CPA LEVEL II

EXAM PAPER: I.1.1.MANAGERIAL FINANCE

REVISION NOTES AUGUST 2021
PRESENTATION
The main objective of this Exam revision is to provide necessary exam tips, planning, and
time management for the exam, the way of tackling questions, extracting data from case
studies, Practice exam technique, and making links between different topics.

SECTION 1: NATURE AND SCOPE OF FINANCIAL MANAGEMENT

1.1 INTRODUCTION
Financial Management is concerned with planning, directing, monitoring, organizing and
controlling monetary resources of an organization. Financial Management simply deals with
management of money matters.
1.2 MEANING OF FINANCE
Finance is defined as the provision of money at the time, it is required. Finance is the art and
science of managing money. There is no human being, without blood. Similarly, there is no
organization that does not require finance, irrespective of the activity, it is engaged in.

1.3 FUNCTIONS AND IMPORTANCE OF FINANCE

In general, the term “Finance” is understood as the provision of funds, as and when needed.
Finance is the essential requirement—sine qua non—of every organization.

Required Everywhere: All activities, be it production, marketing, human resources

development, purchases and even research and development, depend on the adequate and
timely availability of finance both for commencement and their smooth continuation to
completion. Blood is needed for every human being. Similarly, there is no organization that
does not require finance, irrespective of its activities. The way blood is required for a person to
live, so be the finance to any firm for its survival and growth. Finance is regarded as the life-
blood of every business enterprise.

Efficient Utilization—More Important: Finance function is the most important function of all
business activities. The efficient management of business enterprise is, closely, linked with the
efficient management of its finances. The need of finance starts with the setting up of business.
Its growth and expansion require more funds. Funds have to be raised from various sources.
Such sources have to be selected keeping in view their relation to the implications, in
particular, its risks attached. Receiving money, alone, is not important. Terms and conditions,
while receiving money are more important. Cost of funds is an important element. Its
utilization is rather more important. If funds are utilized properly, repayment would be
possible and easier, too. Care has to be exercised to match the inflow and outflow of funds.
Needless to say, profitability of any firm is dependent on its cost as well as its efficient
utilization

1.4 FINANCE AND RELATED DISCIPLINES

Financial Management is not an independent area, but an integral part of overall management.
Financial Management is a wide subject that brings together much of the material that are
found in other subjects and uses other disciplines as its tools. Despite this, it is an interesting
course that brings the best out of an average student. Financial Management involves the use
of accounting knowledge, economic models, mathematical rules, systems analysis and
behavioral science for the specific purpose of assisting management in its functions of
financial planning and control.

It draws on related subjects in the following ways:

i. Financial Accounting
The balance sheet of given company could be regarded as a statement of the results of
financial management. A “healthy balance sheet” indicates skillful financial
management.
ii. Management Accounting
Management Accounting gives the techniques of information generation such as costs
and profitability of projects, the projection of cash flows, the effect of departure from
previous from established plans.
iii. Law
The law governs almost everything which a financial manger does. E.g payment of
dividends is subject to restriction of the law; rising of funds by means of share issue
needs compliance with the company law.
iv. Economics
Economics help the Financial Manager to have knowledge of what goes on outside the
business world.
v. Behavioral Science
Enables Managers to understand the behavior of investors.
vi. Quantitative Methods
Statistical and mathematical techniques through quantitative methods and the Financial
Management combine to give a reasonable forecast and risk analysis e.g variance
measurement is useful in risk analysis; time series is useful in forecasting.

1.5 MEANING AND DEFINITION—FINANCIAL MANAGEMENT

The general meaning of finance refers to the provision of funds, as and when needed.
However, as management function, the term ‘Financial Management’ has a distinct meaning.
Financial management deals with the study of procuring funds and its effective and judicious
utilization, in terms of the overall objectives of the firm, and expectations of the providers of
funds. The basic objective is to maximize the value of the firm. The purpose is to achieve
maximization of share value to the owners, i.e. equity shareholders. The objective of every
company is to create value for its shareholders. Market price of equity share is the barometer
for showing the real ‘Value’. The basic objective of financial management is to maximize the
shareholders’ wealth, represented by the market value of equity shares.
Financial Management is concerned with three activities:
 Anticipating financial needs, which means estimating requirements of the firm in terms
of long-term and short-term needs or investment in fixed and current assets.
 Acquiring financial resources from different sources to meet the financial needs.
 Allocating funds to maximize shareholders’ wealth.
The term financial management has been defined differently by various authors. Some of the
authoritative definitions -are given below:
1. “Financial Management is concerned with the efficient use of an important economic
resource, namely, Capital Funds.” – Solomon
2. “Financial Management is concerned with the managerial decisions that result in the
acquisition and financing of short-term and long-term credits for the firm.” – Phillioppatus
3. “Financial Management is concerned with the acquisition, financing and management of
assets with some overall goal in mind.”– James C. Van Horne
4. “Financial Management deals with procurement of funds and their effective utilization in
the business.” – S.C. Kuchhal From the above definitions, two basic aspects of financial
management emerge. A. Procurement of funds. B. Effective and judicious utilization of funds.
Financial management has become so important that it has given birth to Financial
Management as a separate subject.
1.6 NATURE OF FINANCIAL MANAGEMENT
Financial management refers to that part of management activity, which is concerned with the
planning and controlling of firm’s financial resources. Financial management is a part of
overall management. All business decisions involve finance. Where finance is needed, role of
finance manager is inevitable. Financial management deals with raising of funds from various
sources, dependent on the availability and existing capital structure of the organization. The
sources must be suitable and economical to the organization. Emphasis of financial
management is more on its efficient utilization, rather than raising of funds alone. The scope
and complexity of financial management has been widening with the growth of business in
different diverse directions. As business competition increases, with a greater pace, more
support of financial management is needed, in a more innovative way to make the business
grow, ahead of others.
1.7 IMPORTANCE—FINANCIAL MANAGEMENT
The main importance of financial management can be listed as under:
1. It is necessary for the smooth running of the organization.
2. It facilitates to evaluate the profitability of operational activities of the organization.
3. From the view point of profitability, decision-making is geared at all functional levels.

1.8 NEED OF FINANCIAL MANAGEMENT

Financial management is concerned with optimum utilization of resources. Resources are

limited, particularly in developing countries. So, the focus, everywhere, is to take maximum
benefit, in the form of output, from the limited inputs. Financial management is needed in
every type of organization, be it public or private sector. Its importance exists equally in both
profit oriented and non-profit organizations. In fact, need of financial management is more in
loss-making organizations to turn them to profitable enterprises. Study reveals many
organizations have sustained losses, due to absence of professional financial management.

1.9 SCOPE—FINANCIAL MANAGEMENT

Over the years notable changes have occurred in financial management both in its scope and
areas of coverage. Study of changes that have taken place, over the years, is known as “Scope
of Financial Management”. For easy understanding of changes, it is necessary to divide the
scope of financial management into two approaches. Broadly, the two approaches and their
emphasis are:
 Traditional Approach—Procurement of Funds
 Modern Approach—Effective Utilization of Funds

Traditional Approach
The scope of finance function was treated in the narrow sense as procurement or arrangement
of funds. A finance manager was treated as just provider of funds, when organization felt its
need. The utilization or administering resources was considered outside the purview of the
finance function. It was felt that the finance manager had no role to play in the decision-
making for its utilization. Others used to take decisions regarding its application in the
organization, without the involvement of finance personnel. Finance manager had been
treated, in fact, as an outsider with a very specific and limited function, supplier of funds, to
perform when the need of funds was felt by the organization. As per this approach, the
following aspects only were included in the scope of financial management:
(i) Estimation of requirements of finance.
(ii) Arrangement of funds from financial institutions.
(iii) Arrangement of funds through diverse financial instruments such as shares,
debentures, bonds and loans.
(iv) Looking after the accounting and legal work connected with the raising of
funds,
(v) Preparation of financial statements and managing cash levels needed to pay
day-to-day maturing obligations.
Limitations
The traditional approach was evolved during the 1920s and 1930s period and continued till
1950. The approach had been discarded due to the following limitations: (i) No Involvement in
Application of Funds: The finance manager had not been involved in decision-making of the
allocation of funds. He had been ignored in internal decision-making process and treated as an
outsider. (ii) No Involvement in Day-to-day Management: The focus was on providing long-
term funds from a combination of sources. This process was more of one time happening. The
finance manager was not involved in day-to-day administration of working capital
management. Smooth functioning of the firm depends on working capital management, where
the finance manager was not involved and allowed to play any role. (iii) Not Associated in
Decision-making–Allocation of Funds: The issue of allocation of funds was kept outside his
functioning. He had not been involved in decision making for its judicious utilization.
(iv) Outsider-looking-in Approach: The subject of finance has moved around the suppliers of
funds (investors, financial institutions, banks, etc.) who are outsiders. The approach has been
outsider-looking-in approach, since finance manager has never been involved in internal
decision-making process. Raising finance was an infrequent event. Its natural implication was
that the issues involved in working capital management were not in the purview of the finance
function. In nutshell, during the traditional phase, the finance manager was called upon, in
particular, when his speciality was required to locate new sources of funds, as and when the
requirement of funds was felt.
The following issues, as pointed by Solomon, were ignored in the scope of financial
management, under this approach:
(A) Should an enterprise commit capital funds to a certain purpose?
(B) Do the expected returns meet financial standards of performance?
(C) How should these standards be set and what is the cost of capital funds to the enterprise?
(D) How does the cost vary with the mixture of financing methods used? The traditional
approach has failed to provide answers to the above questions due to narrow scope. Traditional
approach has outlived its utility in the changed business situation. The scope of finance
function has undergone a sea change, with the emergence of different capital instruments.

Modern approach has started during mid-1950s. The approach and utility of financial
management has started changing in a revolutionary manner. Modern approach provides
answers to those questions which traditional approach has failed to provide. Financial
management is considered as vital and an integral part of overall management. Its scope is
wider, as it covers both procurement of funds and its efficient allocation. Allocation is not a
just haphazard process. Its effective utilization and allocation among various investments helps
to maximize shareholders’ wealth. The emphasis of Financial Management has been shifted
from raising funds to the effective and judicious utilization of funds. The modern approach is
analytical way of looking into the financial problems of the firm.
The main contents of this new approach are:
(A) What is the total volume of funds an enterprise should commit?
(B) What specific assets an enterprise should acquire?
(C) How should the funds required be financed?

1.10. Managerial finance functions

Financial management is concerned with the acquisition, financing and management of

assets with some overall goals in mind. It is the study of principle decisions of finance with
overall objective of maximizing shareholder’s wealth. There are four important managerial
finance functions. These are:

a) Investment of Long-term asset-mix decisions: These decisions (also referred to as capital

budgeting decisions) relates to the allocation of funds among investment projects. They refer
to the firm’s decision to commit current funds to the purchase of fixed assets in expectation of
future cash inflows from these projects. Investment proposals are evaluated in terms of both
risk and expected return. Investment decisions also relates to recommitting funds when an old
asset becomes less productive. This is referred to as replacement decision.
b) Financing decisions: Financing decision refers to the decision on the sources of funds to
finance investment projects. The finance manager must decide the proportion of equity and
debt. The mix of debt and equity affects the firm’s cost of financing as well as the financial
risk. This will further be discussed under the cost of capital and capital structure.

c) Division of earnings decision/Dividends decisions: The finance manager must decide

whether the firm should distribute all profits to the shareholders, retain them, or distribute a
portion and retain a portion. The earnings must also be distributed to other providers of funds
such as preference shareholder, and debt providers of funds such as preference shareholders
and debt providers. The firm’s dividend policy may influence the determination of the value of
the firm and therefore the finance manager must decide the optimum dividend – payout ratio
so as to maximize the value of the firm.

d) Liquidity decision: The firm’s liquidity refers to its ability to meet its current obligations
as and when they fall due. It can also be referred to as current assets management. Investment
in current assets affects the firm’s liquidity, profitability and risk. The more current assets a
firm has, the more liquid it is. This implies that the firm has a lower risk of becoming
insolvent but since current assets are non-earning assets the profitability of the firm will be
low.

Routine functions/Routine staff responsibilities

For the effective execution of the managerial finance functions, routine functions have to be
performed. These decisions concern procedures and systems and involve a lot of paper work
and time. In most cases these decisions are delegated to junior staff in the organization. Some
of the important routine functions are:
a) Supervision of cash receipts and payments
b) Safeguarding of cash balance
c) Custody and safeguarding of important documents
d) Record keeping and reporting

The finance manager will be involved with the managerial functions while the routine
functions will be carried out by junior staff in the firm. He must however, supervise the
activities of these junior staff.
1.11. The objectives/goals of a business
*FINANCIAL GOALS
1. Profit maximization – This is a traditional and a cardinal objective of a business. This is
so for the following reasons:
 To earn acceptable returns to its owners. (i.e. Must not be less than bank rates +
inflation + risk)
 So as to survive (through plough backs)
 To meet its day to day obligations.
2. To maximize the net worth/Wealth maximization i.e. the difference between total assets
and total liabilities. This is important because:
 It influences company’s share prices.
 It facilitates growth (plough backs).
 It boosts the company’s credit rating.
  This is what owners claim from the company.
**NON-FINANCIAL GOALS
1. To maximize welfare of employees – Happy employees will contribute to the profitability.
This includes the reasonable salaries, the transport facilities, the medical facilities for the
employee and his family and the recreation facilities (sporting facilities).
2. Interests of customers – the company has to provide quality goods at fair prices and have
honest dealings with customers.
3. Welfare of the society (Corporate social responsibility) – the company has to maintain
sound industrial relations with the society like to avoid pollution and contribution to social
causes e.g. Pension & Health contributions, etc.
4. Fair dealing with suppliers. A company must meet its obligations on time and avoid
dishonor of obligations.
5. Duty to the government: A company should pay taxes promptly, go by government plans
and operate within legal framework.

BASIC OBJECTIVE OF FINANCIAL MANAGEMENT

There is little agreement in the literature as to what the objectives of firms are or even what
they ought to be. However, most writers on financial management make the assumption that
the primary objective of a firm is to maximize the wealth of its shareholders i.e. to maximize
the market value of the company’s equities. Although it is generally agreed that the financial
objective of the firm should be the maximization of owner’s economic welfare, however, there
is disagreement as to how the economic welfare of owners can be maximized. Two well-
known and widely discussed criteria which are put forth for this purpose are:
 Profit maximization and
 Wealth maximization

PROFIT MAXIMIZATION AS A PRIMARY OBJECTIVE

Traditionally, the business has been considered as an economic institution. As such, it has
developed a common and unique measurement of efficiency vis profit. It is therefore, rational
to assume profit maximization as a natural business objective. The appropriateness of this
objective is justified on any of the following counts:
 A human being, performing any economic activity rationally, aims at utility
maximization.
It is argued that utility can be easily measured in terms of profits. Thus profit
maximization is justified on the ground of rationality.
 Profit maximization ensures economic natural selection and in the ultimate end
only profit maximize rs survive.
  The firm by pursuing its objectives of profit maximization also maximizes
social economic welfare.
 A free competitive capital market, in spite of the absence of competition in
product markets will allocate monopoly rights over capital to those who can use
it most profitably.
Thus profit maximization will be a motive force to acquire the monopoly
powers in the imperfect product markets.
LIMITATIONS OF PROFIT MAXIMIZATION AS A PRIMARY OBJECTIVE
 It is argued that profit maximization is a consequence of perfect competition and in the
face of imperfect modern markets today, it cannot be a legitimate objective of the firm.
 It is also argued that profit maximization as a business objective developed in the early
19th century, when the characteristic features of the business structure were self-
financing, private property and single entrepreneurship. The only aim of the single
owner then was to enhance his individual wealth and personal power, which could
easily be satisfied by the profit maximization objective.
However, in the contemporary placing of things, ownership and management are
separated. In this changed business structure, the owner manager of the 19th century
has been replaced by professional manager who has to reconcile the conflicting
objectives of the parties connected with the business firm. In this new business
environment, profit maximization is regarded as unrealistic, difficult, inappropriate
immoral.
The objective also suffers from the following limitations:
 Accounting profits are not the same as “economic” profits. Accounting profits can be
manipulated to some extent by choices of accounting policies.
 A company might make an accounting profit without having used its resources in the
most profitable way possible. There is a difference between the accounting concepts of
historical cost and economic concept of opportunity cost which is the value that should
have been obtained by using resources in their most profitable alternative way.
 Profits are reported every year (with half-year interim results for quoted companies).
They are measures of short-term performance, whereas a company’s performance
should ideally be judged over a long term.
 Profits on their own take no account of the volume of investment that it has taken to
earn the profit. Profits must be related to the volume of investment to have any real
meaning. Hence, measures of financial achievement such as
1) Accounting return on capital employed
2) Earnings per share (EPS)
 3) Yields on investment, such as dividend yield as a percentage of stock
market value are usually calculated to enhance better interpretation.

WEALTH MAXIMISATIO AS A PRIMARY OBJECTIVE

The use of the objective of wealth maximization or net present worth maximization has been
advocated as an appropriate and operationally feasible criterion to choose among the
alternative financial actions. Wealth maximization means maximizing the net present value
(or wealth) of a course of action. The net present value of a course of action is the difference
between the gross present value of the benefits of the action and the amount of investment
required to achieve those benefits. The gross present value of a course of action is found out
by discounting or capitalizing its benefits at a rate which reflects their timing and uncertainty.
A financial action which has a positive action resulting in negative NPV should be rejected
because if accepted it would cause diminution in existing wealth.
Between a number of desirable mutually exclusive projects the one with the highest NPV
should be adopted. The wealth or NPV of the firm will be maximized if this criterion is
followed in making financial decisions.
Other objectives of the financial management include the following:
a) Social responsibility
The firm must decide whether to operate strictly in their shareholders’ best interests or be
responsible to their employers, their customers, and the community in which they operate.
The firm may be involved in activities which do not directly benefit the shareholders, but
which will improve the business environment. This has a long term advantage to the firm and
therefore in the long term the shareholder’s wealth may be maximized.
b) Business Ethics

Related to the issue of social responsibility is the question of business ethics. Ethics are
defined as the “standards of conduct or moral behavior”. It can be thought of as the
company’s attitude toward its stakeholders, that is, its employees, customers, suppliers,
community in general creditors, and shareholders. High standards of ethical behavior demand
that a firm treat each of these constituents in a fair and honest manner. A firm’s commitment
to business ethics can be measured by the tendency of the firm and its employees to adhere to
laws and regulations relating to:
 Product safety and quality
 Fair employment practices
 Fair marketing and selling practices
 The use of confidential information for personal gain
 Illegal political involvement
 Bribery or illegal payments to obtain business.
1.12. The finance manager
The finance Manager is a key personnel who is responsible for the day to day financial
services and record keeping of the organization. He must have proper understanding of those
aspects of legislation which impact upon corporate organizations. Such legislation will include
Companies Acts, health and safety regulations, laws relating to consumer protection and
consumer rights to contrast and agency, employment law and laws relating to protection of the
environment.
A Finance Management will need to familiarize himself with taxation law as well as establish
the reasons why all aspects of Business Taxation are relevant to Finance Strategy.
Additionally he must be conversant with the section on corporation tax which impinges both
on policy formulation and decision-making, this topic being important for investment
appraisal.Other aspects of taxation to be recalled include the tax shield relating to the taking on
of debt in a company’s capital structure, while he should be aware of foreign tax credits
relating to double taxation agreements, whereby most countries give credits in respect of
income remitted to other countries which has already been taxed in the host country.
The Finance Manager should know the workings and implication of tax havens, which are
used by large organizations-usually multinational corporations – to defer payment of tax on
funds earned prior to them being remitted to the parents company’s host country or used for
investment purposes. Such havens will be expected to impose only low rates of tax on income
earned by resident subsidiaries or low withholding taxes on dividends remitted, to have
satisfactory financial services able to provide adequate support facilities and to possess
political and currency stability.

1.13. Stakeholders
Stakeholders are individuals or groups who are affected by the activities of the firm. They can
be classified as internal, connected and external.
The various stakeholder groups in a firm can be classified as follows.
Stakeholder groups
Internal Employees and pensioners
Managers
Directors
Connected Shareholders
Debt holders (bondholders)
Customers
Bankers
Suppliers
Competitors
External Government
Pressure groups
Local and national communities
Professional and regulatory bodies
1.13.1. Objectives of stakeholder groups
The various groups of stakeholders in a firm will have different goals which will depend in
part on the particular situation of the enterprise. Some of the more important aspects of these
different goals are as follows:
 Ordinary (equity) shareholders: Ordinary (equity) shareholders are the providers of
the risk capital of a company. Usually their goal will be to maximize the wealth which
they have as a result of the ownership of the shares in the company.
 Trade payables (creditors): Trade payables have supplied goods or services to the
firm. Trade payables will generally be profit-maximizing firms themselves and have
the objective of being paid the full amount due by the date agreed.
 Long-term payables (creditors): Long-term payables, which will often be banks,
have the objective of receiving payments of interest and capital on the loan by the due
date for the repayments. Where the loan is secured on assets of the company, the lender
will be able to appoint a receiver to dispose of the company's assets if the company
defaults on the repayments. To avoid the possibility that this may result in a loss to the
lender if the assets are not sufficient to cover the loan, the lender will wish to minimise
the risk of default and will not wish to lend more than is prudent.
 Employees: Employees will usually want to maximize their rewards paid to them in
salaries and benefits, according to the particular skills and the rewards available in
alternative employment. Most employees will also want continuity of employment.
 Government: Government has objectives which can be formulated in political terms.
Government agencies impinge on the firm's activities in different ways including
through taxation of the firm's profits, the provision of grants, health and safety
legislation, training initiatives and so on. Government policies will often be related to
macroeconomic objectives such as sustained economic growth and high levels of
employment.
 Management: Management has, like other employees (and managers who are not
directors will normally be employees), the objective of maximizing its own rewards.
Directors, and the managers to whom they delegate responsibilities, must manage the
company for the benefit of shareholders. The objective of reward maximization might
conflict with the exercise of this duty.
1.13.2. The agency theory and problem

An agency relationship arises where one or more parties called the principal contracts/hires
another called an agent to perform on his behalf some services and then delegates decision
making authority to that hired party (Agent). In the field of finance shareholders are the
owners of the firm. However, they cannot manage the firm because:
 They may be too many to run a single firm.
 They may not have technical skills and expertise to run the firm
  They are geographically dispersed and may not have time.
Shareholders therefore employ managers who will act on their behalf. The managers are
therefore agents while shareholders are principal. Shareholders contribute capital which is
given to the directors which they utilize and at the end of each accounting year render an
explanation at the annual general meeting of how the financial resources were utilized. This is
called stewardship accounting.
In the light of the above shareholders are the principal while the management are the agents.
Agency problem arises due to the divergence or divorce of interest between the principal and
the agent. The conflict of interest between management and shareholders is called agency
problem in finance.
There are various types of agency relationship in finance exemplified as follows:
1. Shareholders and Management
2. Shareholders and Creditors
3. Shareholders and the Government
4. Shareholders and Auditors
5. Headquarter office and the Branch/subsidiary.
1. SHAREHOLDERS AND MANAGEMENT

There is near separation of ownership and management of the firm. Owners employ
professionals (managers) who have technical skills. Managers might take actions, which are
not in the best interest of shareholders. This is usually so when managers are not owners of
the firm i.e. they don’t have any shareholding. The actions of the managers will be in conflict
with the interest of the owners. The actions of the managers are in conflict with the interest of
shareholders will be caused by:
i)Incentive Problem
Managers may have fixed salary and they may have no incentive to work hard and maximize
shareholders wealth. This is because irrespective of the profits they make, their reward is
fixed. They will therefore maximize leisure and work less which is against the interest of the
shareholders.
ii)Consumption of “Perquisites”

Prerequisites refer to the high salaries and generous fringe benefits which the directors might
award themselves. This will constitute directors remuneration which will reduce the dividends
paid to the ordinary shareholders. Therefore, the consumption of perquisites is against the
interest of shareholders since it reduces their wealth.
iii)Different Risk-profile

Shareholders will usually prefer high-risk-high return investments since they are diversified
i.e. they have many investments and the collapse of one firm may have insignificant effects on
their overall wealth. Managers on the other hand, will prefer low risk-low return investment
since they have a personal fear of losing their jobs if the projects collapse. (Human capital is
not diversifiable). This difference in risk profile is a source of conflict of interest since
shareholders will forego some profits when low-return projects are undertaken.
iv) Different Evaluation Horizons

Managers might undertake projects which are profitable in short-run. Shareholders on the
other hand evaluate investments in long-run horizon which is consistent with the going
concern aspect of the firm. The conflict will therefore occur where management pursue short-
term profitability while shareholders prefer long term profitability.
v) Management Buy Out : The board of directors may attempt to acquire the business of the
principal. This is equivalent to the agent buying the firm which belongs to the shareholders.
This is inconsistent with the agency relationship and contract between the shareholders and the
managers.

vi) Pursuing power and self-esteem goals: This is called “empire building” to enlarge the
firm through mergers and acquisitions hence increase in the rewards of managers.
vii) Creative Accounting: This involves the use of accounting policies to report high profits
e.g stock valuation methods, depreciation methods recognizing profits immediately in long
term construction contracts etc.

Solutions to Shareholders and Management Conflict of Interest

1. Pegging/attaching managerial compensation to performance

This will involve restructuring the remuneration scheme of the firm in order to enhance the
alignments/harmonization of the interest of the shareholders with those of the management e.g.
managers may be given commissions, bonus etc. for superior performance of the firm.
2. Threat of firing: This is where there is a possibility of firing the entire management team
by the shareholders due to poor performance. Management of companies has been fired by the
shareholders who have the right to hire and fire the top executive officers.

3. The Threat of Hostile Takeover: If the shares of the firm are undervalued due to poor
performance and mismanagement. Shareholders can be threatened to sell their shares to
competitors. In this case the management team is fired and those who stay on can lose their
control and influence in the new firm. This threat is adequate to give incentive to management
to avoid conflict of interest.

4. Direct Intervention by the Shareholders

Shareholders may intervene as follows:

 Insist on a more independent board of directors.

 By sponsoring a proposal to be voted at the AGM
  Making recommendations to the management on how the firm should be run.
5. Managers should have voluntary code of practice, which would guide them in the
performance of their duties.

6. Executive Share Options Plans

In a share option scheme, selected employees can be given a number of share options, each of
which gives the holder the right after a certain date to subscribe for shares in the company at a
fixed price. The value of an option will increase if the company is successful and its share
price goes up. The theory is that this will encourage managers to pursue high NPV strategies
and investments, since them as shareholders will benefit personally from the increase in the
share price that results from such investments.
However, although share option schemes can contribute to the achievement of goal
congruence, there are a number of reasons why the benefits may not be as great as might be
expected, as follows:
 Managers are protected from the downside risk that is faced by shareholders. If the
share price falls, they do not have to take up the shares and will still receive their
standard remuneration, while shareholders will lose money.
 Many other factors as well as the quality of the company’s performance influence share
price movements. If the market is rising strongly, managers will still benefit from
share options, even though the company may have been very successful. If the share
price falls, there is a downward stock market adjustment and the managers will not be
rewarded for their efforts in the way that was planned.
 The scheme may encourage management to adopt ‘creative accounting’ methods that
will distort the reported performance of the company in the service of the managers’
own ends.
7. Incurring Agency Costs

Agency costs are incurred by the shareholders in order to monitor the activities of their agent.
The agency costs are broadly classified into 4.
a) The contracting cost. These are costs incurred in devising the contract between the
managers and shareholders. The contract is drawn to ensure management act in the best
interest of shareholders and the shareholders on the other hand undertake to compensate the
management for their effort. Examples of the costs are negotiation fees, legal costs of
drawing the contracts fees and costs of setting the performance standard.
b) Monitoring Costs
This is incurred to prevent undesirable managerial actions. They are meant to ensure that both
parties live to the spirit of agency contract. They ensure that management utilizes the financial
resources of the shareholders without undue transfer to themselves.
Examples are:
 External audit fees
 Legal compliance expenses e.g. Preparation of financial statement according to
international accounting standards, company law, capital market authority
requirement, stock exchange regulations etc.
 Financial reporting and disclosure expenses
 Investigation fees especially where the investigation is instituted by the
shareholders.
 Cost of instituting a tight internal control system (ICS).
c) Opportunity Cost/Residual Loss This is the cost due to the failure of both parties to act
optimally.e.g.:
 Lost opportunities due to inability to make fast decision due to tight internal control
system
 Failure to undertake high risk high return projects by the manager leads to lost profits
when they undertake low risk, low return projects.
d) Restructuring Costs – e.g. new Internal Control System, business process reengineering
etc.
2. SHAREHOLDERS AND CREDITORS/BOND/DEBENTURE HOLDERS

Bondholders are providers or lenders of long term debt capital. They will usually give debt
capital to the firm on the strength of the following factors:
 The existing asset structure of the firm
 The expected asset structure of the firm
 The existing capital structure or gearing level of the firm
 The expected capital structure of gearing after borrowing the new
debt.
b) Assets/investment substitution
In this case, the shareholders and bond holders will agree on a specific low risk project.
However, this project may be substituted with a high risk project whose cash flows have high
standard deviation. This exposes the bondholders because should the project collapse, they
may not recover all the amount of money advanced.
c) Payment of High Dividends
Dividends may be paid from current net profit and the existing retained earnings. Retained
earnings are an internal source of finance. The payment of high dividends will lead to low
level of capital and investment thus reduction in the market value of the shares and the
bonds.A firm may also borrow debt capital to finance the payment of dividends from which no
returns are expected. This will reduce the value of the firm and bond.

d) Under investment
This is where the firm fails to undertake a particular project or fails to invest money/capital in
the entire project if there is expectation that most of the returns from the project will benefit
the bondholders. This will lead to reduction in the value of the firm and subsequently the
value of the bonds.
e) Borrowing more debt capital
A firm may borrow more debt using the same asset as a collateral for the new debt. The value
of the old bond or debt will be reduced if the new debt takes a priority on the collateral in case
the firm is liquidated. This exposes the first bondholders/lenders to more risk.

Solutions to agency problem

The bondholders might take the following actions to protect themselves from the actions of the
shareholders which might dilute the value of the bond. These actions include:
1. Restrictive Bond/Debt Covenant
In this case the debenture holders will impose strict terms and conditions on the borrower.
These restrictions may involve:
a) No disposal of assets without the permission of the lender.
b) No payment of dividends from retained earnings
c) Maintenance of a given level of liquidity indicated by the
amount of current assets in relation to current liabilities.
d) Restrictions on mergers and organisations
e) No borrowing of additional debt, before the current debt is
fully serviced/paid.
f) The bondholders may recommend the type of project to be
undertaken in relation to the riskness of the project.
2. Callability provisions
These provisions will provide that the borrower will have to pay the debt before the expiry of
the maturity period if there is breach of terms and conditions of the bond covenant.
3. Transfer of Asset
 The bondholder or lender may demand the transfer of asset to him on giving debt or loan to
the company. However the borrowing company will retain the possession of the asset and
the right of utilization.
 On completion of the repayment of the loan, the asset used as a collateral will be
transferred back to the borrower.
4. Representation
The lender or bondholder may demand to have a representative in the board of directors of the
borrower who will oversee the utilization of the debt capital borrowed and safeguard the
interests of the lender or bondholder.
5. Refuse to lend
If the borrowing company has been involved in un-ethical practices associated with the debt
capital borrowed, the lender may withhold the debt capital hence the borrowing firm may not
meet its investments needs without adequate capital. The alternative to this is to charge high
interest on the borrower as a deterrent mechanism.
6. Convertibility: On breach of bond covenants, the lender may have the right to convert the
bonds into ordinary shares.
3. AGENCY RELATIONSHIP BETWEEN SHAREHOLDERS AND THE
GOVERNMENT
Shareholders and by extension, the company they own operate within the environment using
the charter or licence granted by the government. The government will expect the company
and by extension its shareholders to operate the business in a manner which is beneficial to the
entire economy and the society.

The government in this agency relationship is the principal while the company is the agent.
It becomes an agent when it has to collect tax on behalf of the government especially
withholding tax and PAYE. The company also carries on business on behalf of the government
because the government does not have adequate capital resources. It provides a conducive
investment environment for the company and share in the profits of the company in form of
taxes. The company and its shareholders as agents may take some actions that might prejudice
the position or interest of the government as the principal. These actions include:

 Tax evasion: This involves the failure to give the accurate picture of the earnings or
profits of the firm to minimize tax liability.
 Involvement in illegal business activities by the firm.
 Lukewarm response to social responsibility calls by the government.
 Lack of adequate interest in the safety of the employees and the products and services
of the company including lack of environmental awareness concerns by the firm.
 Avoiding certain types and areas of investment coveted by the government.
Solutions to the agency problem
The government can take the following actions to protect itself and its interests.
1. Incur monitoring costs
E.g. the government incurs costs associated with:
 Statutory audit
 Investigations of companies under Company Law
 Back duty investigation costs to recover tax evaded in the past
 VAT refund audits

2. Lobbying for directorship (representation)

The government can lobby for directorship in companies which are deemed to be of strategic
nature and importance to the entire economy or society e.g directorship in RWANDAIR,
CIMERWA, BDF, KFH, BK etc.
3. Offering investment incentives
To encourage investment in given areas and locations, the government offers investment
incentives in form of capital allowances.
4. Legislations
The government has provided legal framework to govern the operations of the company and
provide protection to certain people in the society e.g. regulation associated with disclosure of
information, minimum wages and salaries, environment protection etc.
5. The government can calculate the sense and spirit of social responsibility on the
activities of the firm, which will eventually benefit the firm in future.

4. AGENCY RELATIONSHIP BETWEEN SHAREHOLDERS AND AUDITORS

Shareholders appoint auditors as per the provisions of the Rwandan Companies Law. The
auditors are supposed to monitor the performance of the management on behalf of the
shareholders. They act as watchdogs to ensure that the financial statements prepared by the
management reflect the true and fair view of the financial performance and position of the
firm.
Since auditors act on behalf of shareholders they become agents while shareholders are the
principal. The auditors may prejudice the interest of the shareholders thus causing agency
problems in the following ways:
a) Colluding with the management in performance of their duties whereby their
independence is compromised.
b) Demanding a very high audit fee (which reduces the profits of the firm) although
there is insignificant audit work due to the strong internal control system existing in
the firm.
c) Issuing unqualified reports which might be misleading the shareholders and the
public and which may lead to investment losses if investors rely on such misleading
report to make investment and commercial decisions.
d) Failure to apply professional care and due diligence in performance of their audit
work.
Solutions to the conflict
1. Firing: The auditors may be removed from office by the shareholders at the
AGM.
2. Legal action: Shareholders can institute legal proceedings against the auditors
who issue misleading reports leading to investment losses.
3. Disciplinary Action – ICPAR.
Professional bodies have disciplinary procedures and measures against their members
who are involved in un-ethical practices. Such disciplinary actions may involve:
 Suspension of the auditor
 Withdrawal of practicing certificate
 Fines and penalties
 Reprimand
 4. Use of audit committees and audit reviews.
5. HEAD OFFICE AND SUBSIDIARY/BRANCH
BANK OF KIGALI /BPR ATLAS MARA, I&M BANK RWANDA , COGEBANQUE have
diverse operations set up in the different geographical locations. The HQ acts as the principal
and the subsidiary as an agent thus creating an agency relationship. The subsidiary
management may pursue its own goals at the expense of overall corporate goals. This will
lead to sub-optimisation and conflict of interest with the headquarter.
This conflict can be resolved in the following ways:
a) Frequent transfer of managers
b) Adopt global strategic planning to ensure commonality of vision
c) Having a voluntary code of ethical practices to guide the branch managers

1.14. Not for profit organisations

This category of organisation includes public sector bodies such as the National Health
Service or local councils, charitable bodies e.g., Oxfam, and other organisations whose
purpose is to serve the broader community interests, rather than the pursuit of profit. In broad
terms, such organisations seek to serve the interests of society as a whole, and so they give
non-financial objectives priority of place.

It is reasonable to argue that they best serve society's interests when the gap between the
benefits they provide, and the cost of that provision is greatest. This is commonly termed
value for money, and it is not dissimilar to the concept of profit maximisation, but for the fact
that public welfare is being maximised rather than profit.

In practice it is incredibly difficult to quantify, for example, the benefits from an operation
such as the UK's National Health Service. How does one put a value on a life which has been
prolonged by "x" number of years, or on the easing of pain which is brought about by the
replacement of an arthritic joint? The benefits extend beyond factors which can be measured
in purely financial terms. Nonetheless, financial criteria can be used to appraise the extent to
which such organisations offer value for money, and hence make good use of the funds
provided to them.

Value for money may be described as " getting the best possible combination of services
from the least resources." This means maximising the benefits for the lowest possible cost, and
is usually accepted as requiring the application of economy, effectiveness and efficiency.
Economy measures the inputs that are required to achieve a certain level of outputs.
Effectiveness measures the extent to which a service achieves its declared objectives/goals.
Efficiency combines the other two measures to show the ratio of inputs : outputs. When an
operation is efficient it will produce the maximum number of goods/services relative to the
inputs required for their production. The three "Es" are the fundamental prerequisite of
achieving Value For Money.

The major difficulty for public sector bodies lies in precisely how to measure the achievement
of the non-financial objectives. Value for money as a concept assumes that there is a yardstick
against which to measure success i.e., achievement of objectives. In reality, the indicators of
success are open to debate. For example, in the Health Service is success measured in terms of
fewer patient deaths per hospital admission, shorter waiting lists for operations, average speed
of patient recovery? etc., etc. As long as objectives are difficult to specify, so too will it
remain difficult to specify where there is value for money. Comparative performance
measures are useful, but care must be taken not to read too much into limited information.
TOPIC 2 SOURCES OF FINANCES, FINANCIAL MARKETS &VENTURE
CAPITAL

2.1 SOURCES OF FINANCES

2.1.1. INTRODUCTION

Finance is the lifeblood of business concern, because it is interlinked with all activities performed by
the business concern. In a human body, if blood circulation is not proper, body function will stop.
Financial requirement of the business differs from firm to firm and the nature of the requirements on
the basis of terms or period of financial requirement may be broadly classified into two parts: Long
term and short-term financial requirements.

 Long-term Financial Requirements or Fixed Capital Requirement

Long-term financial requirement means the finance needed to acquire land and building for business
concern, purchase of plant and machinery and other fixed expenditure. Long-term financial
requirement is also called as fixed capital requirements. Fixed capital is the capital, which is used to
purchase the fixed assets of the firms such as land and building, furniture and fittings, plant and
machinery, etc. Hence, it is also called a capital expenditure.

 Short-term Financial Requirements or Working Capital Requirement

This kind of expenditure is to meet with the help of short-term financial requirements which will meet
the operational expenditure of the firms. Short-term financial requirements are popularly known as
working capital.

2.1.2. SOURCES OF FINANCE

Sources of finance mean the ways for mobilizing various terms of finance to the industrial concern.
Sources of finance may be classified under various categories according to the following important
heads:

1. Based on the Period

Sources of Finance may be classified under various categories based on the period.
Long-term sources: Finance may be mobilized by long-term or short-term. When the finance
mobilized with large amount and the repayable over the period will be more than five years, it may be
considered as long-term sources. Share capital, issue of debenture, long-term loans from financial
institutions and commercial banks come under this kind of source of finance. Long-term source of
finance needs to meet the capital expenditure of the firms such as purchase of fixed assets, land and
buildings, etc.
Long-term sources of finance include:
 Equity Shares
 Preference Shares
 Debenture
 Long-term Loans
 Fixed Deposits
Short-term sources: Apart from the long-term source of finance, firms can generate finance with the
help of short-term sources like loans and advances from commercial banks, moneylenders, etc. Short-
term source of finance needs to meet the operational expenditure of the business concern.
Short-term source of finance include:
 Bank Credit
 Customer Advances
 Trade Credit
 Factoring
 Public Deposits
 Money Market Instruments
2. Based on Ownership
Sources of Finance may be classified under various categories based on the period:
An ownership source of finance includes:
 Shares capital, earnings
 Retained earnings
 Surplus and Profits
Borrowed capital include:
 Debenture
 Bonds
 Public deposits
 Loans from Bank and Financial Institutions.
3. Based on Sources of Generation
Sources of Finance may be classified into various categories based on the period.
Internal source of finance includes
 Retained earnings
 Depreciation funds
 Surplus
External sources of finance may be including:
 Share capital
 Debenture
 Public deposits
 Loans from Banks and Financial institutions
4. Based in Mode of Finance
Security finance may be including:
 Shares capital
 Debenture
Retained earnings may include :
● Retained earnings
● Depreciation funds
Loan finance may include
 Long-term loans from Financial Institutions
 Short-term loans from Commercial banks.
The above classifications are based on the nature and how the finance is mobilized from various
sources. But the above sources of finance can be divided into three major classifications:
 Security Finance
 Internal Finance
 Loans Finance

1. EQUITY FINANCE
For small companies, this is personal savings (contribution of owners to the company). For large
companies’ equity finance is made of ordinary share capital and reserves; (both revenue and capital
reserves). Equity finance is divided into the following classes:
a) ORDINARY SHARE CAPITAL – this is raised from the public from the sale of ordinary
shares to the shareholders. This finance is available to limited companies. It is a permanent
finance as the owner/shareholder cannot recall this money except under liquidation. It is thus a
base on which other finances are raised.
Ordinary share capital carries a return that is variable (ordinary dividends). These shares carry
voting rights and can influence the company’s decision making process at the AGM.
These shares carry the highest risk in the company (high securities – documentary claim to) because of:
a) Uncertainty of return
b) Cannot ensure refund
c) Have residual claims – claim last on profits, claim last on assets.
However, this investment grows through retention.
Rights of ordinary shareholders
1. Right to vote
a. elect BOD
b. Sales/purchase of assets
2. Influence decisions:
a) Right to residual assets claim
b) Right to amend company’s by-laws
 c) Right to appoint another auditor
d) Right to approve merger acquisition
e) Right to approve payment of dividends
Reasons why ordinary share capital is attractive despite being risky
 Shares are used as securities for loans (a compromise of the market price of a share).
 Its value grows.
 They are transferable at capital gain.
 They influence the company’s decisions.
 Carry variable returns – is good under high profit
 Perpetual investment – thus a perpetual return
 Such shares are used as guarantees for credibility.
Advantages of using ordinary share capital in financing.
 They facilitate projects especially long-term projects because they are permanent..
 Its cost is not a legal obligation.
 It lowers gearing level – reduces chances of receivership/liquidation.
 Used with flexibility – without preconditions.
 Such finances boost the company’s credibility and credit rating.
 Owners contribute valuable ideas to the company’s operations (during AGM by professionals).

Rights Issues:
A rights issue is a method of raising new share capital by inviting existing shareholders to pay cash for
new shares in proportion to their existing shareholding. For example, a rights issue on a one for four
basis at 300c per share is inviting shareholders to subscribe for one new share for every four shares
they currently hold at a price of Frw3 per new share.
A rights issue may be made by any type of company, public or private, listed or unlisted. We are
mainly concerned however, with listed companies. Advantages of rights issues include:
- Cheaper than offers for sale to the general public
- More beneficial to existing shareholders than an offer to the general public as it gives existing
shareholders a discount on the market price for new shares
- Shareholders voting rights will be unaffected if they take up the rights offer
The offer price of a rights issue will be lower than the current market price of shares; however it must
be above the nominal value of the shares. If current market price is below nominal value, then a rights
issue is not possible.
The theoretical ex rights price (market price after a rights issue):
When a rights issue is announced, all existing shareholders have the right to subscribe for new shares
and so there are rights attached to the existing shares. The shares are therefore described as being ‘cum
rights’ (with rights attached) and are traded cum rights. On the first day of dealings in the newly issues
shares, the rights no longer exist and the old shares are now ‘ex rights’ (without rights attached). In
theory, the new market price will be the consequence of an adjustment to allow for the discount price
of the new issue, and a theoretical ex rights price can be calculated.
Example:
F plc. has 1,000,000 ordinary shares of Frw1 in issue, which have a market price on 1/9/12 of Frw2.10
per share. The co makes a rights issue and offers its shareholders the right to subscribe for one new
share at Frw1.50 each for every four shares held. After the announcement of the issue, the share price
fell to Frw1.95 but just prior to the issue being made it had recovered to Frw2 per share.
Required: Calculate the theoretical ex rights price.
Solution:
1,000,000 shares at cum rights value of Frw2 = Frw2,000,000
250,000 shares issued at Frw1.50 = Frw375,000
---------------
Theoretical value of 1,250,000 shares = Frw2,375,000
The theoretical ex rights price is Frw2,375,000 / 1,250,000 = Frw1.90 per share.
The value of a right:
The value of rights is the theoretical gain a shareholder would make by exercising his rights.
In the above example, where the price offered in the rights issue is Frw1.50 per share and the market
price is expected to be Frw1.90 then the value of a right can be calculated as Frw1.90 - Frw1.50 = 40c.
A shareholder would then expect to gain 40 cent for each new share he buys.
The value of rights attaching to old shares is calculated in the same way. If the value of rights on a new
share is 40 cent and there is a one in four rights issue, the value of rights attaching to each existing
share is 40 / 4 = 10 cent.
To calculate the value of a right attaching to an old share the following formula can be used:
Value of a right: Ex rights price – issue price
-----------------------------------
N
Where N = number of old shares held for every one share
Using the formula on the above example:
1.90 – 1.50
-------------- = .10
4
The theoretical gain or loss to shareholders:
The possible courses of action open to shareholders are;
- To exercise their rights i.e. buy the new shares at the rights price. This will maintain their
proportion of total equity in the company
- To renounce the rights and sell them on the market. This will reduce their percentage of equity
in the company.
- To renounce part of the rights and take up the remainder. This strategy is often adopted by
shareholders who want to take up the offer but do not have the necessary cash. If the
shareholder sells some of his rights he will raise cash and can use that to purchase the
remaining rights shares.
- To do nothing at all. In this case the rights not taken up may be sold on the shareholders behalf,
however the shareholder could also lose wealth and it is up to the shareholder to take effective
action to maintain his existing wealth.

PRACTICE QUESTIONS
QN
A local supermarket chain wishes to increase the number of its retail outlets in the country. The board
of directors of the company have decided to finance the acquisition by raising funds from the existing
shareholders through a one for four rights issue. The recently published income statement of the
company for the year ended 31 October 2002 has the following information:

Frw’000’
Turnover 246,750
Profit before interest and tax 18,900
Interest 8,300
Profit before taxation 9,600
Corporate tax 2,850
Profit after taxation 6,750
Ordinary dividends 3,000
Retained profit for the year 3,750

The share capital of the company consists of 12 million ordinary shares with a par value of Frw5 per
share. The shares of the company are currently being traded on the Stock Exchange with a
price/earnings ratio of 22 times. The board of directors has decided to issue the shares at a discount of
20 per cent on the current market value.
Required:
a) The theoretical ex-rights price of an ordinary share of the company.
b) The price at which the rights in the company are likely to be traded.
c) Assuming an investor held 4,000 ordinary shares of the company before the rights issue
announcement, evaluate the following options and identify the best option to the investor.
i) Exercise the rights.
ii) Sell the rights
iii) Do nothing.
ANSWER:
a) Since the current MPS is not given, compute the MPS from Earnings Per Share (EPS) and P/E
ratio.
 EPS = Profits after tax = 6.75 M = 0.56
No. of Ord. Shares 12 M shares
MPS = EPS x P/E Ratio
= 0.56 x 22 =
= Frw12.32
The subscriptions/issue price for a rights issue is 90% of MPS (at 10% discount)
Use price = 90% x 12.32 = 11.09
Before rights issue, 4 shares @ MPS 12.32 = 49.28
On rights issue 1 share @ Frw11.09 = 11.09
Total 5 shares 60.37

60.37
Theoretical ex-right MPS =  Sh.12.07
5
b) Value of a right = MPS – Ex-right
= 12.32 – 12.07 = 0.25
c) i) Exercise the right and buy new shares @ Frw11.09 each.
- Current number of shares 4000
- New shares ¼ x 4000 1000
5000 shares
After rights issue 5000 shares x 12.07 = 60,350
Cost of buying new 1000 shares @ 11.09 each (11,090)
49,260*
ii) Sell the rights
She has 4000 rights/shares to enable her to buy 1000 new shares therefore
4000 shares @ Frw12.07 ex-right MPS = 48,280
and cash from sale of 4000 rights @ Frw0.25 = 1,000
Net wealth 49,280
iii) Do nothing
She will have 4000 shares each valued at ex-right MPS of 12.07 = Frw48,280
Note: If she exercises the right or sells the rights, the wealth does not change. The difference in the
above figures is due to approximation error.

QN
The Moon Company Ltd. has issued 10,000,000, Frw 10 par equity shares which are at present selling
for Frw 30 per share. It has also issued 5,000,000 warrants, each entitling the holder to buy one equity
share. The warrants are protected against dilution.
(a) The company has plans to issue rights to purchase one new equity share at a price of Frw 20
per share for every four shares held.
Required:
(i) Calculate the theoretical ex-rights price of Moon Company Ltd.’s equity shares.
(ii) The theoretical value of a right of the Moon Company Ltd. before the shares sell
ex-rights.
(b) The chairman of the company receives a phone call from an angry shareholder who owns
100,000 shares. The shareholder argues that he will suffer a loss in his personal wealth due to
this rights issue, because the new shares are being offered at a price lower than the current
market value.
The chairman assures him that his wealth will not be reduced because of the rights issue, as
long as the shareholder takes appropriate action.
Required:
(i) Explain whether the chairman is correct. What should the shareholder do?
(ii) A statement showing the effect of the rights issue on this particular shareholder’s
wealth, assuming:
 He sells all the rights.
 He exercises one half of the rights and sells the other half.
 He does nothing at all.
(iii) Are there any real circumstances which might lend support to the shareholder’s
claim?
ASNWER
(a) (i) The firm will make a one for four rights issue

4 existing shares @ Frw 30 = 120

 1 new share @ Frw 20 = 20
5 shares valued at Frw 140

140
Ex – right M.P.S = Frw = Frw 28
5
(ii) Value of right = cum – right ex – right
M.P.S M.P.S
= 30 – 28 = Frw 2.00
(b) (i) The chairman is right. If the market is efficient, there is no dilution in wealth if the
shareholder either exercises the rights or sells the rights.
Wealth is diluted if the rights issue is ignored.
(ii) Wealth before rights issued = 100,000 shares x 30 = Frw 3,000,000
The investor has 100,000 rights attached to 100,000 shares and priced at Frw 2.00 per right.
After the rights issue, shares will sell at Frw 28.00

Sell the rights

Wealth in shares = 100,000 shares x Frw 28 2,800,000
Cash from sale = 100,000 rights x Frw 2.0 200,000
Total wealth 3,000,000

Exercise one – half of the rights and sell the other half
NOTE
100 000
New shares bought given a 1 for 4 rights issue = x 50% = 12,500 shares at Frw 20.
4

Total shares = (100,000 + 12,500) @ Frw 28 = 3,150,000

Sale of 100,000 x 50% = 50,000 rights @ Frw 2= 100,000
Cash spent buying 12,500 shares @ Frw 20 (250,000)
Net wealth 3,000,000

Do nothing (ignore rights issue)

The investor will remain with the original 100,000 shares valued at Frw 28 each after rights issue
Net wealth = Frw 28 x 100,000 = Frw 2,800,000
(iii) It is possible for the shareholder’s claim to be realistic if
The new capital raised is not invested but is misused
If the new capital is invested in a project whose rate of return is lower than the firm’s cost of capital
If the market is inefficient and ex – right M.P.S is infact not Frw 28 hence loss in wealth of investors
who exercise the right.
If market is efficient and the project is highly profitable, the future share price will raise leading to
increase in wealth of the investor.

QN
Madawa Company Limited, a public quoted company, intends to raise additional share capital through
a rights issue. The number of issued ordinary shares currently stands at 100 million shares. Each
shareholder will have a right to purchase one share for every five shares currently held. The current
market price per share is Frw60 while the rights price has been fixed at Frw50 per share.
Required:
i) Calculate the theoretical value of a right in Madawa Company Limited
ii) Determine the theoretical ex-rights price of a share in the company

ANSWER

One for 5 rights issue.

5 existing shares @ Frw60 = 300
1 new shares @ Frw50 = 50
6 shares Shs.350
Ex-right M.P.S = Frw 350 = Frw58.333
6
 Value of a right = Frw60 cum-right – Frw58.333 = Frw1.667

QN :
The Clifford Corporation has announced a rights offer to raise Frw30 million for a new journal, the Journal
of Financial Excess. This journal will review potential articles after the author pays a nonrefundable
reviewing fee of Frw3,000 per page. The stock currently sells for Frw40 per share, and there are 3.6 million
shares outstanding.
a. What is the maximum possible subscription price? What is the minimum?
b. If the subscription price is set at Frw32 per share, how many shares must be sold? How many rights will it
take to buy one share?
c. What is the ex-rights price? What is the value of a right?
d. A shareholder with 2,000 shares before the offering has no desire (or money) to buy additional shares
offered as rights. What is his portfolio value before and after the rights offer?

Rights:
To avoid dilution of shareholders, as well as to save money on flotation costs(Flotation cost is the
total cost incurred by a company in offering its securities to the public. They arise
from expenses such as underwriting fees, legal fees and registration fees), many companies offer
their current shareholders the right to buy new shares before these shares are issued to the public. The rights
price is typically lower than the current stock price.
a. Maximum price = Frw40, the current stock price.
Minimum price = Frw0. When the price is Frw0, this is equivalent to a stock dividend.
b. Shares sold = Funds needed / Share price = 30 mil / 32 = 937,500.
Rights needed to buy one new share = 3.6 mil / 937,000 = 3.84 rights
c. Value of company after it raises Frw30 mil = 3.6 mil * Frw40 + Frw30 mil = Frw174 mil
New shares issued = 937,500 (see above).
Total shares = 3.6 mil + 937,500 = 4,537,500
New share price = Value / number of shares = 174,000,000 / 4,537,500 = Frw38.35
Value of one right = Old price - New price = 40 - 38.35 = Frw1.65
d. Assuming, rights cannot be detached and sold to other investors,
Value before offer = 2,000 * 40 = 80,000
Value after offer = 2,000 * 38.35 = 76,700

b) RETAINED EARNINGS
i) Revenue Reserves
These are undistributed earnings. Such reserves are retained for the following reasons:
 To make up for the fall in profits so as to sustain acceptable risks.
 To sustain growth through plough backs. They are cheap source of finance.
 They are used to boost the company’s credit rating so they enable further finance to be
obtained.
 It lowers the company’s gearing ratio – reduces chances of receivership/liquidation.

ii) Capital Reserves

1. It is raised by selling shares at a premium. (The difference between the market price (less
floatation costs) and par value is credited to the capital reserve).
2. Through revaluation of the company’s assets. This leads to a fictitious entry which is of the
nature of a capital reserve.
3. By creation of a sinking fund.
c) PREFERENCE SHARE CAPITAL (Quasi-Equity)
It is also called quasi-equity because it combines features of equity and those of debt. It is preference
because it is preferred to ordinary share capital that is:
i) It is paid dividends first – preferred to dividend
ii) It is paid asset proceeds first – preferred to assets.
Unlike ordinary share capital, it has a fixed return. It carries no voting rights. It is an unsecured
finance and it increases the company’s gearing ratio.
CLASSIFICATION
i) Redeemable Class
Redeemable preferential shares are bought back by issuing company after minimum redemption period
but before expiring of maximum redemption period after which they become creditors.

ii) Irredeemable Preference Shares

Are perpetual preference shares as they will not be redeemed in the company’s lifetime unless it is
under liquidation, (it is permanent).

iii) Non-Participative Preference Shares

These do not claim any money over and above their par value, but are usually cumulative and
redeemable.
V) Cumulative Preference Shares
These can claim arrears e.g. if a company sold 10% Frw20 preference shares and did not pay dividends
for the next two years, then in the third year shareholders will claim:

10% x 20 x 3yrs= Frw 6 less withholding tax:

= Frw 6 less 5% of Frw 0.30
= Frw 5.70 net
vi) Non-Cumulative Preference Shares
These cannot claim interest in arrears.
vii) Convertible
These can be converted into ordinary shares (which is optional).
Conversion ratio = par value of ordinary share/par value of preference shares e.g if par value of
10 1
ordinary shares is Frw10 and that of preference shares is Frw20, then conversion ratio =  i.e for
20 2
every preference share you get 2 ordinary shares.
Conversion price par value of preference shares/no. of ordinary shares to be acquired.
20
=  Rwf 10
2
Example
Company XYZ Ltd has sold 10,000 ordinary shares of Frw30 (partly called up) plus 20,000 Frw45
preference shares, which are convertible. Compute the total number of ordinary shares after
conversion.
Solution
Conversion ratio = 30/45 = 2/3 for every 2 preference shares you get 3 ordinary shares.
20,000 3
x = 30,000 ordinary shares.
1 1
45
Conversion price =  Rwf 30
3/ 2
Total = 40,000 ordinary shares after conversion.

viii) Non-Convertible Preference Shares.

These cannot be converted into ordinary shares.

2. DEBT FINANCE
Debt finance is a fixed return finance as the cost (interest) is fixed on the par value (face value of debt).
It is ideal to use if there’s a strong equity base. It is raised from external sources to qualifying
companies and is available in limited quantities. It is limited to:
i) Value of security.
ii) Liquidity situation in a given country. It is ideal for companies where gearing allows
them to raise more debt and thus gearing level.
Classification of Debt Finance
Loan finance – this is a common type of debt and is available in different terms usually short term.
Medium term loans vary from 2 - 5 years. Long-term loans vary from 6 years and above
The terms are relative and depend on the borrower. This finance is used on the basis of Matching
approach i.e. matching the economic life of the project to the term of the loan. It is prudent to use
short-term loans for short-term ventures i.e. if a venture is to last 4 years generating returns, it is
prudent to raise a loan of 4 years maturity period.
Conditions under Which Loans Are Ideal
a) When the company’s gearing level is low (the level of outstanding loans is low.
b) The company’s future cash flows (inflows and their stability) must be assured. The company
must be able to repay the principal and the interest.
c) Economic conditions prevailing. The company must have a long-term forecast of the
prevailing economic condition. Boom conditions are ideal for debt.
d) When the company’s market share guarantees stable sales.
e) When the company’s anticipated future expansion programs, justify such borrowing.

Requirements for raising loan

a) History of the company and its subsidiaries.
b) Names, ages, and qualifications of the company’s directors.
c) The names of major shareholders – 51% plus i.e. owner who must give consent.
d) Nature of the products and product lines.
e) Publicity of the product.
f) Nature of the loan – either secured, floating or unsecured.
g) Cash flow forecast.

Reasons why commercial banks prefer to lend short term loans

a) Long-term forecasts are not only difficult but also vague as uncertainties tend to jeopardise
planning e.g. political and economic factors.
c) Short-term loans are profitable. This is because interest is high as in overdrafts.
d) Long term finance loses value with time due to inflation.
e) Cost of finance – in the long term, the cost of finance may increase and yet they cannot pass
such a cost to borrowers since the interest rate is fixed.
f) Commercial banks do credit analysis that is limited to short term situations.
3. Bills of Exchange
Bills of Exchange are a source of finance in particular in the export trade. A Bill of Exchange is an
unconditional order in writing addressed by one person to another requiring the person to whom it is
addressed to pay to him as his order a specific sum of money. The commonest types of bills of
exchange used in financing are accommodation bills of exchange. For a bill to be a legal document; it
must be:
a) Drawn by the drawer.
b) Bear a stamp duty
c) Acceptable by the drawee
e) Mature in time.
It is used to raise finance through:
i) Discounting it.
ii) Negotiating
iii) Giving it out as security.
Advantages of Using a Bill as a Source of Finance
 They are a faster means of raising finance (if drawer is credible).
 Is highly negotiable/liquid investment
 Does not require security
 Does not affect the gearing level of the company
 It is unconditional and can be invested flexibly
 It is useful as a source of finance to finance working capital
 It is used without diluting capital.

4 Lease Finance
Leasing is a contract between one party called lessor (owner of asset) and another called lessee where
the lessee is given the right to use the asset (without legal ownership) and undertakes to pay the lessor
periodic lease rental charges due to generation of economic benefits from use of the assets. Leases can
be short term (operating leases) in which case the lessor incurs the operating and maintenance costs of
the assets or long term (finance leases) in which the lessee maintains and insure the assets.

Lease finance is ideal under the following conditions:

a) When the asset depreciates faster.
b) When the asset is subject to obsolescence
c) When the available asset cannot meet the contemplated expansion program
d) When the asset’s cost is prohibiting
e) If the asset is required seasonally
f) If the asset can generate returns to pay off lease charges in the short run.

Advantage of Leasing an Asset

 It does not tie up the company’s funds in an asset.
 The arrangement may ensure lessor bears the maintenance costs reducing the companies
operating costs.
 The company has the option to purchase assets at the expiry of the lease period at which time it
will know the viability of the asset.
 The company (lessee) will enjoy the lease charges as allowable expenses thus reducing taxable
income and tax liability.
 Lease finance enables the lessee to use the asset to create financial surpluses which may then
be used to buy assets.
 It is usually a long-term arrangement which enables the company to plan returns expected and
operations which may be carried out.

Disadvantage of Leasing an Asset

 It is a pre-conditional finance (as on the use of asset)
 In the long term the lease charges may out-weigh the cost of buying own asset.
 It is available for a selected asset and this limits flexibility.
 It is useful for financing fixed assets and not working capital
 Lease finance may not be renewed leading to loss of business.
 Lease financing lowers the company’s credit rating (i.e. the asset in the balance sheet is shown
as leased asset).

5. Overdraft Finance
This finance is ideal to use as bridging finance in sense that it should be used to solve the company’s
short term liquidity problems in particular those of financing working capital . It is usually a secured
finance unless otherwise mentioned. Overdraft finance is an expensive source of finance and the over-
reliance on it is a sign of financial imprudence as it indicates the inability to plan or forecast financial
needs.

Advantages of Overdraft Finance

 It is useful in financial crisis which an accountant cannot forecast due to abrupt fall in profits
thus liquidity problems.
 In some cases it may be secured on goodwill thus making it flexible finance.
 It does not entail preconditions and is therefore investible in high-risk situations when the firm
would not have finance in normal circumstances.
 It is raised faster and as usual is ideal to invest in urgent ventures e.g. documentary investments
e.g. treasury bonds, shares, treasury bills, housing bonds etc.
 If not used for a long period of time – it does not affect the company’s gearing level and
therefore does not relate to company’s liquidation or receivership.
 Less formalities/procedures involved.
Disadvantages of Overdraft Finance
 It is expensive as the interest rates of overdrafts are much higher than bank rates.
 The use of this finance is an indication of poor financial management principle.
 It may be misused by management because it does not carry pre-conditions
 Being a short-term financial arrangement, it can be recalled at short notice leaving the company
in financial crisis.
6. Plastic Money (Credit Card Finance)
This is finance of a kind whereby a company will make arrangements for the use of the services of a
credit card organisations (through the purchase of credit cards) in return for prompt settlement of bills
on the card and a commission payable on all credit transactions. This is used to finance goods and
services of working capital in nature such as the payment of fuel, spare-parts, medical and other general
provisions and it is rare for it to finance raw materials or capital items.
Limitations of Credit Cards as a Source of Finance
i) These cards lead to overspending on the part of the holder and as such may disorganize the
organization’s cash budget and cash planning.
ii) Limited as to the activities they can finance as they are ideal for financing working capital
items and not fixed assets in which case they are not a profitable source of finance.
iii) They are expensive to obtain and maintain because of associated cost such as ledger fees,
registration, insurance, commission expenses, renewal fees etc.
iv) It is a short-term source and is open only to a few establishments in which case a company can
obtain goods and services from those establishments that can accept them.
v) Entail a lot of formalities to obtain e.g. guarantees, presentation of bank statements and even
charging assets that are partially pledged to secure expenses that may be incurred using these
cards.
vi) They may be misused by dishonest employees who may use them to defraud the organisation
off goods and services which may not benefit such organisations.
vii) Credit card organisation may suspend the use of such cards without notice and this will
inconvenience the holder who may not meet his/her ordinary needs obtained through these
cards.
7. Debenture Finance
A form of long term debt raised after a company sells debenture certificates to the holder and raises
finance in return. The term debenture has its origin from ‘DEBOE’ which means ‘I owe’ and is thus a
certificate or document that evidences debt of long term nature whereby the person named therein will
have given the issuing company the amount usually less than the total par value of the debenture.
These debentures usually mature between 10 to 15 years but may be endorsed, negotiated, discounted
or given as securities for loans in which case they will have been liquidated before their maturity date.
The current interest rate is payable twice a year and it is a legal obligation.
Classification
i) Secured Debentures
These are those types of debentures which a company will secure usually in two ways, secured with a
fixed charge or with a floating charge.
a) Fixed Charge – a debenture is secured with a fixed charge if it can claim on a specific asset.
b) Floating charge – if it can claim from any or all of the assets which have not been pledged as
securities for any other form of debt.
ii) Naked Debentures
These are not secured by any of the company’s assets and as such they are general creditors.
iii) Redeemable Debentures
These are the type of debentures, which the company can buy back after the minimum redemption
period and before the maximum redemption period (usually 15 years) after which holders can force the
company to receivership to redeem their capital and interest outstanding.
iv) Irredeemable Debentures (perpetuities)
These are never bought back in which case they form permanent source of finance for the company.
However, these are rare and are usually sold by company’s with a history of stable ordinary dividend
record.
v) Classification according to convertibility
Convertible debentures – Can be converted into ordinary shares although they can also be converted
into preference shares.
vi) Non-convertible debentures
These cannot be converted into ordinary preference shares and they are usually redeemable.
vii) Sub-ordinate debentures
Usually last for as long as 10 years and they are sold by financially strong companies. Such are not
secured and they rank among general creditors in claiming on assets during liquidation. This means
that they are sub-ordinate to senior debt but superior to ordinary and preference share capital.

2.2. VENTURE CAPITAL

2.2.1. Introduction
Venture capital is capital that is invested (or is available for investing) in private companies.
The venture capital may be provided by a wealthy individual, or it may be provided by a
venture capital firm that manages a venture capital fund. (A venture capital fund consists of
money from investors for investing in private company equity.)

Venture capitalists are therefore investment specialists who raise pools of capital to fund new
ventures which are likely to become public corporations in return for an ownership interest.
They buy part of the stock of the company at a low price in anticipation that when the
company goes public, they would sell the shares at a higher price and therefore make a
considerably high profit.

Venture capitalists seek to invest cash in return for shares in private companies with high
growth
potential. They seek a high return, which is often realised through a stock market listing.
Venture capital may be invested in young start-up companies, but is more commonly invested
in small companies that already have a track record of business development and which need
additional finance to grow. These companies may have borrowed as much money as their
banks are prepared to lend, and do not have enough equity capital (from the existing owners or
retained profits) to expand at the rate or scale required.

Venture capital organisations have been operating for many years. There are now quite a large
number of such organisations. For example:
(a) The British Venture Capital Association is a regulatory body for all the institutions that
have joined it as members.
(b) Investors in Industry plc, or the 3i group as it is more commonly known, is the biggest and
oldest of the venture capital organisations. It is involved in many venture capital schemes in
Europe, Singapore, Japan and the US.

Venture capitalists want to invest in companies that will be successful. The 3i group's publicity
material states that successful investments have certain common characteristics:
 Highly motivated individuals with a strong management team in place
 A well -defined strategy
 A clearly defined target market
 Current revenue between $1m and $100m
 A proven ability to outperform your competitors
 Innovation
The types of venture that capitalists might invest will involve:
a) Business start-ups – When a business has been set up by someone who has already
put time and money into getting it started, the group may be willing to provide finance
to enable it to get off the ground. With start-ups, venture capital often prefers to be one
of several financial institutions putting in venture capital.
b) Business development – The group may be willing to provide development capital for
a company which wants to invest in new products or new markets or to make a
business acquisition, and so which so needs a major capital injection.
c) Management buyout – A management buyout is the purchase of all or parts of a
business from its owners by its managers.
d) Helping a company where one of its owners wants to realize all or part of his
investment. The venture capital may be prepared to buy some of the company’s
equity.

2.2.2.Attributes of venture capital

i) Equity participation – Venture Capital participate through direct purchase of shares or
fixed return securities (debentures and preference shares)
ii) Long term investment – venture capital is an investment attitude that necessitates the
venture capitalists to wait for a long time (5 – 10 years) to make large profits (capital
gains).
iii) Participation in Management – Venture capitalists give their Marketing, Planning and
Management Skills to the new firm. This hands – on Management enable them protect
their investment.

2.2.3. Role of Venture Capital in Economic Development

The types of venture that capitalists might invest will involve:

a) Business start-ups – When a business has been set up by someone who has already
put time and money into getting it started, the group may be willing to provide finance
to enable it to get off the ground. With start-ups, venture capital often prefers to be one
of several financial institutions putting in venture capital.
b) Business development – The group may be willing to provide development capital for
a company which wants to invest in new products or new markets or to make a
business acquisition, and so which so needs a major capital injection.
c) Management buyout – A management buyout is the purchase of all or parts of a
business from its owners by its managers.
d) Helping a company where one of its owners wants to realize all or part of his
investment. The venture capital may be prepared to buy some of the company’s
equity.

2.2.4. Funding Venture Capital

Some other organisations are engaged in the creation of venture capital funds. In these the
organisation raises venture capital funds from investors and invests in management buyouts or
expanding companies. The venture capital fund managers usually reward themselves by taking
a percentage of the portfolio of the fund's investments.

When a company's directors look for help from a venture capital institution, they must
recognise that:
(a) The institution will want an equity stake in the company.
(b) It will need convincing that the company can be successful (management buyouts of
companies which already have a record of successful trading have been increasingly favoured
by venture capitalists in recent years).
(c) It may want to have a representative appointed to the company's board, to look after its
interests, or an independent director (the 3i group runs an Independent Director Scheme).

The directors of the company must then contact venture capital organisations, to try to find one
or more which would be willing to offer finance. Typically, a venture capitalist will consider
offering finance of $500,000 upwards. A venture capital organisation will only give funds to a
company that it believes can succeed.

A venture capitalist may also agree to invest in some redeemable preference shares as well as
equity, but will want a suitable proportion of the company’s equity as part of the financing
arrangement. When a venture capitalist invests in new equity for a company, the company’s
bank may also be prepared to lend more, because the company is now seen as a lower credit
risk. A survey has indicated that around 75% of requests for venture capital are rejected on an
initial screening, and only about 3% of all requests survive both this screening and further
investigation and result in actual investments.
The venture capital organisation (‘VC' below) will take account of various factors in deciding
whether or not to invest.

Factors in investment decisions

The nature of the company's Viability of production and selling potential
product
Expertise in production Technical ability to produce efficiently
Expertise in management Commitment, skills and experience
The market and competition Threat from rival producers or future new entrants
Future profits Detailed business plan showing profit prospects that
compensate for risks
Board membership To take account of VC's interests and ensure VC has
say in future strategy
Risk borne by existing owners Owners bear significant risk and invest significant part
of their overall wealth

2.2.5.Reasons for Significant Growth in Venture Capital in the Developed Countries

i)Public attitude i.e a favourable attitude by the public at large towards entrepreneurship,
success as well as failure.
ii) Dynamic financial system e.g efficient stock exchange and a competitive banking
system.
iii) Government support – e.g taxation system to encourage venture capital e.g tax
concessions and investment allowance taxes.
iv) Establishment of venture capital institutions e.g investors in the industry.
v) Growth in the number of Management buyers (MBO) which have created a demand for
equity finance.

2.2.6. Constraints of Venture Capital in Rwanda

1. Lack of enough number of investors, hence inadequate equity capital.
2. Inefficiencies of stock market – RSE is inefficient and investors cannot sell the shares
in future. Prices do not reflect all the available information in the market.
3. Infrastructural problems – this limits the growth rate of small firms which need raw
materials and unlimited access to the market factors of production.
4. Lack of managerial skills on part of venture capitalists and owners of the firm.
5. Focus on low risk ventures e.g confining to low technology, low growth sectors with
minimum investment risks.
6. Conservative approach by the venture capitalists.
7. Delay in project evaluation e.g months or more hence entrepreneurs loose interest in
the project.
8. Lack of government support and inefficient financial system.

2.2.7.Key elements for the success of venture capital in any country.

 A broad-based (and less family based) entrepreneurial traditional societies and

government encouragement for innovations, creativity and enterprise.
 A less regulated and controlled business and economic environment where attractive
customer opportunities exists or could be created from high-tech and quality products.
 Existence of disinvestments mechanisms, particularly over-the counter stock exchange
catering for the needs of venture capitalists.
 Fiscal incentives which render the equity investment more attractive and develops ‘equity
cult’ in investors.
 A more general, business and entrepreneurship oriented education system where
scientists and engineers have knowledge of accounting, finance and economics and
accountants understand engineering or physical sciences.
 An effective management education and training programme for developing
professionally competent and committed venture capital managers; they should be trained
to evaluate and manage high technology, high risk ventures.
 A vigorous marketing thrust, promotional efforts and development strategy, employing
new concepts such as venture fair clubs, venture networks, business incubators etc. for
the growth of venture capital.
 Linkage between universities/technology institutions, Research and Development.
Organisations, industry, and financial institutions including venture capital firms.
 Encouragement and funding or Research and Development by private public sector
companies and the government for ensuring technological competitiveness.

2.3. FINANCIAL MARKETS

2.3.1. DEFINITION
Financial markets term refers to an elaborate system of the financial institution and
intermediaries and arrangement put in place and developed to facilitate the transfer of funds
from surplus economic units (savers) to deficit economic units (investors).
2.3.2. FUNCTIONS OF FINANCIAL MARKETS/INSTITUTIONS IN THE ECONOMY
1. Distribution of financial resources to the most productive units. Savings are transferred
to economic units that have channels of alternative investments. (Link between buyers
and sellers).
2. Allocation of savings to real investment.
3. Achieving real output in the economy by mobilizing capital for investment.
4. Enable companies to make short term and long term investments and increase liquidity
of shares.
5. Provision of investment advice to individuals through financial experts.
6. Enables companies to raise short term and long term capital/funds
7. Means of pricing of securities e.g R.S.E. index shares indicate changes in share prices.
8. Provide investment opportunities. Savers can hold financial instrument for investment
made.
2.3.3. FINANCIAL MARKETS TYPES
Financial markets are broadly classified into 2:
1. Capital Markets
2. Money Markets
Capital markets are sub-divided into 2:
a) Security markets e.g stock exchange dealing with instruments such as shares,
debentures etc.
b) Non-security/instrument market e.g mortgage, capital leases, security market is sub-
divided into 2.
 Primary market
 Secondary market

CAPITAL MARKET
These are markets for long term funds with maturity period of more than one year. E.g of
Financial instruments used here are debentures, terms, loans, bonds, warrants, preference
shares, ordinary shares etc.

The capital market serves as a way of allocating the available capital to the most efficient
users. Capital market financial institution includes:
1. Stock exchange
2. Development bank
3. Hire purchase companies
4. Building societies
5. Leasing firms

Functions of Capital Markets are:

a) Providing long term funds which are necessary for investment decisions.
b) Provide advice to investors as to which investments are viable.
c) Long term investments are made liquid, as the transfer between shareholders is
facilitated.
d) Facilitates the international capital inflow.
e) Facilitating the liquidation and marketing of a long term
f) Acting as a channel through which foreign investments find their way into the market.

Money/discount markets
 Are discount and acceptance financial institutions
 This is a market for S.T funds maturing in one year. Money market works through
financial institutions. It facilitates transfer of capital between savers and users.
 The transfer can be direct (from saver to investor) and indirectly through an intermediary).
 Foreign exchange market is also part of money market.
 The money market or discount market is the market for short term loans.

Financial Instruments in Money market include:

1. Commercial paper
2. Treasury bills
3. Bills of exchange
4. Promissory notes
5. Bank overdrafts
6. Bankers certificate of deposit

These instruments are sold by commercial banks, merchant banks, discounting houses,
acceptance houses, and government.

Primary Markets
These are markets that deal with securities that have been issued for the first time. The money
flows directly from transferor (saver of money) to transferee (investing person). They
facilitate capital formation.
Economic Advantage of Primary Markets
1. Raising capital for business.
2. Mobilizing savings
3. Government can raise capital through sale of Treasury bonds
4. Open market operation to effect monetary policy of the government i.e control of
excess liquidity in the economy
5. It is a vehicle for direct foreign investment.

Economic Advantage/Role of Secondary Markets in the Economy

1. It gives people a chance to buy shares hence distribution of wealth in economy.
2. Enable investors realize their investments through disposal of securities.
3. Increases diversification of investments
4. Improves corporate governance through separation of ownership and management.
This increases higher standards of accounting, resource management and transparency.
5. Privatisation of parastatals . This gives individuals a chance for ownership in large
companies.
6. Parameter for health economy and companies
7. Provides investment opportunities for companies and small investors.

2.3.4. THE STOCK EXCHANGE MARKET

2.3.4.1.The Idea and Development of a Stock Exchange
Stock exchange (also known as stock markets) are special “market places” where already held
stocks and bonds are bought and sold. They are, in effect, a financial institution, which
provides the facilities and regulations needed to carry out such transactions quickly,
conveniently and lawfully.
Stock exchanges developed along with, and are an essential part of the free enterprises system.
(No stock exchanges exist in the communist world outside Hong Kong and Macao – which
have special status, and Taiwan which is also claimed by China).
The need for this kind of market came about as a result of two major characteristics of joint
stock company (Public Limited Company), shares.

1. First of all, these shares are irredeemable, meaning that once it has sold them, the
company can never be compelled by the shareholder to take back its shares and give
back a cash refund, unless and until the company is winding up and liquidates.

2. The second characteristic is that these shares are, however, very transferable and can be
bought and resold by other individuals and organizations, freely, the only requirement
being the filling and signing of a document known as a share transfer form by the
previous shareholder. The document will then facilitate the updating of the issuing
companies. shareholders register.

2.3.4.2. Definition of a stock exchange

Organized and regulated financial market where securities are bought and sold at prices
governed by the forces of demand and supply. Stock exchanges impose stringent rules, listing
requirements, and statutory requirements that are binding on all listed and trading parties.
2.3.4.3. Establishment of Rwanda Stock Exchange (RSE)
The Rwanda Stock Exchange Limited was incorporated on 7th October 2005 with the
objective of carrying out stock market operations. The Stock Exchange was demutualized from
the start as it was registered as a company limited by shares. The company was officially
launched on 31st January 2011.
2.3.4.5. Functions of the Rwanda Stock Exchange
The basic function of a stock exchange is the raising of funds for investment in long-term
assets.
Stock exchanges have multiple roles in the economy. This may include the following:
Raising capital for businesses: The Stock Exchange provides companies with the facility to
raise capital for expansion through selling shares to the investing public.
Mobilizing savings for investment: When people draw their savings and invest in shares, it
leads to a more rational allocation of resources because funds, which could have been
consumed, or kept in idle deposits with banks, are mobilized and redirected to promote
business activity resulting in stronger economic growth and higher productivity levels of firms.
Corporate governance: By having a wide and varied scope of owners, companies generally
tend to improve management standards and efficiency to satisfy the demands of the
stakeholders. Creating investment opportunities for small investors
Government capital-raising for development projects: Governments at various levels may
decide to borrow money to finance infrastructure projects by selling bonds.
Barometer of the economy: At the stock exchange, share prices rise and fall depending,
largely, on market forces. Therefore, the movement of share prices and in general of the stock
indexes can be an indicator of the general trend in the economy.

2.3.4.6.THE ROLE OF STOCK EXCHANGE IN ECONOMIC DEVELOPMENT

1. Raising Capital for Businesses
The Stock Exchange provides companies with the facility to raise capital for expansion
through selling shares to the investing public.
2. Mobilising Savings for Investment
When people draw their savings and invest in shares, it leads to a more rational allocation of
resources because funds which could have been consumed, or kept in idle deposits with banks
are mobilized and redirected to promote commerce and industry.
3. Redistribution of Wealth
By giving a wide spectrum of people a chance to buy shares and therefore become part-owners
of profitable enterprises, the stock market helps to reduce large income inequalities because
many people get a chance to share in the profits of business that were set up by other people.

4. Improving Corporate Governance

By having a wide and varied scope of owners, companies generally tend to improve on their
management standards and efficiency in order to satisfy the demands of these shareholder. It
is evident that generally, public companies tend to have better management records than
private companies.

5. Creates Investment Opportunities for Small investors

As opposed to other business that require huge capital outlay, investing in shares is open to
both the large and small investors because a person buys the number of shares they can afford.
Therefore the Stock Exchange provides an extra source of income to small savers.

6. Government Raises Capital for Development Projects

The Government and even local authorities like corporations may decide to borrow money in
order to finance huge infrastructural projects such as sewerage and water treatment works or
housing estates by selling another category of shares known as Bonds. These bonds can be
raised through the Stock Exchange whereby members of the public buy them. When the
Government gets this alternative source of funds, it no longer has the need to overtax the
people in order to finance development.
7. Barameter of the Economy
At the Stock Exchange, share prices rise and fall depending, largely, on market forces. Share
prices tend to rise or remain stable when companies and the economy in general show signs of
stability. Therefore their movement of share prices can be an indicator of the general trend in
the economy.

Advantages of Investing In Shares

1. Income in form of dividends
When you have shares of a company you become a part-owner of that company and therefore
you will be entitled to get a share of the profit of the company which come in form of
dividends. Furthermore, dividends attract a very low withholding tax of 5% only.

2. Profits from Capital Appreciation

Shares prices change with time, and therefore when prices of given shares appreciate,
shareholders could take advantage of this increase and set their shares at a profit.

3. Share Certificate can be used as a Collateral

4. Shares are easily transferable
The process of acquiring or selling shares is fairly simple, inexpensive and swift and therefore
an investor can liquidate shares at any moment to suit his convenience.

5. Availability of Investment Advice: An investor can still benefit from trading in shares
even though he may not be having the technical expertise relevant to the stock market.
6. Participating in Company Decisions: By buying shares and therefore becoming a part-
owner in an enterprise, a shareholder gets the right to participate in making decisions about
how the company is managed.
STOCK MARKET TERMINOLOGY
1. BROKER
 A dealer at the market who buys and sells securities on behalf of the public investors.
 He is an agent of investors
 He is the only authorized person to deal with the quoted securities. He is authorized by
BNR
 He obtains the suitable deal for his clients/investors, gives financial advice and charges
commission for his services.
 He doesn’t buy or sell shares in his own right hence he cannot be a market marker.
 He must maintain standards set by the stock exchange.

2. JOBBERS/SPECULATORS
 This is a dealer who trades in securities in his own right as a principal.
 He can set prices and activate the market through his own buying and selling hence he
is a market maker.
 He engages in speculation and earns profit called Jobbers’ turn (selling price – buying
price).
 He does not deal with members of the public unlike brokers. However, brokers can
buy and sell shares through jobbers.

There are 3 types of jobbers

a) Bulls
 A jobber buy shares when prices are low and hold them in anticipation that the price
will rise and sell them at gain.
 When a market is dominated by bulls (buyers predominate sellers), it is said to be
bullish The share prices are generally rising.
 Therefore the market is characterized by an upward trend in security prices.
 It signifies investors confidence/optimism in the future of economy.
b) Bears
 A speculator/jobber who sells security on expectation of decline in prices in future.
 The intention is to buy same securities at lower prices in future thereby making a gain.
 When market is dominated by bears (sellers predominate buyers) it is said to be bearish
 It is characterized by general downward trend in share prices. It signifies investors
pessimism about the future prospects of the economy.
c) Stags
 This is a jobber found in primary markets
 He buys new securities offered to the public and believes that they are undervalued.
 He believes the price will rise and sell them at a gain to the ultimate investors
 Stags are vital because they ensure full subscription of the share issue.

3, Underwriting
 This is the assumption of risk relating unsubscribed shares
 When new shares are issued, they may be underwritten/unsubscribed. A merchant
banker agrees, under a commission to take up any shares not bought by the public.
 They therefore ensure that all new issues are successful
 Underwriters are very important in pry markets and play the following roles:
 Advice firms on most suitable issue price
  Ensure shares are fully subscribed by taking up all unsubscribed shares
 Advice the firms on where to source funds to finance floatation costs.
4. Blue Chips
 Are first class securities of firms which have sound share capital and are internationally
reputable.
 They have very good dividend record and are highly demanded in the markets.
Individuals holding such securities are reluctant to sell them because of their high
value.
5. Going short or long on a share
 This is the process of selling (going short) or buying (going long) on a share that one
does not have/own
 The aim is to make gain from assumed change in the market value of shares
 It is aided by brokers in countries where it is practiced
 Investors going short or long are required to pay a premium called margin on the
transaction.
TRADING MECHANISM AT RSE
1. An investor approaches a broker who takes his bid/offer to the trading floor.
2. At the trading floor, the buying and selling brokers meet and seal the deal.
3. The investor is informed of what happened/transpired at the trading floor through a contract
note. The note is sent to buying and selling investors.
The note contains details such as:
 Number of shares bought or sold
 Buying/selling price
 Charges/commission payable etc.
4. Settlement is made through the brokers.
5. Old share certificate is cancelled (for selling investor) and a new one is issued in the name of
buying investor.
Factors to Consider when Buying Shares of a Company
1. Economic conditions of the country and other non-economic factors e.g. unfavourable climatic
conditions and diseases which may lead to low productivity and poor earnings.
2. State of management of the company e.g are the B.O.D. and key management personnel of
repute? They should be trusted and run the company honestly and successfully.
3. Nature of the product dealt in and its market share e.g is the product vulnerable to weather
conditions? Is it subject to restrictions?
4. Marketability of the shares – how fast or slowly can the shares of the firm be sold?
5. Diversification i.e does the company have a variety of operations e.g multi-products so that if
one line of business declines, the other increases and the overall position is profitable.
6. Company’s trading partners (local and abroad) and its competitors.
7. Prospects of growth of the firm due to expected growth in demand of products of the firm.

Factors Affecting/Influencing Share Prices

All sorts of influences affect share prices. These influences include:
1. The recent profit record of the company especially the recent dividend paid to shareholders and
the prospects of their growth and stability.
2. The growth prospects of the industry in which the company operates.
3. The publication of a company’s financial results i.e. Balance Sheet and profit and loss
statement.
4. The general economic conditions situations e.g boom and recession e.g during boom, firms
would have high profits hence rise in prices.
5. Change in company’s management e.g entry and exit of prominent corporate personalities.
6. Change on Government economic policy e.g spending, taxes, monetary policy etc. These
changes influence investors’ expectations.
7. Rumour and announcements of impending political changes eg. General elections and new
president will cause anxiety and uncertainty and adversely affect share prices.
8. Rumours and announcement of mergers and take-over bids. If the shareholders are offered
generous terms/prices in a take-over, share prices could rise.
 9. Industrial relations eg strikes and policies of other firms.
10. Foreign political developments where the economy heavily depends on world trade.
11. Changes in the rate of interest on Government securities such as Treasury Bills may make
investors switch to them. Exchange rates will also encourage or discourage foreign investment
in shares.
12. Announcement of good news eg that a major oil field has been struck or a major new
investment has been undertaken. The NPV of such investment would be reflected in share
prices.
13. The views of experts e.g articles by well-known financial writers can persuade people to buy
shares hence pushing the prices up.
14. Institutional buyers such as insurance companies can influence share prices by their actions.
15. The value of assets and the earnings from utilization of such assets will also influence share
prices.

2.3.4. CAPITAL MARKET AUTHORITY (CMA)

Capital Market Authority (CMA) is a public institution established by Law No.23 /2017 of 31/05/2017
responsible for developing and regulating the capital markets industry, commodities exchange and
related contracts, collective investment schemes and warehouse receipts system.
The Authority is responsible for:
1. Implementing the Government policy on Capital Market;
2. Preparing draft policies on capital market;
3. Advising Government on policy relating to the capital market;
4. Promoting public awareness on the capital market and develop such market;
5. Elaborating action plans and conducting studies in order for CMA to achieve its mission;
6. Formulating principles and regulations for the capital market;
7. Making regulations governing capital market business in accordance with the Law regulating capital
market in Rwanda;
8. Controlling and supervising all capital market activities with a view to maintain proper code of
conduct and acceptable practices on the capital market;
9. Registering capital market business and related instruments provided for by the Law regulating
capital market in Rwanda;
10. Issuing, suspending, and withdrawing licenses and approvals related to capital market business;
11. Seeking to achieve fairness, efficiency and transparency in the functioning of the capital market;
12. Protecting citizens and investors in capital market from unfair and unsound practices or practices
involving fraud, deceit, cheating or manipulation;
13. Monitoring, supervising, and take actions with regard to the compliance with this Law and
regulations thereto related as well as with the Law regulating capital market in Rwanda and
regulations thereto related;
14. Co-operating and collaborating with other regulatory bodies in accordance with the provision of the
Law regulating capital market in Rwanda;
15. Consulting concerned organs prior to making any decision to modify principles and regulations of
the profession that may have impact on the functioning of the capital market;
16. Keeping adequately and timely records of decisions made in the accomplishment of CMA mission;
17. Accomplishing any other mission assigned by the Law regulating capital market in Rwanda.

MARKET EFFICIENCY AND ITS IMPLICATIONS

Market Efficiency
Efficient markets are those markets that operate at low costs, prices security efficiently and allocates
funds to firms and organizations with the most promising real investment opportunities.
From the above definition there are three types of market efficiency:
1. Operational efficiency – (low costs)
2. Pricing efficiency – (efficient price)
3. Allocational efficiency – (allocates funds)

Operational Efficiency
These market prices transaction services and cost which are as low as possible given the efforts
associated with having these services provided.
Pricing efficiency (fair game)
These implies that the market prices security i.e security price reflect all the available information
security prices adjust quickly and in an unbias manner to incorporate any new information as it
becomes available. Since new information is not predictable the security prices will follow a random-
walk.
Allocation efficiency
These implies that the markets allocates fund to firms with the most promising real investments
opportunities. Allocation efficiency assumes operational and pricing efficiency.
The most important efficiency to F.M is the pricing efficiency to enable him to maximize shareholders
wealth.

Forms of market price efficiency:

-Weak form
In this form the current security prices reflect information regarding the historical pattern of price
movement. Therefore no trading strategy based on historical prices can yield above normal return.
-Semi-Strong form
In this form, the current security prices incorporate historical pattern of price movements as well as all
public available information about the company. An investor cannot out perform (do better) than the
market by analyzing any public available information about any company.
-Strong form
In this form, the current security prices already incorporate all public as well as privately held
information. It implies that even those accessible to confidential (price sensitive) information cannot
use it to derive superior returns or results.
Implications of market efficiency
1. Timing of financial policy e.g issue of redemption of shares. In an efficient there is no need
of timing financial policy e.g issue or sale of share since nobody knows the direction that the
market will take e.g today’s low may be the highest in the next ten years.
2. Issue of shares at a discount – In an efficient market, the current security price reflect all
available/relevant information. There is therefore no need for significant price discount to
encourage investors to buy. If a firm issues shares at the current market prices it raises funds at
a fair cost and investors also obtain a fair return of the risks assumed.
3. Creative Accounting : In an efficient market there is no need to manipulate financial
statement calculations to influence share prices since security prices only respond to fundamental
information. Efficient market cannot be fooled.
4. Merger as an investment decision – In an efficient market, purchase of a share is zero NPV
transaction. This implies that if the firm acquires another at its current market capitalization, it
simply breaks even. This question a rationale behind many mergers.
5. Use of NPV as an appraisal technique – NPV analysis assumes market efficiency i.e the
returns offered by the investments are commensurate with the risks assumed. Use of NPV in
an efficient market can provide misleading results.
Theories that explain the behaviour of yield curve:
Yield Curve is a curve basically that shows the trade off between the yield of a debt (Kd) instrument
and its term (period to marketing).
Term structure of interest rates refers to the relationship between the yield to maturity and the terms
of the debt instrument

% Yield Yield curve

Kd

n(term of maturity)
Theories – Term Structure theories
1. The expectation theory
This states that the shape of the yield curve depends on the markets expectations about future
interest rates. If future interest rates are expected to rise, the shape of the yield curve will be
upward sloping.
2. Liquidity preference theory
This states that investors normally prefer liquidity (cash) to other investments even the low
risky one like Treasury bills. Investors therefore expect to be paid a high premium for being
deprived of their liquidity for longer periods. The normal upward rising shape of the yield
curve can be explained by this theory.
3. Segmental Market Theory
This states that the market short term and long term debt instruments are separate and distinct.
The shape of the yield curve depends on the demand and supply forces in each market. There
is a ‘wiggle’ (form of disturbance) in the yield curve where the two markets meet.
The forces in each market are weakest where the wiggle occurs.

% yield
Kd
Wiggle

Short term Long term

debt debt

n (maturity period)
Implications
The current shape of the yield reflects ( ) the market expectation about future interest. There is need
to inspect current shape of the yield curve on designing lending and borrowing schemes.

e.g an upward rising yield curve indicates that interest rates are expected to rise. The firm should
therefore avoid long term on variable rates, instead it can borrow long term at fixed rate or short term
on variable rates.
TOPIC 3: COST OF CAPITAL AND CAPITAL STRUCTURE

3.1. COST OF CAPITAL

The cost of capital is the minimum required rate of return on the investment project that keeps
the present wealth of shareholders unchanged. It therefore represents a financial standard for
allocating the firm’s funds supplied by owners and creditors to the various investments
projects in the most efficient manner.
The capital structure of a typical company will include the following types of long-term
capital:
a) Ordinary share capital
b) Preference share capital
c) Debentures
To determine the optimal finance combination, company will need to calculate the cost of each
particular finance being used and also the combined cost of capital i.e. the composite cost of
capital.
COST OF EQUITY CAPITAL
This is the ordinary shareholders’ required rate of return, which equates the PV of the expected
dividends with the market value of the share. It reflects the return shareholders would obtain if
cash flows were paid out as dividends. It is based on dividend valuation model, which states
that ex-dividend share price =
d1 𝑑2 d3 dn
do= 1 + 2 + 3 + ⋯………… 𝑛
(1+𝑘𝑒) (1+𝑘𝑒) (1+𝑘𝑒) (1+𝑘𝑒)
where:
d =the constant dividend per share
ke =cost of equity capital
n =year (i.e. time period)
Assuming the dividend continues forever, the ex-dividend share price =
MVe =d / ke
And which means that the cost of capital equals:
Ke=dividend / Market value i.e ke=de / MVe
ASSUMPTIONS OF DIVIDEND VALUATON MODEL
1. No issue expenses
2. All shareholders have the same marginal rate of time preference i.e. future
expectations.
3. Cost of lending and borrowing are the same.
4. The dividend for which the funds are required will be of the same risk type as existing
dividend.
5. No taxation
6. All shareholders have perfect information about the company’s future
Cost of equity capital without growth in dividend
This is calculated using the formula bellow:
Ke = d /Mve
Where:
D =the constant dividend
Ke =cost of equity capital
Mve =market value per share ex-div
 Where the market value given is cum-div i.e. dividend is incorporated in the
market value given. Do not use it. Ascertain the amount of the dividend and
deduct it from the figure given to become ex-div.
Example 3.1.
 10m Frw1 ordinary shares currently valued at Frw 3.00 per share finance Temiyemi plc. a
dividend of Frw6 m is due for payment.
You are required to calculate the cost of equity capital
Ke = d × 100% i.e 6m ×100%
mve 30m – 6m
= 25%
The market value of Frw 3.00 given is cum div because the dividend has not been
paid but about to be paid.
COST OF CAPITAL WITH GRWOTH IN DIVIDEND
In practice, shareholders expect dividend to increase yearly and not to remain constant to
perpetuity. The cost of equity capital given and expected growth in dividend is expressed
as follows:
. ke = do(1 + g) + g or ke =d1 + g
mve mve
Where:
DO = latest / current dividend paid / payable
d1 = dividend payable in year one (expected, next year)
incorporating element of growth.
g = growth rate
Ke = cost of equity capital
n = year (i.e time period)
Mve = market value per share ex – div
Example 3.2

Mende Nig plc has an authorized share capital of Frw50m of Frw1. 80% of the share capital
had been issued and each is currently valued at 3.20 Frw. dividend amounting to Frw16m was
recently paid. The estimated growth rate is 18%.
Required: calculate the cost of the equity.
Solution
i. Issued share capital = 80% of Frw50 i.e Frw40m
ii. DPS =16M /40m shares i.e 0.4 m
iii. Ke = (do( 1 + g) )/mve +g
Ke = (0.4 (1.18)/3.20) +0.18
Ke = 32,75%

ESTIMATING THE GROWHT RATE

Where the value of the growth rate (g) is not given and there is enough data to enhance its
computation, then the growth rate should be computed.
1. Dividend growth method
𝑛−1 𝑙𝑑
g = √ − 1 or
𝐵𝑑
𝑛 𝑙𝑑
g = √ − 1
𝐵𝑑
where:
g = growth rate
ld = latest dividend
Bd =Base dividend
N = number of years data provided / number of growth

2. Gordon’s growth method / investment on earnings model

g =r × b
Where,
g = Growth rate
r = Return on investment
b = Retention ratio/ Rate i.e Proportion of earnings retained.
THE ASSUMPTIONS OF GORDON’S GROWTH MODEL

1. Assumes the shares are quoted and a market price exists.

2. Assumes the shareholder’s growth expectations are accurately reflected by ‘g’.
3. Future changes in share price are ignored which represent a potential gain / loss.
THE MAJOR OBJECTON TO THE GROWTH MODEL METHODS
A serious objections to the ‘growth’ model method of calculating the cost of equity capital is
that there must be great practical difficulties for shareholders in deciding what the rate of
growth should be.
Example 3.3
You are given the following information about flair plc, which is financially equity –financed
company. The number of shares in issue is 150,000 of Frw1 each.
Current dividend Frw6,158
Market value per share Frw3,42
Current Earnings Frw62,858
Net Assets Frw315,000
Dividend -5 years ago Frw2,473
You are required to estimate the cost of equity capital for the company.
Solution
Ke = 6,158 (Frw1.20)/(150,000 +Frw 3,42) + 20
Ke = 21.4%

Working:
Calculation of the growth rate
n Ld
g = √ − 1
Bd
5 6,158
g = √2,473 − 1
5
g = √2.4900 − 1
g = 20%
Note: where the question gives the number of years of dividend as in the above Example,
then the 5 year is used direct (number of growth); but where the dividend for the years are
given by year, then use n-1 (number of years data provided) as in the Example below.
Using Gordon’s growth model
g = r × b

62,858
r = × 100 =20%
315,000
𝟔𝟐,𝟖𝟓𝟖 − 𝟔,𝟏𝟓𝟖
b = =90%
𝟔𝟐,𝟖𝟓𝟖
g = 0.20 × 0,90 =18%
do ( 1 + g)
Ke = + g
mve
6,158 (1.18)
Ke = 20 + .18
150,000 × 𝑅𝑤𝑓3.42

Ke = 19.4%
Example 3.4
Oluoke Nig.plc is financed by Frw60m Frw1 ordinary shares currently valued at 156 Frw per
share.
The results of the last five financial years are as follows:
Yr Earnings Dividends
20×4 Frw 20m Frw 15.6m
20×3 Frw 18m Frw 15m
 20×2 Frw 16m Frw 13.2m
20×1 Frw 15.4m Frw 12.3m
20×0 Frw 13.9m Frw 11.1m
Calculate the company’s cost of Equity
SOLUTION
𝐝𝐨 ( 𝟏 + 𝐠)
Ke = + 𝐠
𝐦𝐯𝐞
𝟐𝟔 ( 𝟏.𝟎𝟗)
Ke = + . 𝟎𝟗
𝟏𝟓𝟔
ke = 27.17%
working:
calculation of the growth rate
𝐧−𝟏 𝐋𝐝
g = √ − 𝟏
𝐄𝐝
𝟓−𝟏 𝟏𝟓,𝟔𝐦
g = √ − 𝟏
𝟏𝟏.𝟏𝐦
𝟓
g = √𝟐. 𝟒𝟗𝟎𝟎 − 𝟏
g = 9%

CAPITAL ASSET PROCING MODEL (CAPM)

Capital asset pricing model (CAPM) – CAPM is a technique that is used to establish the
required rate of return of an investment given a particular level of risk. According to CAPM,
the total business risk of the firm can be divided into 2:
Systematic Risk – This is the risk that affects all the firms in the market. This risk cannot
be eliminated/diversified. It is thus called undiversifiable risk. Since it affects all the firms
in the market, the share price and profitability of the firms will be moving in the same
direction i.e. systematically. Examples of systematic risk are political instability, inflation,
power crisis in the economy, power rationing, natural calamities – floods and earthquakes,
increase in corporate tax rates and personal tax rates, etc. Systematic risk is measured by a
Beta factor.

Unsystematic risk – This risk affects only one firm in the market but not other firms. It is
therefore unique to the firm thus unsystematic trend in profitability of the firm relative to the
profitability trend of other firms in the market. The risk is caused by factors unique to the firm
such as:
 Labour strikes by employees of the firm;
 Exit of a prominent corporate personality;
 Collapse of marketing and advertising programs of the firm on launching of a new
product;
 Failure to make a research and development breakthrough by the firm, etc

CAPM relates the expected return from an investment (Rs i.e. ke) to the degree of risk from the
investment. The required rate of return Is made up of two parts:
(i) Risk free return
(ii) Risk premium
CAPM is only concerned with systematic risk. According to the model, the required rate of
return will be highly influenced by the Beta factor of each investment.
The risk premium is calculated by applying the project’s beta factor (β) to the difference
between the market return and the risk free rate of the return;
RS=Rf + β (Rm – Rf)
Where:
RS = Minimum required rate of return / cost of equity capital.
Rf = Risk free of return
Rm = Market portfolio’s expected rate of return
 β = Risk measurement
(Rm – Rf) = Market premium risk
β (Rm – Rf) = Risk premium

THE ASSUMPTIONS OF CAPM

1. There is no taxation
2. There is no inflation
3. There is only on risk-free rate of borrowing
4. All investor hold a diversified portfolio.
5. All investors are rational and risk averse.
6. All investors have the same one period time horizon.
7. The beta co-efficient is measurable.

Limitations of using CAPM in investment decisions

The greatest practical problems with the use of the CAPM in capital investment decisions are
as follows.
(a) It is hard to estimate returns on projects under different economic environments, market
returns under different economic environments and the probabilities of the various
environments.
(b) The CAPM is really just a single period model. Few investment projects last for one year
only and to extend the use of the return estimated from the model to more than one time period
would
require both project performance relative to the market and the economic environment to be
reasonably stable. In theory, it should be possible to apply the CAPM for each time period,
thus arriving at successive discount rates, one for each year of the project's life. In practice,
this would exacerbate the estimation problems mentioned above and also make the discounting
process much more cumbersome.
(c) It may be hard to determine the risk-free rate of return. Government securities are
usually taken to be risk-free, but the return on these securities varies according to their term to
maturity.
(d) Some experts have argued that betas calculated using complicated statistical techniques
often overestimate high betas, and underestimate low betas, particularly for small companies.
Example 3.5
Calculate the cost of equity capital for Akwa-Ibom plc from the data given below, using the
Capital Asset Pricing Model;
Beta coefficient for Akw-Ibom plc 0.5%
Expected rate of return on risk free securities 8%
Expected return on the market portfolio 12%
Solution
RS=Rf + β (Rm – Rf)
RS= 8 + 0.5 (12 – 8)
RS = 8 + 0.5 (4)
RS= 8 + 2
RS= 10%
Example 3.6
KK Ltd is an all equity firm whose Beta factor is 1.2, the interest rate on T. bills is currently at
8.5% and the market rate of return is 14.5%. Determine the cost of equity Ke, for the
company.
Solution
Rf = 8.5% Rm = 14.5% Beta of equity = 1.2
Ke = Rf + (Rm – Rf)BE
= 8.5% + (14.5% - 8.5%) 1.2
= 8.5% + (6%)1.2
= 15.7%
Example 3.7
Q plc has a β of 1.5 .The market is giving a return of 12% and the risk free rate is 5%
Required: What will be the required return from Q plc?
Solution: Required return = 5% +(12% – 5%) 1.5 = 15.5%
Example 3.8
R plc has a β of 0.8.The market is giving a return of 16% and the risk free rate is 8%.
Required: What will be the required return from R plc?
Solution: Required return = 8% +(16% – 8%) 0.8 = 14.4%
Example 3.9
S plc is giving a return of 20%. The stock exchange as a whole is giving a return of 25%, and
the return on government securities is 8%.
Required: What is the β of S plc?
Solution
20% = 8%
+ (25% –
8%) β 17β
= 12 β =
¹²⁄₁₇ = 0.706
Example 3.10
T plc is all equity financed. It wishes to invest in a project with an estimated β of 1.4, which is
significantly different from the business risk characteristics of T’s current operations. The
project requires an outlay of Frw100,000 and is expected to generate returns of Frw15,000 p.a.
in perpetuity. The market return is 11% and the risk free rate is 6%.
Required: Estimate the minimum return that T will require from the project and assess
whether or not the project is worthwhile
Solution
Required return = 6% + (11% – 6%) 1.4 = 13%
df @ 10% PV @ 10%
0 (100,000) 1 (100,000)
1 – ∞ 15,000 p.a. ¹⁄₀.₁₃ 115,385
NPV +15,385
The NPV is positive and so the project is worthwhile.

COST OF PREFERENCE SHARE CAPITAL

The estimation of the cost of fixed interest of fixed dividend capital is much easier than the
estimation of the cost of ordinary capital because the received by the holder of the security is
fixed by contract and will not fluctuate in amount.
𝐝
kp = × 𝟏𝟎𝟎
𝐌𝐯𝐩
where:
kp = Cost of preference share capital
d = Last / current dividend paid / payable
mvp =Market value of preference shares ex-div

Cost of redeemable preference shares

The cost of debt capital already issued is the rate of interest (IRR) which equates the current
market value with the discounted future cash receipts of the security i.e
d1 d2 d3 dn
mvp = 1 +𝑘𝑝1 + 1 +𝑘𝑝2 + 3
+ ⋯ …. + IRR
1 +𝑘𝑝 1 +𝑘𝑝𝑛

COST OF DEBENTURE CAPITAL

This is the minimum rate of return required by debenture holders in order to maintain their
existing market value.
Bank loan
A bank loan is a loan of a specific amount from a bank for a set period. Repayment may be
in instalments or at the end of the loan, and interest will be payable on the amount
outstanding. Security is likely to be in the form of a floating charge over the company's
assets.
Loan notes
Loan notes are issued by the company, backed by a written acknowledgement of the debt
given under seal containing provisions on payment of interest and the terms of repayment
of principal. It may be held by more than one lender. Loan notes of listed companies can be
traded, and they may be redeemable (repayable at a certain time), convertible (can be
converted into share capital at a certain time) or irredeemable.
The cost of debt may differ because:
(i) Loan note holders can trade the loan notes and may therefore accept a lower yield
in return for better liquidity.
(ii) The security that the bank demands may differ from the security given to the loan
note holders. A lower rate of interest may be accepted in return for stronger
security.
(iii) The loan notes cover a different period from the bank loan. When the loan notes
were issued, expectations about the level of interest rates and the business and
financial risks faced by WEB may have been different.
Cost of irredeemable Debentures

This is the minimum rate of return required by debenture holders in order to maintain their
existing market value. Is it calculated as follows:
𝐅 (𝟏−𝐭)
Kd = × 𝟏𝟎𝟎
𝐌𝐯𝐝
Where:
Kd = Cost of debt capital
F = Latest / current interest paid / Payable
Mvd = Market value of debt ex-int
T = corporation tax rate
Example 3.11
ABC plc has in issue, 12% Frw500m irredeemable debentures currently valued at Frw84%.
Interest is due for payment within the next 2 weeks. Corporation tax rate is 35%.
Required: Calculate the cost of the debenture capital.
Solution
𝐅 (𝟏−𝐭)
Kd = × 𝟏𝟎𝟎
𝐌𝐯𝐝
𝟏𝟐 (𝟏−.𝟑𝟓)
Kd = × 𝟏𝟎𝟎
𝟖𝟒−𝟏𝟐
𝟏𝟐 (.𝟔𝟓)
Kd = × 𝟏𝟎𝟎
𝟕𝟐
𝟕.𝟖
Kd = × 𝟏𝟎𝟎
𝟕𝟐
Kd = 10.83%

Cost of redeemable debt

The cost of debt capital already issued is the rate of interest (IRR) which equates the current
market value with the discounted future cash receipts of the security i.e
𝐹2 (1−𝑡) 𝐹3 (1−𝑡) 𝐹𝑛 (1−𝑡)
Mvd = 𝐹(1 − 𝑡) + 1+𝑘𝑑2 + +⋯ 𝐼𝑅𝑅
1+𝑘𝑑3 1+𝑘𝑑𝑛
Alternative method
The effective after tax cost of the redeemable debt can be calculated using the following
formula:
(𝑟+1) + √(1 + 𝑟)2 −4𝑟𝑡
ECCC= 2
Where:
ECC =Effective after tax interest rate
R =Normal / quoted pre-tax interest rate
T =corporation tax rate
Example 3.12
XYZ plc is financed by Frw10, 10% redeemable debentures currently quoted at Frw100 each.
The debentures would be redeemed in 10 years’ time at par. Corporation tax is at 30%.
Required: Calculate the cost of debentures.
Solution
Yr CF DF@5% PV DF@8% PV
0 (100) 1 (100) 1 (100)
1-10 10 7.7217 77 6.7101 67
1-10 (3) 7.7217 (23) 6.7101 (20)
10 100 0.6139 61 0.4632 46
15 (7)

Interpolation:
NPV
IRR = LR + LR-× (HR –LR)
NPVs
15
IRR = 5 + × (8 – 5)
22
IRR = 7.05%
Solution Using The Alternative Method
Formula:
(𝑟+1) + √(1 + 𝑟)2 −4𝑟𝑡
ECCC= 2
(0.10+1) + √(1 + 0.10)2 −4×.10×.30
ECCC= 2
−.90 + √1.21− .12
ECCC= 2
−.90 + √1.09
ECCC= 2
−.90 + 1.044
ECC= 2
=7.2%
WEIGHTED AVERAGE COST OF CAPITAL (W.A.C.C.)
This is also called the overall or composite cost of capital. Since various capital components
have different percentage cost, it is important to determine a single average cost of capital
attributable to various costs of capital. This is determined on the basis of percentage cost of
each capital component.
Weighted average cost of capital is the average cost of the company's finance (equity, bonds,
bank loans) weighted according to the proportion each element bears to the total pool of
capital.

The weighted average cost of capital is calculated by weighting the costs of the individual
sources of finance according to their relative importance as sources of finance. We have
looked at the costs of individual sources of capital for a company. But how does this help us
to work out the cost of capital as a whole, or the discount rate to apply in DCF investment
appraisals?
In many cases it will be difficult to associate a particular project with a particular form of
finance. A company's funds may be viewed as a pool of resources. Money is withdrawn from
this pool of funds to invest in new projects and added to the pool as new finance is raised or
profits are retained. Under these circumstances it might seem appropriate to use an average
cost of capital as the discount rate.
 The correct cost of capital to use in investment appraisal is the marginal cost of the funds
raised (or earnings retained) to finance the investment. The weighted average cost of capital
(WACC) might be considered the most reliable guide to the marginal cost of capital, but only
on the assumption that the company continues to invest in the future, in projects of a standard
level of business risk, by raising funds in the same proportions as its existing capital
structure.
Market value weight or proportion of each capital component.
E P D
W.A.C.C = K e    K p    K d 1  T  
V V V
Where: Ke, Kp and Kd = Percentage cost of equity, preference share capital and debt capital
respectively
E, P and D = Market value of equity, preference share capital and debt capital respectively.
NB: Market value = Market price of a security x No. of securities.
V = Total market value of the firm = E + P + D.
Example 3.13
The following is the capital structure of XYZ Ltd as at 31/12/2002.
Shs.M
Ordinary share capital FRW10 par value 400
Retained earnings 200
10% preference share capital FRW20 par 100
value 200
12% debenture FRW100 par value 900
Additional information
1. Corporate tax rate is 30%
2. Preference shares were issued 10 years ago and are still selling at par value MPS = Par
value
3. The debenture has a 10 year maturity period. It is currently selling at FRW90 in the
market.
4. Currently the firm has been paying dividend per share of FRW5. The DPS is expected
to grow at 5% p.a. in future. The current MPS is FRW40.
Required
A) Determine the WACC of the firm.
B) What are the weaknesses associated with WACC when used as the discounting rate, in
project appraisal.
a)i)Compute the cost of each capital component
Cost of equity (Ke) – Since the growth rate in dividends is given, use the constant growth rate
dividend model to determine the cost of equity.
d0 = FRW5 P0 = FRW40 g = 5%
d0 1  g 51  0.05
Ke  g   0.05  0.18125  18.13%
P0 40
Cost of perpetual preference share capital (Kp) – preference shares are still selling at par thus
MPS = par value. If this is the case, Kp = coupon rate = 10%.
MPS = Par value = FRW20
Dp = 10% x FRW20 = FRW2
DPS dp Sh.2
Kp     10%
MPS Pp Sh.20
Cost of debentures (Kd) – the debenture has a 10 year maturity period. It is thus a redeemable
fixed return security thus the cost of debt is equal to yield to maturity.
Redemption yield:
Interest charges p.a. = 12% x FRW100 par = FRW12
value = 10 years
Maturity period (n) = FRW100
Maturity value (m) = FRW90
 Current market value (Vd) = 30%
Corporate tax rate (T)

Int1  T   M  Vd 
1
K d  YTM  RY  n
M  Vd ½
1
Sh.12(1  0.3)  (100  90)
= 10  9.9%  10%
(100  90)½
ii) Compute the market value of each capital component
Market value of Equity (E) = MPS x No. of ordinary shares
Sh.400 MDSC
= Sh.40 x = 1,600
Sh.10parvalue
Market value of preference share capital (P)
= Par value, since MPS = Par value per share = 100
Market value of debt (D) = Vd x No. of debentures
Sh.200 Mdebentures
= Sh.90 x = 180
Sh.100parvalue
E + P + D = V = total Market Value = 1,880
iii) Compute W.A.C.C using Ke = 18.13%, Kp = 10%, Kd(1-T) = 10%
a) Using weighted average cost method,, WACC =
E P D
= K e    K p    K d 1  T  
V V V
 1,600   100   180 
= 18.13%   10%   10% 
 1,880   1,880   1,880 
= 15.43 + 0.5319 + 0.9574
= 0.169193
≈ 16.92%
b) By using percentage method,
WACC = Total monetary cost
Total market value (V)
Where: Monetary cost = % cost x market value of capital
Monetary cost of E = 18.13% x 1,600= 290.08
Monetary cost of P = 10% x 100 = 10.00
Monetary cost of D = 10% x 180 = 18.00
318.08
Total market value (V) 1,880
318 .08
Therefore WACC = x100 = 16.92%
1,880
B) Weaknesses of WACC as a discounting rate
WACC/Overall cost of capital has the following problems as a discounting rate:
 It can only be used as a discounting rate assuming that the risk of the project is equal to the
business risk of the firm. If the project has higher risk then a percentage premium will be
added to WACC to determine the appropriate discounting rate.
 It assumes that capital structure is optimal which is not achievable in real world.
 It is based on market values of capital which keep on changing thus WACC will change
over time but is assumed to remain constant throughout the economic life of the project.
 It is based on past information especially when determining the cost of each component e.g
in determining the cost of equity (Ke) the past year’s DPS is used while the growth rate is
estimated from the past stream of dividends.

MARGINAL COST OF CAPITAL

This is cost of new finances or additional cost a company has to pay to raise and use additional
finance is given by:
Total cost of marginal finance x 100
Cost of finance (COF)
Cost of finance may be computed using the following information:
i) Marginal cost of each capital component.
ii) The weights based on the amount to raise from each source.
a) Investors usually compute their return basing their figures on market values or cost of
investment.
b) Investors purchase their investment at market value and as such, the cost of finance to
the company must be weighted against expectations based on the market conditions.
c) Investments appreciate in the stock market and as such the cost must be adjusted to
reflect such a movement in the value of an investment.

1. Marginal cost of equity

D1
MCE = x100 (for zero growth firm)
Po  f
Also cost of equity
D1
Ke = (for normal growth firm)
Po  f
Where: d1 = expected DPS = d0(1+g)
P0 = current MPS
f = floation costs
g = growth rate in equity
2. Cost of preference share capital:
Dp
Kp = x100
Po  f
Where: Kp = Cost of preference
Dp = Dividend per share
Po = MPS (Market price per share)
F = Flotation costs
3. Cost of debenture
Int(1  T)
Kd 
Vd  f
Where: Kd = Cost of debt
Int = interest
Po = Market price for debenture (at discount)
f = flotation costs
t = Tax rate
4. Just like WACC, weighted marginal cost of capital can be computed using:
i) Weighted average cost method
ii) Percentage method
Example
XYZ Ltd wants to raise new capital to finance a new project. The firm will issue 200,000
ordinary shares (Frw10 par value) at Frw16 with Frw1 floatation costs per share, 75,000 12%
preference shares (Frw20 par value) at Frw18 with Frw150,000 total floatation costs, 50,000
18% debentures (Frw100 par) at Frw80 and raised a Frw5,000,000 18% loan paying total
floatation costs of Frw200,000. Assume 30% corporate tax rate. The company paid 28%
ordinary dividends which is expected to grow at 4% p.a.

Required
a) Determine the total capital to raise net of floatation costs
b) Compute the marginal cost of capital
Solution
a) Frw’000’
Ordinary shares 200,000 shares @ Frw16 3,200,000
Less floatation costs 200,000 shares @ Frw1 200,000 3,000
Preference shares 75,000 shares @ Frw18 1,350,000
Less floatation cost (150,000) 1,200
Debentures 50,000 debentures @ Frw80 3,000,000
 Floatation costs -____ 3,000
Loan 5,000,000
Less floatation costs (200,000) 4,800
Total capital raised 12,000
b) Marginal cost of equity Ke
d (1  g)
Ke 0 g
P0  f
d0 = 28% x Frw10 par = Frw2.80
g = 4%
f = Frw1.00
P0 = Frw16
2.80(1.04)
Therefore marginal = Ke   0.04 = 0.234 = 23.4%
16  1
Marginal cost of preference share capital Kp
Kp = dp
P0-f
dp = 12% x Frw20 par = Frw2.40
P0 = Frw18
f = Floatation cost per share = Frw150,000 = Frw2.00
75,000 shares
Kp = 2.40 = 0.15 = 15%
18 – 2
Marginal cost of debenture Kd:
Kd = Int (1-t)
Vd-f
f = 0
Vd = Frw80
Int = 18% x Frw100 par = Frw18
T = 30%

Kd = 18(1-0.3) = 0.1575 = 15.75%

80

Marginal cost of loan Kd

Kd = Int (1-t)
Vd-f

T = 30%
Vd = Frw5 million
f = Frw0.2 million
Int = 18% x Frw5M = Frw0.9M
Kd = 0.9 (1-0.3) = 0.13125 = 13.13%
5 – 0.2
Source Amount to raise % marginal cost Maturity cost
before f. costs
Frw’000’ Frw’000’
Ordinary shares 3,200 23.4% 748.8
Preference shares 1,350 15.0% 203.5
Debenture 3,000 15.75% 472.5
Loan 5,000 13.13% 656.5
12,550 2,080.3
Weighted marginal cost = 2,080.3 x 100 = 16.58%
12,550
PRACTICE QN
URWURI Investments Ltd. wishes to raise funds amounting to Frw.10 million to finance a project in
the following manner:
Frw.6 million from debt; and
Frw.4 million from floating new ordinary shares.
The present capital structure of the company is made up as follows:
1. 600,000 fully paid ordinary shares of Frw.10 each
2. Retained earnings of Frw.4 million
3. 200,000, 10% preference shares of Frw.20 each.
4. 40,000 6% long term debentures of Frw.150 each.
The current market value of the company’s ordinary shares is Sh.60 per share. The expected
ordinary share dividends in a year’s time is Frw.2.40 per share. The average growth rate in
 both dividends and earnings has been 10% over the past ten years and this growth rate is
expected to be maintained in the foreseeable future.
The company’s long term debentures currently change hands for Frw.100 each. The
debentures will mature in 100 years. The preference shares were issued four years ago and still
change hands at face value.
Required:
(i) Compute the component cost of:
- Ordinary share capital;
- Debt capital
- Preference share capital.
(ii) Compute the company’s current weighted average cost of capital.
(iii) Compute the company’s marginal cost of capital if it raised the additional Frw.10
million as envisaged. (Assume a tax rate of 30%).
ANSWER:
(i) Cost of equity
do(1  g)
Ke = +g
Po
do(1+g) = Frw 2.40
Po = Frw 60
g = 10%
2.40
Ke = + 0.10 = 0.14 = 14%
60
Cost of debt capital (Kd)
Since the debenture has 100years maturity period then Kd = yield to maturity =
redemption.
1
Int(1 - T)  (m - vd)
Kd = n
(m  vd) 1
2
m = Maturity/per value = Frw 150
vd = market value = Frw. 100
n = number of years to maturity =100
Int = Interest = 6% x Sh. 150 = Frw.9 p.a
T = Tax rate = 30%
1
9(1 - 0.3)  (150 - 100)
Kd = 100  6.8 x 100 = 5.441%
(150  100) 1 125
2
Cost of preference share capital Kp
Kp = Coupon rate = 10% since MPS = par value
(ii) WACC or overall cost of capital Ko
M.V of equity = 600,000 shares x Frw 60 MPS 36
M.V of debt = 40,000 debentures x Sh 100 4
4
M.V of preference shares = 200,000 shares x Frw 20
44

Ke = 14% Kd = 5.44% Kp = 10%

36 4 4
Ko = WACC = 14% + 5.44% +10% = 12.86%
44 44 44

The Frw 10M will be raised as follows:

Frw 6M from debt
Frw 4M from shares
Since there are no floatation costs involved then:
Marginal cost of debt = 5.4%
Marginal cost of ordinary share capital = 14%
4 6
Therefore marginal cost of capital = 14% + 5.55% = 8.86%
10 10
TOPIC 4 CAPITAL STRUCTURE AND GEARING
1. Introduction
Capital is the major part of all kinds of business activities, which are decided by the size, and
nature of the business concern. Capital may be raised with the help of various sources. If the
company maintains proper and adequate level of capital, it will earn high profit and they can
provide more dividends to its shareholders.

2. Meaning of Capital Structure

Capital structure refers to the kinds of securities and the proportionate amounts that make up
capitalization. It is the mix of different sources of long-term sources such as equity shares,
preference shares, debentures, long-term loans and retained earnings.
The following definitions clearly initiate the meaning and objective of the capital structures.
According to the definition of Gerestenbeg , “Capital Structure of a company refers to the
composition or make up of its capitalization and it includes all long-term capital resources”.
According to the definition of James C. Van Horne , “The mix of a firm’s permanent long-
term financing represented by debt, preferred stock, and common stock equity.

FINANCIAL STRUCTURE
The term financial structure is different from the capital structure. Financial structure shows
the pattern total financing. It measures the extent to which total funds are available to finance
the total assets of the business.
 Financial Structure = Total liabilities
 Financial Structure = Capital Structure + Current liabilities.
Financial Structures Capital Structures
1. It includes both long-term and short-term 1. It includes only the long-term sources of
sources of funds funds.
2. It means the entire liabilities side of the 2. It means only the long-term liabilities of the
balance sheet. company.
3. Financial structures consist of all sources 3. It consists of equity, preference and retained
of capital. earning capital.
4. It will not be more important while 4. It is one of the major determinations of the
determining the value of the firm. value of the firm.
Example 7.18
From the following information, calculate the capitalization, capital structure and financial
structures.
Statement of financial position
LIABILITIES ASSETS
Equity share capital 50,000 Fixed assets 25000
Preference share capital 5000 Goodwill 10000
Debentures 6000 Stock 15000
Retained earnings 4000 Bills receivables 5000
Bills payables 2000 Debtors 5000
Creditors 3000 Cash in hand/bank 10000
70,000 70,000
i)Calculation of Capitalization
Sources Amount
1 Equity share capital 50000
2 Preference share capital 5000
3 Debentures 6000
61000
ii)Calculation of Capital Structures
 Sources Amount Proportion
1 Equity share capital 50000 76.92
2 Preference share capital 5000 7.69
3 Debentures 6000 9.23
4 Retained earnings 4000 6.16
65000 100%
iii) Calculation of Financial Structure
LIABILITIES Amount Proportion
Equity share capital 50,000 71.42
Preference share 5000 7.14
capital
Debentures 6000 8.58
Retained earnings 4000 5.72
Bills payables 2000 2.85
Creditors 3000 .29
70,000 100%
3. FACTORS AFFECTING THE CAPITAL STRUCTURE
1. Availability of securities – This influences the company’s use of debt finance which
means that if a company has sufficient securities, it can afford to use debt finance in
large capacities.
2. Cost of finance (both implicit and explicit) – If low, then a company can use more of
debt or equity finance.
3. Company gearing level – if high, the company may not be able to use more debt or
equity finance because potential investors would not be willing to invest in such a
company.
4. Sales stability – If a company has stable sales and thus profits, it can afford to use
various finances in particular debt in so far as it can service such finances.
5. Competitiveness of the industry in which the company operates – If the company
operates in a highly competitive industry, it may be risky to use high levels of debt
because chances of servicing this debt may be low and may lead a company into
receivership.
4. GEARING
Financial decision is one of the integral and important parts of financial management in any
kind of business concern. A sound financial decision must consider the board coverage of the
financial mix (Capital Structure), total amount of capital (capitalization) and cost of capital
(Ko). Capital structure is one of the significant things for the management, since it influences
the debt equity mix of the business concern, which affects the shareholder’s return and risk.
Hence, deciding the debt-equity mix plays a major role in the part of the value of the company
and market value of the shares. The debt equity mix of the company can be examined with the
help of leverage.

4.1 Operating gearing

Operating gearing is a measure of the extent to which a firm’s operating costs are fixed rather
than variable as this affects the level of business risk in the firm. Operating gearing can be
measured in a number of different ways, including:

Firms with a high proportion of fixed costs in their cost structures are known as having “high
operating gearing”.
Hence, if the sales of a company vary:
- The greater the operating gearing the greater the EBIT variability.
- The level of operating gearing will be largely a result of the industry in which the firm
operates.
Example 7.19
Two firms have the following cost structures:
Firm A (FRW million) Firm B (FRW million)
Sales 5.0 5.0
Variable costs (3.0) (1.0)
Fixed costs (1.0) (3.0)
EBIT 1.0 1.0

What is the level of operating in each and what would be the impact on each of a 10% increase
in sales?
Answer:
• Operating gearing can be calculated as follows:
Fixed costs/variable costs Firm A: 1/3 = 0.33 Firm B: 3/1 = 3
Firm B carries a higher operating gearing because it has higher fixed costs.
• Its operating earnings will therefore be more volume-sensitive:

Firm A (FRW Firm A 10% Firm B (FRW Firm B (10%

million) increase million) increase)
Sales 5.0 5.5 5.0 5.5
Variable (3.0) (3.3) (1.0) (1.1)
costs
Fixed costs (1.0) (1.0) (3.0) (3.0)
EBIT 1 1.2 1 1.4
Firm B has enjoyed an increase in EBIT of 40% whilst firm A has had an increase of only
20%. In the same way a decrease in sales would bring about a greater fall in B’s earnings than
in A’s.
Uses of Operating Leverage
• Operating leverage is one of the techniques to measure the impact of changes in sales
which lead for change in the profits of the company.
• If any change in the sales, it will lead to corresponding changes in profit.
• Operating leverage helps to identify the position of fixed cost and variable cost.
• Operating leverage measures the relationship between the sales and revenue of the
company during a particular period.
• Operating leverage helps to understand the level of fixed cost which is invested in the
operating expenses of business activities.
• Operating leverage describes the overall position of the fixed operating cost.
4. 2 Financial Leverage
Financial gearing is a measure of the extent to which debt is used in the capital structure.
Financial leverage is defined as “the ability of a firm to use fixed financial charges to magnify
the effects of changes in EBIT on the earnings per share”. It involves the use of funds obtained
at a fixed cost in the hope of increasing the return to the shareholders. “The use of long-term
fixed interest bearing debt and preference share capital along with share capital is called
financial leverage or trading on equity”.
Financial leverage may be favourable or unfavourable depends upon the use of fixed cost
funds.
Favourable financial leverage occurs when the company earns more on the assets purchased
with the funds, then the fixed cost of their use. Hence, it is also called as positive financial
leverage.
Unfavourable financial leverage occurs when the company does not earn as much as the
funds cost. Hence, it is also called as negative financial leverage.
Financial leverage can be calculated with the help of the following formula:
FL =OP/PBT, where,
FL = Financial leverage
OP = Operating profit (EBIT)
 PBT = Profit before tax.
Degree of Financial Leverage
Degree of financial leverage may be defined as the percentage change in taxable profit as a
result of percentage change in earnings before interest and tax (EBIT). This can be calculated
by the following formula:
DFL=Percentage change in taxable Income/Percentage change in EBIT
It can be measured in a number of ways:

Note: Where two companies have the same level of variability in earnings, the company with
the higher level of financial gearing will have increased variability of returns to shareholders.
4.3. Combined leverage
When the company uses both financial and operating leverage to magnification of any change
in sales into a larger relative changes in earning per share. Combined leverage is also called as
composite leverage or total leverage. Combined leverage expresses the relationship between
the revenue in the account of sales and the taxable income.
Combined leverage can be calculated with the help of the following formulas:
CL = OL × FL
CL =C/OP×OP/PBT=C/PBT
Where,
CL = Combined Leverage
OL = Operating Leverage
FL = Financial Leverage
C = Contribution
OP = Operating Profit (EBIT)
PBT= Profit Before Tax
Degree of Combined Leverage
The percentage change in a firm’s earning per share (EPS) results from one percent change in
sales. This is also equal to the firm’s degree of operating leverage (DOL) times its degree of
financial leverage (DFL) at a particular level of sales.
Degree of contributed coverage =Percentage change in EPS/Percentage change in sales
Example 7.20
Kumar company has sales of Frw. 25,000,000. Variable cost of Frw. 12500,000 and fixed
cost of Frw 50,000 and debt of Frw 12,50,000 at 8% rate of interest. Calculate combined
leverage.
Sales 25,000,000
Less: Variable cost 15,000,000
Contribution 10,000,000
Less: Fixed costs 5,000,000
Operating profit 5,000,000
Calculation of financial leverage= Contribution /Operating Profit =
10000000/5000000=2
Calculation of operating leverage
Earnings before interest and Tax 5,000,000
Less: Interest on debenture(8%*12500000) 1,000,000
Earning before Tax 4,000,000
Operating leverage =Operating Profit/Earning Before Tax /=5,00,0004,00,000
=1.25
Combined leverage =Operating leverage* Financial leverage
 Combined leverage = 2 × 1.25 = 2.5
4.4.PECKING ORDER THEORY
Pecking order theory has been developed as an alternative to traditional theory. This theory is
based on the view that companies will not seek to minimise their WACC. Instead they will
seek additional finance in an order of preference , or ‘pecking order’.
Pecking order theory states that firms will prefer retained earnings to any other source of
finance, and then will choose debt, and last of all equity. The order of preference will be:

4.4.1 Reasons for following pecking order

(a) It is easier to use retained earnings than go to the trouble of obtaining external finance
and have to live up to the demands of external finance providers.
(b) There are no issue costs if retained earnings are used, and the issue costs of debt are lower
than those of equity.
(c) Investors prefer safer securities, that is debt with its guaranteed income and priority on
liquidation.
(d) Some managers believe that debt issues have a better signalling effect than equity issues
because the market believes that managers are better informed about shares' true worth than
the market itself is. Their view is the market will interpret debt issues as a sign of confidence,
that businesses are confident of making sufficient profits to fulfil their obligations on debt and
that they believe that the shares are undervalued. By contrast the market will interpret equity
issues as a measure of last resort, that managers believe that equity is currently overvalued
and hence are trying to achieve high proceeds whilst they can. However, an issue of debt may
imply a similar lack of confidence to an issue of equity; managers may issue debt when they
believe that the cost of debt is low due to the market underestimating the risk of default and
hence undervaluing the risk premium in the cost of debt. If the market recognises this lack of
confidence, it is likely to respond by raising the cost of debt.

4.4.2 Consequences of pecking order theory

(a) Businesses will try to match investment opportunities with internal finance provided this
does not mean excessive changes in dividend payout ratios.
(b) If it is not possible to match investment opportunities with internal finance, surplus
internal funds will be invested; if there is a deficiency of internal funds, external finance will
be issued in the pecking order, starting with straight debt.
(c) Establishing an ideal debt-equity mix will be problematic, since internal equity funds will
be the first source of finance that businesses choose, and external equity funds the last.

4.4.3 Limitations of pecking order theory

(a) It fails to take into account taxation, financial distress, agency costs or how the
investment opportunities that are available may influence the choice of finance.
(b) Pecking order theory is an explanation of what businesses actually do, rather than what
they should do. Studies suggest that the businesses that are most likely to follow pecking order
theory are those that are operating profitably in markets where growth prospects are poor.
There will thus be limited opportunities to invest funds, and these businesses will be content to
rely on retained earnings for the limited resources that they need.
 TOPIC 5: CAPITAL BUDGETING /INVESTMENT DECISIONS
5.1. THE NATURE OF INVESTMENT DECISIONS AND THE APPRAISAL
PROCESS

1. Definition

Capital Budgeting Decisions refers to firm’s decision to invest its current funds most
efficiently in long-term assets in anticipation of expected flow of benefits over several years in
the future. It is the process of identifying, analyzing and selecting investment projects whose
returns are expected to extend beyond one year.
2. Types of capital budgeting investments
1. New projects (require investment in fixed assets)
2. Expansion projects (increasing existing capacity)
3. Diversification projects (spreading of risk across a number of investments)
4. Replacement and modernization projects (i.e. improving operating efficiency, reducing
costs, increasing quality).
5. Research and Development projects
6. Miscellaneous projects
7. Mutually Exclusive projects: These are alternative options, which serve the same
purpose and compete with one another. If one investment is undertaken others will
have to be excluded. Two or more projects that cannot be pursued simultaneously – the
acceptance of one prevents acceptance of the other.
8. Independent projects: These serve different purpose and do not compete with each
other and acceptance or rejection of one doesn’t directly eliminate the other. For
instance a company may want to introduce a new product line and at the same time
may want to replace a machine which is currently producing a different product
depending on the availability of funds and profitability of the two projects. These two
projects can be evaluated and considered independently from each other.
9. Contingent projects: A contingent project is one where acceptance or rejection of
which is dependent on decision to accept or reject one or more other projects.
Contingent projects may be complementary or substitutes whereby the choice of one
investment may necessitate that one or more projects should also be undertaken.
3. FACTORS TO CONSIDER WHILE ASSESSING INVESTMENT PROJECTS
1. Cost of investment project: Appraisers must have information regarding total
investment required for the project and the sources of funds to be used.
2. Estimated life of project: Information regarding the estimated life of the project and
the estimated scrap value of the project at the end of its useful life must also be known.
3. Estimated net cash inflows from project: The decision makers should be informed
not only about the amount of cash inflow, but also the expected time of receipt of all
cash flows.
4. Estimated residual value of project at the end of its life if applicable: Appraisers
seek to know the residual value of the project as it affects the current valuation based
on NPV and also the decision of investment.
5. Cost of capital: The cost of equity which is the equity shareholders expected return
and the cost of debt calculated on a weighted basis is the cost of capital.
6. Taxation implications on project: Tax forming a major porting of corporate cash
outflows need to be considered in detail. Companies may take their gearing decisions
based on tax liability.
7. Inflation rates and effect on project: Projects with long gestation periods need to be
very carefully analyzed. Inflation can give wrong projection of earnings affecting the
overall profitability of the firm.
4. IMPORTANCE OF CAPITAL BUDGETING
1. These decisions expose the company’s funds to risk and if not well made can lead the
company in liquidation.
2. They involve commitment of large amount of funds and can result in heavy losses to
the company if not carefully planned.
3. Impact on the value of the firm. Decisions resulting in profitable ventures increase the
value of the firm and add to the shareholder’s wealth.
4. Investment decisions are among the company’s most difficult decisions. They are an
assessment of future events, which are difficult to predict i.e. it is a complex problem
to correctly estimate future cash flows of an investment. Economic, political, social and
technological forces cause the cash flow uncertainty.
5. Any company will invest finance for the sake of deriving a return which is useful
6. Such decisions are importance because they will influence the company’s size (fixed
assets, sales, and retained earnings).
7. They increase the value of the company’s shares and thus its credibility.
8. The fact that they are irreversible means that they have to be made carefully to avoid
any mistake which can lead to the failure of such investment.
9. Any company will invest finance for the sake of deriving a return which is useful for
four main reasons:
a) To reward creditors by paying them regular return in form of interest and repayment
of their principal as and when it falls due.
b) To be able to retain part of their earnings for plough back purposes which facilitates
not only the company’s growth present and the future but also has the implication of
increasing the size of the company in sales and in assets.
c) For the increase in share prices and thus the credibility of the company and its ability
to raise further finance.
d) Such a return is necessary to keep the company’s operations moving smoothly and thus
allow the above objective to be achieved.
10. Due to heavy capital outlay, more attention is required to avoid loss of huge sums of
money which in the extreme may lead to the closure of such a company. However,
these decisions are influenced by:
i) Political factors – Under conditions of political uncertainty, such decisions cannot be
made as it will entail an element of risk of failure of such investment. Thus political
certainty has to be analysed before such decisions are made, such factors must be
taken into account such that the company forecasts the inflows and outflows within
given
limitations such as the degree of competition, performance of economy, changing
tastes etc. which influence ability to generate sufficient return from a venture which
will pay not only interest but principal on such funds invested.
ii) Technological factors – These influence the returns of the company because such
technology will affect the company’s ability to utilise its assets to the utmost ability in
particular if such assets become obsolete and cannot generate good returns or the
output of such machines may be low with time and may not meet planned expectations
which in most cases will have an impact on inflows from a venture.
5. CLASSIFICATION OF CAPITAL BUDGETING TECHNIQUES
These can be classified under 2 broad categories:
1. Techniques under certainty
There is perfect knowledge about the cash flows, their timings and magnitude.
a) Traditional methods
 Payback period method
 Accounting rate of return method
b) Modern methods (Discounted cash flow techniques)
  NPV – Net present value method
 IRR – Internal rate of return method
 PI – Profitability index method
For the above two (a & b) methods to be used, they have to meet the following:
i) They should rank ventures available in the investment market according to their
viability i.e. they should identify which method is more viable than others.
ii) They should rank a venture first if the venture brings in return earlier and in large lump
sums than if a venture brought in late and less inflows over the same period.
iii) Should rank any other projects as and when it is available in the investment market.
Such methods should take into account that all returns (inflows), must be cash returns
as it is necessary to be able to finance the cost of the venture.
2. Techniques under uncertainty and risk
The decision maker does not have perfect knowledge about future outcomes but is able to
predict the outcomes and their associated probabilities
1. Decision trees/Theory models
2. Sensitivity analysis
3. Scenario analysis
4. Simulation analysis
5. Portfolio theory analysis
6. Capital Asset pricing model
7. Arbitrage Pricing model
6. INVESTMENT

Investment can be divided into capital expenditure and revenue expenditure and can be
made in non-current assets or working capital. Investment is any expenditure in the
expectation of future benefits.
We can divide such expenditure into two categories: capital expenditure and revenue
expenditure.
Capital expenditure is expenditure which results in the acquisition of non-current assets or
an improvement in their earning capacity. It is not charged as an expense in the income
statement; the expenditure appears as a non-current asset in the statement of financial position.
Revenue expenditure is charged to the income statement and is expenditure which is
incurred:
(a) For the purpose of the trade of the business - this includes expenditure classified as
selling and distribution expenses, administration expenses and finance charges
(b) To maintain the existing earning capacity of non-current assets
7. INVESTMENT DECISION MAKING PROCESS
A typical model for investment decision making has a number of distinct stages:
1 Origination of proposals
Investment opportunities do not just appear out of thin air. They must be created. An
organisation must therefore set up a mechanism that scans the environment for potential
opportunities and gives an early warning of future problems. A technological change that
might result in a drop in sales might be picked up by this scanning process, and steps should be
taken immediately to respond to such a threat. Ideas for investment might come from those
working in technical positions. A factory manager, for example, could be well placed to
identify ways in which expanded capacity or new machinery could increase output or the
efficiency of the manufacturing process. Innovative ideas, such as new product lines, are more
likely to come from those in higher levels of management, given their strategic view of the
organization’s direction and their knowledge of the competitive environment.
2 Project screening
Each proposal must be subject to detailed screening. So that a qualitative evaluation of a
proposal can be made, a number of key questions such as those below might be asked before
any financial analysis is undertaken. Only if the project passes this initial screening will more
detailed financial analysis begin.
 What is the purpose of the project?
 Does it 'fit' with the organisation's long-term objectives?
  Is it a mandatory investment, for example to conform with safety legislation?
 What resources are required and are they available, eg money, capacity, labour?
 Do we have the necessary management expertise to guide the project to completion?
 Does the project expose the organisation to unnecessary risk?
 How long will the project last and what factors are key to its success?
 Have all possible alternatives been considered?
3 Analysis and acceptance
The analysis stage can be broken down into a number of steps.
Step 1 Complete and submit standard format financial information as a formal investment
proposal.
Step 2 Classify the project by type (to separate projects into those that require more or less
rigorous financial appraisal, and those that must achieve a greater or lesser rate of return in
order to be deemed acceptable).
Step 3 Carry out financial analysis of the project.
Step 4 Compare the outcome of the financial analysis to predetermined acceptance criteria.
Step 5 Consider the project in the light of the capital budget for the current and future
operating periods.
Step 6 Make the decision (go/no go).
Step 7 Monitor the progress of the project.
4 Monitoring the progress of the project
During the project's progress, project controls should be applied to ensure the following:
 Capital spending does not exceed the amount authorized.
 The implementation of the project is not delayed.
 The anticipated benefits are eventually obtained.
5.2. TECHNIQUES UNDER CERTAINTY
5.2. 1.NON-DISCOUNTED CASH FLOW TECHNIQUES
A. NON-DISCOUNTED CASH FLOW TECHNIQUES (TRADITIONAL METHODS)
1. PAYBACK PERIOD METHOD
This method gauges the viability of a venture by taking the inflows and outflows over time to
ascertain how soon a venture can payback and for this reason PBP (or payout period or payoff)
is that period of time or duration it will take an investment venture to generate sufficient cash
inflows to payback the cost of such investment. This is a popular approach among the
traditional financial managers because it helps them ascertain the time it will take to recoup in
form of cash from operations the original cost of the venture.
This is also defined as the number of years required to recover the original cash outlay
invested in a project. Minimum period/time in which a project recoups/repays the initial
investment. It is the amount of time it takes for cash inflows equal to cash outflows.
Steps of calculating the PBP
1. Determine the initial investment
2. Determine the annual net cash flows (NCF)
3. Reduce the initial investment by the net cash inflows
4. The year in which the initial investment has been completely repaid is payback period
Methods of calculating the PBP
There are two methods:
1. Under uniform annual incremental cash inflows – If the project generates equal
constant cash inflows then the PBP can be computed by dividing cash outlay by annual
cash inflows then the payback period (PBP) will be given by:
PBP = Initial cost of the venture/Annual incremental cost
Example
If a venture costs 37,910/= and promises returns of 10,000/= per annum indefinitely then the
37,910
PBP = =3.79 years
10,000
The shorter the PBP the more viable the investment and thus the better the choice of such
investments
2. Discounted PBP

The discounted payback period is the number of periods taken in recovering the investment
outlay on the present value basis. The discounted payback period still fails to consider the
cash flows occurring after the payback period. Consider the example below:
Example
3 DISCOUNTED PAYBACK ILLUSTRATED
Cash Flows
(Rs) Simple Discounted NPV at
C0 C1 C2 C3 C4 PB PB 10%
P -4,000 3,000 1,000 1,000 1,000 2 yrs – –
PV of cash flows -4,000 2,727 826 751 683 2.6 yrs 987
Q -4,000 0 4,000 1,000 2,000 2 yrs – –
PV of cash flows -4,000 0 3,304 751 1,366 2.9 yrs 1,421

2. Under non-uniform cash inflows:

If the project undertaken unequal cash inflows then the PBP can be calculated by adding up
the cumulative cash inflows over the life of the project until the total is equal to the cash
outlay.

Under non-uniformity PBP computation will be in cumulative form and this means that the net
cash inflows are accumulated each year until initial investment is recovered.
Example
Assume a project costs Sh.80,000 and will generate the following cash inflows:
Cash inflows Accumulated inflows
Inflows year 1 = 10,000 10,000
Inflows year 2 = 30,000 40,000
Inflows year 3 = 15,000 55,000
Inflows year 4 = 20,000 75,000
Inflows year 5 = 30,000 105,000
The Sh.80,000 cost is recovered between year 4 and 5. During year 5 (after year 4) Sh.5,000 is
(80,000 – 75,000) is required out the total year 5 cash flows of 30,000.
5,000
Therefore the PBP = 4yrs  = 4.17 years
30,000
Example
Cedes limited has the following details of two of the future production plans. Only one of
these machines will be purchased and the venture would be taken to be virtually exclusive.
The Standard model costs Frw50,000 and the Deluxe cost Frw88,000 payable immediately.
Both machines will require the input of the following:
i) Installation costs of Frw20,000 for Standard and Frw40,000 for the Deluxe
ii) A Frw10,000 working capital through their working lives.
Both machines have no expected scrap value at end of their expected working lives of 4 years
for the Standard machine and six years for the Deluxe. The operating pre-tax net cash flows
associated with the two machines are:
Year 1 2 3 4 5 6
 Standard 28,500 25,860 24,210 23,410 - -

Deluxe 36,030 30,110 28,380 25,940 38,500 35,100

The deluxe machine has only been introduced in the market and has not been fully tested in the
operating conditions, because of the high risk involved the appropriate discount rate for the
deluxe machine is believed to be 14% per annum, 2% higher than the rate of the standard
machine. The company is proposing the purchase of either machine with a term loan at a fixed
rate of interest of 11% per annum, taxation at 30% is payable on operating cash-flows one year
in arrears and capital allowance are available at 25% per annum on a reducing balance basis.
Required: For both the Standard and the Deluxe machines, calculate the payback period.
Solution
Establish the cash flows as follows:
Pre-tax inflows (EBDT) XX
Less depreciation = capital allowance (XX)
Earnings before tax XX
Less tax (XX)
Earnings after tax XX
Add back capital allowance/depreciation XX
Operating cash flows XX

Note :Depreciation is a non-cash item thus when deducted for tax purposes, it should be
added back to eliminate the non-cash flow effects.
Cash flows for standard machine:
Year 1 2 3 4 5

Pretax inflow 28,500 25,850 24,210 23,410 -

Less : depreciation 17,500 13,125 9,844 7,383 -
Taxable cash inflows 11,000 12,735 14,366 16,027
Tax @ 30% 1 yr in arrears -___ 3.300 (3,831) (4,310) (4,808)
11,000 9,435 10,545 11,717 (4,808)

Add back: depreciation 17,500 13,125 9,844 7,383 -

Operating cash flows 28,500 22,560 20,389 19,100 (4,808)
Add working capital realized - - - 10,000 -
Total cash flows 28,500 22,560 20,389 29,100 (4,808)

Cash flows for Deluxe machine

Year 1 2 3 4 5 6 7

Pretax inflows 36,030 30,110 28,380 25,940 38,560 35,100 -

Less 32,000 24,000 18,000 13,500 10,125 7,594 -
(depreciation) 4,030 6,110 10,380 12,440 28,435 27,506 -
- (1,209) (1,833) (3,114) (3,732) (8,531) (8,252)
Tax @ 30% in
arrears 4,030 4,901 8,547 9,326 24,703 18,975 (8,252)

Inflows after tax 32,000 24,000 18,000 13,500 10,125 7,594 -

Add back capital 28,901 26,547 22,826 34,828 26,569 (8,252)
Allowance - - - - - 10,000 -
36,030 28,599 26,547 22,826 34,828 36,569 (8,252)
Add back
w/capital
Total cash flows
Standard Deluxe
 Cost 50,000 + 20,000 70,000 88,000 + 40,000
128,000

Year Cash flows Accumulated Cash Accumulated

flows
1 28,500 28,500 36,030 36,030
2 22,560 51,060 28,901 64,931
3 20,389 71,449 26,547 91,478
4 29,100 100,549 22,826 114,304
5 (4,808) 95,741 34,828 149,132
6 - - 36,569 185,701
7 - - ( 8,252) 179,449
* Pay back period for standard: Initial capital of Sh.7,000 is recovered during year 3. After year
2, we require 70,000 – 9,060 = 18,940 to recover initial capital out of year 3 cash flows of Sh.20,389.
* Applying the same concept for Deluxe, payback period would be:
128,000  114 ,304
4 = 4.39 years
34,828
Example: Assume a project costs FRW80,000 and will generate the following cash inflows:
Cash inflows Accumulated inflows
Inflows year 1 = 10,000 10,000
Inflows year 2 = 30,000 40,000
Inflows year 3 = 15,000 55,000
Inflows year 4 = 20,000 75,000
Inflows year 5 = 30,000 105,000
The FRW80,000 cost is recovered between year 4 and 5. During year 5 (after year 4)
FRW5,000 is (80,000 – 75,000) is required out the total year 5 cash flows of 30,000.
5,000
Therefore the PBP = 4yrs  = 4.17 years
30,000
Acceptance Rule of Payback Period (PBP)
Using PBP method a company will accept all those ventures whose payback period is less than
that set by the management and will reject all those ventures whose PBP is more than that set
by the management. Alternatively, PBP may be gauged against the term of the loan in which
case the PBP method will give a high ranking to all those ventures paying back before the term
of the loan and the highest ranking will be given to those projects with shortest PBP.
However, in assessing the viability of a venture it is also important to see which venture brings
returns earlier, other things being equal.

Advantages of Payback Period

1. It is cheap as it does not call for use of computer and does not require a lot of analyst
time.
1. Simple to understand and easy to apply.
2. It chooses the project that has the shortest PBP and thus minimizes the financial and
business risks associated with future returns.
3. Choosing that project that pays back earlier improves the liquidity position of the
company.
4. PBP is realistic for those companies which intend to re-invest intermediary returns.
Projects which generate big returns early will be chosen so that such returns can be re-
invested to generate more profits to the company before the lenders can be paid back.
5. It uses cash flows rather than accounting profits
6. It can be used as a screening device as a first stage in eliminating obviously
inappropriate projects prior to more detailed evaluation
 7. It can be used when there is a capital rationing situation to identify those projects
which generate additional cash for investment quickly.
Disadvantages of Payback Period
1. It ignores time value of money.
2. It ignores the timing of cash flows within the payback period
3. It does not take into account cash flows after the end of payback period as well as cash
flows over the entire life of the project.
4. It is difficult to determine the maximum acceptable payback period. There is no
rational basis for setting a maximum payback period – it is arbitrary
5. It is not consistent with the objective of maximizing the market value of the company
shares. Shares values do not depend on payback period of investment but depend on
the profitability of the project undertaken.
6. Payback period assumes that cash flows occur evenly throughout the year and that cash
inflows for a fraction of a year can be calculated proportionately, which is unrealistic.
7. It ignores the risk of future cash flows
8. It may lead to excessive investment in short term projects
9. Unable to distinguish between projects with the same payback period

Accounting Rate of Return Method (ARR)

ARR (return on investment (ROI) or Average rate of return) method uses accounting
information as revealed by financial statement to measure the profitability of investment
proposals or assess the viability of investment proposal by dividing the average income after
tax by average investment. The investment would be equal to either the original investment
plus the salvage value divided by two or the initial investment divided by two or dividing the
total of the investment book value after depreciating by the life of the project. This method is
also known as financial statement method or book value method. The rate of return on asset
method or adjusted rate of return method is given by:
ARR = Average income x 100 or Average income – Average depreciation
Average investment Initial investment
i. When it is mentioned as Account rate of return in problem:
ARR = Average Annual EAT or PAT*100/original Investment (OI)
OI= Original Investment + Additional NWC + Installation Charges+ Transport charges
ii. Whenever Average rate of return is mentioned in problem
ARR= Average Annual EAT*100/Average Investment (AI)
AI: (original investment-scrap value)1/2 + Additional NWC +Scrap value
iii. If only ARR is mentioned use any one of the above but the last is more preferable.
Unlike PBP, this method will ascertain the profitability of an investment and it will give
results which are consistent with those given by return ratios.
Example
Frw
Project X cost 500,000
Scrap value 100,000
Stream of income before depreciation and taxes are as follows:

Frw
Year 1 100,000
Year 2 120,000
Year 3 140,000
Year 4 160,000
Year 5 200,000
Let tax = 50% and depreciation straight line. Calculate the accounting rate of return.
Solution
Depreciation = 500,000 – 100,000 = Frw80, 000
5 years
Year 1 2 3 4 5

Income 100,000 120,000 140,000 160,000 200,000

Less depreciation 80,000 80,000 80,000 80,000 80,000
Earnings before tax EBT 20,000 40,000 50,000 80,000 120,000
Less tax @ 50% (10,000) (20,000) (30,000) (40,000) (60,000)
EAT 10,000 20,000 30,000 40,000 60,000

Average income (EAT) = 160,000/5=32,000

Average investment = (500,000 + 100,000) ½ = 300,000
Or ARR = Average income x 100 = 32,000 x 100 = 10.67%
Average investment 300,000
Note : The best method of depreciation to use should be that which will produce larger
depreciation changes in the 1st few years of the assets life and lesser changes in the later years
because this will produce a higher tax shield to the company with higher value of inflows.
Thus reducing balance is preferred as compared to sum of digits and straight line method.
The salvage value should be treated as follows:
If the asset produces a salvage value at the end of the year, this will increase inflows for
payback period. This value is only used to ascertain how much the company will reduce
original cost of investment to obtain average investment
Acceptance Rule of Accounting Rate of Return (ARR)
ARR method will accept those projects whose ARR is higher than that set by management or
bank rate and it will give highest ranking to ventures with highest ARR and reject if ARR is
less than predetermined ARR or cut off rate.
Advantages
1. It is easy to understand and easy to calculate.
2. The impact of the project on a company’s financial statement can also be specified
3. ROCE is still the commonest way in which business unit performance is measured
and evaluated, and is certainly the most visible to shareholders
4. Managers may be happy in expressing project attractiveness in the same terms in
which their performance will be reported to shareholders, and according to which
they will be evaluated and rewarded.
5. The continuing use of the ARR method can be explained largely by its utilization of
balance sheet and P&L account magnitudes familiar to managers, namely profit and
capital employed.
Disadvantages
1. It fails to take account of the project life or the timing of cash flows and time value
of money within that life
2. It uses accounting profit, hence subject to various accounting conventions.
3. There is no definite investment signal. The decision to invest or not remains
subjective in view of the lack of objectively set target ARR.
4. Like all rate of return measures, it is not a measurement of absolute gain in wealth
for the business owners.
 5. The ARR can be expressed in a variety of ways and is therefore susceptible to
manipulation

5.2.2. MODERN METHODS OR DCF i.e. DISCOUNTED CASH FLOW

TECHNIQUES
The Discounted Cash Flow Techniques take into consideration almost all deficiencies of non-
discounted techniques as listed below:
– Benefits and costs occurring during the project’s entire life
– Time value of money
Three common methods are used:
- Net present value
- Internal rate of return
- Profitability index
1. Present Value Concept
1.1.Value
Individuals have different perception and interpretations of value. Not all aspects of value are
tangible or even measurable. Value can be defined from different concepts.

Book Value (BV): It is the value at which assets are shown in the balance sheet.
BV=Cost-Depreciation

Market Value (MV):This is the value at which the asset is currently trading in the market as
determined by interaction of demand and supply for that asset
Net Realizable Value (NRV):This is the value an asset can fetch in the market less cost
incurred in selling the asset.
Liquidation Value: It is the price an individual asset will fetch in the market if the business
operations are stopped and all assets sold. This value is likely to be less than all the other
value.
Intrinsic Value: It is the present value of all expected cash flows discounted at the investors
required rate of return. In an efficient market, the market value and the intrinsic value should
be equal.
This concept acknowledges the fact that a shilling losses value with time and as such if it is to
be compared with a shilling to be received in the N year then the two must be at the same
values. This means that an investor’s analytical power is increased by his/her ability to
compare cash inflows and outflows separated from each other by time. He/she should be able
to work in the reverse direction i.e. from future cash flows to their present values.

2. Present Value of a Lumpsum

Usually an investor would wish to know how much he/she would give up now to get a given
amount in year 1, 2, … n. In this situation he would have to decide at what rate of discount
also known as time preference rate, he/she will use to discount the anticipated lumpsum using
this rate by applying the following formula:
L
Pv 
1  K n
Where: Pv = Present value
L = Lumpsum
K = Cost of finance or time preference rate
n = given year.
This implies that if the time preference rate is 10%, the present value of 1/= to e received at the
end of year 1 is:
1
Pv   0.909
1.1
The present value of inflows to be received in the 2nd year to Nth year, will be equal to:
 A
Pv 
1  K N
Where: A = annual cash flows
N = Number of years
Also, the present value of a shilling to be received at a given point in time can in addition to
using the above formula can be found using the present value tables.

Example
Suppose that an investor can expect to receive:
40,000 at the end of year 2
70,000 at the end of year 6
100,000 at the end of year 8
Compute his present (value) if his time preference is 12%.
L 40,000 70,000 100,000
Pv    _
1  K N
1.12 2
1.12  6
1.12 8
= Frw107,740.26
Using tables:
= 40,000(0.7992) + 70,000(0.5066) + 100,000(0.4039)
= 107,820
3. Present Value of an Annuity
An individual investor may not necessarily get a lumpsum after some years but rather get a
constant periodic amount i.e. an annuity for certain number of years. The present value of an
annuity receivable where the investor time preference is 10% equal to:
A
Pv (A)  I = time preference rate
1  i
E.g. Pv of 1/= to be received after 1 year if time preference rate is 10%.
1
=  0.909
1  0.1
A 1
After 2 years it will be:   0.8264
1  i2
1.12
1st year - 0.9090
2nd year - 0.8264
3rd year - 0.7513
4th year - 0.6830
Total - 3.1697

4. Present Value of Uneven Periodic Sum

In investment decisions it is very rare to get even periodic returns and in most cases a company
will generate a stream of uneven cash inflows from a venture and the present value of those
uneven periodic sums is equal to:

A1 A2 A3 AN
Pv     ..... 
1  K 1 1  K 2 1  K 3 1  K N
Equation
 1  K 
At
Pv 
t

Where: At = Uneven cash inflows at time t

Pv = Present value
K =Cost of finance
Example
A company contemplates to receive Frw:
20,000 in year 1
18,000 in year 2
24,000 in year 3
Nil in year 4
 40,000 in year 5
Cost of this finance is 12%
Required: Compute present value of that finance
Solution
30,000 18,000 24,000 40,000
Pv    
1.12 
1
1.12 
2
1.12 
3
1.12 5
= 80,915.004
5. Net Present Value Method
The method discounts inflows and outflows and ascertains the net present value by deducting
discounted outflows from discounted inflows to obtain net present cash inflows i.e the present
value method will involve selection of rate acceptable to the management or equal to the cost
of finance and this will be used to discount inflows and outflows and net present value will be
equal to the present value of inflow minus present value of outflow. If net present value is
positive you invest, If NPV is negative you do not invest.
Pv(inflow) – Pv(outflows) = NPV
Note: Initial outflow is at period zero and their value is their actual present value. With this
method, an investor can ascertain the viability of an investment by discounting outflows. In
this case, a venture will be viable if it has the lowest outflows.
 A1 A2 A3 AN 
NPV      .....   C
 1  K  1  K  1  K  1  K N 
1 2 3

Where: A = annual inflow

K = Cost of finance
C = Cost of investment
N = Number of years
Example
Cost of investment = 100,000/=, interest rate = 10%, inflows year 1 = 80,000/= year 2 =
50,000/=
80,000 50,000
NPV =   100 ,000
1.1 1.12
= 14,049 positive hence invest.
Example
Jeremy limited wishes to expand its output by purchasing a new machine worth Frw 170,000
and installation costs are estimated at Frw40,000/=. In the 4th year, this machine will call for
an overhaul to cost Frw80, 000. Its expected inflows are:
Frw
Year 1 60,000
Year 2 72,650
Year 3 35,720
Year 4 48,510
Year 5 91,630
Year 6 83,715
This company can raise finance to purchase machine at 12% interest rate.
Compute NPV and advise management accordingly.
Solution
Frw
Cost of machine at present value 170,000
Installation cost 40,000
210,000
Overhaul cost in the 4th year = 80,000
Discounting factor = (1.12)4
Therefore present value =80,000 = Frw50,841.446
(1.12)4
Total present value of investment=260,841.45
 60,000 72,650 35,720 48,510 91,630 83,715
PV inflows =     
(1.12) 1.12 2
1.12K  (1.12) 4 1.12 5 1.12 6
3

= 262,147.28
Therefore: NPV = 262,147.28 – 260,841.45
NPV = 1,305.83
The NPV is positive and I would advise the management to invest.

Example
RWAMO limited intends to purchase a machine worth Frw1,500,000 which will have a
residue value Frw200,000 after 5 years useful life. The saving in cost resulting from the use of
this machine are:
Frw
Year 1 800,000
Year 2 350,000
Year 3 -
Year 4 680,000
Year 5 775,000
Using NPV method, advice RWAMO Company whether this machine should be purchased if
the cut off rate is 14% and acceptable saving in cost is 12% of the cost of the investment.
Solution
Years 1 2 3 4 5
Saving 800,000 350,000 - 680,000 775,000
Scrap value - - - - 200,000
Total 800,000 350,000 - 680,000 975,000
amount

800 ,000 350,000 680,000 975,000

NPV =     1,500,000
1.14 1 1.14 2 1.14 4 1.14 5
= 1,880,067.1 – 1,500,000
= 380,067.07
380,067 .0
Return = x100 = 25.337% > 12% hence invest.
1,500,000

ACCEPT OR REJECT RULE OF NPV

Under this method, a company should accept an investment venture if N.P.V. is positive i.e. if
present value of cash outflows exceeds that of cash inflows or at least is equal to zero. (NPV
≥0). This will rank ventures giving the highest rank to that venture with highest NPV because
this will give the highest cash inflow or capital gain to the company.
Advantages of NPV
1. A project with a positive NPV increases the wealth of the company’s, thus
maximize the shareholders wealth.
2. Takes into account the time value of money and therefore the opportunity
cost of capital.
3. Discount rate can be adjusted to take account of different level of risk
inherent in different projects.
4. Unlike the payback period, the NPV takes into account events throughout the
life of the project.
5. Superior to the internal rate of return because it does not suffer the problem of
multiple rates of return
6. Better than accounting rate of return because it focuses on cash flows rather
than profit.
7. NPV technique can be combined with sensitivity analysis to quantify the risk
 of the projects result.
8.It can be used to determine the optimum policy for asset replacement.
The net present value method of investment appraisal has a number of advantages over
other methods:
(i) It is based on cash flows not accounting profit unlike ROCE. Accounting profits
are subject to a number of different accounting treatments and cash flows can add
to the wealth of the shareholders via increased dividends.
(ii) NPV looks at cash flows throughout the whole of an investment period unlike
payback, which ignores cash flows after the end of the payback period. This avoids
the incorrect rejection of projects with later high returns, although it is unlikely in
practice that payback would be used in isolation.
(iii) NPV incorporates the time value of money by using discounted cash flows
whereas ROCE and payback do not. This means that it takes account of the fact
that Frw1 today is worth more than Frw1 in one year's time. Discounted payback
can be used but this will still ignore cash flows after the payback period.
(iv) NPV is viewed as being technically superior to IRR and simpler to calculate. It
reflects the amount of the initial value rather than a relative measure of return and
represents the change in total market value that will occur if the investment project
is accepted. Other investment appraisal methods do not directly show the potential
increase in shareholder wealth, which is a primary financial management objective.
(v) The NPV method is superior for ranking mutually exclusive projects in order of
attractiveness. IRR will give an incorrect indication where discount rates are less
than the IRR of incremental cash flows.
(vi) Where cash flow patterns are non-conventional, for example where the sign of the
net cash flow changes in successive periods, there may be several IRRs which
decision makers must be aware of to avoid making the wrong decision. NPV
however can accommodate these non-conventional cash flows.
(vii) When discount rates are expected to differ over the life of the project, such
variations can be incorporated easily into NPV calculations, but not into IRR
calculations.
(viii) An assumption underlying the NPV method is that any net cash inflows generated
during the life of the project will be reinvested at the cost of capital (that is, the
discount rate). The IRR method, on the other hand, assumes these cash flows can
be reinvested to earn a return equal to the IRR of the original project, which is not
necessarily reasonable.

Disadvantages of NPV
1. NPV assumes that firms pursue an objective of maximizing the wealth of
their shareholders.
2. Determination of the correct discount rate can be difficult.
3. Non-financial managers may have difficulty understanding the concept.
4. The speed of repayment of the original investment is not highlighted.
5. The cash flow figures are estimates and may turn out to be incorrect.
6. NPV assumes cash flows occur at the beginning or end of the year, and is not
a technique that is easily used when complicated, mid-period cash flows are
present.

Limitations of net present value techniques

(i) Shareholder wealth maximization: NPV is based on the assumption that the primary
aim of the organisation is to maximise the wealth of the ordinary shareholders. This
is valid for many companies, but in some investment decisions there may be other
overriding factors that make the NPV approach less relevant. This is particularly true
when the investment under consideration is fundamental to the strategic direction of the
business.
(ii) Public sector problems: The technique is difficult to apply in the public sector, partly
due to methods of accounting, and partly because other organisational aims will be more
important than the maximisation of profit. Public sector operations are commonly judged
in terms of economy, efficiency and effectiveness, and the NPV approach can only
provide a partial answer to these issues.
(iii) Discount rate :A major problem in the use of NPV in practice is the choice of the
discount rate. It is generally accepted that the rate to be used should be the cost of
capital, but this in itself may be difficult to determine. The problem is particularly tricky
when the size of the investment means that the company will need to acquire a
significant amount of additional capital, and there is uncertainty about the cost of new
funds.
(iv) Risk: A related problem to the choice of the discount rate is the incorporation of risk.
The simplest approach is to apply a risk premium to the cost of capital, but the amount of
this is subjective. Other approaches include the use of sensitivity analysis and probability
analysis, but these too have limitations, and involve the use of subjective judgements.
(v) Subjectivity: It follows from (iv) that NPV techniques may appear to be very scientific
and rational whereas in fact there is a large component of subjectivity in the assumptions
and forecasts used. However, this subjectivity is masked by the precise format in which
results are communicated.
(vi) Cash flow timing: The technique assumes that all cash flows arise at the end of the
time period (which is usually one year). This is obviously untrue, and large fluctuations
in this pattern may distort the results. Breaking the analysis down into small periods
leads to complication, and may be unsatisfactory due to the problems of forecasting in
such a precise way.
(vii) Long-term measure: Although the NPV approach may lead to the correct financial
decision in the long-term, this timescale may be too long to be appropriate for the
business to use in practice. For example, it could lead to an unacceptable reduction in
short-term accounting profits which will impact upon the share price and on confidence
in the company. Similarly, it may conflict with incentive arrangements for managers,
which are usually geared to short-term profitability.
(viii) Non quantifiable costs and benefits: Some costs and benefits that arise are not
quantifiable. There may be important non-financial factors that are relevant to the
decision, but which are difficult to quantify. For example, undertaking a new investment
may enhance the standing of the company, making it more attractive to customers,
investors and potential employees. This could have an important impact on the
performance of the company, but cannot be quantified in an NPV analysis.

IRR (INTERNAL RATE OF RETURN)

This method is a discounted cash flow technique which uses the principle of NPV. It is
defined as the rate which equates the investment outlay with the present value of cash inflow
received after a given period of time. This also implies that the rate of return is the discount
rate which makes NPV = 0.
IRR = Pv (cash inflows) = Pv(cash outflows) or IRR is the cost of capital when NPV = 0.
It is also called internal rate of return because it depends wholly on the outlay of investment
and proceeds associated with the project and not a rate determined outside the venture.

A1 A2 A3 AN
IRR  C     ..... 
1  r  1
1  r 2
1  r 
3
1  r N
A = inflow for each period
C = Cost of investment
The value r can be found by:
i) Trial and error
ii) By interpolation
iii) By extrapolation
i) Trial and error method
a)
Select any rate of interest at random and use it to compute NPV of cash
inflows.
b) If rate chosen produces NPV lower than the cost, choose a lower rate.
c) If the rate chosen in (a) above gives NPV greater than the cost, choose a higher
rate. Continue the process until the NPV is equal to zero and that will be the
IRR.
Example :A project costs 16,200/= and is expected to generate the following inflows:
Frw
Year 1 8,000
Year 2 7,000
Year 3 6,000
Compute the IRR of this venture.
Solution
1st choice 10%
8,000 7,000 6,000
  = 17,565.74 > cost, choose a higher rate.
1.11 1.12 1.13
2nd choice 14%
8,000 7,000 6,000
  = 16,453.646
1.14  1
1.14  2
1.14 3
3rd choice 15%
8,000 7,000 6,000
  = 16,194.625
1.15 1 1.152 1.153
IRR lies between 14% and 15%.
ii) Interpolation method
Difference
PV at rate of 14% = 16,453.646
253.646
PV required = 16,200.000
-5.375
PV at rate of 15% = 16,194.625

Therefore, r denotes required rate of return

253 .646
Therefore, IRR = 14% + x (15% - 14%)
253 .646  5.375
= 14% + 0.98%
= 14.98%
A
Similarly, IRR  a%  x (b%  a%
A B
Where, a%=discount rate that gives positive NPV, b%=discount rate that gives negative NPV,
A=positive NPV and B=negative NPV.
 253 .646
Therefore, IRR = 14% + x(15% - 14%)
253 .646  5.375
= 14% + 0.98%
= 14.98%
Acceptance Rule of IRR
IRR will accept a venture if its IRR is higher than or equal to the minimum required rate of
return which is usually the cost of finance also known as the cut off rate or hurdle rate, and in
this case IRR will be the highest rate of interest a firm would be ready to pay to finance a
project using borrowed funds and without being financially worse off by paying back the loan
(the principal and accrued interest) out of the cash flows generated by that project. Thus, IRR
is the break-even rate of borrowing from commercial banks.

(a) Strengths of IRR

 The main advantage of the IRR method is that the information it provides is more easily
understood by managers than NPV, especially non-financial managers. It gives a relative
measure of the value of a proposed investment in the form of a percentage which can be
compared with the company's cost of capital or the rates of interest and inflation.
 IRR is a discounted cash flow method and so takes account of the time value of money:
the concept that Frw1 received today is not equal to Frw1 received in the future.
 IRR considers cash flows over the whole of the project life and is sensitive to both the
amount and the timing of cash flows.

Weaknesses of IRR
 IRR ignores the relative sizes of investments. It therefore does not measure the absolute
increase in company value, and therefore shareholder wealth, which will be created by an
investment.
 Where cash flow patterns are non-conventional, for example cash flows change from
positive to negative during the life of the project, there may be several IRRs which
decision makers must be aware of to avoid making the wrong decision. When discount
rates are expected to differ over the life of the project, such variations can be
incorporated easily into NPV calculations, but not into IRR calculations.
 Mutually exclusive projects are two or more projects from which only one can be chosen.
Examples include the choice of a factory location or the choice of just one of a number of
machines. The IRR and NPV methods can, however, give conflicting rankings as to
which project should be given priority. Where there is a conflict, NPV always offers the
technically correct investment advice.
 Despite the advantages of the NPV method over the IRR method, the IRR method is
widely used in practice.

PROFITABILITY INDEX (P.I.)

Profitability index is the ratio of the present value of cash inflows, at the required rate of
return, to the initial cash outflow of the investment.
P.I. (benefit-cost ratio) = Present value of inflows
Present value of cash outlay
Decision rule:
 Accept : PI is greater than 1
 Reject: PI is less than 1
Example :A company is faced with the following 5 investment opportunities:
Cost PV P.I = Total P.v___ P.I Ranking
Initial capital
1. 500,000 150,000 1.3 4
2. 100,000 40,000 1.4 3
3. 400,000 40,000 1.1 5
4. 200,000 100,000 1.5 2
5. 160,000 90,000 1.6 1
This company has 750,000/= available for investment projects, 3 and 4 are mutually exclusive.
All of the projects are divisible. Which group should be selected in order to maximize the
NPV. Indicate this NPV figure.
Solution
Using P.I. to rank the projects in order of preference 5, 4, 2, 1, 3.
In order to maximize NPV, the following projects combination should be selected:
Frw
Funds available for investment 750,000
Cost of project: 5 160,000
4 200,000
2 100,000
1 290,000 (750,000)
NIL
290,000
NPV = 90,000 + 100,000 + 40,000 + x150,000 = 317,000
500,000
Advantages of profitability index
a) Simple to use and understand.
b) The element of NPV in the venture will indicate which venture is more powerful as the
most profitable venture will have the highest P.I. as the difference or net P.I. will
continue to the company’s profitability.
c) It acknowledges time value for money and at the same time the NPV of a venture at its
present value which is consistent with investment appraisal requirements.

Disadvantages of profitability index

a) It may be useful under conditions of uncertain cost of finance used to discount inflows
and yet this cost is a complex item due to the implicit and explicit element.
b) It may be difficult to ascertain if the economic life of a venture is long and it yields
large inflows because their discounting may call for use of computers that are
expensive.

NPV AND IRR COMPARED

-Single investment decision: A single project will be accepted if it has a positive NPV at the
required rate of return. If it has a positive NPV then, it will have an IRR that is greater than the
required rate of return
-Mutually exclusive projects: Two projects are mutually exclusive if only one of the projects
can be undertaken. In this circumstance the NPV and IRR may give conflicting
recommendation.
The reasons for the differences in ranking are:
 NPV is an absolute measure but the IRR is a relative measure of a project’s viability.
 Reinvestment assumption. The two methods are sometimes said to be based on different
assumptions about the rate at which funds generated by the project are reinvested. NPV
assumes reinvestment at the company’s cost of capital, IRR assumes reinvestment at the
IRR.
5.3. NPV layout
When answering an NPV question, you may find it helpful to use the following layout.
Year 0 Year 1 Year 2 Year 3 Year 4
Sales receipts X X X
Costs (X) (X) (X)
Sales less costs X X X
Taxation (X) (X) (X) (X)
Capital expenditure (X)
Scrap value X
Working capital (X) X
Tax benefit of tax dep'n X X X X
(X) X X X (X)
Discount factors @
post-tax cost of capital X X X X X
Present value (X) X X X (X)

5.2.3. ADJUSTMENT WITH NPV

5.2.3. 1. Allowing for inflation
Inflation is a feature of all economies, and it must be accommodated in financial planning.
There are two types of the cash flows:
 Real cash flows (cash flows in current prices) should be discounted at a real
discount rate, which is a return ignoring inflation.
 Nominal cash flows (the actual expected cash flows at future prices, ie including
inflationary increases) should be discounted at a nominal discount rate, which is a rate
relating to current market rates of return.

So far we have not considered the effect of inflation on the appraisal of capital investment
proposals. As the inflation rate increases so will the minimum return required by an investor.
For example, you might be happy with a return of 5% in an inflation-free world, but if
inflation were running at 15% you would expect a considerably greater yield.

The nominal interest rate incorporates inflation. When the nominal rate of interest is higher
than the rate of inflation, there is a positive real rate. When the rate of inflation is higher than
the nominal rate of interest, the real rate of interest will be negative.

The relationship between real and nominal rates of interest is given by the Fisher formula:
(1 + n) = (1 + r)(1 + i)
Where i = rate of inflation
r = real rate of interest
n = nominal rate of interest
Illustration
A company is considering investing in a project with the following cash flows.
Time Actual cash flows
Rwf
0 (15,000)
1 9,000
2 8,000
3 7,000
The company requires a minimum return of 20% under the present and anticipated conditions.
Inflation is currently running at 10% a year, and this rate of inflation is expected to continue
indefinitely. Should the company go ahead with the project?
Let us first look at the company's required rate of return. Suppose that it invested Rwf1,000
for one year on 1 January, then on 31 December it would require a minimum return of
Rwf200. With the initial investment of Rwf1,000, the total value of the investment by 31
December must therefore increase to Rwf1,200. During the course of the year the purchasing
value of the dollar would fall due to inflation. We can restate the amount received on 31
December in terms of the purchasing power of the dollar at 1 January as follows.
Amount received on 31 December in terms of the value of the pound at 1 January
= Rwf1, 200 = Rwf1, 091 (1.10)1
In terms of the value of the dollar at 1 January, the company would make a profit of Rwf91
which represents a rate of return of 9.1% in 'today's money' terms. This is the real rate of
return. The required rate of 20% is a nominal rate of return (sometimes called a money
rate of return). The nominal rate measures the return in terms of the dollar which is, of
course, falling in value. The real rate measures the return in constant price level terms.
The two rates of return and the inflation rate are linked by the equation, (1 + n) = (1 + r)(1 + i)
where all rates are expressed as proportions.
In our example, (1 + 0.2) = (1 + r)(1 + 0.1)
1.2
1+r = = 1.091
1.1
r = 9.1%
Do we use the real rate or the nominal rate?
The rule is as follows.
 If the cash flows are expressed in terms of the actual number of dollars that will be
received or paid on the various future dates, we use the nominal rate for discounting.
 If the cash flows are expressed in terms of the value of the dollar at time 0 (that is, in
constant price level terms), we use the real rate.
The cash flows given above are expressed in terms of the actual number of dollars that will
be received or paid at the relevant dates (nominal cash flows). We should, therefore, discount
them using the nominal rate of return.

A The advantages and misuses of real values and a real rate of return

Although generally companies should discount money values at the nominal cost of
capital, there are some advantages of using real values discounted at a real cost of capital.
 When all costs and benefits rise at the same rate of price inflation, real values are
the same as current day values, so that no further adjustments need be made to
cash flows before discounting. In contrast, when nominal values are discounted at
the nominal cost of capital, the prices in future years must be calculated before
discounting can begin
 The government might prefer to set a real return as a target for investments, as
being more suitable than a commercial money rate of return.

Costs and benefits which inflate at different rates

Not all costs and benefits will rise in line with the general level of inflation. In such cases, we
can apply the nominal rate to inflated values to determine a project's NPV.
Illustration
Rice is considering a project which would cost Rwf5,000 now. The annual benefits, for four
years, would be a fixed income of Rwf2,500 a year, plus other savings of Rwf500 a year in
year 1, rising by 5% each year because of inflation. Running costs will be Rwf1,000 in the
first year, but would increase at 10% each year because of inflating labour costs. The general
rate of inflation is expected to be 7½% and the company's required nominal rate of return is
16%. Is the project worthwhile? Ignore taxation.
Solution
The cash flows at inflated values are as follows.
Year Fixed income Other savings Running costs Net cash flow
Rwf Rwf Rwf Rwf
1 2,500 500 1,000 2,000
2 2,500 525 1,100 1,925
3 2,500 551 1,210 1,841
4 2,500 579 1,331 1,748
The NPV of the project is as follows.
Year Cash flow Discount factor 16% PV
Rwf Rwf
0 (5,000) 1.000 (5,000)
1 2,000 0.862 1,724
2 1,925 0.743 1,430
3 1,841 0.641 1,180
4 1,748 0.552 965
+ 299
The NPV is positive and the project would seem therefore to be worthwhile.

Briefly, the following rules apply:

 When you have the nominal cash flows, discount with nominal discount rate
 When you have the real cash flows, discount with real discount rate

Assume: a) We are given the nominal cash flows and real discount rate
Option 1:
 Use the given nominal cash flows
 Convert real discount rate into nominal discount rate and thereafter discount
Option 2:
 Convert nominal cash flows into real cash flows
 Discount using the given real discount rate
Illustration 2.20
Year 0 1 2 4
Nominal cash flows (in (500) 250 300 400
millions Rwf)
Real discount rate given was 7% and the inflation rate was
Option 1:
 Convert real discount rate into nominal discount rate and thereafter discount using
Fisher formula
(1 + n) = (1 + r)(1 + i)
n = (1 + r)(1 + i)-1
n = (1 + 7%)(1 + 9%)-1
n = (1 .07)(1 .09)-1
n = 1.663-1
n = 0.1663
n = 16.63%
 Discount nominal cash flows using the obtained nominal discount rate

Year 0 1 2 3
Nominal cash (500) 250 300 400
flows
DF (16.63%)-n 1.000 0.857 0.735 0.630
PV (500) 214.3 220.5 252
NPV=186

Option 2:
 Convert nominal cash flows into real cash flows
Year 0 1 2 3
Nominal cash (500) 250 300 400
flows
DF (1+9%)-n 1.000 0.857 0.735 0.630
PV (500) 229.25 252.6 308.8 Real cash
flows
  Discount using the given real discount rate
Year 0 1 2 3
Real cash flows (500) 229.25 252.6 308.8
DF (1+7%)-n 1.000 0.857 0.735 0.630
PV (500) 214.3 220.5 252
NPV=186.8

Assume: b) We are given the real cash flows and nominal discount rate
Option 1:
 Use the given real cash flows
 Convert nominal discount rate into real discount rate and thereafter discount

Option 2:
 Convert real cash flows into nominal cash flows
 Discount using the given nominal discount rate

Illustration
Year 0 1 2 4
Nominal cash flows(in (600) 300 400 350
millions Rwf)
Nominal discount rate given was 19% and the inflation rate was 6%
STEPS
Option 1:
 Convert nominal discount rate into real discount rate and thereafter discount
(1  n)  (1  r )(1  i )
(1  n)
r 1
(1  i)
(1.19)
r 1
(1.06)
r  1.1265  1
r  0.1265
 Discount using the given real discount rate
Year 0 1 2 3
Nominal cash flows (in millions Rwf) (600) 300 400 350
-n
Real DR (12.265) 1.000 0.891 0.794 0.707
PV (600) 267.3 317.6 247.5
NPV =232.4
Option 2:
 Convert real cash flows into nominal cash flows
Year 0 1 2 3
Real cash flows (in millions (600) 300 400 350
Rwf)
Inflation factor (1.06)n 1.000 1.06 1.124 1.191
Nominal cash flows (in (600) 318 449.6 416.85
millions Rwf)
 Discount Nominal cash flows using the given nominal discount rate
Year 0 1 2 3
Nominal cash flows (in (600) 318 449.6 416.85
millions Rwf)
Nominal DR(1.19)-n 1.000 0.840 0.706 0.593
PV (600) 267.1 317.4 247.2
NPV=231.7
Note:
To be realistic, impact of inflation should be considered. All cash flows are assumed to be
nominal, unless stated otherwise.
5.2.3. 2. ADJUSTMENTS WITH THE TAXATION
There are three additional considerations associated with including taxation:
 Good – Any investment in a capital asset will give rise to a capital
allowance. The capital allowance will lead to a reduction in the amount of
tax subsequently paid – CASH INFLOW
 Bad – We would expect the investment to generate additional profits, these
in turn would lead to additional tax payable – CASH OUTFLOW
 Ugly – Sometimes the examiner may delay all cash flow associated with
taxation by one year, this is done to reflect the delays between tax arising
and being paid. Take care and read the question carefully.
Corporation tax charged on a company’s profits is a relevant cash flow for NPV purposes. It is
assumed, unless otherwise stated in the question, that:

 operating cash inflows will be taxed at the corporation tax rate

 operating cash outflows will be tax deductible and attract tax relief at the corporation
tax rate
 tax is paid one year after the related operating cash flow is earned
 investment spending attracts capital or WDAs which get tax relief (see the section
below)
 the company is earning net taxable profits overall (this avoids any issues of carrying
losses forwards to reduce future taxation).

Use the following approach for examination questions:

Capital allowances/WDAs
For tax purposes, a business may not deduct the cost of an asset from its profits as depreciation
(in the way it does for financial accounting purposes). Instead the cost must be deducted from
taxable profits in the form of ‘capital allowances’ or WDAs. The basic rules are as follows:
 WDAs are calculated on a reducing balance basis (usually at a rate of 25%
 the total WDAs given over the life of an asset equate to its fall in value over the
period (i.e. the cost less any scrap proceeds)
 WDAs are claimed as early as possible
 WDAs are given for every year of ownership except the year of disposal
 in the year of sale or scrap a balancing allowance (BA) or charge arises (CA).
Frw
Original cost of asset X
Cumulative capital allowances claimed (X)
___
Written down value of the asset X
Disposal value of the asset (X)
 ___
BA or BC X
___

EXAMPLE:
A company buys an asset on the last day of the accounting period for Frw26,000. It will be
used on a project for three years after which it will be disposed of on the final day of year 3.
Tax is payable at 30% one year in arrears, and capital allowances are available at 25%
reducing balance.
Required:
(a) Calculate the WDA and hence the tax savings for each year if the proceeds on disposal of
the asset are Frw12,500.
(b) If net trading income from the project is Frw16,000 pa and the cost of capital is 8%
calculate the NPV of the project.
Solution
(a) Time Tax saving Timing of
@ 30% tax relief
Frw Frw
T0 Initial investment 26,000
T0 WDA @ 25% (6,500) 1,950 T1
Written down value 19,500
T1 WDA @ 25% (4,875) 1,463 T2
__________
Written down value 14,625
T2 WDA @ 25% (3,656) 1,097 T3
Written down value 10,969
Sale proceeds (12,500)
T3 BC (1,531) (460) T4

Time T0 T1 T2 T3 T4
Frw Frw Frw Frw Frw
Net trading 16,000 16,000 16,000
inflows
Tax payable (30%) (4,800) (4,800) (4,800)
Initial (26,000)
investment

Scrap 12,500
proceeds
Tax relief on WDAs 1,950 1,463 1,097 (460)
___________________________________________________________
Net cash (26,000) 17,950 12,663 24.797 5,260
flows
____________________________________________________________
DF @ 8% 1.000 0.926 0.857 0.794 0.735
____________________________________________________________

PV (26,000) 16,622 10,852 19,689 3,866

NPV Frw17,297
5.2.3. 3.INCORPORATING WORKING CAPITAL
Investment in a new project often requires an additional investment in working capital, i.e. the
difference between short-term assets and liabilities.
The treatment of working capital is as follows:
 initial investment is a cost at the start of the project
 if the investment is increased during the project, the increase is a relevant cash outflow
 at the end of the project all the working capital is ‘released’ and treated as a cash
inflow.

EXAMPLE
A company anticipates sales for the latest venture to be Frw300,000 in the first year. Sales are
then expected to increase at a rate of 8% pa over the three-year life of the project. Working
capital equal to 10% of annual sales is required and needs to be in place at the start of each
year.Calculate the working capital flows?
Solution
T0 T1 T2 T3
Frw Frw Frw Frw
Sales 300,000 324,000 349,920
Working capital required 30,000 32,400 34,992
Step 2: Work out the incremental investment required each year, remembering to release all
the working capital at the end of the project
T0 T1 T2 T3
Frw Frw Frw Frw
Working 32,400-30,000 34,992-32,400
Capital investment (30,000) (2,400) (2,592) 34,992

DEALING WITH QUESTIONS WITH BOTH TAX AND INFLATION.

 Combining tax and inflation in the same question does not make it any more difficult
than keeping them separate.
 Questions with both tax and inflation are best tackled using the money method.
 Inflate costs and revenues, where necessary, before determining their tax implications.
 Ensure that the cost and disposal values have been inflated (if necessary) before
calculating WDAs.
 Always calculate working capital on these inflated figures, unless given.
 Use a post-tax money discount rate.

Proforma
EXAMPLE
Ackbono Co is considering a potential project with the following forecasts:
Now T1 T2 T3
Initial investment (Frwmillion) (1,000)
Disposal proceeds (Frwmillion) 200
Demand (millions of units) 5 10 6
Further information provided:
 The initial investment will be made on the first day of the new accounting period.
 The selling price per unit is expected to be Frw100 and the variable cost Frw30 per
unit. Both of these figures are given in today’s terms.
 Tax is paid at 30%, one year after the accounting period concerned.
 WDA's are available at 25% reducing balance.
 The company has a real required rate of return of 6.8%.
 General inflation is predicted to be 3% pa but the selling price is expected to inflate at
4% and variable costs by 5% pa
Required: Determine the NPV of the project. N.B:Work in Frw millions.
Solution

Frw millions T0 T1 T2 T3 T4
Sales (W1) 520 1082 675
Variable costs (W1) (158) (331) (208)
_____ _____ _____
Net trading inflows 362 751 467
Tax payable (30%) (109) (225) (140)
Initial investment (1,000)
Scrap proceeds 200
Tax relief on WDAs (W2) 75 56 109
_____ _____ _____ _____ _____
Net cash flows (1,000) 362 717 498 (31)
DF @ 10% (W3) 1 0.909 0.826 0.751 0.683
_____ _____ _____ _____ _____
PV (1,000) 329 592 374 (21)
 NPV 274
_____
Then,
Time Frwm Tax saving Timing of

tax relief
Frwm
T0 Initial investment 1000
T1 WDA @ 25% (250) 75 T2
_____
Written down value 750
T2 WDA @ 25% (188) 56 T3
_____
Written down value 562
Sale proceeds (200)
_____
T3 BA 362 109 T4

5.2.3.4. LEASE VERSUS BUY DECISIONS

1. The nature of leasing
Rather than buying an asset outright, using either available cash resources or borrowed funds,
a business may lease an asset. Leasing is a contract between a lessor and a lessee for hire of a
specific asset by the lessee from a manufacturer or vendor of such assets. The lessor has
ownership of the asset and so provides the initial finance for the asset. The lessee has
possession and use of the asset on payment of specified rentals over a period.
Examples of lessors
 Banks
 Insurance companies
Types of asset leased
 Office equipment
 Computers
 Cars
 Commercial vehicles
 Aircraft
 Ships
 Buildings
2. Types of leasing
We distinguish three types of leasing:
a) Operating leases (lessor responsible for maintaining asset)
b) Finance leases (lessee responsible for maintenance)
c) Sale and leaseback arrangements
a. Operating lease
Operating lease is a lease where the lessor retains most of the risks and rewards of ownership.
Operating leases are rental agreements between a lessor and a lessee, for a relatively short
period of time. It is useful to think of operating leases as short-term rental agreements.
(a) The lessor supplies the equipment to the lessee.
(b) The lessor is responsible for servicing and maintaining the leased equipment
(c) The period of the lease is fairly short, less than the expected economic life of the asset. At
the end of one lease agreement, the lessor can either lease the same equipment to someone
else, and obtain a good rent for it, or sell the equipment second-hand.
b. Finance leases
A finance lease is a lease that transfers substantially all of the risks and rewards of ownership
of an asset to the lessee. It is an agreement between the lessee and the lessor for most or all of
the asset's expected useful life.
There are other important characteristics of a finance lease.
(a) The lessee is responsible for the upkeep, servicing and maintenance of the asset.
(b) The lease has a primary period covering all or most of the useful economic life of the
asset. At the end of this period, the lessor would not be able to lease the asset to someone else,
because the asset would be worn out or near the end of its useful life. The lessor must therefore
ensure that the lease payments during the primary period pay for the full cost of the asset as
well as providing the lessor with a suitable return on his investment.
(c) At the end of the primary period the lessee can normally continue to lease the asset for an
indefinite secondary period, in return for a very low nominal rent, sometimes called a
'peppercorn rent'. Alternatively, the lessee might be allowed to sell the asset on a lessor's
behalf (since the lessor is the owner) and perhaps to keep most of the sale proceeds.
Example: A motor lease
The primary period of a lease to acquire a motor car might be three years, with an agreement
by the lessee to make three annual payments of Frw6,000 each. The lessee will be responsible
for repairs and servicing, road tax, insurance and garaging. At the end of the primary period of
the lease, the lessee may have the option either to continue leasing the car at a nominal rent
(perhaps Frw250 a year) or to sell the car and pay the lessor 10% of the proceeds.

KEY DIFFERENCES BETWEEN OPERATING AND FINANCE LEASES

Finance lease
A finance lease is an agreement between the user of the leased asset and a provider of finance
that covers the majority of the asset's useful life.
Key features of a finance lease
(i) The provider of finance is usually a third party finance house and not the original
provider of the equipment.
(ii) The lessee is responsible for the upkeep, servicing and maintenance of the asset.
(iii) The lease has a primary period, which covers all or most of the useful economic
life of the asset. At the end of the primary period the lessor would not be able to
lease the equipment to someone else because it would be worn out.
(iv) It is common at the end of the primary period to allow the lessee to continue to
lease the asset for an indefinite secondary period, in return for a very low nominal
rent, sometimes known as a 'peppercorn' rent.
(v) The lessee bears most of the risks and rewards and so the asset is shown on the
lessee's balance sheet.
Operating leases are rental agreements between a lessor and a lessee
Key features of an operating lease
(i) The lessor supplies the equipment to the lessee.
(ii) The lessor is responsible for the upkeep, servicing and maintenance of the asset.
(iii) The lease period is fairly short, less than the expected economic life of the asset. At
the end of one lease agreement the lessor can either lease the same equipment to
someone else and obtain a rent for it or sell it second-hand.
(iv) The asset is not shown on the lessee's balance sheet.

c. Sale and leaseback

Sale and leaseback is when a business that owns an asset agrees to sell the asset to a financial
institution and lease it back on terms specified in the sale and leaseback agreement.
The business retains use of the asset but has the funds from the sale, whilst having to pay rent.
A common form of sale and leaseback arrangement has involved commercial property. A
company might sell its premises to a bank or finance company (to raise cash) and then lease
back the premises under a long-term leasing arrangement.
3. Attractions of leasing
Attractions include the following.
(a) The supplier of the equipment is paid in full at the beginning. The equipment is sold to the
lessor, and other than guarantees, the supplier has no further financial concern about the asset.
(b) The lessor invests finance by purchasing assets from suppliers and makes a return out of
the lease payments from the lessee. The lessor will also get capital allowances (tax allowable
depreciation) on the purchase of the equipment.
(c) Leasing may have advantages for the lessee:
(i) The lessee may not have enough cash to pay for the asset, and would have difficulty
obtaining a bank loan to buy it. If so the lessee has to rent the asset to obtain use of it at all.
(ii) Finance leasing may be cheaper than a bank loan.
(iii) The lessee may find the tax relief available advantageous.
Operating leases have further advantages.
(a) The leased equipment does not have to be shown in the lessee's published statement of
financial position, and so the lessee's statement shows no increase in its gearing ratio.
(b) The equipment is leased for a shorter period than its expected useful life. In the case of
high technology equipment, if the equipment becomes out of date before the end of its
expected life, the lessee does not have to keep on using it. The lessor will bear the risk of
having to sell obsolete equipment second-hand. A major growth area in operating leasing in
the UK has been in computers and office equipment (such as photocopiers and fax machines)
where technology is continually improving.
4. Lease or buy decisions
The decision whether to lease or buy an asset is a financing decision which interacts with the
investment decision to buy the asset. The assumption is that the preferred financing method
should be the one with the lower PV of cost. We identify the least-cost financing option by
comparing the cash flows of purchasing and leasing. We assume that if the asset is purchased,
it will be financed with a bank loan; therefore the cash flows are discounted at an after-tax
cost of borrowing.
The cost of capital that should be applied to the cash flows for the financing decision is the
cost of borrowing. We assume that if the organisation decided to purchase the equipment, it
would finance the purchase by borrowing funds (rather than out of retained funds). We
therefore compare the cost of purchasing with the cash flows of leasing by applying this cost
of borrowing to the financing cash flows.
The cash flows of purchasing do not include the interest repayments on the loan as these
are dealt with via the cost of capital.
An important cash flow difference between leasing and buying is that:
 With buying the asset, the company receives the tax allowances (tax-allowable
depreciation).
 With leasing, the lessor and not the lessee receives these allowances.
With leasing, the lease rentals are allowable for tax purposes, and there are consequently
savings in tax cash flows.
A simple example: Brown Co has decided to invest in a new machine which has a ten year
life and no residual value. The machine can either be purchased now for Frw50,000, or it can
be leased for ten years with lease rental payments of Frw8,000 per annum payable at the end
of each year. The cost of capital to be applied is 9% and taxation should be ignored.
Solution
Present value of leasing costs
PV = Annuity factor at 9% for 10 years × Frw8,000= 6.418 × Frw8,000 = Frw51,344
If the machine was purchased now, it would cost Frw50,000. The purchase is therefore the
least-cost financing option.
Note: Once the decision has been made to acquire an asset for an investment project, a
decision still needs to be made as to how to finance it. The choices that we will consider are:
 lease
 Buy.
The NPVs of the financing cash flows for both options are found and compared and the lowest
cost option selected. The finance decision is considered separately from the investment
decision. The operating costs and revenues from the investment will be common in each case.
Only the relevant cash flows arising as a result of the type of finance are included in the NPV
calculation.
Numerical analysis
The benefits of leasing vs purchasing (with a loan) can be assessed by an NPV approach:
Step 1 the costs of leasing (payments, lost capital allowances and lost scrap revenue)
Step 2 the benefits of leasing (savings on loan repayments = PV of loan = initial outlay)
Step 3 discounting at the post tax cost of debt.
Step 4 calculate the NPV – if positive it means that the lease is cheaper than the post-tax
cost of a loan
- An alternative method is to evaluate the NPV of the cost of the loan and the NPV of the
cost of the lease separately, and to choose the cheapest option.
- Note that the cost of the loan should not include the interest repayments on the loan eg
the NPV of the repayments on a loan for Frw10,000 repayable in 1 year at 10% interest is
Frw10,000 when discounted at 10% - so the cost of a loan is just its initial time 0 value, here
Frw10,000.
- In numerical questions you can assume that the lessee is not able to claim capital allowances
unless told otherwise.

Advantages of leasing:

- Increased flexibility – Short term/operating leases are cancellable hence convenient

when the asset is needed temporary.
- Avoidance of investment initial outlay – The firm is able to secure full use of the asset
without immediate heavy initial capital investment.
- Off-balance sheet financing – In case of operating lease, lease obligations are not
shown in the balance sheet. They do not affect the gearing of the firm. The firm’s
borrowing position is thus not affected. Operating leases is thus called off-balance
sheet financing.
- Leasing does not require a collateral – It is also less expensive compared to a bank
loan. In long term (finance) leases, the lessor is given a chance to buy the asset.
- Lease charges are tax allowable hence a tax shield/saving for the firms
- No risk of obsolescence – the firm can revoke the lease e.g in case of operating leasing
thus it avoids risk of ownership

Eg: Mallen and Mullins has decided to install a new milling machine. The machine costs
$20,000 and it would have a useful life of five years with a trade-in value of $4,000 at the end
of the fifth year. A decision has now to be taken on the method of financing the project.
(a) The company could purchase the machine for cash, using bank loan facilities on which the
current rate of interest is 13% before tax.
(b) The company could lease the machine under an agreement which would entail payment of
$4,800 at the end of each year for the next five years. The rate of tax is 30%. If the machine is
purchased, the company will be able to claim a tax depreciation allowance of 100% in Year 1.
Tax is payable with a year's delay.
Solution: Cash flows are discounted at the after-tax cost of borrowing, which is at 13% * 70%
= 9.1%, say 9%.
The cheapest option would be to purchase the machine.
An alternative method of making lease or buy decisions is to carry out a single financing calculation with the
payments for one method being negative and the receipts being positive, and vice versa for the other method.

The negative NPV indicates that the lease is unattractive and the purchasing decision is better, as the net savings
from not leasing outweigh the net costs of purchasing.
Illustration: ABC Ltd has decided to acquire a piece of equipment costing Frw 240 000 of
five years. The equipment is expected to have no salvage value ate the end and the company
uses straight-line depreciation method on all it Fixed Assets. The company has two financing
alternative methods available, leasing or borrowing. The loan has an interest rate of 15%
requiring equal-year-end installments to be paid. The lease would be set at a level that would
amortize the cost of equipment over the lease period and would provide the lessor with a 14%
return on capital. The company‘s tax rate is 40%.
Required:
o Compute the annual lease payments.
o Compute the PV of the cash out flow under lease financing
o Calculate the annual loan installment payment
o For each of the 5 years, calculate the interest and the principal component of
the loan repayment.
o Calculate the PV of after tax cash flow under the loan alternative
o Which alternative is better and why?
Solution:
 240 000 = A + A PVAF 14%, 4 years

240 000 = A (1 + 2.9137)

A= 240 000 = Frw 61, 323

3.9137

b) Year Lease payments Lease Rental Net Payments PVIF 14% PVs
Tax shield (40%)

0 61 323 - 61 323 1.000 61 323

1 61 323 (24 529) 36 794 0.9174 33 755
2 61 323 (24 529) 36 794 0.8417 30 970
3 61 323 (24 529) 36 794 0.7722 28 412
4 61 323 (24 529) 36 794 0.7084 26 065
5 61 323 (24 529) (24 529) 0.6499 (15 941)
Total PV‘s 164 584

c) Annual Loan Installments

240 000 = A PVAF 15%, 5 years

A = 240 000 = Frw 71 595
3.3522

 Loan Amortization Schedule

Year bal. at Installment Interest Principle Outstanding Bal. the

beg.
1 240 000 71 595 36 000 35 595 204 405
2 204 405 71 595 30 661 40 934 163 471
3 163 471 71 595 24 521 47 074 116 397
4 116 397 71 595 17 460 54 135 62 262
5 62 262 17 595 9 339 62256 6*

* rounding off error

Depreciation of the asset = 240 000 – 0 = 48 000

5
e)
Year Depreciation Interest Total Tax shield (40%) Cash flows PVIF 9% Pv‘s
(71595-tax)

1 48 000 36 000 84 000 33 600 37 995 0.9174 34 857

2 48 000 30 661 78 661 31 464 40 131 0.8417 33 778
3 48 000 24 521 72 521 29 008 42 587 0.7722 32 886
4 48 000 17 460 65 460 26 184 45 411 0.7084 32 169
5 48 000 9 339 57 339 23 936 48 659 0.6499 31 623
165 313
f) Decision:
Leasing is better than borrowing because it‘s cheaper and results in lower cost of transaction.

N.P.V of leasing = 240 000 – 164 584 = Frw 75, 416

N.P.V of borrowing = 240 000 – 165 313 = Frw 74 687
Net benefit of leasing 729
5.2.3.5. ASSETS REPLACEMENT DECISIONS

DCF techniques can assist asset replacement decisions, to decide how frequently an asset should be
replaced. When an asset is being replaced with an identical asset, the equivalent annual cost method can
be used to calculate an optimum replacement cycle.

When an asset is newly purchased the asset’s efficiency and resale value will be very high
while the maintenance costs will be relatively low. However as the asset is ageing it may
become more expensive to operate and maintain. The longer replacement is deferred, the
more expensive will the operating and the affected asset. Equally, replacement of assets
involves an outlay of capital expenditure which would be deferred when the decision to
replace is postponed. The realizable value of an asset will decline as the asset gets older and
more worn.
Early replacement means that a higher resale value should be obtained for existing equipment.
When considering replacement certain items are of paramount importance.

1. The capital cost i.e. outlay of the new asset.

2. The operating, maintenance costs, repairs costs and costs of servicing.
3. Scrap value i.e. resale value
4. Revenue where applicable.

TYPES OF REPLACEMENT

There are two types of replacement of an existing asset with a new, but identical asset. Two
assets are termed identical if they produce the same cash flows i.e. both the existing asset and
the replacing asset have the same financial characteristic. The problem is therefore simple one
of deciding on “how frequently the asset should be replaced” i.e what is the optimum
replacement cycle?
NON – IDENTICAL REPLACEMENT DECISION
When an asset is replaced or to be replaced by an asset of a different type, the two assets are
said to be non- identical once they produce different cash flows. The decision is now “when
should the existing asset be replaced “ i.e. what is the optimal replacement cycle?

METHODS OF DECIDING OPTIMUM REPLACEMENT CYCLE

There are basically three methods of deciding the optimum replacement cycle and each
method will give the same recommendation if well applied.
1. The annual equivalent value method (EAC)
2. The lowest common multiple method (LCM)
3. Finite horizon method

EQUIVALENT ANNUAL COST METHOD (EAC)

When there is no inflation, this is the quickest method of deciding the optimum replacement
cycle. To begin, it is necessary to calculate the present value of costs for each replacement
cycle but over one cycle only. The PV arrived at for each of the various years are not
comparable, because they refer to different time periods, whereas replacement is continuous.
The equivalent annual cost method of comparing these cash flows is to calculate, for each
length of replacement cycle an annuity (annual cost) which has the same present value,
discounted cost of capital, as the cost of repeated cycles of the various lengths under
consideration.

𝑃𝑉 𝑜𝑣𝑒𝑟 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑦𝑐𝑙𝑒

EAC = 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑜𝑟 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
LOWEST COMMON MUTIPLE METHOD (LCM)

The lowest common multiple method is to estimate cash flows over a period of time which is
the lowest common multiple of all the replacement cycles under consideration.
Thus for replacement cycles of 1, 2, 3, 4yrs, the LCM of time in 12years.in twelve years there
would be :
(a) 12 complete replacement cycles of 1 year or
(b) 6 complete replacement cycles of 2 year or
(c) 4 complete replacement cycles of 3 year or
(d) 3 complete replacement cycles of 4 years.
We are to discount these cash flows over the lowest common multiple time period. The option
with the lowest present value of cost will be the optimum replacement cycle.

FINITE HORIZON
In practice when the maximum life of the asset is more than about 4 years, the lowest common
multiple method becomes a very long and tedious process thus giving rise to the finite horizon
method.
If the maximum life were say, the replacement options would be every 1, 2, 3, 4, 5, 6 or
7years, and the LCM would be 420. The finite horizon method is to calculate the present value
of cost over a “ significant” time period (perhaps 15 or 20 years), because the present values of
cash flows beyond this period are unlikely to affect the relative costs of the replacement
options.

PROCEDURE REQUIRED IN SOLVING IDENTICAL REPLECEMENT PROBLEMS

Identify the optimal replacement policy of the existing asset making use of EAC or LCM
method.

PROCEDURE REQUIRED IN SOLVING NON- IDENTICAL REPLECEMENT

PROBLEMS
1. Identify the optimal replacement policy of the new asset making use of EAC or LCM
method.
2. Identify the value of the optimal policy and discount to infinity. ALTERNATIVELY use
the value as derived in (1) above and apply the EAC approach full .ANOTHER is to use
the figure calculated in (1) above and add one to the relevant option for application to
infinity.
3. Combine your answer in (2) above with the various replacement alternatives available for
the existing asset

EXAMPLE
A new machine costs Frw120,000 and may be sold at the end of any year at the following
prices:
Year (end) 1 2 3 4 5
Selling price (Frw) 75,000 49,000 30,000 16,500 9,000
Studies of the machine’s performance indicate the maintenance costs are:
Year (end) 1 2 3 4 5
Maintenance costs (Frw) 15,000 18,000 22,500 30,000 45,000

How often should a new car with identical characteristic be bought if the average total cost per
period is to be minimized? Cost capital is 10%
Solution:
EVERY ONE YEAR
Yr CF DF@ 10% PV
0 (120,000) 1.000 (120,000)

1 (15,000) 0.91 (13,650)

1 75,000 0.91 68,250
(65,400)
EVERY TWO YEARS
Yr CF DF@10% PV
0 (120,000) 1.0000 (120,000)

1 (15,000) 0.91 (13,650)

2 (18,000) 0.83 (14,940)

2 49,500 0.83 68,250
(10792)

EVERY THREE YEARS

Yr CF DF@10% PV
0 (120,000) 1.000 (120,000)

1 (15,000) 0.91 (13,650)

2 (18,000) 0.83 (14,940)

3 (22,500) 0.75 (16,875)

3 30,000 0.75 22,500
(142,965)
EVERY FOUR YEARS
Yr CF DF@10% PV
0 (120,000) 1.000 (120,000)

1 (15,000) 0.91 (13,650)

2 (18,000) 0.83 (14,940)

3 22,500 0.75 (16,875)

4 (30,000) 0.68 (20,400)

4 16,500 0.68 11,220
(174,645)

EVERY FIVE YEARS

Yr CF DF@10% PV
0 (120,000) 1.000 (120,000)

1 (15,000) 0.91 (13,650)

2 (18,000) 0.83 (14,940)

3 (22,500) 0.75 (16,875)

4 (30,000) 0.68 (20,400)

5 (45,000) 0.62 (27,900)

5 9,000 0.62 5,580
(174,645)
Calculation of EAC

EAC for Yr 1 (65,400) / 0.91 = (71,868)

EAC for Yr 2 (107,920) / 1.74 = (62,023)

EAC for Yr 3 (65,400) / 2.49 = (57,416)

EAC for Yr 4 (65,400) / 3.17 = (55,093)

EAC for Yr 5 (65,400) / 3.79 = (54,930) ****

DECISION: replace every 5 years.

REPLACEMENT OF ASSETS- CONT’D
Example
Estate Developers purchased a machine five years ago at a cost of Frw7,500. The machine
had an expected economic life of 15 years at the time of purchase and a zero estimated salvage
value at the end of 15 years. It is being depreciated on a straight line basis and currently has a
book value of Frw5,000. The Financial Manager has conducted a feasibility study aimed at
acquiring a new machine for Frw12,000 and is depreciated over its 10 years useful life. The
new machine will expand sales from Frw10,000 to Frw11,000 per annum and will reduce
labour and materials usage sufficiently to cut operating cost from Frw7,000 to Frw5,000. The
salvage value of the new machine is Frw2,000 at the end of useful life. The current market
value of the old machine is Frw1,000 and tax is 40%. The firms cost of capital is 10%. The
financial manager wishes to make a decision on whether to replace the old machine with a
new one and he seeks your held.
N.B. The decision to replace takes into account the following:
a) Estimate the actual cash outlay attributable to the new machine
b) Determine the incremental cash flows.
c) Compute the NPV of incremental cash flows.
d) Add up the present value of the expected salvage value to the P.V. of the incremental
cash flow.
e) Ascertain whether the NPV (net present value) is positive or whether the IRR (internal
rate of return) exceed the cost in which case invest if its positive.
Solution
a) Initial capital for new machines Frw
Cash price of new machine 12,000
Less market value of old machine (1,000)
Less tax shield on sale of old machine:
Market value 1,000
Less net book value 5,000
Loss on disposal 4,000
Tax shield = 40% x 4,000 (6,000)
Increamental initial capital 9,400

12,000  2,000
b) Depreciation of new machine = = 1,000
10 yrs
5,000  0
Depreciation of old machine = = 500
10 yrs
Increamental depreciation 500

NB: The NBV of old machine after 5 years is Frw5,000. This NBV will be depreciated
over the remaining 10 years.
 Determine operating cash flows:
Increamental sales = 11,000 – 10,000 1,000
Savings in labour costs = 5,000 – 7,000 2,000
Increamental EBDT 3,000
Less increamental depreciation (non-cash item) (500)
Increamental EBT 2,500
Less tax @ 40% 1,000
Increamental EAT 1,500
Add back increamental depreciation 500
Annual cash flow 2,000

Terminal cash flows at end of year 10 is equal to increamental salvage value.

New machine salvage value 2,000
Less old machine salvage value 0
2,000
Compute the NPV @10% cost of capital:
1  (1.1) 10
P.V of cash flows = 2000 x  2,000 xPVAF10% ,10  2,000 x 6.145 12,290
0.10
1
P.V of salvage value = 2,000 x
 
1.110
 2,000 xPVIF10% ,10  2,000 x 0.386 772
13,062
Less increamental initial capital (9,400)
Increamental N.P.V 3,662
Replace the old machine

5.2.3.6. SPECIFIC INVESTMENT DECISIONS-CAPITAL RATIONING

Capital rationing is a situation in which a company has a limited amount of capital to invest
in potential projects, such that the different possible investments need to be compared with
one another in order to allocate the capital available most effectively. If an organisation is in a
capital rationing situation it will not be able to enter into all projects with positive NPVs
because there is not enough capital for all of the investments.
Soft capital rationing is brought about by internal factors; hard capital rationing is brought
about by external factors.
Soft capital rationing may arise for one of the following reasons.
(i) Management may be reluctant to issue additional share capital because of concern
that this may lead to outsiders gaining control of the business.
(ii) Management may be unwilling to issue additional share capital if it will lead to a
dilution of earnings per share.
(iii) Management may not want to raise additional debt capital because they do not
wish to be committed to large fixed interest payments.
(iv) Management may wish to limit investment to a level that can be financed solely
from retained earnings. They may not want to grow the company too quickly.
Hard capital rationing may arise for one of the following reasons.
(i) Raising money through the stock market may not be possible if share prices are
depressed.
(ii) There may be restrictions on bank lending due to government control.
(iii) Lending institutions may consider an organisation to be too risky (eg, too highly
geared, poor prospects) to be granted further loan facilities.
(iv) The costs associated with making small issues of capital may be too great.
SINGLE AND MULTI-PERIOD CAPITAL RATIONING
a)Single –period capital rationing
There is a shortage of funds in the present period which will not arise in following periods.
Note that the rationing in this situation is very similar to the limiting factor decision that we
know from decision making. In that situation we maximize the contribution per unit of
limiting factor.
b)Multi-period capital rationing
A more complex environment where there is a shortage of funds in more than one period.
This makes the analysis more complicated because we have multiple constraints and
multiple outputs. Linear programming would have to be employed.
PRACTICAL METHODS OF DEALING WITH CAPITAL RATIONING
- Practical steps to deal with capital rationing include:
(a) Leasing
(b) Entering into a joint venture with a partner
(c) Delaying one of then projects to a later period
(d) Issuing new capital (if possible)
PROCEDURE OF MARGINAL COSTING EXTENDED TO CAPITAL RATIONING
1. Positive contribution
2. Contribution per limiting factor
3. Rank the projects in order of contribution per limiting factor
4. Select based on the ranking carried out.

Let us consider the example below for a ranking demonstration:-

Example
Borno Pic is considering four projects, A, B,C and D, which have the fallowing estimated
cash flows and NPVs ( at a cost of capital of 10 %)

Projects Year 0 year 1 year2 NPV

A (10,000) 6,000 7,000 +1,240
B (20,000) 14,000 10,000 +991
C (30,000) 10,000 28,000 +2,230
D (40,000) 30,000 20,000 +3,801

Without capital rationing, all four projects would be viable investments

a) If the projects are divisible

If there is a restriction to the amount of finance available, so that only Frw60,000 is available
in year o, the company will optimize its return by maximizing the NPV generated per Frw1
spent in year 0 as follows:

Project NPV Outlay in year PI=NPV /Io (Ranking)

in year 0
A 1,240 0.124 1st
B 991 0.050 4th
C 2,230 0.074 3rd
D 3,801 0.095 2nd

The Frw60,000 available would be spent as follows:

Project ranking outlay NPV
A 1st 10,000 1,240
B 2nd 40,000 3,801
rd
C (balance)* 3 10,000 743
60,000 5,784

743=10/40*3,801
By spending the balancing Frw10,000 0nproject C, one third of the full investment would be
made to earn one-third of the NPV. It is interesting to note that the discount rate of return
(IRR) for each of the four projects would be as follows:

Projects IRR (approx) Ranking

A 19% 1st
B 14% 4th
C 15% 3rd
D 16% 2nd
It is no coincidence that the ranking of project in order of IRR gives the same priority listing
as that of the NPV: OUTLAY ratio. This coincidence arises only when there is single period
rationing and at the same time no projects involve capital expenditure in any other year.
OPPORTUNITY COST OF CAPITAL
The projects selected from above exampled were A, D and a part of C, therefore it could be
stated that:
(a) Any project which does not have an IRR at least as great as that of project C ( about
15% ) should be rejected; and
(b) If any project suddenly appeared which offered a return in excess of the IRR of project
C, it should be accepted at the expense of some (or all ) of project C, and then even
possibly at the expense of project D or A

b) If the projects are not divisible

 Select the combination of the projects but not exceeding the funds available
 Choose the combination with the highest NPV
Example
Funds available=300 million Frw
Initial outlays in Frw
Projects millions NPV
A 100 80
B 60 50
C 70 35
D 200 96
Step one: Projects Combinations
Possible combinations
1 A+B+C=100+60+70=230/300
2 A+B=100+60=160/300
3 A+D=200+100=300/300
4 C+D=70+200=270/300
5 B+C=60+70=130/300
6 B+D=60+200=260/300
Step two: NPV combinations based on the outlays combinations made
NPV combinations Projects Ranking
1 A+B+C=80+50+35=165 2
2 A+B=80+50=130 5
3 A+D=80+96=176 1
4 C+D=35+96=131 4
5 B+C=50+35=85 6
6 B+D=50+96=146 3
Summary
With the indivisible projects
Funds available=300 millions FRW
NPV=176 millions Frw
5.2.3. ADJUSTED PRESENT VALUE (APV)

Adjusted Present Value (APV) is used for the valuation of projects and companies. It takes the net
present value (NPV), plus the present value of debt financing costs, which include interest tax shields,
costs of debt issuance, costs of financial distress, financial subsidies, etc. So why do we use Adjusted
Present Value instead of NPV in evaluating projects with debt financing? To answer this, we first need
to understand how financing decisions (debt vs. equity) affect the value of a project.

The value of a project financed with debt may be higher than that of an all equity-financed one since
the cost of capital often decreases with leverage, turning some negative NPV projects into positive
ones. Thus, under the NPV rule, a project may be rejected if it’s financed with only equity, but may be
accepted if it’s financed with some debt. Moreover, the APV approach takes into consideration the
benefits of raising debts (e.g. interest tax shield), which NPV does not do. As such, APV analysis is
widely preferred in highly leveraged transactions.

The Adjusted Present Value approach takes into consideration the benefits of raising debts (e.g. interest
tax shield), which NPV does not do. As such, APV analysis can be preferred in highly leveraged
transactions. In financial modeling, it’s common practice to use Net Present Value with firm’s the
Weighted Average Cost of Capital as the discount rate, which determines the un-levered value of the
firm (its enterprise value) or the unlevered value of a project.The present value of net debt is deducted
to arrive at equity value, if that’s what is desired.

Adjusted Present Value assumptions

We make the following simplifying assumptions before using the APV approach in the valuation of a
project:
The project’s risk is equal to the average risks of other projects within the firm, which is also the risk
of the firm. In other words, the project in question is a “typical” project that the firm usually takes on.
In this case, the relevant discount rate for the project is based on the risk of the firm. Corporate taxes
are the only important market imperfection at the level of debt chosen. This means that we focus only
on the interest tax shields, and ignore the effects generated by the costs of debt issuance and financial
distress. All debt is perpetual.

Unlevered cost of capital

The APV method uses unlevered cost of capital to discount free cash flows, as it initially assumes
that the project is fully financed by equity. To find the unlevered cost of capital, we must first find the
project’s unlevered beta. Unlevered beta is a measure of the company’s risk relative to that of the
market. It is also referred to as “asset beta”, because without leverage, a company’s equity beta is equal
to its asset beta.To retrieve a company’s beta, we can look up the company on financial resource sites.
The unlevered cost of capital is calculated as:
Unlevered cost of capital (rU) = Risk-free rate + beta * (Expected market return – Risk-free
rate).

The Adjusted Present Value for valuation

The APV method to calculate the levered value (VL) of a firm or project consists of three steps:
Step 1
Calculate the value of the unlevered firm or project (VU), i.e. its value with all-equity financing. To do
this, discount the stream of FCFs by the unlevered cost of capital (rU).

Step 2
Calculate the net value of the debt financing (PVF), which is the sum of various effects, including:
PV(Interest tax shields) – our main focus
PV(Issuance costs)
PV(Financial distress costs)
PV(Other market imperfections)
Step 3
Sum up the value of the unlevered project and the net value of debt financing to find the adjusted
present value of the project. That is, VL = VU + PVF.

Applications of Adjusted Present Value

The APV method is most useful when evaluating companies or projects with a fixed debt schedule, as
it can easily accommodate the side effects of financing such as interest tax shields. APV breaks down
the value of a project into its fundamental components and thus provides useful information needed to
refine the transaction and monitor its execution. Leveraged buyouts (LBOs), where one firm
acquires another firm using debt to finance the purchase, are a classical situation where APV is used.
APV method is the most practical for this situation because of the changing capital structure. It has
been noted that the company‘s gearing level has an implication for both the value of equity and the
overall cost of capital. The viability of an investment project would depend partly on how it is financed
and partly on how the method of financing affects the company‘s gearing. Investment projects can be
evaluated using NPV method by discounting the cash flows at the projects overall cost of capital or the
risk adjusted discount rate.

An alternative method of carrying out project appraisal is use of NPV method involving 2 stages:
 Evaluate a project as if its an all equity financed to determine the base case NPV
 Make adjustments to allow for the effect of the method of financing that has been used

APV = Base case NPV + PV of financing effect

Illustration
Assume XYZ ltd is considering a project which costs Frw100 000 to be financed by 50% equity with
a cost of 21.6% and 50% debt with a pre-tax cost of 12%.
The financing method would maintain the company‘s overall cost of capital to remain unchanged.
The project is estimated to generate cash flows of Frw36 000 p.a. before interest charges and
corporate tax at 33%.
Required:
Evaluate the project using:
NPV method
APV method
Solution:
B E
 Ko = Kd (I – T) ( /V) + Ko ( /V)
 0.12 (1 – 0.33) 0.5 + 0.216 (0.5)
 14.82%
After tax cash flows = 36 000 (1 – 0.33) = 24120
NPV = ( 24120) -100
000 0.1482
= Frw62 753
Amounts of debt = 50% (162 753) = Frw81376.5
Amount of equity = 50% (162 753) = Frw81376.5
 Kel = Keu + (1 – T) (Keu – Kd) B/E
0.216 = Keu + (1- 0.33) (Keu – 0.12)
0.5/0.5 Keu = 0.177485029
Step 1 Base Case NPV = 24120 – 100 000
0.177485029 =
35899
APV =Base case NPV + PV of the interest tax shield (tcB)
=35899 + 0.33 (81376.5)
=Frw62753
Decision:
Accept because NPV > 0
APV and NPV method produce the same conclusion since the capital structure remains constant.
However, the NPV and APV method will produce different results in cases where the financing
method used changes the firm ‘s capital structure.
Illustration:
Assumes in the above illustration that the entire project was to be financed by debt.
The APV would be:
APV = 35899 + 0.33 (100
000) = Frw68 899
APV is a better method where initial capital is raised in such a way that it changes the capital
structure proportions. It can be used to evaluate the effect of the method of financing a project
and therefore is better than NPV.
 However, APV has the following Limitations:
 Computation of the cost of a no equity-financed company may not be easy.
 Identifying all costs associated with the method of financing would be difficult e.g. the transaction
costs, agency cost, etc.

QUESTION THREE
The managers of Strayer plc are investigating a potential Sh.25 million investment. The
investment would be a diversification away from existing mainstream activities and into the
printing industry. Sh.6 million of the investment would be financed by internal funds, Sh.10
million by a rights issue and Sh.9 million by long term loans. The investment is expected to
generate pre-tax net cash flows of approximately Sh.5 million per year, for a period of ten
years. The residual value at the end of year ten is forecast to be Sh.5 million after tax. As the
investment is in an area that the government wishes to develop, a subsidized loan of Sh.4
million out of the total Sh.9 million is available. This will cost 2% below the company’s
normal cost of long-term debt finance, which is 8%.
Strayer’s equity beta is 0.85, and its financial gearing is 60% equity, 40% debt by value. The
average equity beta in the printing industry is 1.2, and average gearing 50% equity, 50% debt
by market value.
The risk free rate is 5.5% per annum and the market return 12% per annum.
Issue costs are estimated to be 1% for debt financing (excluding the subsidized loan), and 4%
for equity financing. These costs are not tax allowable.
The corporate tax rate is 30%.
Required:
(a) Estimate the Adjusted Present Value (APV) of the proposed investment.
(b) Comment upon the circumstances under which APV might be a better method of
evaluating a capital investment than Net Present Value (NPV).

Solution
(a) Assuming the risk of companies in the printing industry is similar to that of Strayer’s
new investment, the beta of the printing industry will be used to estimate the discount
rate for the base case NPV. Ungearing the beta of the printing industry:

E 50
Asset beta = equity beta x  1.2x  0.706
E  D(1  t) 50  50(1  0.30)

Using the capital asset pricing model:

Ke ungeared = 5.5% + (12% - 5.5%)0.706 = 10.09% or approximately 10%.
Annual after tax cash flows = Sh.5 million (1 – 0.3) = Sh.3,500,000
From annuity tables with a 10% discount rate:
Sh.
Present value of annual cash flows 3,500,000 x 6.145 21,507,500
= 1,930,000
Present value of the residual value 5,000,000 x 0.386 23,437,500
= 25,000,000
(1,562,500)
Less initial investment
Base case NPV

Financing side effects relate to the tax shield on interest payments, the subsidized loan, and
issue costs associated with external financing.

Tax relief:
Sh.5 million 8% loan. Interest payable is Sh.400,000 per year, tax relief is Sh.400,000 x 0.3 =
Sh.120,000 per year
Sh.4 million subsidized loan. Interest is Sh.240,000 per year, tax relief Sh.72,000 per year.
Total annual tax relief Sh.192,000 per year.
The present value of this tax relief, discounted at the risk free rate of 5.5% per year is:
Sh.192,000 x 7.541 = Sh.1,447,872
(The tax relief on interest payments allowed by government is assumed to be risk free. The
mid-point between 5% and 6% in annuity tables is used. N.B. discounting at a rate higher than
the risk free rate could be argued, especially if the company might be in a non taxpaying
position in some years.)
Subsidy:
The company saves 2% per year on Sh.4,000,000 or Sh.80,000, or Sh.80,000 x (1 – 0.30) =
Sh.56,000 after tax.
As this is a government subsidy it is assumed to be risk free and will be discounted at 5.5%
per year.
Sh.56,000 x 7.541 = Sh.422,296

Issue costs: Sh.

Debt Sh.5 million x 1% = 50,000
Equity Sh.10 million x 4% = 400,000
450,000
The adjusted present value is estimated to be:
(Sh.1,562,500) + Sh.1,447,872 + Sh.422,296 – Sh.450,000 = (Sh.142,332)
Based upon these estimates the project is not financially viable.
(b) APV may be a better technique to use than NPV when:
 There is a significant change in capital structure as a result of the investment.
 The investment involves complex tax payments and tax allowances, and/or has periods
when taxation is not paid.
 Subsidized loans, grants or issue costs exist.
 Financing side effects exist (e.g. the subsidized loan) which require discounting at a
different rate than that applied to the mainstream project.
Advantages and disadvantages of the adjusted present value (APV)
The adjusted present value present the practical advantages and theoretical disadvantages as
detailed below:

5.3. INVESTMENT APPRAISAL UNDER UNCERTAINTY

A major reservation of any investment appraisal decision is that the figures used in the
calculations are only estimates and stand to be uncertain. Clearly if any of the cash flows used
in the decision turn out to be different from what was estimated, the decision itself could be
affected. In this chapter we will look at four approaches that attempt to either reduce the
problem or quantify the possible effect of the problem.

5.3.1. RISK AND UNCERTAINTY

Risk analysis can be applied to a proposed capital investment where there are several possible
outcomes and, on the basis of past relevant experience, probabilities can be assigned to the
various outcomes and estimated cash flows that could prevail.
Uncertainty analysis can be applied to a proposed capital investment where there are several
possible outcomes but there is little past relevant experience to enable the probability of the
alternative outcomes to be predicted. There are a wide range of techniques for incorporating
risk into project appraisal.
Scenario:
A risky situation is one where we can say that there is a 70% probability that returns from a
project will be Frw150,000 and a 30% probability that returns will be less than Frw50,000.
This is more risky than an investment where there is a 70% probability that returns will be
Frw110,000 and a 30% probability that returns will be Frw90,000. The variability of returns,
which could be measured statistically, is lower with this second investment, which is why it is
less risky.

If, however, no information can be provided about the probabilities of different the returns
from the project, we are faced with an uncertain situation. For example, we might estimate that
returns from an investment could be anything between Frw150,000 and Frw50,000, but we
can’t estimate probabilities. This would be uncertainty about the investment returns.

In general, risky projects are those whose predicted possible future cash flows, and hence the
project returns, are more variable. The greater the variability, the greater the risk.

The problem of risk is more acute with capital investment decisions than other decisions for
the following reasons.
(a) Estimates of capital expenditure might be for several years ahead, such as for major
construction projects. Actual costs may escalate well above budget as the work progresses.
(b) Estimates of benefits will be for several years ahead, sometimes 10, 15 or 20 years ahead
or even longer, and such long-term estimates can at best be approximations.

5.3.2. EXPECTED VALUES (EV)

it is weighted average of different outcome based on their probability of occurrences
= outcome x probability
Eg.
Demand (A) Probability(B) Expected Values (EV) C= AxB
100 0.2 or 20% 20
200 0.1 or 10% 20
500 0.45 or 45% 225
100 0.25 or 25% 25
Total 1<100% 290
5.3.3 SENSITIVITY ANALYSIS
Sensitivity analysis assesses how responsive the project's NPV is to changes in the variables
used to calculate that NPV. Sensitivity analysis is one particular approach to uncertainty
analysis. The certainty equivalent approach is another; this involves the conversion of the
expected cash flows of the project to riskless equivalent amounts.
The NPV could depend on a number of uncertain independent variables.
 Selling price
  Sales volume
 Cost of capital
 Initial cost
 Operating costs
 Benefits

The basic approach of sensitivity analysis is to calculate the project's NPV under alternative
assumptions to determine how sensitive it is to changing conditions. An indication is thus
provided of those variables to which the NPV is most sensitive (critical variables) and the
extent to which those variables may change before the investment results in a negative NPV.

Sensitivity analysis therefore provides an indication of why a project might fail. Management
should review critical variables to assess whether or not there is a strong possibility of events
occurring which will lead to a negative NPV. Management should also pay particular attention
to controlling those variables to which the NPV is particularly sensitive, once the decision has
been taken to accept the investment.

A simple approach to deciding which variables the NPV is particularly sensitive to is to

calculate the sensitivity of each variable:

Sensitivity =NPV *%
Present value of project variable
The lower the percentage, the more sensitive is NPV to that project variable as the variable
would need to change by a smaller amount to make the project non-viable.
As a guide, the percentage change in variables that will change our decision can be calculated
as follows depending on the variable under consideration:
1. Sensitivity to Outlay = (NPV of the project/PV of outlay) X 100%
2. Sensitivity to contribution = ( NPV of the project / PV of contribution) X 100%
3. Sensitivity to sales volume/ units = (NPV of the project / PV of sales volume (units) )
x 100%
4. Sensitivity to sales value = ( NPV of the project / PV of sales value) X 100%
5. Sensitivity to variable cost = (NPV of the project / PV of variable cost ) X 100%
6. Sensitivity to project’s life = ( Project’s life – BEP Project’s life / Project’s life)/ 100%
7. Sensitivity to Cost of capital = (( IRR – COC ))/ COC ) /100%
8. Sensitivity to incremental fixed cost = (NPV of the project / PV of incremental fixed
cost)/ 100%
Example:
Year Outlay Savings Running cost
0 (100,000) - -
1 42,000 14,000
2 56,000 24,500
3 84,000 35,000
4 105,000 42,000
The company’s cost of capital is 10%
You are required to calculate:
a. The project’s viability
b. (i) The project’s sensitivity to the outlay
(ii) The project’s sensitivity to the savings
(iii) The project’s sensitivity to the running cost.
Solution
a) First step is to calculate the NPV
Yr CF DF@10% PV
 0 (100,000) 1.000 (100,000)
1 28,000 0.9091 25,455
2 31,500 0.8264 26,032
3 49,000 0.7513 36,814
4 63,000 0.6830 43,029
NPV 31,330
The project is viable, it has a + NPV of Frw 31,330
B) i) SM of the Outlay
Computation of PV of Outlay
SM = ( NPV/PV of Outlay ) X 100%
SM = (31,330/100,000) X 100%
SM = 31.33%
Interpretation
The outlay can rise i.e increase by a s much as 31.33% and the project will still be viable. Or if
the outlay increases by more than 31.33% the project becomes unviable
i) SM of Savings
Computation of PV of Savings
Yr CF DF@10% PV
1 42,000 0.9091 38,182
2 56,000 0.8264 46,278
3 84,000 0.7513 63,109
4 105,000 0.6830 71,715
Total Savings 219,284
SM = ( NPV / PV of Savings) X 100%
SM = ( 31,330 / 219,284) X 100%
SM = 14,29%
Interpretation
Savings should not fall / reduce by more than 14.29% or else the project becomes unviable.
ii) SM of running cost
Computation of PV of Running Costs
Yr CF DF@10% PV
1 14,000 0.9091 12,727
2 24,500 0.8264 20,247
3 35,000 0.7513 26,296
4 42,000 0.6830 28,686
Total of running cost 87,956

SM = (NPV / PV of running cost) X 100%

SM = (31,330/ 87,956) X 100%
SM = 35, 62%
Interpretation
(i) Running cost can increase by as much as 35.62% and the project will still be viable
(ii) If running cost should increase above 35.62% the project becomes unviable

Example 2
Gbenga has just set up a company, Gbengashin Manufacturing Plc and estimates its cost of
capital to be 15%. His first project involves investing in Frw 150,000 of equipment with a life
of 15 years and a final scrap value of Frw 15,000
The equipment will be used to produce 15,000 deluxe pairs of rain boots per annum generating
a contribution of Frw 2,750 per pair. He estimates that annual fixed costs will be Frw 15,000
per annum
(a) Determine on the basis of the above figures, whether the project is worthwhile; and
(b) Calculate the sensitivity of your calculations to:
(i) Initial investment;
(ii) Annual sales volume;
(iii) Annual fixed costs
(iv) Scrap value; and
(v) Cost of capital
By finding what percentage changes in the above figures would cause your decision in (a) to
change.
Solution
a) Computation of the NPV
Yr Item CF DF@15% PV
0 Equip (150,000) 1.000 (150,000)
1-15 Contribution 41,250 5.8474 241,205
1-15 Annual FC (15,000) 5.8474 (87,711)
15 S. Value 15,000 0.1229 1,844
5,338
Decision: The project has a + NPV it is therefore worthwhile.
b) i) Initial Investment
SM = (NPV /PV of outlay) X 100%
SM = (5,338 / 150,000) X 100%
= 3.56%
iii) Annual Sales Volume
SM = ( NPV/ PV of Sales volume) X 100%
SM = (5,338/241,205) X 100%
SM = 2.21%

iv) Annual Fixed Costs

SM = (NPV / PV of Annual Fixed costs) X 100%
SM = (5,338 / 87,711) X 100%
SM = 6.09%
v) Scrap Value
SM = (NPV/PV of Scrap Value) X 100%
SM = (5,338/1,844) X 100%
SM = 289,48%
vi) Cost of Capital i.e IRR
Trial and Error: at 15% the project produced a + NPV of Frw 5,338
We try 20% for possible – NPV

Yr Item CF DF@20% PV
0 Equip (150,000) 1.0000 (150,000)
1-15 Contribution 41,250 4.6755 192,864
1-15 Annual FC (15,000) 4.6755 (70,133)
15 SV 15,000 0.0649 974
(26,295)
Interpolation NPV1 =5,338; R1 =15%; R2 = 20% and NPV2 = (26,295).
Example: Sensitivity analysis
Kenney Co is considering a project with the following cash flows.

Cash flows arise from selling 650,000 units at Frw10 per unit. Kenney Co has a cost of capital
of 8%.
Required: Measure the sensitivity of the project to changes in variables.
Solution
The PVs of the cash flow are as follows.

The project has a positive NPV and would appear to be worthwhile. The sensitivity of each
project variable is as follows.
(a) Initial investment

In other words, the project will only just provide the required investment return if the cost of
the investment is 14.6% higher than estimated, assuming that the value of all the other cash
flows for the investment are as estimated.
(b) Sales volume

In other words, the project will only just provide the required investment return if sales
volume is
12.8% lower than estimated, assuming that the value of all the other cash flows for the
investment are as estimated.
(c) Selling price

(d) Variable costs

(e) Cost of capital. We need to calculate the IRR of the project. Let us try discount rates of
15% and 20%. The cost of capital can therefore increase by 132% before the NPV becomes
negative.

The elements to which the NPV appears to be most sensitive are the selling price followed by
the sales volume. Management should thus pay particular attention to these factors so that they
can be carefully monitored.
Weaknesses of this approach to sensitivity analysis
These are as follows.
(a) The method requires that changes in each key variable are isolated, assuming that all other
values in the estimated cash flows are unchanged. However, management may be more
interested in the combination of the effects of changes in two or more key variables.
(b) Looking at factors in isolation is unrealistic since they are often interdependent.
(c) Sensitivity analysis is analysis when there is uncertainty. It does not examine the
probability that any particular variation in costs or revenues might occur.
(d) Critical factors may be those over which managers have no control.
(e) In itself it does not provide a decision rule. Parameters defining acceptability of an
investment project, given the uncertainty, must be laid down by managers.
Sensitivity analysis analyses the effect of changes made to variables in the problem in order to
determine their effect on the decision. First we calculate the NPV of the project on the basis of
the best estimates. Then we calculate what % change (or sensitivity) in each of the variables
would result in a NPV of zero (i.e. the breakeven position – any further change would change
the decision).By considering the sensitivity of each variable we can ascertain which variables
are the most critical and therefore perhaps need more work confirming our estimates.
Example 1
Daina has just set up a new company and estimates that the cost of capital is 15%. Her first
project involves investing in Frw150,000 of equipment with a life of 15 years and a final scrap
value of Frw15,000. The equipment will produce 15,000 units p.a. generating a contribution of
Frw2.75 each. She estimates that additional fixed costs will be Frw15,000 p.a..
(a) Determine, on the basis of the above figures, whether the project is worthwhile
(b) Calculate the sensitivity to change of:
i. the initial investment
ii. the sales volume p.a.
iii. the contribution p.u.
iv. the fixed costs p.a.
v. the scrap value
vi. the cost of capital
Solution
DF @15% PV
-
0 Cost -150,000 1
150,000
1-15 Contribution 41,250 p.a 5.847 241,189
1-15 Fixed costs (15,000) p.a 5.847 -87,705
15 scrap 15000 0.123 1,845
NPV 5,329
5,329
i)Sensitivity of initial investment * 100%  3.55%
150,000
5,329
ii) Sensitivity of sales volume  * 100%  2.21%
241,189
5,329
iii)Sensitivity of contribution per unit  * 100%  2.21%
241,189
5,329
iii)Sensitivity of fixed costs  * 100%  6.08%
87,705
5,329
iv)Sensitivity of scrap value  * 100%  289%
1,845
DF @20% PV
-
0 Cost -150,000 1
150,000
 1-15 Contribution 41,250 p.a 4.675 192,844
1-15 Fixed costs (15,000) p.a 4.675 -70,125
15 scrap 15000 0.065 975
NPV (26,306)
5,329
IRR  15%  * 5%  15.84%
(5,329  26,306)
0.84
iv)Sensitivity of cost of capital  * 100%  5.6%
15
5.3.4. THE CERTAINTY-EQUIVALENT APPROACH
Another method is the certainty-equivalent approach. By this method, the expected cash
flows of the project are converted to riskless equivalent amounts. The greater the risk of an
expected cash flow, the smaller the certainty-equivalent value (for receipts) or the larger the
certainty-equivalent value (for payments). As the cash flows are reduced to supposedly certain
amounts, they should be discounted at a risk free rate. This concept will be covered in detail
later in this text, but the risk free rate is effectively the level of return that can be obtained
from undertaking no risk.
Example: Certainty-equivalent approach
Dark Ages Co, whose cost of capital is 10%, is considering a project with the following
expected cash flows.

The project seems to be worthwhile. However, because of the uncertainty about the future
cash receipts, the management decides to reduce them to 'certainty-equivalents' by taking only
70%, 60% and 50% of the years 1, 2 and 3 cash flows respectively. The risk-free rate is 5%.
On the basis of the information set out above, assess whether the project is worthwhile.
Solution
The risk-adjusted NPV of the project is as follows.

The project’s certainty-equivalent NPV is negative. This means that the project is too risky
and should be rejected. The disadvantage of the 'certainty-equivalent' approach is that the
amount of the adjustment to each cash flow is decided subjectively.
Eg.
Cost of Capital =10 %
Years Cfs DF at 10% Present value
0 (10,000) 1 (10,000)
1 7,000 0.909 6,363
2 5,000 0.826 4,130
3 5,000 0.751 3,733
NPV + 4,248
Management decided to reduce future cfs by taking only 70%, 60% and 50% for year1, year2
and year3 respectively
Required: On the basis of the information assess whether the project is worthwhile
Solution
Years Cfs DF at 10% PV
0 (10,000) 1 (10,000)
1 4,900 0.909 4454
2 3,000 0.826 2478
3 2,500 0.751 1877
NPV =(1,191)
The project is too risky.

5.3.5. PROBABILITY ANALYSIS

A probability analysis of expected cash flows can often be estimated and used both to
calculate an expected NPV and to measure risk. A probability distribution of 'expected cash
flows' can often be estimated, recognizing there are several possible outcomes, not just one.
This may be used to do the following:
Step 1 Calculate an expected value of the NPV.
Step 2 Measure risk, for example in the following ways.
(a) By calculating the worst possible outcome and its probability
(b) By calculating the probability that the project will fail to achieve a positive NPV
(c) By calculating the standard deviation of the NPV
Example: Probability estimates of cash flows
A company is considering a project involving the outlay of Frw300,000 which it estimates will
generate cash flows over its two-year life at the probabilities shown in the following table.
Cash flows for project
Year one

Year two

The company's cost of capital for this type of project is 10% DCF. You are required to
calculate the expected value (EV) of the project's NPV and the probability that the NPV will
be negative.
Solution
Step 1 Calculate expected value of the NPV.
First we need to draw up a probability distribution of the expected cash flows. We begin by
calculating the present values of the cash flows.
And then,

Step 2 Measure risk.

Since the EV of the NPV is positive, the project should go ahead unless the risk is
unacceptably high. The probability that the project will have a negative NPV is the probability
that the total PV of cash inflows is less than Frw300,000. From the column headed 'Total PV
of cash inflows', we can establish that this probability is 0.0625 + 0.125 + 0.0625 + 0.125 =
0.375 or 37.5%. This might be considered an unacceptably high risk.
Problems with expected values
There are the following problems with using expected values in making investment decisions.
 An investment may be one-off, and 'expected' NPV may never actually occur. For
example, if there is a 50% probability that the NPV will be + Frw10,000 and a 50%
probability that it will be Frw(2,000), the EV of the NPV is + Frw4,000. On this basis
the project will go ahead. However, an NPV of Frw4,000 is not expected to happen.
The NPV will be either plus Frw10,000 or minus Frw2,000.
 Assigning probabilities to future events and outcomes is usually highly subjective.
 Expected values do not evaluate the range of possible NPV outcomes.
Question used to calculate the expected 1) Cfs, 2) NPV
Eg. Initial investment = Frw 300,000
Cash flows for the project
year 1
Cfs Probability
100,000 0.25
200,000 0.50
300,000 0.25
Year 2
If Cfs in year 1 is Probability Cfs in year2
Frw 100,000 0.25 -
0.50 100,000
0.25 200,000
1
Frw 200,000 0.25 100,000
0.50 200,000
0.25 300,000
1
Frw 300,000 0.25 200,000
0.50 300,000
0.25 350,000
1
The company’s cost of capital for this type of project is 10% Dcf. You are
required to calculate the expected value (EV) of the project’s NPV and the
probability that the NPV will be negative.
Solution
Y2 Sum of Cfs Joint probability
AxB
100 0.25 0 100 + 0 = 100 0.25 x 0.25 = 0.0625 6.250
0.25 100 0.50 100 100 + 100 = 200 0.25 x 0.50 = 0.125 25
0.25 200 100 + 200 = 300 0.25 x 0.25 = 0.0625 18.750
0.50 200 200 0.25 100 200 + 100 = 300 0.50 x 0.25 = 0.125 37.500
0.50 200 200 + 200 = 400 0.50 x 0.50 = 0.250 100
0.25 300 200 + 300 = 500 0.50 x 0.25 = 0.125 62.500
0.25 300 300 0.25 200 300 + 200 = 500 0.25 x 0.25 = 0.0625 31.250
0.50 300 300 + 300 = 600 0.25 x 0.50 = 0.125 75
0.25 350 300 + 350 = 650 0.25 x 0.25 = 0.0625 40.625
Total expected CFS
396.875
Year 1 PV PV year 2 Sum of PV Joint Sum of
probability present values
90.9 = 100x0.909 0.25 0 x 0.826 90.9 + 0 = 90.9 0.0625 56.1825
0.50 82.6 =100 x 0.826 90.9 + 82.6 = 173.5 0.1250 21.6875
0.25 165.2 = 200 x 0.826 90.9 + 165.2 = 256.1 0.0625 16.00625
181.8 = 200 x 0.909 0.25 82.6 = 100 x 0.826 181.8 + 82.6 = 264.4 0.1250 33.05
165.2 = 200 x 0.826 181.8 +165.2 = 347 0.250 86.75
0.50 247.8 = 300 x 0.826 181.8 + 247.8 = 429.6 0.1250 53.7

0.25
272.7 = 300 x 0.909 0.25 165.2 = 200 x 0.826 272.7 + 165.2 = 437.9 0.0625 27.36875
247.8 = 300 x 0.826 272.7 + 347.8 = 520.5 0.125 65.0625
0.50 289.1 = 350 x 0.826 272.7 + 289.1 = 561.8 0.0625 35.1125

0.25

Total ∑PV 342.35575

Less initial outlay {300)
NPV = 42.35575

5.3.6. OTHER RISK ADJUSTMENT TECHNIQUES

Other risk adjustment techniques include the use of simulation models, discounted payback
and risk adjusted discount rates.
a) SIMULATIONS

Simulation is a technique which allows more than one variable to change at the same time.
Simulation will overcome problems of having a very large number of possible outcomes, also
the correlation of cash flows (a project which is successful in its early years is more likely to
be successful in its later years).
Essentially, the stages are as follows:
 identify the major variables
 specify the relationship between the variables
 attach probability distributions to each variable and assign random numbers to reflect
the distribution
 simulate the environment by generating random numbers
 record the outcome of each simulation
 repeat the simulation many times to be able to obtain a probability distribution of the
possible outcomes
Example: Simulation model
The following probability estimates have been prepared for a proposed project.

The cost of capital is 12%. Assess how a simulation model might be used to assess the
project's NPV.
Solution
A simulation model could be constructed by assigning a range of random number digits to
each possible value for each of the uncertain variables. The random numbers must exactly
match their respective probabilities. This is achieved by working upwards cumulatively from
the lowest to the highest cash flow values and assigning numbers that will correspond to
probability groupings as follows.

* Probability is 0.15 (15%). Random numbers are 15% of range 00 – 99.

** Probability is 0.40 (40%). Random numbers are 40% of range 00 – 99 but starting at 15.
*** Probability is 0.30 (30%). Random numbers are 30% of range 00 – 99 but starting at 55.
For revenue, the selection of a random number in the range 00 and 14 has a probability of
0.15. This probability represents revenue of Frw40,000. Numbers have been assigned to cash
flows so that when numbers are selected at random, the cash flows have exactly the same
probability of being selected as is indicated in their respective probability distribution above.
Random numbers would be generated, for example by a computer program, and these would
be used to assign values to each of the uncertain variables. For example, if random numbers
37, 84, 20, 01, 56 and 89 were generated, the values assigned to the variables would be as
follows.

A computer would calculate the NPV many times over using the values established in this way
with more random numbers, and the results would be analyzed to provide the following.
(a) An expected NPV for the project
(b) A statistical distribution pattern for the possible variation in the NPV above or below this
average.The decision whether to go ahead with the project would then be made on the basis of
expected return and risk.
An investor is considering introducing a new cheap ball pens into the market, this would
involve purchasing a plant costing Frw 30 DM with UEL of 5years depreciated on SLM
salvage is nil. Due to the market uncertainty, the sale price variable cost and sale volume
of the new ball pen is estimated probabilistically as follows,
selling price value probability
Frw
30 0.2
40 0.6
50 0.2
Variable value Cost Probability Sale value Volume probability
Frw 10 0.2 4M 0.2
Frw 20 0.5 6M 0.5
Frw 30 0.3 8M 0.3
Company cost of capital is 12% and corporate tax is 30%.
Required:
1. Expected NPV of the new product
2. Simulate NPV calculations using random numbers (76 20 55, 64 82 50, 02 74 29, 53
08 58, 16 01 51, 16 69 14, 55 36 86, 54 35 24, 23 52 39, 36 99 47)
3. The probability that the product simulation
Techniques that allows more than one variable to change art time. It considers Probability –
random numbers
Solution
1. Expected selling price = (30 x 0.2) + (40 x0.6) + (50x0.2) = 40
Expected Sale volume = (4M x 0.2) + (6Mx0.5) + (8Mx0.3) = 6.2M
Expected variable cost = (10x0.2) + (20x0.5) + (30x0.3) = 2 + 10 + 9 = 29
Depreciation
Initial cost = 300M
Scrap value = 0
UFL = 5years
300M
Depreciation expenses = 5 = 60M
Selling price 40
Sale volume 6.2M
Total sales (revenues) 248M
Less variable cost (21 x 6.2) (130.2M)
PBDT 117.8M
Less depreciation (60)
PBT 57.8M
Less taxation at 30% (17.34)
PAT 40.46
Add back depreciation 60M
Net cash flows 100.46

Expected NPV = (40.46 x 3.605) – 300M = (154.1417M)

Cash flows = PBDT (1-t) + D
whereby t = tax rate and D = depreciation
= 57.8(1-0.3) + 60M = 100.46
variable cost (40 – 21) x 6.2
contribution 19 x 6.2 =

ii) relate probability with cash flows

Selling price value Selling price Cumulative Range
probability probability
30 0.2 0.2 (20%) 1 – 19
40 0.6 0.8 (80%) 20 – 79
50 0.2 1 (100%) 80 – 99
Variable cost
Value Probability Cumulative Range
probability
10 0.2 0.2 1 – 19
20 0.5 0.7 20 – 69
30 0.3 1 70 – 99
Sales volume
Value Probability Cumulative Range
probability
4M 0.2 0.2 1 – 19
6M 0.5 0.7 20 – 69
8M 0.3 1 70 -99

Random numbers
Random Range value Variable Variable Sale Sale PBDT CFs ∑NPV
numbers number cost cost volume volume (sales
 Random value Random volume price –
Number Number variable
cost) x
sales
volume
1 76 40 20 20 55 6M 120M 102 67.71
2 64 40 82 30 50 6M 60M 60 (83.7)
3 02 30 74 30 29 6M 0M 18 (235,11)
4 53 40 08 10 58 6M 180M 144 219.12
5 16 30 01 10 51 6M 120M 102 67.71
6 16 30 69 20 14 4M 40M 46 (134.17)
7 55 40 36 20 86 8M 160M 130 168.65
8 54 40 35 20 24 6M 120M 102 67.71
9 23 40 52 20 39 6M 120M 102 67.71
10 36 40 99 30 47 6M 60m 60 (83.7)
cfs = PBDT (1 –t) + D
cfs = 120(1 -3%) + 60 =
Annuity factor at 12% is 3.605
Eg.
PBDT 120
(60)
PBT 60
tax 3% (18)
42
Add back 60
102
cfs = PBT(1 – t) + D = (120 – 60) x 0.7 + 60 = 102
∑NPV 67.71+(86.7)+ (235.11)+ 219.12+67071+(134.17)+ 168.65+67.71+67.71+(83.7)
Expected NPV = 10 = =
10
12.193
Number of places where we have positive NPV 6
Probability of success = = 10 ≈ 60%
number of random numbers

b) DISCOUNTED PAYBACK (ADJUSTED PAYBACK)

The discounted payback period (DPP) is the time it will take before a project's cumulative
NPV turns from being negative to being positive. The payback method of investment
appraisal, discussed in Chapter 7, recognizes uncertainty in investment decisions by focusing
on the near future. Short-term projects are preferred to long-term projects and liquidity is
emphasized.

The discounted payback period is the length of time before the cumulative PV of cash inflows
from the projects begins to exceed the initial outflow. It is similar to the payback method, but
uses discounted cash flows rather than non-discounted cash flows to measure the payback
period.
Discounted payback uses discounted cash flows. This is also known as adjusted payback.
For example if we have a cost of capital of 10% and a project with the cash flows shown
below, we can calculate a discounted payback period.
The DPP is early in year 4. It may be approximated as 3 years + [1,390/(1,390 + 19,100)] × 12
months = 3 years 0.8 months, say 3 years 1 month. A company can set a target DPP, and
choose not to undertake any projects with a DPP in excess of a certain number of years, say
five years.
Advantages and disadvantages of discounted payback period
The approach has all the perceived advantages of the payback period method of investment
appraisal: it is easy to understand and calculate, and it provides a focus on liquidity where this
is relevant. In addition, however, it also takes into account the time value of money. It
therefore bridges the gap between the theoretically superior NPV method and the regular
payback period method. However, it does differ from NPV in that the discount rate used is the
unadjusted cost of capital whereas NPV often uses an adjusted rate to reflect project risk
and uncertainty.
Because the DPP approach takes the time value of money into consideration, it produces a
longer payback period than the non-discounted payback approach, and takes into account
more of the project's cash flows.

Another advantage it has over traditional payback is that it has a clear accept-or-reject
criterion. Using payback, acceptance of a project depends on an arbitrarily determined cut-off
time. Using DPP, a project is acceptable if it pays back within its lifetime. DPP still shares one
disadvantage with the payback period method: cash flows which occur after the payback
period are ignored (although as the DPP is longer than the payback period, fewer of these is
ignored).
One way of dealing with risk is to shorten the payback period required. A maximum
payback period can be set to reflect the fact that risk increases the longer the time period
under consideration. However, the disadvantages of payback as an investment appraisal
method (discussed in Chapter 5) mean that discounted payback cannot be recommended as a
method of adjusting for risk.

Eg. Initial investment = 500Frw

cfs 1 2 3
300 250 70
DR = 10%
PBP = cumulative cfs
1. 300 300
2. 250 550
3. 70 620
200
PBP = 1 + 250 = 1.8
= 1 year
0.8 * 12 = 9.6 = 9months
0.6 * 30 = 18 days
PBP = 1year, 9months, and 16days
DPBP
Years Cfs A DF at 10% B Discounted cfs AXB
1 300 0.909 272.7
2 250 0.826 206.5
3 70 0.751 52.57
20.8
Discounted Pay back period = 2 + 52.57 = 2.39 ≈ 2.4
2years
Cumulated discounted cfs 500 – 272.2
272.2
479.2 227.3 – 206.5
531.7
c) RISK-ADJUSTED DISCOUNT RATES
Investors want higher returns for higher risk investments. The greater the risk attached to
future returns, the greater the risk premium required. Investors also prefer cash now to later
and require a higher return for longer time periods. In investment appraisal, a risk-adjusted
discount rate can be used for particular types or risk classes of investment projects to reflect
their relative risks. For example, a high discount rate can be used so that a cash flow which
occurs quite some time in the future will have less effect on the decision. Alternatively, with
the launch of a new product, a higher initial risk premium may be used with a decrease in the
discount rate as the product becomes established.
The Adjusted discount rate (ADR) adds the risk margin to the nominal Discount rate
ADR = DR + Risk margin
Eg DR = 10% risk margin = 3%
Adjusted discount rate = DR + RM
= 0.10 + 0.03
≈13%

PRACTICE QUESTIONS
QN 1.
Rainbow Co, a medium-sized company specialising in the manufacture and distribution of
equipment for babies and small children, is evaluating a new capital expenditure project. In a
joint venture with another separate company, it has invented a remote controlled pushchair,
one of the first of its kind on the market. It has been unable to obtain a patent for the invention,
but is sure that it will monopolise the market for the first three years. After this, it expects to
be faced with stiff competition.
The details are set out below.
(1) The project has an immediate cost of Frw2,100,000.
(2) Sales are expected to be Frw1,550,000 per annum for years 1 to 3, falling to Frw650,000
per annum for the two years after that. No further sales of the product are expected after
the end of this five-year period.
(3) Cost of sales is 40% of sales.
(4) Distribution costs represent 10% of sales.
(5) 20% of net profits are payable to the joint venture partner the year after the profits are
earned.
(6) The company's cost of capital is 5%.
Required
(a) Calculate the net present value of the project at the company's required rate of return.
Assume that all cash flows arise annually in arrears unless otherwise stated. Conclude
whether the project is financially viable.
(b) Calculate the project's internal rate of return (IRR) to the nearest percent.
(c) Calculate the project's simple payback period. Assume all cash flows arise at the end of
the year apart from the immediate investment costs.
QN 2
It is now June 2018. TUBURA Co manufactures bicycles for the UK and European markets,
and has made a bid of Frw150 million to take over HEZA Co, their main UK competitor,
which is also active in the German market. TUBURA currently supplies 24% of the UK
market and HEZA has a 10% share of the same market.
TUBURA anticipates labour savings of Frw700,000 per year, created by more efficient
production and distribution facilities, if the takeover is completed. In addition, the company
intends to sell off surplus land and buildings with a balance sheet value of Frw15 million,
acquired in the course of the takeover.
Total UK bicycle sales for 2017 were Frw400 million. For the year ended 31 December 2017,
HEZA reported an operating profit of Frw10 million, compared with a figure of Frw55 million
for TUBURA. In calculating profits, HEZA included a depreciation charge of Frw0.5 million.
Note. The takeover is regarded by TUBURA in the same way as any other investment, and is
appraised accordingly.
Required
(a) Despite the theoretical limitations of the payback method of investment appraisal, it is
the method most used in practice.' Discuss this statement briefly.
(b) Assuming that the bid is accepted by HEZA, calculate the payback period (pre-tax) for
the investment, if the land and buildings are immediately sold for Frw5 million less than
the balance sheet valuation, and HEZA's sales figures remain static.
(c) TUBURA has also appraised the investment in HEZA by calculating the present value of
the company's future expected cash flows. What additional information to that required
in (b) would have been necessary?
(d) Explain how and why the UK Government might seek to intervene in the takeover bid
for HEZA.
(e) Suggest four ratios, which TUBURA might usefully compute in order to compare the
financial performance of HEZA with that of companies in the same manufacturing
sector. You should include in your answer a justification of your choice of ratios. Briefly
explain why it is important to base a comparison on companies in the same sector.
QN 3
SHEZO Co is a wholesaler of specialist books which is keen to explore the financial
implications of making a significant investment in equipment and the development of a
website.
Due to the fast-changing nature of the equipment and the Internet software, SHEZO's
management has set a project lifetime of three years, ie the equipment will be replaced at the
end of 2016 and a new website designed. Frw60,000 would be paid for the new equipment on
31 December 2013. The supplier has agreed to pay Frw10,000 as a trade-in price in December
2016.
SHEZO's estimated final sales for the current accounting year (which ends on 31 December
2013) are Frw1,200,000. The company's costs behave in such a way that its contribution to
sales ratio for 2013 is expected to be 40% and its net margin 10%. A considerable proportion
of SHEZO's total fixed costs are marketing expenses. The proposed project will lead to
savings in this area. So, in 2014 fixed costs (at 31 December 2014 prices) will total
Frw316,800.
Sales estimates are shown
below.
Total sales if no Total sales with
investment (at 31 investment (at 31
December 2013 prices) December 2013 prices)
Frw Frw
Year to 31 December 2014 1,240,000 1,288,000
Year to 31 December 2015 1,265,000 1,325,000
 Year to 31 December 2016 1,290,000 1,362,000
From 1 January 2014 inflation will have the following effects on SHEZO’s operations.
(i) Sales prices will increase by 5% per annum.
(ii) All costs (ie variable and fixed) will increase by 10% per annum.
The increase in sales will mean that SHEZO will carry an additional investment in working
capital as follows (all at 31 December 2013 prices).
2013 An initial Frw20,000
2014 Another Frw10,000
2015 Reduced to Frw15,000
2016 Reduced to Frw0
This investment will also be affected by inflation from 1 January 2014, at the same annual rate
as the variable and fixed costs, ie 10%.
The website would be designed and installed during the first four months of 2014. It will cost
Frw150,000 (at 2014 prices) payable at the end of 2014. The suppliers will be paid a
retaining/advisory fee of Frw10,000 in both 2015 and 2016. These are at 31 December 2014
prices and it is anticipated that, due to inflation, they will increase at the same rate as all other
costs. SHEZO has a nominal cost of capital of 10% and pays tax at an annual rate of 30% in
the year profits are earned. It can claim capital allowances on a 25% reducing balance basis.
Required
Advise the management of SHEZO whether it should proceed with the proposed investment.
Your recommendation should be supported by relevant workings and a calculation of NPV.
QN 4
NDIWANO Co, a software company, has developed a new game, 'Fingo', which it plans to
launch in the near future. Sales of the new game are expected to be very strong, following a
favourable review by a popular PC magazine. NDIWANO Co has been informed that the
review will give the game a 'Best Buy' recommendation. Sales volumes, production volumes
and selling prices for 'Fingo' over its four-year life are expected to be as follows
‘

Year 1 2 3 4
Sales and production (units) 150,000 70,000 60,000 60,000
Selling price (Frw per game) Frw25 Frw24 Frw23 Frw22
Financial information on 'Fingo' for the first year of production is as follows:

Direct material cost Frw5.40 per game

Other variable production cost Frw6.00 per game

Fixed costs Frw4.00 per game

Advertising costs to stimulate demand are expected to be Frw650,000 in the first year of
production and Frw100,000 in the second year of production. No advertising costs are
expected in the third and fourth years of production. Fixed costs represent incremental cash
fixed production overheads. 'Fingo' will be produced on a new production machine costing
Frw800,000. Although this production machine is expected to have a useful life of up to ten
years, government legislation allows NDIWANO Co to claim the capital cost of the machine
against the manufacture of a single product. Capital allowances will therefore be claimed on a
straight-line basis over four years.
NDIWANO Co pays tax on profit at a rate of 30% per year and tax liabilities are settled in the
year in which they arise. NDIWANO Co uses an after-tax discount rate of 10% when
appraising new capital investments. Ignore inflation.
Required
(a) Calculate the net present value of the proposed investment and comment on your
findings.
(b) Calculate the internal rate of return of the proposed investment and comment on your
findings.
(c) Discuss the reasons why the net present value investment appraisal method is preferred
to other investment appraisal methods such as payback, return on capital employed and
internal rate of return.
QN 5
TEREZA Co plans to buy a new machine to meet expected demand for a new product,
Product T. This machine will cost Frw250,000 and last for four years, at the end of which time
it will be sold for Frw5,000. TEREZA Co expects demand for Product T to be as follows:
Year 1 2 3 4
Demand (units) 35,000 40,000 50,000 25,000
The selling price for Product T is expected to be Frw12.00 per unit and the variable cost of
production is expected to be Frw7.80 per unit. Incremental annual fixed production overheads
of Frw25,000 per year will be incurred. Selling price and costs are all in current price terms.
Selling price and costs are expected to increase as follows:
Increase
Selling price of Product T: 3% per year
Variable cost of production: 4% per year
Fixed production overheads: 6% per year
Other information
TEREZA Co has a real cost of capital of 5.7% and pays tax at an annual rate of 30% one year
in arrears. It can claim capital allowances on a 25% reducing balance basis. General inflation
is expected to be 5% per year.
TEREZA Co has a target return on capital employed of 20%. Depreciation is charged on a
straight-line basis over the life of an asset.
Required
(a) Calculate the net present value of buying the new machine and comment on your
findings (work to the nearest Frw1,000).
(b) Calculate the before-tax return on capital employed (accounting rate of return) based on
the average investment and comment on your findings.
Discuss the strengths and weaknesses of internal rate of return in appraising capital
investments.
QN 6
DATIVA Co needs to increase production capacity to meet increasing demand for an existing
product, ‘Quago’, which is used in food processing. A new machine, with a useful life of four
years and a maximum output of 600,000 kg of Quago per year, could be bought for
Frw800,000, payable immediately. The scrap value of the machine after four years would be
Frw30,000. Forecast demand and production of Quago over the next four years is as follows:
Year 1 2 3 4
Demand (kg) 1.4 million 1.5 million 1.6 million 1.7 million
Existing production capacity for Quago is limited to one million kilograms per year and the
new machine would only be used for demand additional to this.
The current selling price of Quago is Frw8·00 per kilogram and the variable cost of materials
is Frw5·00 per kilogram. Other variable costs of production are Frw1·90 per kilogram. Fixed
costs of production associated with the new machine would be Frw240,000 in the first year of
production, increasing by Frw20,000 per year in each subsequent year of operation.
DATIVA Co pays tax one year in arrears at an annual rate of 30% and can claim capital
allowances (tax-allowable depreciation) on a 25% reducing balance basis. A balancing
allowance is claimed in the final year of operation.
DATIVA Co uses its after-tax weighted average cost of capital when appraising investment
projects. It has a cost of equity of 11% and a before-tax cost of debt of 8·6%. The long-term
finance of the company, on a market-value basis, consists of 80% equity and 20% debt.
Required
(a) Calculate the net present value of buying the new machine and advise on the
acceptability of the proposed purchase (work to the nearest Frw1,000).
(b) Calculate the internal rate of return of buying the new machine and advise on the
acceptability of the proposed purchase (work to the nearest Frw1,000).
(c) Explain the difference between risk and uncertainty in the context of investment
appraisal, and describe how sensitivity analysis and probability analysis can be used to
incorporate risk into the investment appraisal process.
QN 7
SC Co is evaluating the purchase of a new machine to produce product P, which has a short
product life-cycle due to rapidly changing technology. The machine is expected to cost Frw1
million. Production and sales of product P are forecast to be as follows:
Year 1 2 3 4
Production and sales (units/year) 35,000 53,000 75,000 36,000
The selling price of product P (in current price terms) will be Frw20 per unit, while the
variable cost of the product (in current price terms) will be Frw12 per unit. Selling price
inflation is expected to be 4% per year and variable cost inflation is expected to be 5% per
year. No increase in existing fixed costs is expected since SC Co has spare capacity in both
space and labour terms.
Producing and selling product P will call for increased investment in working capital. Analysis
of historical levels of working capital within SC Co indicates that at the start of each year,
investment in working capital for product P will need to be 7% of sales revenue for that year.
SC Co pays tax of 30% per year in the year in which the taxable profit occurs. Liability to tax
is reduced by capital allowances on machinery (tax-allowable depreciation), which SC Co can
claim on a straight-line basis over the fouryear life of the proposed investment. The new
machine is expected to have no scrap value at the end of the fouryear period.
SC Co uses a nominal (money terms) after-tax cost of capital of 12% for investment appraisal
purposes.
Required
(a) Calculate the net present value of the proposed investment in product P.
(b) Calculate the internal rate of return of the proposed investment in product P.
(c) Advise on the acceptability of the proposed investment in product P and discuss the
limitations of the evaluations you have carried out.
Discuss how the net present value method of investment appraisal contributes towards the
objective of maximising the wealth of shareholders.
QN 8
RUHAPA Co is a manufacturing company that wishes to evaluate an investment in new
production machinery. The machinery would enable the company to satisfy increasing demand
for existing products and the investment is not expected to lead to any change in the existing
level of business risk of RUHAPA Co.
The machinery will cost Frw2.5 million, payable at the start of the first year of operation, and
is not expected to have any scrap value. Annual before-tax net cash flows of Frw680,000 per
year would be generated by the investment in each of the five years of its expected operating
life. These net cash inflows are before taking account of expected inflation of 3% per year.
Initial investment of Frw240,000 in working capital would also be required, followed by
incremental annual investment to maintain the purchasing power of working capital.
RUHAPA Co has in issue five million shares with a market value of Frw3.81 per share. The
equity beta of the company is 1·2. The yield on short-term government debt is 4.5% per year
and the equity risk premium is approximately 5% per year.
The debt finance of RUHAPA Co consists of bonds with a total book value of Frw2 million.
These bonds pay annual interest before tax of 7%. The par value and market value of each
bond is Frw100.
RUHAPA Co pays taxation one year in arrears at an annual rate of 25%. Capital allowances
(tax-allowable depreciation) on machinery are on a straight-line basis over the life of the asset.
Required
(a) Calculate the after-tax weighted average cost of capital of RUHAPA Co.
(b) Prepare a forecast of the annual after-tax cash flows of the investment in nominal terms,
and calculate and comment on its net present value.
Explain how the capital asset pricing model can be used to calculate a project-specific
discount rate and discuss the limitations of using the capital asset pricing model in investment
appraisal.
QN 9
PV Co is evaluating an investment proposal to manufacture Product W33, which has
performed well in test marketing trials conducted recently by the company’s research and
development division. The following information relating to this investment proposal has now
been prepared.
Initial investment Frw2 million
Selling price (current price terms) Frw20 per unit
Expected selling price inflation 3% per year
Variable operating costs (current priceFrw8 per unit
terms)
Fixed operating costs (current price terms) Frw170,000 per year
Expected operating cost inflation 4% per year
The research and development division has prepared the following demand forecast as a result
of its test marketing trials. The forecast reflects expected technological change and its effect
on the anticipated life-cycle of Product
W33.
Year 1 2 3 4
Demand (units) 60,000 70,000 120,000 45,000
It is expected that all units of Product W33 produced will be sold, in line with the company’s
policy of keeping no inventory of finished goods. No terminal value or machinery scrap value
is expected at the end of four years, when production of Product W33 is planned to end. For
investment appraisal purposes, PV Co uses a nominal (money) discount rate of 10% per year
and a target return on capital employed of 30% per year. Ignore taxation.
Required:
(a) Identify and explain the key stages in the capital investment decision-making process,
and the role of investment appraisal in this process.
(b) Calculate the following values for the investment proposal:
(i) net present value;
(ii) internal rate of return;
(iii) return on capital employed (accounting rate of return) based on average
investment; and
(iv) discounted payback period.
Discuss your findings in each section of (b) above and advise whether the investment proposal
is financially acceptable.
QN 10
AGD Co is a profitable company which is considering the purchase of a machine costing
Frw320,000. If purchased, AGD Co would incur annual maintenance costs of Frw25,000. The
machine would be used for three years and at the end of this period would be sold for
Frw50,000. Alternatively, the machine could be obtained under an operating lease for an
annual lease rental of Frw120,000 per year, payable in advance.
AGD Co can claim capital allowances on a 25% reducing balance basis. The company pays
tax on profits at an annual rate of 30% and all tax liabilities are paid one year in arrears. AGD
Co has an accounting year that ends on 31 December. If the machine is purchased, payment
will be made in January of the first year of operation. If leased, annual lease rentals will be
paid in January of each year of operation.
Required
(a) Using an after-tax borrowing rate of 7%, evaluate whether AGD Co should purchase or
lease the new machine.
(b) Explain and discuss the key differences between an operating lease and a finance lease.

(c) The after-tax borrowing rate of 7% was used in the evaluation because a bank had
offered to lend AGD Co Frw320,000 for a period of five years at a before-tax rate of
10% per year with interest payable every six months.
Required
Calculate the annual percentage rate (APR) implied by the bank's offer to lend at 10% per year
with interest payable every six months.
Calculate the amount to be repaid at the end of each six-month period if the offered loan is to
be repaid in equal instalments.
QN 11
Basril Co is reviewing investment proposals that have been submitted by divisional managers.
The investment funds of the company are limited to Frw800,000 in the current year. Details of
three possible investments, none of which can be delayed, are given below.
Project 1
An investment of Frw300,000 in work station assessments. Each assessment would be on an
individual employee basis and would lead to savings in labour costs from increased efficiency
and from reduced absenteeism due to work-related illness. Savings in labour costs from these
assessments in money terms are expected to be as follows:
Year 1 2 3 4 5
Cash flows (Frw'000) 85 90 95 100 95
Project 2
An investment of Frw450,000 in individual workstations for staff that is expected to reduce
administration costs by Frw140,800 per annum in money terms for the next five years.
Project 3
An investment of Frw400,000 in new ticket machines. Net cash savings of Frw120,000 per
annum are expected in current price terms and these are expected to increase by 3.6% per
annum due to inflation during the five-year life of the machines.
Basril Co has a money cost of capital of 12% and taxation should be ignored.
Required
(a) Determine the best way for Basril Co to invest the available funds and calculate the
resultant NPV:
(i) on the assumption that each of the three projects is divisible;
(ii) on the assumption that none of the projects are divisible.
(b) Explain how the NPV investment appraisal method is applied in situations where capital
is rationed.
(c) Discuss the reasons why capital rationing may arise.
(d) Discuss the meaning of the term 'relevant cash flows' in the context of investment
appraisal, giving examples to illustrate your discussion.
QN 12
Leaminger Co has decided it must replace its major turbine machine on 31 December 2012.
The machine is essential to the operations of the company. The company is, however,
considering whether to purchase the machine outright or to use lease financing.
Purchasing the machine outright
The machine is expected to cost Frw360,000 if it is purchased outright, payable on 31
December 2012. After four years the company expects new technology to make the machine
redundant and it will be sold on 31 December 2016 generating proceeds of Frw20,000. Capital
allowances for tax purposes are available on the cost of the machine at the rate of 25% per
annum reducing balance. A full year's allowance is given in the year of acquisition but no
writing down allowance is available in the year of disposal. The difference between the
proceeds and the tax written down value in the year of disposal is allowable or chargeable for
tax as appropriate.
Leasing
The company has approached its bank with a view to arranging a lease to finance the machine
acquisition. The bank has offered two options with respect to leasing which are as follows:
Finance lease Operating
lease
Contract length (years) 4 4
Annual rental Frw135,000 Frw140,000
First rent payable 31 December 2013 31 December
2012
General
For both the purchasing and the finance lease option, maintenance costs of Frw15,000 per year
are payable at the end of each year. All lease rentals (for both finance and operating options)
can be assumed to be allowable for tax purposes in full in the year of payment. Assume that
tax is payable one year after the end of the accounting year in which the transaction occurs.
For the operating lease only, contracts are renewable annually at the discretion of either party.
Leaminger Co has adequate taxable profits to relieve all its costs. The rate of tax on profits can
be assumed to be 30%. The company's accounting year-end is 31 December. The company's
annual after tax cost of capital is 10%.
Required
(a) Calculate the net present value at 31 December 2012, using the after tax cost of capital,
for
(i) purchasing the machine outright;
(ii) using the finance lease to acquire the machine; and (iii)
using the operating lease to acquire the machine.
Recommend the optimal method.
(b) Assume now that the company is facing capital rationing up until 30 December 2013
when it expects to make a share issue. During this time the most marginal investment
project, which is perfectly divisible, requires an outlay of Frw500,000 and would
generate a net present value of Frw100,000. Investment in the turbine would reduce
funds available for this project. Investments cannot be delayed. Calculate the revised net
present values of the three options for the turbine given capital rationing. Advise
whether your recommendation in (a) would change. As their business advisor, prepare
a report for the directors of Leaminger Co that assesses the issues that need to be
considered in acquiring the turbine with respect to capital rationing.
QN 13
Bread Products Co is considering the replacement policy for its industrial size ovens which are
used as part of a production line that bakes bread. Given its heavy usage each oven has to be
replaced frequently. The choice is between replacing every two years or every three years.
Only one type of oven is used, each of which costs Frw24,500. Maintenance costs and resale
values are as follows.
Year Maintenance per annum Resale value
Frw Frw
1 500
2 800 15,600
3 1,500 11,200
Original cost, maintenance costs and resale values are expressed in current prices. That is, for
example, maintenance for a two year old oven would cost Frw800 for maintenance undertaken
now. It is expected that maintenance costs will increase at 10% per annum and oven
replacement cost and resale values at 5% per annum. The money discount rate is 15%.
Required
(a) Calculate the preferred replacement policy for the ovens in a choice between a two year
or three year replacement cycle.
(b) Identify the limitations of net present value techniques when applied generally to
investment appraisal.
QN 14
(a) Explain how cash shortages can restrict the investment opportunities of a business.
(b) Distinguish between 'hard' and 'soft' capital rationing, explaining why a company may
deliberately choose to restrict its capital expenditure.
(c) Filtrex Co is a medium-sized, all equity-financed, unquoted company which specialises
in the development and production of water- and air-filtering devices to reduce the
emission of effluents. Its small but ingenious R & D team has recently made a
technological breakthrough which has revealed a number of attractive investment
opportunities. It has applied for patents to protect its rights in all these areas. However, it
lacks the financial resources required to exploit all of these projects, whose required
outlays and post-tax NPVs are listed in the table below. Filtrex's managers consider that
delaying any of these projects would seriously undermine their profitability, as
competitors bring forward their own new developments. All projects are thought to have
a similar degree of risk.
Project Required outlay NPV
Frw Frw
A 150,000 65,000
B 120,000 50,000
C 200,000 80,000
D 80,000 30,000
E 400,000 120,000
The NPVs have been calculated using as a discount rate the 18% post-tax rate of return
which Filtrex requires for risky R & D ventures. The maximum amount available for this
type of investment is Frw400,000, corresponding to Filtrex's present cash balances, built
up over several years' profitable trading. Projects A and C are mutually exclusive and no
project can be sub-divided. Any unused capital will either remain invested in short-term
deposits or used to purchase marketable securities, both of which offer a return well
below 18% post-tax.
Required
(i) Advise Filtrex Co, using suitable supporting calculations, which combination of
projects should be undertaken in the best interests of shareholders; and
(ii) Suggest what further information might be obtained to assist a fuller analysis.
(d) Explain how, apart from delaying projects, Filtrex Co could manage to exploit more of
these opportunities.

TOPIC 6: WORKING CAPITAL MANAGEMENT

1. Definitions
Working capital, also known as "WC", is a financial metric which represents operating
liquidity available to a business. Along with fixed assets such as plant and equipment, working
capital is considered a part of operating capital. It is calculated as current assets minus current
liabilities. If current assets are less than current liabilities, an entity has a working capital
deficiency, also called a working capital deficit. Net working capital is working capital
minus cash (which is a current asset) and minus interest bearing liabilities (i.e. short term
debt). It is a derivation of working capital that is commonly used in valuation techniques such
as DCFs (Discounted cash flows).

Working Capital = Current Assets − Current Liabilities

A company can be endowed with assets and profitability but short of liquidity if its assets
cannot readily be converted into cash Positive working capital is required to ensure that a firm
is able to continue its operations and that it has sufficient funds to satisfy both maturing short-
term debt and upcoming operational expenses.

Decisions relating to working capital and short term financing are referred to as working
capital management. These involve managing the relationship between a firm's short-term
assets and its short-term liabilities.

2. Approaches to working capital management

a) Conservative approach
under this approach current assets are more than current liabilities. There is high
Asset liquidity than financing liquidity.

Asset liquidity= current assets /non- current assets or current assets/Total assets

Non-current assets Non-current

liability

Current assets
Current liability
Financing liquidity= current liability/ non-current liability or current liability/total liability
Company liquidity = current assets / current liability
This leads to low liquidity risk and low profitability. It indicates long-term finance is being
invested in current assets which has low yield.
b) Hedging /Matching Approach
Current assets are equal to current liability. This leads to moderate liquidity risk, moderated
assets liquidity, moderate financing risk and moderate profitability.
Non-current assets Non-current liability
Current assets Current liability
c)Aggressive Approach

Under this approach current assets are less than current liability leading to high financing
liquidity, low assets and company liquidity. Very high liquidity risk and high profitability.
There should be an attempt to strike a balance between profitability and liquidity risk in
working capital management.

Non-current assets Non-current liability

Current liability
Current assets
3. Factors affecting working capital management
1. Nature of the firm
Service companies that have a short operating cycle and which sell predominantly for cash
basis have a modest working capital requirement. The cycle refers to the amount of time that
elapses from the time when the company makes an outlay to the point when the company
collects cash from sales.
2. Seasonality of operations
Companies with marked seasonality of operations usually have high fluctuating working
capital e.g a company selling ice creams or company selling umbrellas.
3. Market conditions
The degree of competition affects the working capital need of a company eg when competition
is high large stocks may e required to serve customers.
4. Condition of supply
If supply is prompt and adequate the company can manage with small balances of working
capital but if the supply is scanty and unpredictable the company may have to acquire
quantities of current assets to ensure continuity.
4. Importance of working capital management
The finance manager should understand the management of working capital because of the
following reasons:
a) Time devoted to working capital management
A large portion of a financial manager’s time is devoted to the day to day operations of the
firm and therefore, so much time is spent on working capital decisions.
b) Investment in current assets
Current assets represent more than half of the total assets of many business firms. These
investments tend to be relatively volatile and can easily be misappropriated by the firm’s
employees. The finance manager should therefore properly manage these assets.
c) Importance to small firms
A small firm may minimise its investments in fixed assets by renting or leasing plant and
equipment, but there is no way it can avoid investment in current assets. A small firm also has
relatively limited access to long term capital markets and therefore must rely heavily on short-
term funds.
d) Relationship between sales and current assets
The relationship between sales volume and the various current asset items is direct and close.
Changes in current assets directly affects the level of sales. The finance management must
therefore keep watch on changes in working capital items.
5. Operating/cash or working capital cycle
Operating or working capital cycle is defined as the period between the payment of cash to
creditors(i.e. cash out flow) and the receipt of cash from debtors (i.e. cash inflow)

Creditors Raw-materials Work-in-progress

 Finished goods

Cash

Debtors Bad debts

The operating cycle is the length of time it takes to acquire inventory of raw materials,
convert them to finished product, sell them and collect cash from sales. Thus operating cycle
begins life as inventory. It is converted to accounts receivables when it is sold and it is finally
converted to cash when we collect cash from sales.
The cash cycle is the number of days that passes before we collect the cash from sales
measured from when we actually pay for the inventory. Cash cycle is therefore the difference
between operating cycle and accounts its payable
Differences
Operating cycle tells a complete story of time it takes to convert inventory procured to cash
through collection of sales, whereas cash cycle explains the time interval between when
inventory procured is paid for and is converted to cash through sales.Operating cycle tells the
financial implication of various policies of a firm in its working capital management. Cash
cycle on the other hand attempts to explain the time interval required by a firm to meet its
financial obligation.
OVER CAPITALISATION (UNDER TRADING)
Over capitalization occurs where a company commits excessive capital into the company’s
trading activities, so that there are excessive stock, debtors and cash, and very few creditors. If
a company manages its working inefficiently, i.e. if working capital is excessive and the
company becomes over –capitalized the return on capital employed would be lower than
what it should be and long term funds would be unnecessarily “tied up” when they could be
invested elsewhere to earn profits.Over-capitalization should not exist if there is good
management of working capital, but the “warning signal” of excessive working capital would
be poor accounting ratios.The ratio below are to judge whether the investment in working
capital is reasonable are:
A) Sales/working capital. The volume of sales as multiple of the working capital
investment should indicate whether in comparison with previous year or with similar
companies, the total volume of working capital is too high.
B) Liquidity ratios also called working capital ratios.
They indicate ability of the firm to meet its short term maturing financial obligation/current
liabilities as and when they fall due.
The ratios are concerned with current assets and current liabilities. They include:
a) Current ratio = Current Assets
Current liabilities
This ratio indicates the No. of times the current liabilities can be paid from current assets
before these assets are exhausted. The most recommended ratio is 2.0 i.e. the current asset
must at least be twice as high as current liabilities.
b) Quick/acid test ratios =Current Asset - Stock
Current liabilities
Is a more refined current ratio which exclude amount of stock of the firm. Stocks are excluded
for two basic reasons:
i) They are valued on historical cost basis
ii) They may not be converted into cash very quickly
The ratio therefore indicates the ability of the firm to pay its current liabilities from the more
liquid assets of the firm.
c) Cash ratio = Cash in hand/bank + short term marketable securities
 Current liabilities
This is a refinement of the acid test ratio indicating the ability of the firm to meet its current
liabilities from its most liquid resources. Short term marketable securities refers to short term
investment of the firm which can be converted into cash within a very short period e.g
commercial paper and treasury bills.
a) Net working capital Ratio =Networking Capital x 100
Net Assets
Where Net Assets or Capital employed = Total Assets – Current liability. This ratio indicates
the proportions of total net assets which is liquid enough to meet the current liabilities of the
firm. It is expressed in % term.
C) TURNOVER PERIOD.
Excessive turnover periods for stock and debtor or a low period of credit taken from suppliers
would indicate whether the volume of stock or debtors is unnecessarily high, or the volume of
creditors too low.
THE TURNOVER PERIODS MAY BE CALCULATED AS FOLLOW
12 months 12 moths
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝑹𝑴 𝒔𝒕𝒐𝒄𝒌 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝒔𝒕𝒐𝒄𝒌
1. Raw materials = 𝒂𝒏𝒏𝒖𝒂𝒍 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔 × 52 weeks OR 𝑨𝒏𝒏𝒖𝒂𝒍 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔 × 52 weeks
365 days 365 days

12 months 12 moths
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝑹𝑴 𝒔𝒕𝒐𝒄𝒌 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝑾𝑰𝑷
2. Work in progress = 𝒂𝒏𝒏𝒖𝒂𝒍 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔
× 52 weeks OR 𝒄𝒐𝒔𝒕 𝒐𝒇 𝒔𝒂𝒍𝒆𝒔 × 52 weeks
365 days 365 days

12 months 12 moths
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝑭𝑮 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝑭𝑮
3. Finished goods = 𝒄𝒐𝒔𝒕 𝒐𝒇 𝒔𝒂𝒍𝒆𝒔 𝒑.𝒂
× 52 weeks OR 𝑪𝑶𝑺𝑻 𝑶𝑭 𝑺𝑨𝑳𝑬𝑺 𝑷.𝑨 ×52 weeks
365 days 365 days

12 months 12 moths
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝑹𝑴 𝒔𝒕𝒐𝒄𝒌 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝒅𝑹𝑺
4. Drs T/o periods = 𝒂𝒏𝒏𝒖𝒂𝒍 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔
× 52 weeks OR 𝑨𝑺𝑨𝑳𝑬𝑺 𝑷.𝑨 × 52 weeks
(Average collection 365 days 365 days
Period)
12 months 12 moths
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒄𝒓𝒆𝒅𝒊𝒕𝒐𝒓𝒔 𝒄𝒍𝒐𝒔𝒊𝒏𝒈 𝑪𝑹𝑺
5. Raw materials = × 52 weeks OR × 52 weeks
𝒄𝒓𝒆𝒅𝒊𝒕 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔 𝑷𝑨 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆𝒔 𝑷𝑨
365 days 365 days
Example
The table below gives information extracted from the annual accounts of management for
the past three years. You are required to calculate the length of working capital cycle year
by assuming 365days in the year.

NAKUX Enterprise–extract from annual account

Year1 year2 year 3
FRW FRW FRW
Stocks raw materials 108,000 145,800 180,000
Work in progress 75,600 97,200 93,360
Finished goods 86,400 129,600 142,875
Purchases 518,400 702,000 720,000
Cost of good sols 756,000 972,000 1,098,360
Sales 864,000 1,080,000 1,118,000
Debtors 172,800 259,2000 297,000
Trade creditors 86,400 105,300 126,000

Solution
Year1 year2
year3
1. Raw material =RM stock * 365days 76.0 75.8 91.3
Purchase
2. Work in progress =WIP * 365days 36.5 36.5 31.0
Cost of sales
3. Finished goods =finished goods *365days 41.1 48.7 47.5
Cost of sales

4. Drs T/O period =debtors *365days 73.0 87.6 91.3

(Average collection sales
Period)

5. Crs T/O periods = creditors

6. (average payment purchase *365days (60.8) (54.8)
(63.9)
period)

TOTAL LENGTH OF CYCLE 166.4 193.8

197.2

UNDER CAPITALIZATION (OVERTRADING)

Overtrading occurs when a company tries to do too much, to quickly with too little capital. So
that is it trying to support too large a volume of trade with the little capital resource at its
disposal.
An overtrading business can be operating at a profit; nevertheless it will eventually run into
serious trouble because it is short of fund and this liquidity trouble system from the fact that it
does not have enough capital to provide the cash to pay its debts as they fall due.
SYMPTOMS OF OVERTRADING
a) A rapid increase in sales turnover
b) A rapid increase in the volume of current assets and possible also of fixed assets. Stock
turnover periods might slow down, which means that the rate of increase in stocks and
debtors would be even greater than the rate of increase in sales turnover.
c) Increase in assets financed by a small increase in proprietors’ capital (eg. Retained profit)
while most increase are financed by:
i) trade creditors (repayment period to creditors become much slower)
ii) Encroachment on the limit approved for overdraft
d) Overhead cost might increase substantially, so that net benefit margins fall.
e) Gross profit ratio might fall, because of higher purchase cost
f) Some debt ratios and liquidity ratio will alter dramatically. Eg:
i) Ratio of working capital to sales will decline
ii) Ratio of debtors to trade creditors will decline
iii) Current and acid test ratios will fall
iv) Proportion of total assets financed by proprietor’s capital will decline and the
proportion financed by credit will rise-GEARING.

MANAGEMENT DECISION ON WORKING CAPITAL

The management of the various components of working capital involves determining the
Optimal level at which the controllable ones should be maintained at particular time
 i) Level of funds that managed to allocate to the different forms of current assets.
ii) How the current assets should be financed eg. Short or long term.
iii) The relationship between the levels of fixed assets and current assets

OVERTRADING –EFFECTS.
a) Growth stagnation –company finds it difficult to undertake profitable projects
b) Opportunities to invest in attractive –short term venture are lost.
c) Operating plans/budget becomes difficult to implement and thus the profit target
will not be achieved
d) The company may lose its reputation by its failure to fulfill short-term obligation.
e) Rate of return on investment slumps as fixed assets are not efficiently utilized for
the lack of working capital funds.
Example
XYZ Ltd. currently purchases all its raw materials on credit and sells its merchandise on
credit. The credit terms extended to the firm currently requires payment within thirty days of
a purchase while the firm currently requires its customers to pay within sixty days of a sale.
However, the firm on average takes 35 days to pay its accounts payable and the average
collection period is 70 days. On average, 85 days elapse between the point a raw material is
purchased and the point the finished goods are sold.
Required:
Determine the cash conversion cycle and the cash turnover.
Solution
The following chart can help further understand the question:
Inventory Conversion period (85 days)

Receivable collection
Payable deferral Period (70 days)
Period (35 days)

Purchase of Payment for the Sale of Collection of

raw materials raw materials Finished goods receivables

Cash conversion cycle = 85 + 70 - 35 = 120

The cash conversion cycle is given by the following formula:

Cash conversion = Inventory conversion + Receivable collection – Payable deferral
Cycle period period period
For our example:
Cash conversion cycle= 85 + 70 – 35 = 120 days

Cash turnover = 360

Cash conversion cycle
360
=
120
= 3 times
Note also that cash conversion cycle can be given by the following formulae:
  inventory receivables Payables Accruals 
Cash conversion cycle= 360    
 costofsales sales Cashoperatingexpenses
NB: In this chapter we shall assume that a year has 360 days.

6. MANAGEMENT OF CASH, INVENTORY AND RECEIVABLES

Management will use a combination of policies and techniques for the management of
working capital. These policies aim at managing the current assets (generally cash and cash
equivalents, inventories and debtors) and the short term financing, such that cash flows and
returns are acceptable. The management of working capital involves the cash management,
inventory management, debtor’s management and short term financing.
6.1. MANAGEMENT OF CASH
This is the most important Asset for the operations of the business. Cash itself earns no
interest unless invested. The objective of a firm is to minimize the amount of cash held to
conduct normal business. Cash management is concerned with managing of cash inflow and
outflow of the firm by having sufficient and pointing out Deficit or investing surplus cash
Motive for Holding Cash
a. Transaction motive.
b. Precautionary motive.
c. Financing needs.
d. Speculative motive.
e. Inflationary tendencies
Objective of cash management
1. To minimize liquidity risk, i.e. avoidance of technical insolvency.
2. To maximize return on cash as an asset i.e. minimizes cash flow costs.
Cash flow (cash holding cost)
1. Opportunity cost i.e. the investment return.
2. Loss of purchasing power due to inflation.
3. Possibility of theft, embezzlement
4. Cash insurance both in office and in transit.
5. Insurance against theft by employees
Minimization of cash holding costs
1. Invest
2. Bank deposits
3. Treasury bills/ short-term treasury bonds.
4. Invest in highly marketable merchandise or property

Cost of insufficient cash

1. Transaction costs i.e. raising cash
2. Interest charges
3. Loss of trade cash discount
4. Loss of good credit rating
5. Penalty interest for failure to honor obligation

Cash surpluses
A cash surplus may arise over the short term, medium term, or long term.
Possible uses of surplus cash include:
Short term
 Reduce overdraft
 Invest in short-term Treasury
 Stock
 Invest in bank deposit account
 Invest in ‘blue-chip’ shares
Long term:
 Invest in new projects
 Acquire other companies
 Increase dividends
 Buy back shares
 Repay long term loans
SETTING THE OPTIMAL CASH BALANCE
Cash is often called a non-earning asset because holding cash rather than a revenue-generating
asset involves a cost in form of foregone interest. The firm should therefore hold the cash
balance that will enable it to meet its scheduled payments as they fall due and provide a
margin for safety. There are several methods used to determine the optimal cash balance.
These are:

a) The Cash Budget

The Cash Budget shows the firm’s projected cash inflows and outflows over some specified
period.
The cash flow forecast is one of the most important planning tools that an organisation can
use. It shows the cash effect of all plans made within the flow forecasting process and hence
its preparation can lead to a modification of flow forecasts if it shows that there are
insufficient cash resources to finance the planned operations. It can also give management an
indication of potential problems that could arise and allows them the opportunity to take
action to avoid such problems. A cash flow forecast can show four positions. Management
will need to take appropriate action depending on the potential position.
Cash position Appropriate management action
Pay accounts payable early to obtain discount
Attempt to increase sales by increasing accounts receivable and inventories
Short-term surplus Make short-term investments
Increase accounts payable by delaying payments to suppliers
Reduce accounts receivable by improving collection of overdue payments
Arrange a bank overdraft facility, or increase the limit on an existing
Short-term deficit facility
Make long-term investments
Expand& Diversify
Replace/update non-current assets
Long-term surplus Distribute the surplus to shareholders
Raise long-term finance (such as via issue of share capital)
Long-term deficit Consider shutdown/disinvestment opportunities

Proforma of the cash budget

Period 1 2 3 4 5
Frw Frw Frw Frw Frw
Receipts
Cash sales x x x x x
 Receipts from credit
customers x x x x x
Other income x x
x x x x x
Payments
Cash purchases x x x x x
Payments for credit
purchases x x x x x
Rent and rates x x
Wages x x x x x
Light and heat x x
Salaries x x x x x
Telephone x x
Insurance x
x x x x x
Surplus/(deficit) (x) (x) x x x
Balance b/f – (x) (x) (x) x
Balance c/f (x) (x) (x) x x

Additionally, cash flows relating to fixed assets or financing should be included as

appropriate.
Example
The following information related to the proposed budget for K.K Ltd for the months ending
31 December 2018.
Material Administration
Production
Month Sales Purchases Wages Overheads
Overheads
Rwf ‘000’ Rwf ‘000’ Rwf Rwf ‘000’ Rwf ‘000’
‘000’

July 72000 250000 10000 6000 55000

August 97000 31000 12100 6300 6700
September 86000 25500 10600 6000 7500
October 88600 30600 25000 6500 8900
November 102500 37000 22000 8000 11000
December 108700 38800 23000 18200 11500
Additional Information
1. Depreciation expenses are expected to be 0.5%of sales.
2. Expected cash balance in hand on 1 July 2018 is Rwf 72,500,000
3. 50% of total sales are cash sales
4. Assets are to be acquired in the months of August and October at Rwf 8,000,000 and Rwf
25,000,000 respectively
5. An application has been made to the bank for the grant of a loan of Rwf 30,000,00 and it is
hoped that it will be received in the month of November
6. It is anticipated that a dividend of Rwf 35,000,000 will be paid in December
7. Debtors are allowed one month’s credit
8. Sales commission at 3% on sales is paid to the salesmen each month
Required: A cash budget for the six months ending 31 December 2018.
Solution
CASH BUDGET
K.K LTD
Workings I: Depreciation = 0.5% of sales
 July Aug Sept Oct Nov Dec
Sales 72000 97000 86000 88600 102500 108700
Depreciation 360 485 430 443 512.5 543.5

Workings II Cash Production Overheads

July Aug Sept Oct Nov Dec

Production overheads 6000 6300 6000 6500 8000 8200
Less: Depreciation 360 485 430 443 512.5 543.5
Cash production 5640 5815 5570 6057 7487.5 7656.5
overheads

Workings III Receipt from sales

July Aug Sept Oct Nov Dec

Total sales 72000 97000 86000 88600 102500 108700
Cash Sales (50%) 36000 48500 43000 44300 51250 54350
Receipt from Debtors - 36000 48500 43000 44300 51250
Total cash receipts 36000 84500 91500 87500 95550 15560

Workings IV Sales Commission (3% of Sales)

July Aug Sept Oct Nov Dec

Sales 72000 97000 86000 88600 102500 108700

Sales Commission 2160 2910 2580 2658 3075 3261
KK
CASH BUDGET FOR SIX MONTHS ENDING 31 DECEMBER 2018
July Aug Sept Oct Nov Dec Total
RECEIPTS ‘000’ ‘000’ ‘000’ ‘000’ ‘000’ ‘000’ ‘000’

Opening b/d 72500 96340 121690 156495 152567 207485 72500

Cash receipts 36000 84500 91500 87500 95550 105600 500450
Loan - - - - 30000 - 30000
108500 180840 213190 243795 278117 313085 602950
PAYMENTS
Materials - 25000 31000 25500 30600 37000 149100
Wages 10000 12100 10600 25000 22000 23000 102700
Production - 5640 5815 5570 6057 7487.5 3056.5
overheads
Admin overheads - 5500 6700 7500 8900 11000 39600
Cash assets - 8000 - 25000 - - 33000
Dividends - - - - 35000 - 35000
Sales commission 2160 2910 2580 2658 3075 3261 16644
Total payments 12160 59160 56695 91278 70362 . .
Closing balance 96340 121690 156495 152567 207485 196336.5 196336.5
c/d

b) Baumol’s Model
The Baumol’s model is an application of the EOQ inventory model to cash management. Its
assumptions are:
1. The firm uses cash at a steady predictable rate
2. The cash outflows from operations also occurs at a steady rate
 3. The cash net outflows also occur at a steady rate.
Under these assumptions the following model can be stated:
C*  2bT
i
Where:
C* is the optimal amount of cash to be raised by selling marketable securities or by
borrowing.
b is the fixed cost of making a securities trade or of borrowing
T is the total annual cash requirements
i is the opportunity cost of holding cash (equals the interest rate on marketable securities or the
cost of borrowing)
The total cost of holding the cash balance is equal to holding or carrying cost plus transaction
costs and is given by the following formulae:
TC  1 Ci  T b
2 C
Example
ABC Ltd. makes cash payments of Shs.10,000 per week. The interest rate on marketable
securities is 12% and every time the company sells marketable securities, it incurs a cost of
Shs.20.

Required
a) Determine the optimal amount of marketable securities to be converted into cash every
time the company makes the transfer.
b) Determine the total number of transfers from marketable securities to cash per year.
c) Determine the total cost of maintaining the cash balance per year.
d) Determine the firm’s average cash balance.
Solution
2bT
a) C*
i
Where: b = Shs.20
T = 52 x 20,000 = Shs.520,000
i = 12%
2x 20 x520,000
C*   Sh.13,166
0.12
Therefore the optimal amount of marketable securities to be converted to cash every time a
sale is made is Sh.13,166.
T
b) Total no. of transfers=
C*
520 ,000
=
13,166
= 39.5
≈ 40 times
1 T
c) TC  Ci  b
2 C
13,166 x 0.12 520,000 x 20
= 
2 13,166
= 790 + 790 = Shs.1,580
Therefore the total cost of maintaining the above cash balance is Sh.1,580.
d) The firm’s average cash balance = ½C
13,166
=
2
= Shs.6,583
c) Miller-Orr Model
Unlike the Baumol’s Model, Miller-Orr Model is a stochastic (probabilistic) model which
makes the more realistic assumption of uncertainty in cash flows.

Merton Miller and Daniel Orr assumed that the distribution of daily net cash flows is
approximately normal. Each day, the net cash flow could be the expected value of some
higher or lower value drawn from a normal distribution. Thus, the daily net cash follows a
trendless random walk.
From the graph below, the Miller-Orr Model sets higher and lower control units, H and L
respectively, and a target cash balance, Z. When the cash balance reaches H (such as point A)
then H-Z shillings are transferred from cash to marketable securities. Similarly, when the cash
balance hits L (at point B) then Z-L shillings are transferred from marketable securities cash

The Lower Limit is usually set by management. The target balance is given by the following
formula:

1/ 3
3B  2
Z   L

4i 
 
and the highest limit, H, is given by:
H = 3Z - 2L
4Z  L
The average cash balance =
3
Where: Z = target cash balance
H = Upper Limit
L = Lower Limit
b = Fixed transaction costs
i = Opportunity cost on daily basis
δ² = variance of net daily cash flows

Example
XYZ’s management has set the minimum cash balance to be equal to FRW10,000. The
standard deviation of daily cash flow is FRW2,500 and the interest rate on marketable
securities is 9% p.a. The transaction cost for each sale or purchase of securities is FRW20.
Required
a) Calculate the target cash balance
b) Calculate the upper limit
c) Calculate the average cash balance
d) Calculate the spread

Solution
 3b² 
1/ 3
a) Z  L
 4i 
  
 3x 20 x (2,500 )² 
=    10,000
 4x
9% 
 360 
= 7,211 + 10,000 = Sh.17,211
b) H = 3Z – 2L
= 3 x 17,211 – 2(10,000)
= Shs.31,633
4Z  L
c) Average cash balance =
3
4x17,211  10,000
=
3
d) The spread = H–L
= 31,633 – 10,000
= Shs.21,633
Note: If the cash balance rises to 31,633, the firm should invest Shs.14,422 (31,633 – 17,211)
in marketable securities and if the balance falls to Shs.10,000, the firm should sell
Shs.7,211(17,211 – 10,000) of marketable securities.

Example
Wobnig Co is considering using the Miller-Orr model to manage its cash flows. The
minimum cash balance would be Frw200,000 and the spread is expected to be
Frw75,000.
Required: Calculate the Miller-Orr model upper limit and return point, and explain how
these would be used to manage the cash balances of Wobnig Co.
Solution
Calculation of upper limit
The upper limit is the sum of the lower limit and the spread. If we use the minimum
cash balance as the lower limit, the upper limit = 200,000 + 75,000 = Frw275,000

Calculation of return point

The return point is the sum of the lower limit and one-third of the spread. Return point =
200,000 + (75,000/3) = 200,000 + 25,000 =Frw225,000

Use in managing cash balances

The Miller-Orr model provides decision rules about when to invest surplus cash (if a cash
balance increases to a high level), and about when to sell short-term investments (if a cash
balance falls to a low level). By using these decision rules, the cash balance is kept
between the upper and lower limits set by the Miller-Orr model. When the cash balance
reaches the upper limit, Frw50,000 is invested in short-term securities. This is equal
to the upper limit minus the return point (Frw275,000 –Frw225,000). When the cash
balance falls to the lower limit, short-term securities worth Frw25,000 are sold for cash.
This is equal to the return point minus the lower limit (Frw225,000 – Frw200,000).

CASH MANAGEMENT TECHNIQUES

The basic strategies that should be employed by the business firm in managing its cash are:
i) To pay account payables as late as possible without damaging the firm’s credit rating. The
firm should however take advantage of any favourable cash discounts offered.
ii) Turnover inventory as quickly as possible, but avoid stockouts which might result in loss of
sales or shutting down the ‘production line’.
iii) Collect accounts receivable as quickly as possible without losing future sales because of high
pressure collection techniques. The firm may use cash discounts to accomplish this objective.
In addition to the above strategies the firm should ensure that customer payments are converted into
spendable form as quickly as possible. This may be done either through:
a) Concentration Banking
b) Lock-box system.
a) Concentration Banking
Firms with regional sales outlets can designate certain of these as regional collection centre.
Customers within these areas are required to remit their payments to these sales offices, which
deposit these receipts in local banks. Funds in the local bank account in excess of a specified
limit are then transferred (by wire) to the firms major or concentration bank.
Concentration banking reduces the amount of time that elapses between the customer’s mailing
of a payment and the firm’s receipt of such payment.
b) Lock-box system.
In a lock-box system, the customer sends the payments to a post office box. The post office
box is emptied by the firm’s bank at least once or twice each business day. The bank opens the
payment envelope, deposits the cheques in the firm’s account and sends a deposit slip
indicating the payment received to the firm. This system reduces the customer’s mailing time
and the time it takes to process the cheques received.
6.2. MANAGEMENT OF INVENTORY/MATERIAL
This refers to stocks of the product a company is manufacturing for sale and the components
to make up the product. It can take the following forms:
a) Raw-material
b) Work in progress
c) Finished goods
d) Consumables
Motives for holding stock
1. Transaction motive
Holding of inventory facilitates smooth production and sales operations.
2. Pre-cautionary motive
Holding inventory guards against the risk of unpredictable changes in demand and supply
forces and other factors.
Speculative motive
Firms may increase or decrease inventory to take advantage of price fluctuations.
A company should maintain adequate stock of inventory to ensure that production and sales
activity run smoothly.
Determinants of stock to be held
1. Level of sales.
The higher the sales the higher the stock.
2. Style/perishability of product
Where style is not a factor relatively high levels of stocks can be maintained. If fashions
change first it would be risky to keep a high level of stock of finished goods.
3. Length of production cycle
Where the production cycle is long, relatively large stocks are kept.
4. Reliability of suppliers
Where the suppliers are reliable the organization can maintain relatively lower stocks than in a
case where they are not reliable.
5. Efficiency of production and sales schedule
Where the scheduling of sales are efficient i.e. as soon as goods are produced are sold the
inventory of finished will be low.

Objectives of inventory management

The firm is faced with the problem of two conflicting objectives:
1. To maintain a large size of inventory for efficient and smooth production.
2. To maintain a minimum investment in inventory so as to maximize profitability.

NB: in inventory management stock levels should be controlled so that the costs of holding
stocks and stock ordering costs are at minimum. This is done by establishing:
a) When to order
 b) How much to order
Thus stock is maintained at minimum.

Stock holding costs

a) Interest on capital invested in stock
b) Storage charges (rent of store and other associated costs)
c) Stores staffing (store keepers)
d) Equipment maintenance
e) Handling costs
f) Stock taking and audit costs
g) Insurance and security
h) Deterioration and obsolescence costs
i) Pilferage and other damage

Stock ordering costs

a) Transport costs
b) Clerical and administrative costs

Stock out costs

a) Lost contribution through lost sales
b) Loss of future sales
c) Loss of customer goodwill
d) Cost of production stoppages caused by lack of stocks
e) Labor frustrations over stoppages
The firm must determine the optimal level of inventory to be held so as to minimize the
inventory relevant cost.

ECONOMIC ORDER QUANTITY (EOQ)

This is a calculated ordering quantity which minimizes the balance of cost between stock
holding cost and stock ordering cost. This model is given by the following equation:
2DCo
Q 
Cn
Where: Q is the economic order quantity
D is the annual demand in units
Co is the cost of placing and receiving an order
Cn is the cost of holding inventories per unit per order
The total cost of operating the economic order quantity is given by total ordering cost plus
total holding costs.
D
TC = ½QCn + Co
Q
Where: Total holding cost = ½QCn
D
Total ordering cost = Co
Q
The holding costs may include:
1. Cost of tied up capital
2. Storage costs
3. Insurance costs
4. Obsolescence costs
The ordering costs include:
1. Cost of placing orders such as telephone and clerical costs
2. Shipping and handling costs

Under this model, the firm is assumed to place an order of Q quantity and use this quantity
until it reaches the reorder level (the level at which an order should be placed). The reorder
level is given by the following formulae:
 D
R L
360
Where: R is the reorder level
D is the annual demand
L is the lead time in days
ECONOMIC ORDER QUANTITY ASSUMPTIONS
1. There are known stock holding costs
2. There is known fixed ordering costs.
3. The rates of demand are known
4. There are known constant price per unit
5. The replenishment is made immediately
6. Buffer stocks are ignored
Example
ABC Ltd requires 2,000 units of a component in its manufacturing process in the coming year
which costs FRW50 each. The items are available locally and the leadtime in one week. Each
order costs FRW50 to prepare and process while the holding cost is Frw .15 per unit per year
for storage plus 10% opportunity cost of capital.
Required
a) How many units should be ordered each time an order is placed to minimize inventory
costs?
b) What is the reorder level?
c) How many orders will be placed per year?
d) Determine the total relevant costs.
Suggested Solution:
2DCo
a) Q
Cn
Where: D = 2,000 units
Co = Sh.50
Cn = Sh.15 + 10% x 50 = Sh.20
L = 7 days
2x 2,000 x50
Q  100units
20
DL
b) R =
360
2,000 x 7
=
360
= 39 units
D
c) No. of orders =
Q
2,000
=
100
= 20 orders
D
d) TC = ½QCn + Co
Q
2,000
= ½(100)(20) + (50)
100
= 1,000 + 1,000
= Frw.2,000
Under the basic EOQ Model the inventory is allowed to fall to zero just before another order is
received.

EXISTENCE OF QUANTITY DISCOUNTS

Frequently, the firm is able to take advantage of quantity discounts. Because these discounts affect the
price per unit, they also influence the Economic Order Quantity.
If discounts exists, then usually the minimum amount at which discount is given may be greater than
the Economic Order Quantity. If the minimum discount quantity is ordered, then the total holding cost
will increase because the average inventory held increases while the total ordering costs will decrease
since the number of orders decrease. However, the total purchases cost will decrease.
Illustration
Consider illustration one and assume that a quantity discount of 5% is given if a minimum of 200 units
is ordered.
Required
Determine whether the discount should be taken and the quantity to be ordered.
Decision rule:
If Qd < minimum discount quantity, then order the minimum discount quantity.
If Qd < minimum discount quantity, then order Qd.
Reduction in price due to the purchase in big quantity
Example. (Bulk purchases)
0 →999→0% discount
1000→4999→2% discount.
High order increase and decrease in price, in holding cost, ordering cost
Steps
1. compute EOQ, assuming no discount
2. compute EOQ if there is a discount
3. compute total cost for each range TC = CO + CP + CH, where CP = demand x
purchase price
CO = Nº of order x cost per order, CH = Average stock x CH per unit
4. Choose range with lowest total cost
Eg. D = 30,000 Barres at 12 £ each
Co = 250 £ per order
CH = 20% of purchase price
Discount 0 →4999→0%
5000 →7499→2% discount
7500→Above 2.5 discount

Required: EOQ and bulk

√2𝐷𝐶𝑂 √2𝑥3000𝑥250
1. EOQ if there is no discount = CH = 12 x20% = 2500 barres
2. Determine options available 0%→2%→2.5% discount available→available to choose
3. Determine total cost for each range option available
4. At zero discount %
5. TC = CO + CP + CH
CP = demand x purchase price
CO = nº of order x cost per order
CH = Average stock x CH per unit
Total holding cost
Total ordering cost
CP = D x purchase price per unit = 30,000 x 12 = 360,000£
D 30000
CO = nº of orders x cost per order = Q cost order per unit = = 2500 x 250 = 3000£
Q 2500
CH = Average stock x CH per unit = 2 x 12 x 20% = = 2 x 2.4 = 3000£
TC = CP + CO + CH = 360,000 + 3000 + 3000 = 366,000 £
At 2% discount, what would be the
CP = demand x purchase price = 30,000 x (98% x 12) = 352,800 £
D
CO = Nº order x cost per order or Q x cost per order
D 30,000
= x 250 = 1500 £
Q 5,00
5,000
CH = Average stock x CH per unit = 2 x ( 98% x 12 x 20%) = 5880 £
TC = CP + CO + CH = 352800 + 1500 6+ 5880 = 360,180
At 2.5% of discount
CP = demand x purchase
% of discount
30,000
CP = demand x purchase = 5,00 x 250 = 1000
75000
CH = Average stock s cost per unit = 5,00 (97.5% x 12 x 20%)
= 8190
TC = CP + CH + CO 351000 + 8775 + 1000 =
Summary
0% 2% 2.5%
TC = 360,000 TC = 360,180 TC = 360,775
The lowest total cost would be at 0%

UNCERTAINTY AND SAFETY STOCKS

Usually demand requirements may not be certain and therefore the firm holds safety stock to
safeguard stock out cases. The safety stock guards against delays in receiving orders.
However, carrying a safety stock has costs (it increases the average stock).
Re-order Level
This is that inventory level at which an order should be placed to replenish inventory. It is that
inventory level at which will be maintained for consumption during lead time. Assuming that
usage (demand) is known with certainty and is uniform throughout and that lead time does not
vary then,
Re-order Level =Daily usage x lead-time
Safety stock (Buffer stock)
It is difficult to predict usage and lead time accuracy. Demand for material may fluctuate from
day to day or week to week. Similarly actual lead time may be different from normal leadtime.
If actual usage increases or delivery of inventory is delayed the firm can face problem of stock
out. To guard against stock out the firm may maintain safety stock. This is some minimum or
buffer inventory to act as cushion against expected increases in usage or delay in delivery
time. In this case the re-order level then becomes:
Re-order Level =Safety stock + (Daily usage x lead-time)
Formulas for stock levels:
1. Re-Order level= Maximum Consumption x Maximum Re-order period
2. Minimum Stock Level= Re-order level – Normal Consumption x Normal Re-order period
3. Maximum Stock Level =Re-order Level + Re-order quantity – (Minimum Consumption x
Minimum Reorder period).
Example
In relation to the inventory management, with the following information calculate, (1) Re-
order level (2) Maximum level (3) Minimum level (4) Average level:
Normal usage: 100 units per week
Maximum usage: 150 units per week
Minimum usage: 50 units per week
Re-order quantity (EOQ) 500: units
Log in time: 5 to 7 weeks

ANSWER:
Re-order Level = Maximum consumption × Maximum Re-order period = 150×7=1050 units
Maximum Level= Re-order level+ Re-order quantity –(Minimum consumption ×Minimum
delivery period)= 1050 + 500 – (50 × 5) = 1300 units
Minimum Level = Re-order level – (Normal consumption ×Normal delivery period)
= 1050 – (100 × 6) = 450 units
Average Level
Maximum level + Minimum level
=
 2
= 1300+450
2
= 875 units.
EXAMPLE
The following are the details of two basic raw materials L and S
Usage
Normal usage 100,000Kg per week of each
Maximum usage 150,000Kg per week of each
Minimum usage 50,00Kg per week of each
Re-order quantity:
Material L 600,000Kgs
Material S 1,000,000Kgs
Re-order Period:
Material L 4 to 6 weeks
Material S 2 to 4 weeks
Required:
Calculate for each type of material
i) Re-order level
ii) Minimum stock level
iii) Maximum stock Level
iv) Average stock Level
Just-in-time (JIT) procurement
Under this approach, minimum inventories are held of Finished Goods, Work-in-Progress, and
Raw Materials. The conditions necessary for the business to be able to operate with minimum
inventories include the following:
1.1 Finished Goods:
 a short production period, so that goods can be produced to meet demand (‘demand-
pull’ production)
 good forecasting of demand
 good quality production, so that all production is actually available to meet demand
1.2 Work-in-Progress:
• a short production period. If the production is faster, then the level of WIP will
automatically be lower.
• the flexibility of the workforce to expand and contract production at short notice
1.3 Raw Materials:
 The ability to receive raw materials from suppliers as they are needed for production
(instead of being able to take from inventory). This requires the selection of suppliers
who can deliver quickly and at short notice.
 Guaranteed quality of raw material supplies (so that there are no faulty items holding
up production).
 The flexibility of suppliers to deliver more or less at short notice.
 Tight contracts with suppliers, with penalty clauses, because of the reliance placed on
suppliers for quality and delivery times.
A ‘just-in-time’ approach is a philosophy affecting the whole business. The benefits are not
just cost savings from lower inventory-holding costs and less risk of obsolete inventory, but
benefits in terms of better quality production (and therefore less wastage), greater efficiency,
and better customer satisfaction. Some manufacturing companies have sought to reduce their
inventories of raw materials and components to as low a level as possible. Just-in-time
procurement is a term which describes a policy of obtaining goods from suppliers at the
latest possible time (ie when they are needed) and so avoiding the need to carry any materials
or components inventory.

Introducing JIT might bring the following potential benefits.

 Reduction in inventory holding costs
  Reduced manufacturing lead times
 Improved labor productivity
 Reduced scrap/rework/warranty costs
 Reduced inventory levels mean that a lower level of investment in working capital will
be required.
JIT will not be appropriate in some cases. For example, a restaurant might find it preferable to
use the traditional economic order quantity approach for staple non-perishable food
inventories but adopt JIT for perishable and 'exotic' items. In a hospital, a stock-out could
quite literally be fatal and so JIT would be quite unsuitable.

6.3. MANAGEMENT OF DEBTORS

Debtors or receivables constitutes a substantial portion of current assets of several businesses
and therefore need to be managed efficiently and investment in them kept at optimum level.

In order to keep current customers and attract new ones, most firms find it necessary to offer
credit. Accounts receivable represents the extension of credit on an open account by a firm to
its customers. Accounts receivable management begins with the decision on whether or not to
grant credit.
The total amount of receivables outstanding at any given time is determined by:
a) The volume of credit sales
b) The average length of time between sales and collections.
Accounts receivables=Credit sales per day x Length of collection period
The average collection period depends on:
a) Credit standards which is the maximum risk of acceptable credit accounts
b) Credit period which is the length of time for which credit is granted
c) Discount given for early payments
d) The firm’s collection policy.
Establishing optimum credit policy
A firm investment in debtors depends on:
a) Volume of credit sales,
b) collection period e.g. if a firm credit sales are Frw 300,000 per day and customers on
average take 30days to make payments, then the firm average investment in receivables is
(daily sales x average collection period) =300,000 x 30=9,000,000.
The financial manager can influence the volume of credit sales, collection period and
consequently credit policy.
Credit policy refers to the contribution of 3 decision variables.
a)Credit standards
These are the criteria to decide the types of customers to whom goods should be sold on credit.
When the standards strict the firm will have little uncollectable debts and low sales and vice
versa.
Determinants of credit standards
1. The financial statements, financial rations would be computed to give the firms
measure of liquidity leverage and profitability.
2. Length of time the customer has been in business.
3. Experience of key personnel
4. Rate of growth of the business performance.
5. Records of customers, adherence to credit terms as offered by other suppliers and
financial institutions.
Other subjective qualities 5Cs of credit
1. Character of customers: Honesty and integrity.
2. Capacity of customer: the ability to pay as evidenced by customers, past records, bank
statements, and credit agency records.
3. Capital: as measured by general position of the firm.
4. Collateral: i.e security pledged in case of default.
5. Conditions: i.e general economic conditions
b)Credit terms
The duration of credit is specified and also the discounts offered to customers who pay within
the specified time. The lower the credit period the lower the investment in debtors and vice
versa.
c)Collection efforts
This determines the actual collection period. It involves reminding the debtors in a:
 Politely worded letter,
 Strongly worded letter,
 Sending a representative and then
 Contemplating taking a legal action or writing him off as bad debts.
The firm will have to evaluate its credit policy in terms of both returns and costs of additional
sales. Additional sales should add to companies operating profit but at the same time there will
be additional expenses, administration costs and bad debts losses. The goal of the firm credit
policy is to maximize the value of the firm and investment in receivables should therefore be
carefully evaluated.
Steps
1. Estimate the incremental operating profit.
2. Estimate the additional investment in debtors.
3. Estimate the rate of return (incremental) on additional investment in debtors
4. Compare the rate of return on additional investment with required rate of return.
Example :A firm has current sales of frw 7,200,000. The firms has unutilized capacity
therefore with a view to boost sales, it is considering lengthening its credit policy from 30
days to 45days. The average collection period will also increase from 30 days to 45days. Bad
debts losses are estimated to remain constant at 3% of sales. The firm’s sales are expected to
increase by 360,000. The variable production, administration and selling costs are 70% of
sales. The firm’s corporate tax rate is 35% and its cost of capital is 12%.
Required:Should the firm change its credit policy?

Solution
Incremental sales 360,000
less variable costs (70% x 360,000) (252,000)
Less bad debts(3% x 360,000) (10,800)
97,200
Less tax (35% 97,200) 34,020
Incremental profit after tax 63,180

Incremental investment in debtors

Total sales after change=7,200,000 + 360,000 7,560,000
7,560,000 x 45days 932,054.76
Investment in debtors 365 days
Previous investment debtors 7,200,000 x 30 days 591,781
365days
Incremental investment in debtors 340,274
Incremental rate of return
= (Incremental profit after tax /Incremental investment in debtors x 100%
= (63,180 /340,274) x 100% =18.57%
Recommendation: Since the incremental rate of return (18.57%) is more than the required
rate of return (12%), the firm should change its credit policy from 30days to 45days.
Example: Wholesaler’s credit sales are currently 14,400,000. The firm offers a net 30days
credit terms to its retailers. Of its receivables 3% becomes uncollectible. Variable costs are
70% of sales and the firm requires 20% rate of return of its assets. The wholesaler is
considering the following 3 alternatives credit policy:
1. Keep credit terms of net 30days
2. Change credit terms to net 60days.
3. Change credit terms to net 90days.
Data for each alternative is shown below:
 Net 30 days Net 60 days Net 90 days
Receivable turnover 12times 6times 4times
Annual credit sales 14,400,000 15,600,000 16,400,000
Average accounts receivables 1,200,000 2,600,000 4,100,000
Bad debts percentage 3% 4% 6%
Required: Which policy is preferable?

Solution
Net 30 days Net 60 days Net 90 days
Annual sales 14,400,000 15,600,000 16,400,000
Less variable cost 70% (10,080,000) (10,920,000) (11,480,000)
Contribution 4,320,000 4,680,000 4,920,000
Bad debts (3% 4% 6%) of sales (432,000) (624,000) (984,000)
3,888,000 4,056,000 3,936,000
Less opportunity cost 20% of average debtors 240,000 520,000 820,000
3,648,000 3,536,000 3,116,000
Recommendation: The preferred alternative is net 30days since it gives the highest gains.
NB: For the countries may offer credits to both local and foreign companies.
Risks arising from granting credit to foreign customers
 Foreign debts raise the following special problems. When goods are sold abroad, the
customer might ask for credit. Exports take time to arrange, and there might be complex
paperwork. Transporting the goods can be slow, if they are sent by sea. These delays in
foreign trade mean that exporters often build up large investments in inventories and
accounts receivable. These working capital investments have to be financed somehow.
 The risk of bad debts can be greater with foreign trade than with domestic trade. If a
foreign customer refuses to pay a debt, the exporter must pursue the debt in the debtor's
own country, where procedures will be subject to the laws of that country.
How risks can be managed and reduced
 A company can reduce its investment in foreign accounts receivable by insisting on
earlier payment for goods. Another approach is for an exporter to arrange for a bank to
give cash for a foreign debt, sooner than the exporter would receive payment in the
normal course of events. There are several ways in which this might be done. Where the
exporter asks his bank to handle the collection of payment (of a bill of exchange or a
cheque) on his behalf, the bank may be prepared to make an advance to the exporter
against the collection.
 Negotiation of bills or cheques is similar to an advance against collection, but would be
used where the bill or cheque is payable outside the exporter's country .
 Discounting bills of exchange is where a bank buys the bill before it is due and credits the
value of the bill after a discount charge to the company's account.
 Export factoring could be considered where the exporter pays for the specialist expertise
of the factor in order to reduce bad debts and the amount of investment in foreign accounts
receivable.
 Documentary credits provide a method of payment in international trade, which gives the
exporter a secure risk-free method of obtaining payment. The buyer (a foreign buyer, or a
Rwandan importer) and the seller (a Rwandan exporter or a foreign supplier) first of all
agree a contract for the sale of the goods, which provides for payment through a
documentary credit. The buyer then requests a bank in his country to issue a letter of credit
in favour of the exporter. The issuing bank, by issuing its letter of credit, guarantees
payment to the beneficiary.
 Countertrade is a means of financing trade in which goods are exchanged for other
goods.
 Export credit insurance is insurance against the risk of non-payment by foreign
customers for export debts. If a credit customer defaults on payment, the task of pursuing
 the case through the courts will be lengthy, and it might be a long time before payment is
eventually obtained.
 Premiums for export credit insurance are however very high and the benefits are
sometimes not fully appreciated.
FACTORING OF DEBTORS
This is a method of converting the non-productive Asset of debtors to productive asset of Cash
This is done by selling book debt of a company that specializes on administration and
collection. Factoring can be defined as a business continuing a legal relationship between a
financial institution (factor) and a business concern (client) selling goods or providing
services to trade customer where the factor purchases the client book debts and there after
controls the credit extended to customers and administers the sales ledger.
Aspects of factoring
The main aspects of factoring include the following:
(a) Administration of the client's invoicing, sales accounting and debt collection service
(b) Credit protection for the client's debts, whereby the factor takes over the risk of loss from
bad debts and so 'insures' the client against such losses. This is known as a non-recourse
service. However, if a non-recourse service is provided the factor, not the firm, will decide
what action to take against non-payers.
(c) Making payments to the client in advance of collecting the debts. This is sometimes
referred to as 'factor finance' because the factor is providing cash to the client against
outstanding debts.)

Factoring and short-term finances

Factoring differs from other short-term finances in the following respects.
1. Factoring involves sale of book debts, the client obtains advance cash against the expected
debt collection.
2. Factoring provides flexibility as regards credit facility, one can obtain cash either
immediately or on due dates or on time as and when one needs cash Such flexibility is not
available on other form of credit.
3. Factoring is a unique mechanism which not only provides credit to the client but also
undertakes the total management of debtors.
Cost of factoring
1. Factoring commission or service fee. This is paid for credit evaluation and collection and
other services and cover bad debt losses.
2. The interest on advance granted by the factor to the firm. This is usually higher than the
prevailing bank rate.
Benefits of factoring
The benefits of factoring for a business customer include the following:
.The business can pay its suppliers promptly, and so be able to take advantage of any early
payment discounts that are available.
(a) Optimum inventory levels can be maintained, because the business will have enough
cash to pay for the inventories it needs.
(b) Growth can be financed through sales rather than by injecting fresh external capital.
(c) The business gets finance linked to its volume of sales. In contrast, overdraft limits tend
to be determined by historical balance sheets.
(d) The managers of the business do not have to spend their time on the problems of slow
paying receivables.
(e) The business does not incur the costs of running its own sales ledger department, and
can use the expertise of receivable management that the factor has.
(f) Because they are managing a number of sales ledgers, factors can manage receivables
more efficiently than individual businesses through economies of scale.
An important disadvantage is that accounts receivable will be making payments direct to the
factor, which is likely to present a negative picture of the firm's attitude to customer
relations. It may also indicate that the firm is in need of rapid cash, raising questions about its
financial stability.
Example :A small firm has total credit sales of 8,000,000 and its average collection period is
80 days. The past experience indicates that bad debts losses are around 1% of credit sales.
The firm spends about 120,000 per annum on administering its credit sales. This is avoidable
costs. A factor is prepared to buy the firms debtors. He will charge 2% commission. He will
also pay advance against receivables at interest rate of 18% after withholding 10% as
reserves.
Required: Should the firm engage the factor?
Solution
1. Calculate the average level of receivables
Annual sales x average collection period 8,000,000 x 80days
Number of days in a year 360days
=1,777,778
Advance paid by the factor will be average level of receivables less factoring commission,
reserves and interest on advance.
2. Factoring commission = 2% average receivables 2% x 1,777,778 =35,556
3. Reserves 10% 1,777,778 =177,778
Amount available for advance (1,777,778-35,556-177,778) = 1,564,444
Less Interest to be paid is (18% x 1,564,444 x 80 ) =62,577.76 = 1,501,866
360
Cost of factoring per annum
Factoring commission 35,556 x 360/80 160,002
Interest charges 62,578 x 360/80 281,601
441,603
Benefits
Cost of credit administration 120,000
Cost of bad debts loss (1% x 8,000,000) 80,000
Net costs 241,603
Effective rate of annual cost 241,603 x 100% =15.44%
1,564,444
INVOICE DISCOUNTING :Invoice discounting is the selling of an invoice to a third party
(usually a bank) for a lower (discounted) amount. This way the supplier gets cash immediately
and it is the bank who has to wait for payment (hence the lower or discounted amount).
6.4. MANAGING ACCOUNTS PAYABLES
Payables may be used as a source of short-term finance. If a company delays payment by
a further month then they now have a further months use of the cash. However, delaying
payment may lose the company its credit status with the supplier and could result in
supplies being stopped. Additionally, the company could lose the benefit of any
settlement discount offered by the supplier for early payment. In exactly the same way as
for receivables, we can calculate the annual effective cost of refusing any settlement
discount offered, and compare this with the cost of financing working capital.
Example :A supplier offers a 2% discount if invoices are paid within 10 days of receipt.
Currently we take 30 days to pay invoices and therefore do not receive the discount.
Calculate the annual % effective cost of refusing the discount.
Solution
2 × 100% over 20 days (30-10)
Effective cost = 98
2
= × 365 × 100% p.a.
98 20
= 37% p.a.
TOPIC 7: PORTFOLIO THEORY
In topic 5, we looked at investment decisions for assets held in isolation. That is, we did not
consider the synergistic effects of assets held together. This will, however, be considered in this
chapter.
7.1. Uncertainty of returns

If we were comparing a building society investment with one in shares we would normally require a
higher return from equities to compensate us for their extra risk. In a similar way if we were
appraising equity investments in a food retailing company against a similar investment in a
computer electronics firm we would usually demand higher returns from the electronics investment
to reflect its higher risk.
We can better the return earned by investors on the stock market by investing in a physical asset
offering the same level of risk, we can increase investor wealth and the investment should be adopted.
Unfortunately the required approach is not as simple as this. Investors seldom hold securities in
isolation. They usually attempt to reduce their risks by not” putting all their eggs into one basket” and
therefore hold portfolios of securities. Before we can deduce a risk –adjusted discount rate from stock
exchange returns we need to identify the risks taken by investors in their diversified investment
portfolios.

7.2. The benefits of portfolio diversification

A portfolio is simply a combination of investments. If an investor puts half of his funds into an
engineering company and half into a retail shop then it is possible that any misfortunes in the
engineering company (e.g. a strike) may be to some extent offset by the performance of the retail
investment. It would be unlikely the both would suffer a strike in the same period.
This effect can be demonstrated more formally in the following graphs. Assume we have two
companies, A and B, whose fortunes are inversely correlated (i.e. when A does well B does badly and
vice versa).
Rate of
return
Investment A

Rate of Time
return

Investment B

Both investment A and investment B show fluctuating returns over time. Time
They both have
roughly the same amount of variability, when A does well B does badly, and vice versa.
If both investments are held, the resulting portfolio will generate a greater average (absolute)
return than with either one alone but a greatly reduced risk, because the 'ups' of A cancel with
the 'downs' of B and vice versa.
The same effect can be illustrated by a simple computational example.
Example 1
Mr Mario sells ice by cream from a stall on the seafront at Brighton during the tourist season.
His sales are affected by the British weather which is rather unpredictable. There are two
possible states of the weather: sun and rain. In Brighton, when it is sunny, it is sunny all, but
when it rains, it rains all day. Mr Mario has noticed that during the tourist season half the days
are sunny and half are rainy. When the sun is out he makes a daily contribution of £200, but
when it rains he only makes £20.
A few yards down the road Mr Hashimoto also operates a stall, from which he sells cheap
throw-away Japanese umbrellas which always seem to last one day before the spokes break.
These are very popular with tourists who are caught out by the rain. When it rains, Mr
Hashimoto makes a daily contribution of £200, but when the sun shines, he only makes £20.
State Sun Rain Average Risk
Probability 0.5 0.5
Contribution: ice creams 200 20 110 High
Contribution: umbrellas 20 200 110 High
Although both businesses are profitable, the traders are a bit unhappy about riding the roller-
coaster of risk. Also, they never talk to each other because when Mr Mario is happy, Mr
Hashimoto is miserable and vice versa.
As it happens, one bank holiday Monday, a well known management consultant, Mr Drizzle,
is spending the day on Brighton beach. He succeeds in persuading the two traders to swap
their secrets and pool their resources.
Now both Mr Mario and Mr Hashimoto hold half their stock as umbrellas and half as ice
creams. When it is sunny they both make (1/2 x 200) + (1/2 x 20) = £ 110, and when it rains
they both make (1/2 x 20) + (1/2 x 200) = £ 110.
State Sun Rain Average Risk
Probability 0.5 0.5
Contribution 110 110 110 Zero

Now both men are reasonably happy all the time. They each have as much money as before,
but it is earned risk-free. They even talk to each other.

7.3 Correlation
Correlation is a statistical measure of how strong the connection is between two variables. In
portfolio theory the two variables are the returns of two investments.
High positive correlation means that both investments tend to show increases (or decreases) in
return at the same time:

Return
Portfolio return
A

Time
High negative correlation means that as returns on A increase, returns on B decrease:
Return
Portfolio return
A

Time
The degree of risk reduction possible by combining the investments depends on correlation
between them.

The coefficient of correlation is measured on a scale from -1 (perfect negative correlation) to

+1 (perfect positive correlation). Perfect negative correlation can, but will always, completely
eliminate risk (see Example 1).
A correlation coefficient less than +1 can reduce risk. The further the correlation coefficient is
from + I the greater than the potential risk reduction.]

State why it is that combining two investments with perfect negative correlation might not
completely eliminate risk.
7.4 The risk and return of portfolios
A formal analysis of the combination of two investments is now presented. Because portfolio
theory has its roots in the management of stock exchange investments, this is referred to as the
two-security portfolio. The theory starts by identifying measures of risk and return for an
investment. The analysis is usually presented in terms of rates of return over a single time
period.
For example, if all investment is predicted to rise from a value now of £8,000 to a value in one
year of £9.000, and a dividend of £ 1,000 will be paid in the period; it has a predicted rate of
return of
£9,000  8,000  £1,000
 25%
£8,000
This is just as we have defined return to investors previously - dividend yield plus capital
growth. We also need a measure of the risk of a particular security. Remember that, if possible
returns are R1, R2 …, Rn, with associated probabilities P1, P2… Pn, then the standard deviation
is calculated as
  R  R  Pi Where R is the average return, R P
2
i i i

Example 2 : Suppose we are trying to forecast the possible rates of return of two investments
over the next year. We make predictions as follows:
Economic climate Probability of economic Returns Returns from B
climate from A % %
Recession 0.2 10 6
Stable 0.5 14 15
Expansion 0.3 20 11
1.0
Firstly, calculate the expected return and standard deviation of each investment. This tells us
the risk and return of each security if held in isolation.
Economic Probability Return
 climate P R %
P R RA  RA RA  RA 2
R 0.2 10 2 -5 25
S 0.5 14 7 -1 1
E 0.3 20 6 +5 25
R A  15% Variance of return A = 51
SD,  A = 51
= 7.14
Economic Probability Return
climate P R %
P R RB  RB RB  RB 2
R 0.2 6 1.2 -6 36
S 0.5 15 7.5 +3 9
E 0.3 11 3.3 -1 1
RB  12% Variance of return B = 46
SD,  B= 46
= 6.78

Summary
Investment A B
Expected return 15% 12%
Risk,  7.14 6.78
Consider now constructing a portfolio consisting of one-half of the total amount invested in
investment A and one-half in investment B. Under each economic climate the return of the
portfolio would be the average of A and B. Compute the expected value and standard
deviation of this portfolio:
Portfolio ½ B
Economic Probability Return
climate P R % P R RB  RB RB  RB 2
R 0.2 10  6  8 1.60 5.5 30.25
2
S 0.5 14  15  14.5 7.25 1 1
2
E 0.3 20  11  15.5 4.65 2 4
2
R  13.5% Variance of return B = 35.25
SD,  = 35.25
= 5.93
The portfolio has an expected return which is equal to the weighted average on investment
returns, but its risk as measured by standard deviation, is lower than of the two original
investments.
7.5 Indifference curves
Consider the three possible portfolios constructed so far.
100% A 100% B 50% A and 50% B
Return 15% 12% 13.5%
Risk 7.14 6.78 5.93
Which of these portfolios is preferable? It all depends on the investor’s attitude to risk against
return, which may be depicted diagrammatically as ‘indifference curves’. The following
diagram shows three possible investments (R, S and T), their positions on the graph being
determined by their return /risk combination. The investor who is trying to decide between
them has indifference curves as shown.
Indifference curves
Increasing
Return
benefit
R

T X

Risk

The indifference curves represent alternative combinations of risk and return between which
the investor is indifferent. Obviously each investor will have different indifference curves, but
they will tend to be of the slope indicated above. This is because most investors are averse to
risk, and will demand a higher return to compensate. Thus, the indifference curves represent
the trade-off between risk and return for an individual investor.
In this example, the investor would prefer R to S as it is on a higher indifference curve: The
lower level of risk for S does not adequately compensate for the lower level of return.

Question : Would the investor prefer T to R on the above diagram?

Solution :No - R is on a higher indifference curve than T.

Note that another investor with a more risk-averse attitude may have much steeper
indifference curves (requiring a much greater compensation in return for the same change in
risk) which could mean they have a different order of preference:

Return
R
S
X T

Risk

Here, the investor would prefer S to R.

7. 7. Covariance and correlation
The risk reduction in the last example was made possible by the low correlation between the
investments. Just looking at the possible returns of A and B shows that there is no consistent
positive or negative relationship between them. The correlation coefficient will probably be
just higher than zero.
One way of computing the correlation coefficient is to first compute the covariance, which is
defined as:
Cov x, y   px  x  y  y 
Where x,y are corresponding returns from investments X and Y arising with probability p.
The covariance will be positive for positive correlation and negative for negative correlation
but its size depends on the size of the figures in the original data and is difficult to interpret.
The correlation coefficient is the ratio of the covariance to the product of the two standard
deviations and will vary between -1 and +1.
Cov x , y
Correlation, P x , y 
 x y
(The Greek letter  (rho) is normally used for correlation in portfolio theory, because the
usual symbol R would be confused with return).
The positive covariance tells us there is a positive relationship between returns on A and B but
the strength of the relationship is not quantified. The correlation coefficient indicates that the
positive correlation is quite weak. Significant risk reduction is therefore possible. Note: once
again negative correlation is not necessary for risk reduction.

7.8. Portfolio selection with both risky and risk-free assets

There is a special case of the type security portfolio which is particularly important for our
later studies. This is the case of combining a risk-free security with a risky security.
A ‘risk-free’ security is one which shows no variability in predicted returns. In other
words its return is known with certainly. In practice it can be approximated by an investment
in government stocks or bank deposit accounts at fixed interest (although varying rates of
inflation would mean the real return on these investments becomes uncertain). A risk-free
security has a zero variance, and a zero covariance with any other security (check that this
must be so by examining the formulae for variance and covariance).
The formula for the variance of the two-security portfolio therefore reduces as follows:
VarP  X A VarA  0  0
2

Where VarA = variance of risky investment A.

Taking square roots:  p  X A A
In other words, the portfolio standard deviation is simply the standard deviation of the risky
investment times the proportion of that investment in the portfolio. The expected return of the
portfolio will still be a weighted average of the expected returns of the two investments.
Example 4 : You can invest in government stock, showing a risk-free annual return of 10%
and also in shares in BP plc, which you expect to show a return of 25% p.a., subject to a
standard deviation of 10%. Show the possible returns and risks of portfolio constructed out
these two securities.
Solution
Let XA be the proportional amount of investment in shares in the portfolio.
XA Portfolio expected return Portfolio risk X A A
25% 10%
0.8 (0.8 x 25%) + (0.2 x 10%) = 22% 0.8 x 10% = 8%
0.5 (0.5 x 25%) + (0.5 x 10%) = 17% 0.5 x 10% = 5%

Portfolio
return
25
XAll BP
20 X0.8 BP

15
X0.5 BP

10 All govt. stock

6 8 10 Portfolio risk
2 4
When combining a risk-free security with a risky security, there is a straight line trade-off
between return and risk.
7.9. Portfolio theory and project appraisal
We are now in a position to apply the principles of portfolio theory to project appraisal by a
firm. We cannot yet develop a risk-adjusted discount rate but in considering risk the following
fundamental point should be clear.
The relevant risk of a security (or any investment) is not its own risk but its effect on the risk
of the portfolio to which it is added.
7.9.1 Mixing many risky securities
Portfolio theory its roots in the management of investor’s portfolio of stock exchange
investments and fixed interest stocks. The following sections show how the attempt to identify
an optimal portfolio for investors has led to a comprehensive but simple theory or how the
capital market relates risk and return. This, in turn, will assist us in our attempt to adjust
discount rates to allow for risk.
The previous section considered portfolio of two securities. It is easy to extend this theory to
cover portfolios of many securities, noting that where returns are assessed in percentage terms:
 The expected return of a portfolio is equal to the weighted average of the returns of the
individual securities in the portfolio.
 The risk of the portfolio depends on:
(a) the risk of each security in isolation
(b) the proportions in which the securities are mixed
(c) the correlations between every pair of securities in the portfolio.
When two securities were mixed, the possible portfolios lie on a curve linking the two
securities (see below).

Return
B

Strategy financial management Risk

When three securities are mixed, the possible portfolios lie across an area on the graph like
this: Return

C
A

Risk
When many securities are mixed, the opportunity set is better-quality:
Return

Risk
The shaded area shows the return and risk of all the possible portfolios constructed from the
securities by mixing them in all possible proportions, In the 1950s, H M Markowitz developed
this theory and showed how ‘efficient portfolios’ can be identified.

7.9.2 Efficient portfolios, mean-variance efficiency and the efficient frontier

It is possible to identify which of these portfolios are really worth holding.
A rational risk-averse investor would define an efficient portfolio as one that has:
(a) a higher return than any other portfolio with the same risk
(b) a lower risk than any other with the same return.
This simple approach is known as the mean variance efficiency rule (return = mean or
expected return; risk = variance or standard deviation).
So, out of all the possible portfolios which an investor could make out of his chosen securities,
which are mean variance efficient? (Put another way, which portfolios would the investors
select from, given logical assessment of the mean returns and variances of all those available?)
Return

B
C A

Risk
If we started with portfolio A, in the middle of the opportunity set, then a better portfolio
could be identified by moving upwards (higher return, same risk) or to the left (lower risk,
same return).
Thinking in this way leads us to the conclusion that the efficient portfolios must lie along the
top left hand edge of the opportunity set. This is called the efficient frontier.
Return
Efficient frontier

Risk
All other portfolios can now be ignored. Only the efficient ones need be considered.
Logical investors would eliminate all others.
Notice the shape of this efficient frontier. As we attempt to increase return, risk begins to grow
at an increasing rate.

An optimal portfolio could be identified for any investor by superimposing indifference curves
on the efficient frontier.
Return

Efficient frontier

The optimal portfolio

Risk
However, this so-called optimal portfolio has ignored the existence of fixed interest risk-free
securities. These now need to be introduced. At this stage, it is convenient to build a simplified
model of investor behaviour.
7.9.3 The market portfolio
A few assumptions are now made, in order to build a simple model:
 Investors base their portfolio investment decisions on expected returns, standard
deviation and correlations between all pairs of investments.
 All investors have the same expectations about future outcomes over one-period time
horizon.
 Investors may lend and borrow without limit at the (same) risk-free rate of interest.
 There are no market imperfection investments are infinitely divisible, information is
costless, there are no taxes, transaction cots or interests rate charges, and no inflation.
Some of these assumptions are obviously unrealistic, but they greatly simplify the model-
building process. Furthermore, even if the assumptions are relaxed, the theory will still hold
approximately.

Building the model

(a) Firstly, consider all the portfolios which could be constructed out of risky securities
quoted on the stock market.
(b) Then identifying the efficient portfolios from these.
(c) Then consider mixing any one of these efficient portfolios, A, with a risk-free
investment, Rf:

Return

Efficient portfolios
A
Rf

Risk
If all the investor’s funds were put into the risk-free investment, he would earn the free rate of
interest and have no risk. If all his funds were put into portfolio A, he would have the return
and risk of portfolio A., if he split his investment between Rf and A, the return and risk he
would get would lie anywhere up a line joining Rf and A, depending on the proportions in
which the funds were split.
 Return

Efficient portfolios
A
RF

Risk
The section of the efficient frontier below a now becomes redundant those portfolios are not
so attractive as a combination of A with risk-free investments (the latter have a lower risk
for the same return).

Portfolio A was chosen at random. If we chose one higher up the efficient frontier, the effect
would be better:
Return

A
RF

Risk

Any combination of Rf with portfolio B is better than (‘dominates’) a combination of Rf with

portfolio A (higher return for the same risk).
Proceeding in this way, the best portfolio is M in the following diagram, where a line drawn
from Rf touches the efficient frontier at a tangent:

Return
N

RF

Risk
The surprising conclusion is that:
‘Out of all the possible portfolios that could be constructed from risky investments, only one
portfolio is worth considering-portfolio M.’

A combination of Rf and M produces portfolios which are better than any others in terms of
the return which is offered for any given level of risk.

However, given the existence of risk-free investment, investors would choose from those on
the revised efficient frontier represented by line Rf M.

Portfolios on the line RfM are achieved by mixing portfolio M with risk-free investments.
Portfolios on the line M N are achieved by borrowing at the risk-free rate (remember we
have assumed that the risk-free rate applies to borrowing as well as lending) and investing our
own funds plus borrowed fund in portfolio M.
What is portfolio M?
Because we have assumed that all investors have the same expectations about the future
outcomes of investments, it follows that:

All investors will come to the conclusion that portfolio M is the best portfolio consisting
solely of risky investments to hold.

Now, if any quoted share was not in portfolio M, then nobody would wish to hold it. It would
therefore have no value. We must therefore conclude that:

Portfolio M is includes every risky security which is quote on the market.

Portfolio M is in fact simply a slice of the whole stock market: the proportion shares held in it
are same as the total market capitalisations of the shares on the stock market.
Portfolio M is called the market portfolio
All rational risk-averse investors will hold the market portfolio, according to the model we
have just constructed. Note: it is not necessary for every investor to hold every share on the
stock market. Close replicas of portfolio M may be generated by holding as few as fifteen
shares. Investment in unit trusts will also achieve the same result.

However, all investors do not have the same attitude to risk. By using the market portfolio,
and by either lending or borrowing suitably at the risk-free rate, the investor can choose any
level of risk he likes and can predict the return which the market will give him. This return
will be the best that he could possibly get for the risk taken.
By adding the investor indifference curves, we have:

Return

Investor’s optimal portfolio

Rf

Risk
The trade-off between return and risk which is offered by this sensible use of the capital
market is called the capital market line. This is effectively, as previously mentioned, our new
efficient frontier.
7.9.4 Nature of the capital market line
We have already seen that combinations of risk-free and risky investments give a straight line
trade-off between risk and return.
To draw the capital market line we therefore need only two observations:
 Rf- the risk-free rate of interest, which can be approximated by the return on
government stock;
 RM and  M the risk and return of the market portfolio should contain all risky
investments. This can be estimated by using the risk and return on a stock market index
such as the Financial Times All share Index.
Example 6
An investor has £100 to invest. The following information is available:
RM = 15% (Return on portfolio M)
M = 10% (Risk of portfolio M)
Rf = 6% (Risk-free rate of return).
You are required to plot the capital market line and show that a lending portfolio (of £50
invested at the risk-free rate and £50 invested in portfolio M) and a borrowing portfolio (£50
borrowed at risk-free rate and £150 invested in portfolio M) lie on this line.

7.9.5 Significance of the capital market line

The capital market line tells us for a given level of risk the return an investor should expect on
the stock exchange. It is often referred to a giving the market price of risk. That is if we
choose to take given level of risk on the stock exchange then we can expect a given level of
return.

7.10. Practical aspect of portfolio theory

7.10.1 The relevance of portfolio theory to practical financial management
Our analysis of portfolio theory started by looking at two-security portfolio and was then
developed to deal with portfolios combining many securities with a risk-free security. It would
theoretically be possible for financial managers to assess whether to accept a proposed project
by applying the two-security portfolio theory.
Security A = the company’s existing operations
Security B = the proposed project
On a risk-return graph both 'security A' and 'security A plus security B should be plotted.
When shareholders indifference curves are superimposed on the graph it should be possible to
decide whether the addition of security B increases the shareholders' utility, i.e. whether it
should be accepted.
However, such an analysis would prove very difficult in practice for the fol1owing reasons:
 The risks and returns of the existing operations and of the proposed project will
impossible to estimate accurately.
 Different shareholders will have different attitudes to risk; the concept of a sing set of
shareholder indifference curves is unrealistic.
 The theory examines risks and returns over a single time period only; in practice
managers are responsible over a series of successive time periods.
Portfolio theory is not a practical method of project appraisal for financial manager. However,
it useful1y introduces managers to the concept of risk reduction through diversification, and it
leads on to the capital asset pricing model which is more use in practice. Perhaps portfolio
theory is most valuable for the proportion of each shareholder’s weather.

7.10.2 The limitations of portfolio theory

Several limitations have already been touched on:
 Risk is assessed in terms of the total risk of individual investments, but in practice
much of this risk will be diversified away when the investment is added to an already
well diversified away when the investment is added to an already well diversified
 It is a single period model.
 Plotting indifference curves is a theoretical exercise which is impossible to carry out
accurately in practice.
 Forecasting returns and the correlations between returns will be hazardous in practice.
It should also be noted that measuring risk as the standard deviation of expected returns is not
the only component of risk. There are other costs (e.g. the risk of bankruptcy) associated with
high risk investment strategies.

7.11. ARBITRAGE PRICING THEORY (APT)

Formulated by Ross(1976), the Arbitrage Pricing Theory(APT) offers a testable alternative to the
capital market pricing model(CAPM). The main difference between CAPM and APT is that CAPM
assumes that security rates of returns will be linearly related to a single common factor- the rate of
return on the market portfolio. The APT is based on similar intuition but is much more general.

APT assumes that, in equilibrium, the return on an arbitrage portfolio (i.e. one with zero investment,
and zero systematic risk) is zero. If this return is positive, then it would be eliminated immediately
through the process of arbitrage trading to improve the expected returns. Ross (1976) demonstrated
that when no further arbitrage opportunities exist, the expected return (E(Ri)) can be shown as follows:

E(Ri)=Rf + β1(R1-Rf)+β2(R2 -Rf)+--------+ βn(Rn-Rf)+έi

Where,
E(Ri) is the expected return on the security
Rf is the risk free rate
Βi is the sensitivity to changes in factor i
έi is a random error term.

7.11.1. APT and CAPM compared

The Arbitrage Pricing Theory (APT) is much more robust than the capital asset pricing model for
several reasons:

 The APT makes no assumptions about the empirical distribution of asset returns. CAPM
assumes normal distribution.
 The APT makes no strong assumption about individuals‘ utility functions (at least nothing
stronger than greed and risk aversion).
 The APT allows the equilibrium returns of asset to be dependent on many factors, not just one
(the beta).
 The APT yields a statement about the relative pricing of any subset of assets; hence one need
not measure the entire universe of assets in order to test the theory.
 There is no special role for the market portfolio in the APT, whereas the CAPM requires that
the market portfolio be efficient.
 The APT is easily extended to a multi-period framework.

Since APT makes fewer assumptions than CAPM, it may be applicable to a country like Kenya.
However, the model does not state the relevant factors. Cho(1984) has, however, shown the security
returns are sensitive to the following factors: Unanticipated inflation, Changes in the expected level of
 industrial production, Changes in the risk premium on bonds, and Unanticipated changes in the term
structure of interest rates

Illustration
Security returns depend on only three riskfactors-inflation, industrial production and the aggregate
degree of risk aversion. The risk free rate is 8%, the required rate of return on a portfolio with unit
sensitivity to inflation and zero-sensitivity to other factors is 13.0%, the required rate of return on a
portfolio with unit sensitivity to industrial production and zero sensitivity to inflation and other factors
is 10% and the required return on a portfolio with unit sensitivity to the degree of risk aversion and
zero sensitivity to other factors is 6%. Security i has betas of 0.9 with the inflation portfolio, 1.2 with
the industrial production and-0.7 with risk bearing portfolio—(risk aversion)

Assume also that required rate of return on the market is 15% and stock i has CAPM beta of 1.1

REQUIRED:

Compute security i's required rate of return using

 CAPM
 APT
Using APT Ri = 8% + (13% - 8%)0.9 + (10% - 8%)1.2 + (6% - 8%)(-.7)
 16,3%
Using CAPM Ri = RF + (E(RM) - RF)ßi

Ri = 8% + (15% - 8%)1.1 =15.7%

 LIMITATIONS OF APT
APT does not identify the relevant factors that influence returns nor does it indicate how many factors
should appear in the model. Important factors are inflation, industrial production, the spread between
low and high grade bonds and the term structure of interest rates.

PRACTICE QUESTIONS
QUESTION ONE
Securities D, E and F have the following characteristics with respect to expected return, standard
deviation and correlation coefficients.

Security Expected Return Standard Deviation Correlation Coefficient

D-E D-F E -
F
D 0.08 0.02 0.4 0.6
E 0.15 0.16 0.4 0.8
F 0.12 0.08 0.6 0.8
REQUIRED: Compute the expected rate of return and standard deviation of a portfolio comprised of
equal investment in each security.
QUESTION TWO:The risk free rate is 10% and the expected return on the market portfolio is 15%.
The expected returns for 4 securities are listed below together with their expected betas

SECURITY EXPECTED RETURN EXPECTED BETA

A 17.0% 1.3
B 14.5% 0.8
C 15.5% 1.1
D 18.0% 1.7

REQUIRED:
 On the basis of these expectations, which securities are overvalued? Which are undervalued?
 If the risk-free rate were to rise to 12% and the expected return on the market portfolio rose to
16%, which securities would be overvalued? which would be under-valued? (Assume the
expected returns and the betas remain the same).
QUESTION THREE
XYZ ltd. is considering three possible capital projects for next year. Each project has a 1 year life, and
project returns depend on next years state of the economy. The estimated rates of return are shown
below.

STATE OF THE PROBABILITY RATE OF RETURN

ECONOMY OF OCCURRENCE A B C

Recession 0.25 10% 9% 14%

Average 0.50 14 13 12
BOOM 0.25 16 18 10

REQUIRED:
 Find each project expected rate of return, variance, standard deviation and coefficient of
variation.
 Compute the correlation coefficient between

 A and B
 A and C
 B and C
 Compute the expected return on a portfolio if the firm invests equal wealth on each
asset.
 Compute the standard deviation of the portfolio.
TOPIC 9 : BUSINESS VALUATION
A business may be valued for different reasons such as for merger, takeover, acquisition, or outright
sale or liquidation. In purchasing a business, a buyer will be interested in not only the assets but
also the future income this business is expected to generate.
9.1. BASES OF VALUATION
1. Theoretical value – In theory, if a purchaser buys a business, he is simply buying a stream
of future income flows and to arrive at the actual purchase price the buyer will:
a) Consider the estimated probable cash flows.
b) Discount cash flows to their present value.
c) Add together the separate amounts to give the present value of income stream.
Where future income flows are constant:
1  (1  r ) n 
PV  C 
 r 
Where: PV = Present value of income stream
c = Inflow per annum
r = Discounting rate
n = Number of years the inflows will last
Example
As a result of the purchase of an asset, the income stream will increase by Frw1,000 per annum for
25 years. Assuming a discount rate of 20%, compute the maximum price to be paid for this asset
ignoring taxation.
Solution
Maximum price = Present value of all future cash inflows
Maximum price=Frw10,000 x PVAF20%,25
1  (1.2) 25
= Frw10,000 x =10,000 x 4.9476=Frw49,476
0.20
In practice the income streams are never uniform and have to be estimated from existing income
shown in the recent accounts.
2. Earning method – The business is valued according to the total stream of income it is
expected to generate over its lifetime.
Determination of maintainable earnings
a) The first step in arriving at earning based valuation is to estimate the future maintainable
earnings and if the conditions in the future are expected to be similar to those in the past, it
is then prudent to face the forecast on the historical figures. However, conditions do change
and as such changes in cost and revenue. Therefore, a detailed examination of profits of the
most recent profit and loss account will be necessary to estimate the effects of the changes.
While the information given will depend upon the nature of the business the general
principles to bear in mind must include the trend of sales and gross profit.
b) Analysis of sales and gross profit percentage by:
i) Product lines
ii) Departments
iii) Geographical areas
iv) Customer type.
c) Costs as a percentage of total sales.
d) Unusual fluctuations in the ratios.
e) Necessity of expenditure in the business e.g. excessive remuneration on expenses charged.
f) Inclusion of all costs.
g) Effects of external conditions such as inflation or recession.
However, there are several ways of arriving at the value based on the earnings valuation.
i) Earnings yield valuation
ii) Price earnings ratio valuation
iii) Super profits valuation
i) Earnings Yield Valuation
EY is given by the earnings made by the business expressed as a percentage of the market price of
the business i.e.
EY = Earnings x 100
Market price of equity
EY =EPS x 100 =Earnings to Shareholders
MPS Market value of equity
Therefore Market Value=Earning to shareholders
Earnings yield
Example
Estimated maintainable earnings are Frw240,000 per annum, rate of return required is 25%.
Compute the value of the business.
alue MV) = Earnings x 100
Earning Yield
= 240,000 x 100
0.25
M.V. = Frw960,000
This method can be converted into the theoretical base, especially if the business is going concern.
C 1 
PV  1  
i  1  0.25 
N

Note
As N approaches ∞
Pv = C
r
= 240,000 = Frw960,000
0.25
ii) Price Earning Ratio Valuation
P/E ratio is traditionally used for valuation of shares but it is an important ratio in the valuation of
business. The P/E ratio is the measure of how may years earning would ‘purchase’ the market
value of the business and is given by:
P/E ratio = MV
E
MV = P/E x E
NB: The value of the business can be calculated by taking estimated earnings x P/E ratio.
9.2. VALUATION OF SECURITIES:
The previous methods were ideal for valuing the entire business but it is also necessary to ascertain
the value of part of a business namely shares, or securities or a block of shares in a limited liability
company. The valuation of securities and shares in particular is necessary in the following aspects:
i) To facilitate take-over bids
ii) To allow for mergers.
170 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
 iii) To facilitate for company accounts disclosure
iv) For purposes of acquisitions or disposal of blocks of shares.
v) For purposes of computing capital gains tax (not applicable in Kenya at present)
vi) For tax payer’s executors in assessing the capital transfers processes
vii) For ascertaining stamp duty payable.
However, a number of parties are interested in the value of shares and securities and such will
include:
a) Company shareholders, directors and vendors of the company.
b) The existing and prospective shareholders.
c) Buyers of a company.
d) Transferee and transferor parties, in particular from the point of view of income tax.
e) Income tax department.
The main difficulties in valuation of shares are:
i) Existence and method of valuation of goodwill.
ii) Succession of company’s management
iii) Growth in dividend
iv) Growth in equity.
BASES OF SHARE VALUATION
Share valuation can be done on the basis of income and asset values. However, on the basis of
income a share will be entitled to two forms of income. For this reason the bases of valuing shares
are:
i) Earnings method
ii) Dividend method
iii) Assets method
I) Earnings Method (Or Earning Basis Valuation)
Using the earning valuation method, a company will use its P/E ratio to value its shares.
P/E = MV
E
MV = E x P/E -> value of ordinary share.
The MV can be determined where the estimated earnings have been established by applying the P/E
ratio expected of this type of company.
Example
Company XYZ is expected to generate post tax earnings of FRW200,000 per annum . On account
of company XYZ limited size, a P/E ratio of six (6) is considered more appropriate. The issued
share capital is 1,000,000ordinary shares of FRW50 each.
Required
Value of shares= EPS x P/E
= Earnings per share x P/
= 200,000 x 6 = FRW12.00
1,000,000
Value of Business = Earnings x P/E ratio
MV = E x P/E = FRW200,000 x 6 = FRW1.2 million
ii) Dividend Basis Valuation
Ownership of shares in entities – The owner to receive a cash flow consisting of future dividends
and the value of a share should correspond to the present value of this future cash flow. A
shareholder cannot expect cash flows in perpetuity as he will sell his shares at one time.
171 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
 Po = Do
Ke
d0 (1  g)
Note: Where there is growth in equity, P0 =
Ke  g
Example: Company XYZ pays a dividend of 10% on its FRW60 par value ordinary shares. This
company uses a discount rate of 15%. Assuming no growth, compute the value of its ordinary
share if there’s growth of 5%, what would be the value of this company’s ordinary shares.

a) Po = Do Po = 6 = FRW40 (no growth)

Ke 15%

b) Po = 6(1.05) = Frw63 (5% growth rate)

0.15-0.05
iii) Asset Based Valuation
This method takes into account the entire business with reference to its assets and then divides the
resultant value by the number of shares in an issue to give the per share. The principles are the
same as those in the valuation of businesses computed already. However, if a historical dividend
based on earning based valuation produces a figure which is less than the asset value then there is a
possibility that the buyer may be able to improve the management of the asset being taken over. In
such a case, a buyer would be prepared to pay a price which though excessive in terms of income
might be justified by the underlying assets value.
Example 1:Information extracted from the books of Kent Limited.
FRW FRW
Current liabilities 300,000 Land 250,000
Bank overdraft 50,000 Stock in trade 100,000
350,000 350,000
Stock has a realisable value of FRW80,000 and land FRW300,000. This company is assumed to be
have a share capital of 20,000 ordinary shares.
Compute the value of its shares.
i) Assets method
Assets = L & B 300,000
Stock 80,000
380,000
Liabilities [350,000]
30,000
Value of shares =30,000 = FRW1.50
20,000
Example 2
K & K Company Limited is planning to absorb three other companies so as to realise its sales
records of FRW500,000 per annum. Its accountants have advised the company to maintain such a
size that it will enable its shares to sell at a minimum price of FRW16. The company’s last
published balance sheets indicate the following:
FRW’000’
Ordinary shares of FRW10 each 50,000
Reserves 65,000
172 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
Current liabilities 40,000
Total 155,000
Assets: FRW
Fixed assets 80,000
Current assets 75,000
Total 155,000
Profits for the last 5 years were as follows:
FRW’000’
1. 9,000
2. 6,000
3. 10,000
4. 8,000
5. 17,000
P/E ratio applicable is 12:1
Compute the value of the business indicating the lowest offer price and the highest offer price and
the share value thereof whether it would be viable to take on the three companies if its to maintain
this share value.
P/E RATIO METHOD
P/E = 12:1 Average profits = 10,000,000
Therefore Value of business = 10,000,000 x 12 = FRW120,000,000
Value of shares = FRW120 million = FRW24
5 million shares
ASSETS METHOD
FRW’000’
Assets 155,000
Less: Current liabilities [ 40,000]
115,000
Value of shares =FRW115M = FRW23
5M shares
6.3. VALUATION OF BONDS AND DEBENTURES
This will depend on expected cash flows consisting of annual interest plus the principal amount to
be received at maturity. The appropriate rate of capitalization or discount rate to be applied will
depend upon the riskiness of the bond e.g. government bonds are less risky and will therefore call
for lower discount rates than similar bonds issued by private companies which will call for high rate
of discount.

Valuation of bonds with maturity period

When a bond or debenture has reached maturity, its value can be determined by considering annual
interest payments plus its terminal or maturity and this is done using the P.V. concept to discount
the cash flows and the result will be compared to the market value of the bond to ascertain whether
it has overvalued or undervalued.

 (1  kd)
Int M

t
t 1
(1  kd)n
Where: Int = Annual interest
173 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
 Kd = Required rate of return
M = Terminal/maturity value
n = Number of years to maturity
Example
THP Co is planning to buy CRX Co, a company in the same business sector, and is considering
paying cash for the shares of the company. The cash would be raised by THP Co through a 1 for 3
rights issue at a 20% discount to its current share price.
The purchase price of the 1 million issued shares of CRX Co would be equal to the rights issue
funds raised, less issue costs of Frw320,000. Earnings per share of CRX Co at the time of
acquisition would be 44·8c per share. As a result of acquiring CRX Co, THP Co expects to gain
annual after-tax savings of Frw96,000.
THP Co maintains a payout ratio of 50% and earnings per share are currently 64c per share.
Dividend growth of 5% per year is expected for the foreseeable future and the company has a cost
of equity of 12% per year.
Information from THP Co’s statement of financial position:
Equity and liabilities Frw000
Shares (Frw1 par value) 3,000

Reserves
Non-current liabilities
8% loan notes 5,000
Current liabilities 2,200
Total equity and liabilities 14,500

Required
(a) Calculate the current ex dividend share price of THP Co and the current market
capitalisation of THP Co using the dividend growth model. (4 marks)
(b) Assuming the rights issue takes place and ignoring the proposed use of the funds raised,
calculate:
(i) the rights issue price per share;
(ii) the cash raised;
(iii) the theoretical ex rights price per share; and
(iv) the market capitalization of THP Co.
(c) Using the price/earnings ratio method, calculate the share price and market capitalisation of
CRX Co before the acquisition.
(d) Assuming a semi-strong form efficient capital market, calculate and comment on the post-
acquisition market capitalisation of THP Co in the following circumstances:
(i) THP Co does not announce the expected annual after-tax savings; and
(ii) the expected after-tax savings are made public.

174 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

(e) Discuss the factors that THP Co should consider, in its circumstances, in choosing between
equity finance and debt finance as a source of finance from which to make a cash offer for
CRX Co.
Solution
(a) p0 = d0(1 g)
ke g
d0 = 64c u 50% = 32c per share
g = 5% ke =
12%
0.32(1
Share price = = 4.80

Market capitalisation = Frw4.80 u 3m shares = Frw14.4m

(b) (i) Rights issue price per share = Frw4.80 u (1 – 20%) = Frw3.84
(ii) It is a 1 for 3 rights issue so number of new shares = 3m/3 = 1m
Cash raised = 1m u Frw3.84 = Frw3.84m
(iii) Theoretical ex-rights price = ((3 u Frw4.80) +Frw3.84)/4 = Frw4.56
(iv) Market capitalisation
Frwm
Market capitalisation from part (a) 14.4
Cash raised from rights issue 3.84
Issue costs (0.32)
17.92

The market capitalisation of THP Co after the rights issue is Frw17.92m, and the share
price is Frw17.92/4 = Frw4.48
(c) P/E ratio of THP Co = Share price/earnings per share
= 480/64
= 7.5
Earnings per share of CRX Co = 44.8c
Using the P/E ratio of THP Co:
Share price of CRX Co = 0.448 u 7.5 = Frw3.36
Market capitalisation = Frw3.36 u 1m shares = Frw3.36m
(d) (i) No announcement
In a semi-strong efficient capital market, current share process reflect all relevant
information about past price movements and all knowledge which is available
publicly. If the announcement is not made, the information in the expected savings will
not be reflected in the share price of THP Co.

175 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

 The market capitalisation of THP Co after the acquisition will therefore be equal to its
value after the rights issue plus the market capitalisation of CRX Co less cash paid to
buy CRX Co.
This amounts to:
Frw14.4m (from part a) + Frw3.36m ( from part c) = Frw17.76m
= Frw17.76m
This is equivalent to a share price of Frw4.44 (17.76/4). The market capitalisation has
fallen as, without the information on additional earnings, THP Co has apparently paid
Frw3.52m for a company that is only worth Frw3.36m.
(ii)An announcement is made
In a semi-strong form efficient capital market, the information will be reflected quickly
and accurately in the share price of THP Co.
The value of the business should increase by the present value of the annual after-tax
savings. A quick way to calculate this is to multiply the additional earnings by the P/E
ratio:
Frw96,000 x 7.5 = Frw0.72m
This gives a revised market capitalisation of Frw18.48m (17.76 + 0.72) which is
equivalent to a share price of Frw4.62 (18.48/4).
This makes the acquisition much more attractive to the shareholders of THP Co as their
shareholder wealth has increased. The capital gain on the shares is 14c per share (4.62
– 4.48).
This does however assume that the market has not already anticipated the savings
before they are actually announced.
(e) There are a number of factors to be considered in the choice between debt and equity finance.
Gearing and financial risk
Debt finance tends to be relatively low risk for the debtholder as it is interest-bearing and
can be secured. The cost of debt to a company is therefore relatively low. The greater the
proportion of debt, the more financial risk to the shareholders of the company so the higher
is their required return.
Financial risk can be measured by the gearing ratio. For THP, gearing is currently 68.5%
(5,000/7,300 x 100). If equity finance is used, this will decrease to 45% (5,000/(7,300 +
3,840) x 100%). If debt finance is used, gearing will increase to 121% ((5,000 + 3,840)/7,300
x 100).
The relative acceptability of these levels of gearing depends on THP’s desired level of
financial risk.
Objectives
If the primary financial objective of THP Co is to maximise shareholder wealth, it should
aim to minimise its WACC. This can be achieved by increasing the amount of debt in its
capital structure. The limit to this is the point at which gearing is so high that costs of
financial distress are incurred. For example, bankruptcy risk and restrictive covenants
imposed by debt providers.
Security

176 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

 The choice of finance may be determined by the assets the business is willing or able to offer
as security. This can be in the form of a fixed charge on specific assets, or a floating charge
on a class of assets. More information would be needed on the availability of such assets.
Investors are likely to expect a higher return on unsecured debt to compensate them for the
extra risk.
Expectations
If economic conditions are buoyant, THP Co will be more willing to take on extra debt and
commitment to pay interest than if business is suffering in an economic downturn. Lenders
are also likely to be more cautious and less willing to lend if the economy is struggling.
Control
A key advantage of debt finance for a company’s shareholders is that existing shareholdings
will not be diluted. Debt providers may however impose covenants restricting dividend
payment.
A rights issue will also not dilute existing patterns of ownership and control provided
existing shareholders take up their rights. If the amount of new equity finance required is
sufficiently large, new shares may be issued to new investors, for example in a placing, and
this will dilute existing shareholdings.

Example 1:
MC provides a range of services to the medical and healthcare industry. These services include
providing locum (temporary) cover for healthcare professionals (mainly doctors and nurses),
emergency call-out and consultancy/advisory services to government-funded health organisations.
The company also operates a research division that has been successful in recent years in attracting
funding from various sources. Some of the employees in this division are considered to be leading
experts in their field and are very highly paid.
A consortium of doctors and redundant health-service managers started the company some years
ago. It is still owned by the same people, but has since grown into an organisation employing over
100 full-time staff throughout the UK. In addition, the company uses specialist staff employed in
state-run organisations on a part-time contract basis. The owners of the company are now interested
in either obtaining a stock market quotation, or selling the company if the price accurately reflects
what they believe to be the true worth of the business.
Summary financial statistics for MC and a competitor company, which is listed on the UK Stock
Exchange, are shown below. The competitor company is broadly similar to MC but uses a higher
proportion of part-time to fulltime staff and has no research capability.
MC Competitor
Last year end: Last year
end:
31.3.20X0 31.3.20X0
Shares in issue (m) 10 20
Earnings per share (pence) 75 60
Dividend per share (pence) 55 50
Net asset value (Frwm) 60 75
Debt ratio (outstanding debt as % of total financing) 10 20
177 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
Share price (pence) N/A 980
Expected rate of growth in earnings and dividends (% per 8 7
annum)
Notes
1 The treasurer of the company has provided the forecast growth rate for MC. The forecast for
the competitor is based on published information.
2 The net assets of MC are the net book values of land, buildings, equipment and vehicles plus
net working capital.
3 Sixty per cent of the shares in the competitor company are owned by the directors and their
relatives or associates.
4 MC uses a 'rule-of-thumb' discount rate of 15% to evaluate its investments. The cost of equity
of the competitor has been calculated to be 13%.
5 Assume that growth rates in earnings and dividends are constant per annum.
Required
Assume that you are an independent consultant retained by MC to advise on the valuation of the
company and on the relative advantages of a public flotation versus outright sale.
Prepare a report for the directors that:
(a) Produces a range of share prices at which shares in MC might be issued. Use whatever
information is available. Explain the methods of valuation that you have used and discuss their
suitability for providing appropriate valuation of the company.
(b) Discusses the relative advantages of flotation and direct sale of shares.
(c) Recommends a course of action that the company should take.
Solution :
To: Board of Directors, MC
From: Independent Consultant
Date: 31 December 20X0
Re: Valuation of MC
Introduction
This report deals with the alternative methods available for the valuation of the shares in the
company. It also seeks to highlight some of the key issues to be addressed in arriving at an
appropriate valuation for this type of company, and looks at the relative merits of public flotation
versus an outright sale of the business.
(a) Company valuation
There are three main valuation techniques that could be appropriate in this
situation:
1) Net assets basis
2) Price/earnings ratio
3) Dividend valuation model
These will be discussed in more detail below.

178 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

 (i) Net assets basis
The net asset value of MC is Frw60m or Frw6 per share.
This method is most commonly used to arrive at a break-up value for businesses with a
significant amount of non-current assets. However, it is less appropriate for service
businesses, and in particular for those in which the majority of the value is in the form
of human and/or intellectual capital. In the latter type of company, a net assets valuation
can be attempted if the intangibles are included as assets in the balance sheet. However,
a significant part of the value of MC resides in its research division, and this is not
reflected at all in the company's present balance sheet.
Although it could be argued that items such as brands should be included in the balance
sheet so as to make the market more aware of the true value of the company, in reality it
is extremely difficult both to arrive at and to retain an appropriate measure of these
types of items.
A further argument against the incorporation of this type of intangible is that if the
company is publicly quoted, and if the market shows semi-strong or strong form
efficiency, then the market price of the shares should reflect this information in any
case.
In view of these points, there is little point in attempting a net assets valuation for MC at
the present time. The inappropriateness of this can be illustrated with reference to the
competitor, which would have a theoretical net assets based valuation of Frw75m as
compared with a market capitalisation of Frw196m (Frw9.80 share price u 20m shares
in issue).
(ii) Price/earnings ratio
This method compares the earnings information of the company with that of other
companies of similar size and characteristics that operate in the same markets, to arrive
at an appropriate market price for the shares. The information that has been provided for
the quoted competitor will be used to arrive at an initial price, but this will need to be
adjusted to reflect the fact that the competitor lacks MC's research capability.
The price/earnings (P/E) ratio is calculated by dividing the market price of the
shares by the earnings per share. The competitor has a P/E ratio of 16.3 (980p/60p).
Although this is likely to be above the average for quoted industrial companies as a
whole, it does not appear to be unreasonably high for the medical sector. Given that MC
is forecasting better growth prospects than the competitor, and also has a research
capability, it seems reasonable to value the company on a P/E of around 18 times. This
would value MC at Frw135m (18 u 75p u 10m shares in issue).
However, if the shares were to be offered on the open market, it would be prudent to
price them at a discount to this to reflect the fact that the company would be a new
entrant to the stock market, despite an eleven year trading history. Pricing at a discount
will also make the issue more attractive to investors and thereby help to obtain a good
take-up of shares.
Valuation on a P/E of 18 implies a price of Frw13.50 per share. If the shares were to be
offered at a discount of, say, 15%, this would result in an offer price of around
Frw11.50 per share, and a market capitalisation of Frw115m.
(iii) Dividend valuation model

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 The dividend valuation model has the central assumption that the market value of
shares is directly related to the expected future dividends on those shares. It can be
expressed as:
d0(1 g)
P0 = (ke g)
Since the shares are not yet quoted, it is not possible to say exactly what the
shareholders' net cost of capital is likely to be. However, it might be reasonable to use
the competitor's cost of equity of 13% for an initial estimate. This is better than using
the 'rule of thumb' discount rate of 15%, as MC has a lower financial risk than the
competitor (the debt ratio is much lower) and a higher dividend per share and growth
rate.
This cost of equity can now be used in the dividend valuation model to estimate the
market value of
MC:
d0 (1 g)
P0 =
(ke g)

P0 =
P0 = Frw118.8m
The dividend valuation model values the company at Frw118.8m, or Frw11.88 per
share. This assumes a growth rate of 8%. However, in reality, the potential growth rate
may be higher since the company is currently evaluating investments at a discount rate
that is above the estimated cost of capital. This means that it may be turning down
investments that would in fact add value to the company and hence result in higher
dividends and a higher growth rate.
(b) The relative advantages of flotation and direct sale
The following points should be considered when deciding which option is to be preferred.
(i) Aims of existing owners
The aims of the existing owners are important in determining the best course of action.
If a significant number of the existing consortium wish to maintain control over the
business in the future, then they are more likely to be able to achieve this if the company
is floated rather than sold.
(ii) Market for shares
Flotation will create a wider market for the company's shares. This has the twin
benefits that it will be easier for the company to raise additional capital to finance
expansion, and that the existing shareholders will be able to realise all or part of their
holding. However, if MC is to achieve a good price, the existing owners should aim to
retain the major part of their holding for a reasonable period following the flotation.
(iii) Share option schemes

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 Flotation will allow the company to offer share option schemes to its employees, which
should assist in the recruitment and retention of good staff. This is particularly
important in a company such as MC, where a significant part of the value in the
company is linked to the knowledge base and research capability. Retaining a high
proportion of the key staff will be vital to the success of any change in ownership, and
must be taken into account in the structuring of either the sale or the flotation.
(iv) Costs of flotation
Flotation will be an expensive process and will mean that the company has to comply
with the stringent Stock Exchange regulations. It will put extra administrative burdens
on the management and will cost more to organise than would a direct sale of the
business.
(c) Conclusions and recommendations
(i) Sale price
The calculations suggest that the company should achieve a sale price of at least
Frw120m. This compares with a market capitalisation of the competitor of Frw196m.
Since MC has better growth prospects and also has a research base, which the
competitor lacks, it may be able to achieve a better price than this, but Frw120m should
be regarded as the base price in any negotiations.
(ii) Stock market quotation
It is also recommended that the company should opt for a Stock Market quotation rather than for
a direct sale. Given the current state of the market for this type of stock, it should be able to achieve
a good price, and flotation will also give flexibility to the owners in allowing them to realise a part
of their investment, while at the same time retaining control over the future direction of the
business.
Example
K is contemplating purchasing a 3 year bond worth 40,000/= carrying a nominal coupon rate of
interest of 10%. K required rate of return is 6%.
What should he be willing to pay now to purchase the bond if it matures at par?
Example

BST Motors Co (BST) is a long-established listed company. Its main business is the retailing of
new and used motor cars and the provision of after-sales service. It has sales outlets in most of the
major towns and cities in the country. It also owns a substantial amount of land and property that it
has acquired over the years, much of which it rents or leases on medium-long term agreements.
Approximately 80% of its net current asset value is land and buildings.
The company has grown organically for the last few years but is now considering expanding by
acquisition.
SM owns a number of car showrooms in wealthy, semi-rural locations. All of these showrooms
operate the franchise of a well-known major motor manufacturer. SM is a long-established private
company with the majority of shares owned by the founding family, many of whom still work for
the company. The major shareholders are now considering selling the business if a suitable price
can be agreed. The Managing Director of SM, who is a major shareholder, has approached BST to
see if they would be interested in buying SM. He has implied that holders of up to 50% of SM's
shares might be willing to accept BST shares as part of the deal.
181 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
The forecast earnings of BST for the next financial year are Frw35 million. According to the
Managing Director of SM, his company's earnings are expected to be Frw4 million for the next
financial year.
Financial statistics and other information on BST and SM are shown below:
BST SM
Shares in issue (millions) 25 1.5
Earnings per share (cents) 112.5 153
Dividend per share (cents) 50.6 100
Share price (cents) 1237 N/A
Net asset value attributable to equity (Frwm) 350 45
Debt ratio (outstanding debt as percentage of total market value of 20 0
company)
Forecast growth rate percentage (constant, annualised) 4 5
Cost of equity 9% N/A
SM does not calculate a cost of equity, but the industry average for similar companies is
10% Required
Assume you are a financial manager working with BST. Advise the BST Board on the following
issues in connection with a possible bid for SM:
(a) Methods of valuation that might be appropriate and a range of valuations
for SM within which BST should be prepared to negotiate.
(b) The financial factors relating to both companies that might affect the bid.
(c) Explain the practical considerations in the valuation of shares and
businesses.

Solution 2
(a)Methods of valuation and range of values for SM
Net assets
The book value of SM's net assets attributable to equity shareholders is Frw45 million.
This figure may need to be adjusted for increased or decreased market values of assets,
particularly SM's property holding. However in any case, for a going concern, the book value
of assets is a poor indicator of their economic value, which depends on their income-
generating capacity, rather than their historical cost or realisable value. Here also SM has a
franchise generating earnings that will not be reflected in the balance sheet.
Price/earnings model
SM's existing earnings per share is Frw1.53, and number of shares is 1.5 million, giving total
equity earnings of Frw2.295 million. Taking the 5% growth figure given, next year's earnings
would be Frw2.410 million. However, the managing director is estimating Frw4 million for
next year. This figure cannot be accepted at face value and would need to be substantiated.
In the absence of any better information, BST's P/E ratio could be applied to these earnings
figures. This is 1237/112.5 = 10.996, say 11.

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 The range of values for SM's valuation would be between Frw2.410 million × 11 and Frw4
million × 11 ie between Frw26.5 million and Frw44 million.
This valuation is dependent upon the P/E ratio. Arguably a lower ratio should be used as SM
is unquoted, but it is difficult to say how much lower. Also BST's ratio may not be typical of
the industry.
Dividend valuation model
Again there is a range of values depending on whether the MD's forecast earnings are
believed.
Last year's total dividends were 1.5m × 100 cents = Frw1.5 m. A 5% increase next year would
give Frw1.575 million. The cost of equity for similar firms is 10% and the expected growth
rate 5%.
So on this basis the expected company value = Frw1.575m/(0.1 – 0.05) = Frw31.5 million.
SM 's dividend payout ratio (dividend/earnings) is 100 /153 = 0.654.
Based on the MD's forecast earnings of Frw4 million, next year's dividend would be Frw4m ×
0.654 = Frw2.616 million.
The forecast company value would be Frw2.616 million/(0.1 – 0.05) = Frw52.3 million.
The drawbacks of this method are:
(i) The assumption that SM's cost of equity is the same as similar firms may be
misleading.
(ii) The assumption of constant dividend growth at that rate may be misleading.
Dividend policy may change on takeover.
(iii) Share price is not normally just a function of dividend policy; future expected
earnings are also a key factor.
Summary
Based on valuation of assets and income earning capacity, SM appears to have a value
anywhere between Frw25 million and Frwrw52 million. The higher earnings-based figures
are heavily dependent on the MD's forecast of next year's earnings that may well be
overstated. Because the net asset value is towards the top end of the valuation range, BST
could probably look at a value of between Frw40 million and Frw45 million, but will need
to carry out further investigations on likely asset values.
(b) Financial factors that may affect the bid
Financial factors relating to BST
(i) Like SM, the forecast of next year's earnings may be overstated. Current earnings =
Frw1.125 × 25 million = Frw28.125 million. 4% growth (given) gives Frw29.25
million, but BST's forecast for next year is Frw35 million.
(ii) The total market value of the company's shares is below the net asset value.25m
shares × Frw12.37 = Frw309.25.m that is below the Frw350m net asset value. This may
indicate that the company possesses under-utilised assets, or alternatively that its assets
are overstated in value. On the face of it, the company would be better broken up than
operating as a going concern. All these factors will be of interest to any of SM's

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 shareholders who would be considering receiving BST shares. It will also interest the
market and BST's low market value may mean that it becomes a takeover target itself.
(iii) BST has a fairly high gearing ratio. If BST lacks cash and has to borrow more in order
to buy out those 50%+ shareholders of SM who do not wish to have BST shares, this
may have the effect of increasing the company's cost of capital.
(iv) BST has a lower dividend payout ratio than SM. This may discourage some of SM's
shareholders from accepting BST's shares.
(v) Strategically it is unclear why BST is buying SM; whilst BST may be trying to
diversify, SM may not be a big enough acquisition to make it worth diversifying. There
may be better investment opportunities.
Relevant financial factors relating to SM
(i) Next year's forecast earnings may be overstated. However, some of the directors may
be taking higher salaries than realistic market levels, and the ongoing future
profitability of the company may be higher if these people are replaced with lower cost
managers.
(ii) Like BST, asset value is high. The net asset valuation is in fact higher than some of the
other valuations, and SM's shareholders are unlikely to accept an offer below net asset
value.
(iii) The company is ungeared, which is advantageous, as it enables BST to borrow to fund
part of the acquisition.
(iv) The 'quality' of SM's earnings is probably higher than BST's, as it operates in up-
market areas.
(v) Selling SM to a listed company represents a good way for SM's shareholders to realise
the value of their investment. However, many of the shareholders are likely to lose
their jobs and may find it difficult to find equivalent positions. The bid may therefore be
opposed by a substantial number of shareholders.
(vi) There are likely to be many areas where costs can be saved as a result of the acquisition
of SM. This may make it worthwhile for BST to pay a higher price for SM.
(vii) BST is likely to have good access to SM's business documentation as SM has
contacted BST. This should enable BST to calculate a more accurate valuation.
(c) The fundamental theory of share values states that the realistic market price of a share can
be derived from a valuation of estimated future dividends. The value of a share will be the
discounted present value of all future expected dividends on the shares, discounted at the
shareholders' cost of capital.
If the fundamental analysis theory of share values is correct, the price of any share will be
predictable, provided that all investors have the same information about a company's
expected future profits and dividends, and a known cost of capital.
However, share prices are also affected by a number of other factors.
Marketability and liquidity of shares

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 In financial markets, liquidity is the ease of dealing in the shares, how easily can the shares
can be bought and sold without significantly moving the price?
In general, large companies, with hundreds of millions of shares in issue, and high numbers of
shares changing hands every day, have good liquidity. In contrast, small companies with few
shares in issue and thin trading volumes, can have very poor liquidity.
The marketability of shares in a private company, particularly a minority shareholding, is
generally very limited, a consequence being that the price can be difficult to determine.
Shares with restricted marketability may be subject to sudden and large falls in value and
companies may act to improve the marketability of their shares with a stock split. A stock
split occurs where, for example, each ordinary share of Frw1 each is split into two shares of
50c each, thus creating cheaper shares with greater marketability. There is possibly an
added psychological advantage, in that investors may expect a company which splits its
shares in this way to be planning for substantial earnings growth and dividend growth in the
future.
As a consequence, the market price of shares may benefit. For example, if one existing share
of Frw1 has a market value of Frw6, and is then split into two shares of 50c each, the market
value of the new shares might settle at, say, Frw3.10 instead of the expected Frw3, in
anticipation of strong future growth in earnings and dividends.
Availability and sources of information
An efficient market is one where the prices of securities bought and sold reflect all the
relevant information available. Efficiency relates to how quickly and how accurately prices
adjust to new information. Information comes from financial statements, financial databases,
the financial press and the internet.
It has been argued that shareholders see dividend decisions as passing on new information
about the company and its prospects. A dividend increase is usually seen by markets to be
good news and a dividend decrease to be bad news, but it may be that the market will react to
the difference between the actual dividend payments and the market's expectations of the
level of dividend. For example, the market may be expecting a cut in dividend but if the
actual decrease is less than expected, the share price may rise.
Market imperfections and pricing anomalies
Various types of anomaly appear to support the views that irrationality often drives the stock
market, including the following.
x Seasonal month-of-the-year effects, day-of-the-week effects and also hour-of-the-day
effects seem to occur, so that share prices might tend to rise or fall at a particular time of
the year, week or day.
x There may be a short-run overreaction to recent events. For example, the stock market
crash in 1987 when the market went into a free fall, losing 20% in a few hours.
x Individual shares or shares in small companies may be neglected.
Market capitalisation
The market capitalisation or size of a company has also produced some pricing anomalies.
The return from investing in smaller companies has been shown to be greater than the
average return from all companies in the long run. This increased return may compensate for
the greater risk associated with smaller companies, or it may be due to a start from a lower
base.
185 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
 Investor speculation
Speculation by investors and market sentiment is a major factor in the behaviour of share
prices. Behavioural finance is an alternative view to the efficient market hypothesis. It
attempts to explain the market implications of the psychological factors behind investor
decisions and suggests that irrational investor behaviour may significantly affect share
price movements. These factors may explain why share prices appear sometimes to over-react
to past price changes.

Example 2
(a) Phobis Co is considering a bid for Danoca Co. Both companies are stock-market listed and
are in the same business sector. Financial information on Danoca Co, which is shortly to pay
its annual dividend, is as follows:
Number of ordinary shares 5
million
Ordinary share price (ex div basis) Frw3·30
Earnings per share 40·0c
Proposed payout ratio 60%
Dividend per share one year ago 23·3c
Dividend per share two years ago 22·0c
Equity beta 1·4

Other relevant financial information

Average sector price/earnings ratio 10
Risk-free rate of return 4·6%
Return on the market 10·6%
Required
Calculate the value of Danoca Co using the following methods.
(i) price/earnings ratio method; (ii) dividend growth model;
and discuss the significance, to Phobis Co, of the values you have calculated, in comparison
to the current
market value of Danoca Co. (11 marks)
(b) Phobis Co has in issue 9% bonds which are redeemable at their par value of Frw100 in five
years’ time. Alternatively, each bond may be converted on that date into 20 ordinary shares of
the company. The current ordinary share price of Phobis Co is Frw4·45 and this is expected to
grow at a rate of 6·5% per year for the foreseeable future. Phobis Co has a cost of debt of 7%
per year.
Required
Calculate the following current values for each Frw100 convertible bond:
(i) market value;
(ii) floor value;
(iii) conversion premium. (6 marks)
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(c) Distinguish between weak form, semi-strong form and strong form stock market efficiency,
and discuss the significance to a listed company if the stock market on which its shares are
traded is shown to be semi-
strong form efficient. (8 marks)
solution :
(a) (i) Price/earnings ratio method of valuation
Market value = P/E ratio × EPS
EPS = 40.0c
Average sector P/E ratio = 10
Value of shares = 40.0 × 10 = Frw4.00 per share
Number of shares = 5 million
Value of Danoca Co = Frw20 million
(ii)Dividend growth model method of valuation
Do (1 g)
Po = .
Ke g
Note: The formula sheet in this exam uses re instead of ke
D0 can be found using the proposed payout ratio of 60%.
D0 = 60% × 40c = 24c
2
Proposeddividend
(1 + g) =
Dividendtwo yearsago

(1 + g)2 =
2
1 + g = 1.091 1.045 g =
4.5%
ke = re = E(ri) = Rf + Ei(E(rm) – Rf)
= 4.6 + (1.4 × (10.6 – 4.6))
= 4.6 + (1.4 × 6)
= 13%
0.
Value of shares =

= Frw2.95
Value of Danoca Co = Frw14.75 million

Discussion of the values calculated

P/E ratio

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 The current share price of Danoca is Frw3.30 which equates to a P/E ratio of 8.25
(3.30/0.4). This is lower than the average sector P/E ratio of 10 which suggests that the
market does not view the growth prospects of Danoca as favourably as an average
company in that business sector.
This implies that an acquisition by Phobis could result in improved financial
performance of Danoca, assuming that Phobis has the competences and skills to
transfer to Danoca.
Dividend growth
The dividend growth model method of valuation resulted in a value of Frw14.75m
which is lower than the current market capitalisation of Danoca of Frw16.5m (Frw3.30
× 5m). The current share price may be artificially high due to bid rumours but
shareholders are unlikely to accept a valuation much lower than this.
The dividend growth model uses an estimated expected growth rate and a calculated
cost of equity, both of which are subject to error.
The model assumes that investors act rationally and homogenously and this may not
be true. Shareholders may have different expectations and the stock market may not be
completely efficient, both of which will make this method of valuation less reliable.
(b) (i) Dividend growth model method of valuation Conversion value =
P0(1 + g)nR where P0 = current ex-dividend ordinary share price = 4.45 g =
expected annual growth of the ordinary share price = 6.5% n = number of
years to conversion = 5
R = number of shares received on conversion = 20
Conversion value = 4.45 × (1 + 0.065)5 × 20
= Frw122
The conversion value is higher than the redemption value of Frw100 so conversion is
expected.
The current market value is the sum of the present value of the future interest payments
and the present value of the bond’s conversion value.
Present value of Frw9 interest per annum for five years at 7% = 9 × 4.100 = Frw36.90
Present value of the conversion value = 122.00 × 0.713 = Frw86.99
Current market value of convertible bond = 36.90 + 86.99 = Frw123.89
(ii) Floor value
The floor value is the sum of the present value of the future interest payments and the
present value of the redemption value.
Present value of Frw9 interest per annum for five years at 7% = 9 × 4.100 = Frw36.90
Present value of the redemption value = 100.00 × 0.713 = Frw71.30
Floor value of convertible bond = 36.90 + 71.30 = Frw108.20
(iii) Conversion premium
Conversion premium = current market value – current conversion value

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 Current conversion value = Frw4.45 × 20 =
Frw89.00 Current market value = Frw123.89
Conversion premium = 123.89 – 89.00 = Frw34.89
As an amount per share = 34.89/20 = Frw1.75
(c) Stock market efficiency
If a stock market is efficient, share prices should vary in a rational way and will reflect the
amount of relevant information that is available. The efficient market hypothesis
identifies three forms of efficiency; weak, semi-strong and strong.
Weak form efficiency
Under the weak form hypothesis of market efficiency, share prices reflect all available
information about past changes in the share price.
Since new information arrives unexpectedly, changes in share prices should occur in a
random fashion. If it is correct, then using technical analysis to study past share price
movements will not give anyone an advantage, because the information they use to predict
share prices is already reflected in the share price.
Semi-strong form efficiency
If a stock market displays semi-strong efficiency, current share prices reflect both:
x All relevant information about past price movements and their
implications, and x All knowledge which is available publicly
This means that individuals cannot 'beat the market' by reading the newspapers or annual
reports, since the information contained in these will be reflected in the share price.
Stock markets are usually presumed to be semi-strong efficient.
Strong form efficiency
If a stock market displays a strong form of efficiency, share prices reflect all information
whether publicly available or not:
x From past price changes x
From public knowledge or anticipation
x From specialists' or experts' insider knowledge (eg investment managers)
Significance to a listed company of semi-strong efficiency
The main consequence for financial managers will be that they simply need to concentrate on
maximising the net present value of the company's investments in order to maximise the
wealth of shareholders. Managers need not worry, for example, about the effect on share
prices of financial results in the published accounts because investors will make allowances
for low profits or dividends in the current year if higher profits or dividends are expected in
the future.
There is little point in financial managers attempting strategies that will attempt to mislead the
markets. There is no point for example in trying to identify a correct date when shares should
be issued, since share prices will always reflect the true worth of the company.
The market will identify any attempts to window dress the accounts and put an optimistic
spin on the figures.

189 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

OTHER PRACTICE QUESTIONS
QN 1
Dartinga Co is a stock-market listed company that manufactures consumer products and it is
planning to expand its existing business. The investment cost of Frw5 million will be met by a 1 for
4 rights issue. The current share price of Dartinga Co is Frw2·50 per share and the rights issue price
will be at a 20% discount to this. The finance director of Dartinga Co expects that the expansion of
existing business will allow the average growth rate of earnings per share over the last four years to
be maintained into the foreseeable future.
The earnings per share and dividends paid by Dartinga over the last four years are as follows:
20X3 20X4 20X5 20X 20X7
Earnings per share27.7 29.0 29.0 30.2 32.4
(cents)
Dividend per share12.8 13.5 13.5 14.5 15.0
(cents)
Dartinga Co has a cost of equity of 10%. The price/earnings ratio of Dartinga Co has been
approximately constant in recent years. Ignore issue costs. Required
(a) Calculate the theoretical ex rights price per share prior to investing in the proposed business
expansion.
(b) Calculate the expected share price following the proposed business expansion using the
price/earnings ratio method.
(c) Discuss whether the proposed business expansion is an acceptable use of the finance raised by
the rights issue, and evaluate the expected effect on the wealth of the shareholders of Dartinga
Co.
(d) Using the information provided, calculate the ex div share price predicted by the dividend
growth model and discuss briefly why this share price differs from the current market price of
Dartinga Co.
At a recent board meeting of Dartinga Co, a non-executive director suggested that the company’s
remuneration committee should consider scrapping the company’s current share option scheme,
since executive directors could be rewarded by the scheme even when they did not perform well. A
second non-executive director disagreed, saying the problem was that even when directors acted in
ways which decreased the agency problem, they might not be rewarded by the share option scheme
if the stock market were in decline.
Required
Explain the nature of the agency problem and discuss the use of share option schemes as a way of
reducing the agency problem in a stock-market listed company such as Dartinga Co.

190 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

TOPIC 8: CORPORATE DIVIDNED POLICY AND STRATEGIES

1. INTRODUCTION

The financial manager must take careful decisions on how the profit should be distributed among
shareholders. It is very important and crucial part of the business concern, because these decisions
are directly related with the value of the business concern and shareholder’s wealth. Like financing
decision and investment decision, dividend decision is also a major part of the financial manager.
When the business concerns decide dividend policy, they have to consider certain factors such as
retained earnings and the nature of shareholder of the business concern.

2. Meaning of Dividend

Dividend refers to the business concerns net profits distributed among the shareholders. It may also
be termed as the part of the profit of a business concern, which is distributed among its
shareholders. According to the Institute of Chartered Accountant of India, dividend is defined as
“a distribution to shareholders out of profits or reserves available for this purpose”.

3. TYPES OF DIVIDEND/FORM OF DIVIDEND

Dividend may be distributed among the shareholders in the form of cash or stock. Hence,
Dividends are classified into:

i)Cash Dividend
If the dividend is paid in the form of cash to the shareholders, it is called cash dividend. It is paid
periodically out the business concerns EAIT (Earnings after interest and tax). Cash dividends are
common and popular types followed by majority of the business concerns.
ii) Stock Dividend
Stock dividend is paid in the form of the company stock due to raising of more finance. Under this
type, cash is retained by the business concern. Stock dividend may be bonus issue. This issue is
given only to the existing shareholders of the business concern.
iii)Bond Dividend
Bond dividend is also known as script dividend. If the company does not have sufficient funds to
pay cash dividend, the company promises to pay the shareholder at a future specific date with the
help of issue of bond or notes.
Iv) Property Dividend
Property dividends are paid in the form of some assets other than cash It will distribute under the
exceptional circumstance.

4. DIVIDEND POLICIES AND DECISIONS

Dividend decision of the business concern is one of the crucial parts of the financial manager,
because it determines the amount of profit to be distributed among shareholders and amount of
profit to be treated as retained earnings for financing its long term growth. Hence, dividend decision
plays very important part in the financial management. Dividend decision consists of two important
191 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
concepts which are based on the relationship between dividend decision and value of the firm.
Dividend policy determines the division of earnings between payment to stock holders and re-
investment in the firm. It therefore looks at the following aspects:

i).How much to pay – this encompassed in the four major alternative dividend policies.

 Constant Amount Of Dividend Per Share

 Constant Payout Ratio
 Fixed Dividend Plus Extra
 Residual Dividend Policy

ii)When to pay – paying interim or final dividends

iii)Why dividends are paid – this is explained by the various theories which has to determine the
relevance of dividend payment i.e.:
 Residual dividend theory
 Dividend irrelevance theory (MM)
 Signaling theory
 Bird in hand theory
 Clientele theory
 Agency theory

iv)How to pay: cash or stock dividends.

Dividends decisions are integral part of a firm’s strategic financing decision. It is therefore a plan
of action adopted by management e.g payment of high dividends means less retained earnings and
the firm may have to go to the market to borrow for investment purposes. This will increase its
gearing level.

Solution to the Dividend Puzzle

A firm’s dividend decision may have some relevance to the firm’s share value. The managers
therefore require formulating an optimal dividend policy which will maximize the wealth of the
shareholders (value of shares).

i) HOW MUCH TO PAY: ALTERNATIVE DIVIDENDS POLICIES

a) Constant payout ratio
This is where the firm will pay a fixed dividend rate e.g. 40% of earnings. The DPS would
therefore fluctuate as the earnings per share changes. Dividends are directly dependent on the firms
earnings ability and if no profits are made no dividend is paid. This policy creates uncertainty to
ordinary shareholders especially who rely on dividend income and they might demand a higher
required rate of return.

b) Constant amount per share (fixed D.P.S.)

The DPS is fixed in amount irrespective of the earnings level. This creates certainty and is
therefore preferred by shareholders who have a high reliance on dividend income. It protects the
firm from periods of low earnings by fixing, DPS at a low level. This policy treats all shareholders
192 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
like preferred shareholders by giving a fixed return. The DPS could be increased to a higher level if
earnings appear relatively permanent and sustainable.

c) Constant DPS plus Extra/Surplus

Under this policy a constant DPS is paid every year. However extra dividends are paid in years of
supernormal earnings. It gives the firm flexibility to increase dividends when earnings are high and
the shareholders are given a chance to participate in super normal earnings

The extra dividend is given in such a way that it is not perceived as a commitments by the firm to
continue the extra dividend in the future. It is applied by the firms whose earnings are highly
volatile e.g. agricultural sector.

d) Residual dividend policy

Under this policy dividend is paid out of earnings left over after investment decisions have been
financed. Dividend will only be paid if there are no profitable investment opportunities available.
The policy is consistent with shareholders wealth maximization.

ii) WHEN TO PAY

Firms pay interim or final dividends. Interim dividends are paid at the middle of the year and are
paid in cash .Final dividends are paid at year end and can be in cash or bonus issue.

iii) DIVIDENDS THEORIES (WHY PAY DIVIDENDS)

The main theories are:

1. Residual dividend theory

Under this theory, a firm will pay dividends from residual earnings i.e. earnings remaining
after all suitable projects with positive NPV has been financed. It assumes that a retained
earnings is the best source of long term capital since it is readily available and cheap. This is
because no floatation cash are involved in use of retained earnings to finance new
investments. Therefore, the first claim on earnings after tax and prefere M-M's Proof of the
dividend irrelevancy

Let Po be share price at time t0

P1 be share price at time t1
D1 be dividend per share at time t1
N be number of share at time t0
M be number of new shares at time t0
I be total value of new investment
X be net income at period t1
Ke be cost of equity capital

Using the dividend yield model, the value of a share in time t0 will be
+
PO = D1 P1
(1 + Ke)

The value of the firm will be

193 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021

 +
NPO = ND1 NP1
(1 + Ke)

If M additional shares are sold at period t1 then

+ + -
NPO = ND1 NP1 MP1 MP1
(1 + Ke)
= ND1 + (N + M ) P1 - MP1
(1 + Ke)

If no debt is used then the sources of funds will be equal to the uses of fund.

MP1 + X = I + ND1
MP1 = I + ND1 - X

If we substitute MP1 in the above equation, then

+ (N + M ) - (I + - X)
NPO = ND1 P1 ND1 (1 +
Ke)

= (N + M ) P1 - I + X
(1 + Ke)

Since D1 does not appear, then the dividend decision has no value in determining the value of the firm.
nce dividends will be a reserve for financing investments. Dividend policy is irrelevant and treated
as passive variable. It will not affect the value of the firm. However, investment decisions will.

Advantages of Residual Theory

1. Saving on floatation costs
No need to raise debt or equity capital since there is high retention of earnings which requires no
floatation costs.
2. Avoidance of dilution of ownership
New equity issue would dilute ownership and control. This will be avoided if retention is high.
A high retention policy may enable financing of firms with rapid and high rate of growth.

3. Tax position of shareholders

High-income shareholders prefer low dividends to reduce their tax burden on dividends income.
They prefer high retention of earnings which are reinvested, increase share value and they can gain
capital gains which are not taxable in Kenya.

ii) MM Dividend Irrelevance Theory

Was advanced by Modiglian and Miller in 1961. The theory asserts that a firm’s dividend policy
has no effect on its market value and cost of capital.
They argued that the firm’s value is primarily determined by:
 Ability to generate earnings from investments
 Level of business and financial risk
194 | CPA LEVEL II – MANAGERIAL FINANCE -REVISION NOTES 2021
According to MM dividend policy is a passive residue determined by the firm’s need for investment
funds. It does not matter how the earnings are divided between dividend payment to shareholders
and retention. Therefore, optimal dividend policy does not exist. Since when investment decisions
of the firms are given, dividend decision is a mere detail without any effect on the value of the firm.
They base on their arguments on the following assumptions:
1. No corporate or personal kites
2. No transaction cost associated with share floatation
3. A firm has an investment policy which is independent of its dividend policy (a fixed
investment policy)
4. Efficient market – all investors have same set of information regarding the future of the firm
5. No uncertainty – all investors make decisions using the same discounting rate at all time i.e
required rate of return (r) = cost of capital (k).

Criticism of MM approach
The following are the major criticisms of MM approach:
 MM approach assumes that tax does not exist. It is not applicable in the practical life of the
firm.
 MM approach assumes that, there is no risk and uncertain of the investment. It is also not
applicable in present day business life.
 MM approach does not consider floatation cost and transaction cost. It leads to affect the
value of the firm.
 MM approach considers only single decrement rate, it does not exist in real practice.
 MM approach assumes that, investor behaves rationally. But we cannot give assurance that
all the investors will behave rationally.

iii) Bird-in-hand theory

Advanced by John Litner (1962) and furthered by Myron Gordon (1963). Argues that shareholders
are risk averse and prefer certainty. Dividends payments are more certain than capital gains which
rely on demand and supply forces to determine share prices. Therefore, one bird in hand (certain
dividends) is better than two birds in the bush (uncertain capital gains). Therefore, a firm paying
high dividends (certain) will have higher value since shareholders will require to use lower
discounting rate.

Myron Gorden suggests one of the popular model which assume that dividend policy of a firm
affects its value, and it is based on the following important assumptions:
1. The firm is an all equity firm.
2. The firm has no external finance.
3. Cost of capital and return are constant.
4. The firm has perpetual life.
5. There are no taxes.
6. Cost of capital is greater than growth rate

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Criticism of Gordon’s Model

Gordon’s model consists of the following important criticisms:

 Gordon model assumes that there is no debt and equity finance used by the firm. It is not
applicable to present day business.
 Ke and r cannot be constant in the real practice.
 According to Gordon’s model, there is no tax paid by the firm. It is not practically
applicable.

MM argued against the above proposition: They argued that the required rate of return is
independent of dividend policy. They maintained that an investor can realize capital gains generated
by reinvestment of retained earnings, if they sell shares. If this is possible, investors would be
indifferent between cash dividends and capital gains.

iv) Information signaling effect theory

Advanced by Stephen Ross in 1977. He argued that in an inefficient market, management can use
dividend policy to signal important information to the market which is only known to them.

Example – If the management pays high dividends, it signals high expected profits in future to
maintain the high dividend level. This would increase the share price/value and vice versa.

MM attacked this position and suggested that the change in share price following the change in
dividend amount is due to informational content of dividend policy rather than dividend policy
itself. Therefore, dividends are irrelevant if information can be given to the market to all players.
Dividend decisions are relevant in an inefficient market and the higher the dividends, the higher the
value of the firm. The theory is based on the following four assumptions:
1. The sending of signals by the management should be cost effective.
2. The signals should be correlated to observable events (common trend in the market).
3. No company can imitate its competitors in sending the signals.
4. The managers can only send true signals even if they are bad signals. Sending untrue
signals is financially disastrous to the survival of the firm.
v) Tax differential theory
Advanced by Litzenberger and Ramaswamy in 1979. They argued that tax rate on dividends is
higher than tax rate on capital gains. Therefore, a firm that pays high dividends have lower value
since shareholders pay more tax on dividends. Dividend decisions are relevant and the lower the
dividend the higher the value of the firm and vice versa.

vi) Clientele effect theory

Advance by Richardson Petit in 1977. It stated that different groups of shareholders (clientele)
have different preferences for dividends depending on their level of income from other sources.

Low income earners prefer high dividends to meet their daily consumption while high income
earners prefer low dividends to avoid payment of more tax. Therefore, when a firm sets a dividend
policy, there’ll be shifting of investors into and out of the firm until an equilibrium is achieved.
Low, income shareholders will shift to firms paying high dividends and high income shareholders
to firms paying low dividends. At equilibrium, dividend policy will be consistent with clientele of
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shareholders a firm has. Dividend decision at equilibrium are irrelevant since they cannot cause
any shifting of investors.
vii) Agency theory
The agency problem between shareholders and managers can be resolved by paying high dividends.
If retention is low, managers are required to raise additional equity capital to finance investment.
Each fresh equity issue will expose the managers financing decision to providers of capital e.g
bankers, investors, suppliers etc. Managers will thus engage in activities that are consistent with
maximization of shareholders wealth by making full disclosure of their activities.
This is because they know the firm will be exposed to external parties through external borrowing.
Consequently, Agency costs will be reduced since the firm becomes self-regulating.
Dividend policy will have a beneficial effect on the value of the firm. This is because dividend
policy can be used to reduce agency problem by reducing agency costs. The theory implies that
firms adopting high dividend payout ratio will have a higher due to reduced agency costs.

5.HOW TO PAY DIVIDENDS (MODE OF PAYING DIVIDENDS)

1. Cash and bonus issue
For a firm to pay cash dividends, it should have adequate liquid funds.
However, under conditions of liquidity and financial constraints, a firm can pay stock dividend
(Bank issue).
Bonus issue involves issue of additional shares for free (instead of cash) to existing shareholders in
their shareholding proportion.
Stock dividend/Bonus issue involves capitalization of retained earnings and does not increase the
wealth of shareholders. This is because R. Earnings is converted into shares.
Advantages of Bonus Issue
a) Tax advantages
Shareholders can sell new shares, and generate cash in form of capital gains which is tax exempt
unlike cash dividends which attract 5% withholding tax which is final.
b) Indication of high profits in future:
A Bonus issue, in an inefficient market conveys important information about the future of the
company. It is declared when management expects increase in earning to offset additional
outstanding shares so that E.P.S is not diluted.
c) Conservation of cash
Bonus issue conserves cash especially if the firm is in liquidity problems.
d) Increase in future dividends
If a firm follows a fixed/constant D.P.S policy, then total future dividend would increase due to
increase in number of shares after bonus issue.
Journal entry in case of bonus issue
Dr. R. Earnings (par value)
Cr. Ordinary share capital (par value)
2. Stock Split and Reverse Split
This is where a block of shares is broken down into smaller units (shares) so that the number of
ordinary shares increases and their respective par value decreases at the stock split factor. Stock
split is meant to make the shares of a company more affordable by low income investors and
increase their liquidity in the market.
3. Stock Repurchase

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The company can also buy back some of its outstanding shares instead of paying cash dividends.
This is known as stock repurchase and shares repurchased, (bought back) are called treasury
Stock. If some outstanding shares are repurchased, fewer shares would remain outstanding.
Assuming repurchase does not adversely affect firm’s earnings, E.P.S. of share would increase.
This would result in an increase in M.P.S. so that capital gain is substituted for dividends.
Advantages of Stock Repurchase
1.It may be seen as a true signal as repurchase may be motivated by management belief that firm’s
shares are undervalued. This is true in inefficient markets.
2. Utilization of idle funds
Companies, which have accumulated cash balances in excess of future investments, might find
share reinvestment scheme a fair method of returning cash to shareholders. Continuing to carry
excess cash may prompt management to invest unwisely as a means of using excess cash
E.g: A firm may invest surplus cash in an expensive acquisition, transferring value to another group
of shareholders entirely. There is a tendency for more mature firms to continue with investment
plan even when E (K) is lower than cost of capital.
3. Enhanced dividends and E.P.S.
Following a stock repurchase, the number of shares issued would decrease and therefore in normal
circumstances both D.P.S. and E.P.S. would increase in future. However, the increase in E.P.S is a
bookkeeping increase since total earnings remaining constant.
4. Enhanced Share Price
Companies that undertake share repurchase, experience an increase in market price of the shares.
This is partly explained by increase in total earnings having less and/or market signal effect that
shares are under value.
5. Capital structure
A company’s managers may use a share buyback or requirements, as a means of correcting what
they perceive to be an unbalanced capital structure. If shares are repurchased from cash reserves,
equity would be reduced and gearing increased (assuming debt exists in the capital structure).
Alternatively a company may raise debt to finance a repurchase. Replacing equity with debt can
reduce overall cost of capital due to tax advantage of debt.
6. Employee incentive schemes
Instead of cancelling all shares repurchase, a firm can retain some of the shares for employees share
option or profit sharing schemes.
7. Reduced takeover threat
A share repurchase reduced number of share in operation and also number of ‘weak shareholders’
i.e. shareholders with no strong loyalty to company since repurchase would induce them to sell.
This helps to reduce threat of a hostile takeover as it makes it difficult for predator company to
gain control. (This is referred as a poison pill) i.e. Co.’s value is reduced because of high
repurchase price, huge cash outflow or borrowing huge long term debt to increase gearing.
Disadvantages of stock repurchase
1. High price
A company may find it difficult to repurchase shares at their current value and price paid may be
too high to the detriment of remaining shareholders.
2. Market Signaling
Despite director’s effort at trying to convince markets otherwise, a share repurchase may be
interpreted as a signal suggesting that the company lacks suitable investment opportunities. This
may be interpreted as a sign of management failure.
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3. Loss of investment income
The interest that could have been earned from investment of surplus cash is lost.
11.6. FACTORS TO CONSIDER IN PAYING DIVIDENDS (FACTORS INFLUENCING
DIVIDEND)
1. Legal rules
a) Net purchase rule:States that dividend may be paid from company’s profit either past or present.
b) Capital impairment rule: prohibits payment of dividends from capital i.e. from sale of assets.
This is liquidating the firm.
c) Insolvency rule: prohibits payment of dividend when company is insolvent. Insolvent company
is one where assets are less than liabilities. Insolvent company is one where assets are less than
liabilities. In such a case all earnings and assets of company belong to debt holders and no
dividends is paid.
2. Profitability and liquidity
A company’s capacity to pay dividend will be determined primarily by its ability to generate
adequate and stable profits and cash flow. If the company has liquidity problem, it may be unable to
pay cash dividend and result to paying stock dividend.
3. Taxation position of shareholders
Dividend payment is influenced by tax regime of a country
4. Investment opportunity
Lack of appropriate investment opportunities i.e. those with positive returns (N.P.V.), may
encourage a firm to increase its dividend distribution. If a firm has many investment opportunities,
it will pay low dividends and have high retention.
5. Capital Structure
A company’s management may wish to achieve or restore an optimal capital structure i.e. if they
consider gearing to be too high, they may pay low dividends and allow reserves to accumulate until
a more optimal/appropriate capital structure is restored/achieved.
6. Industrial Practice
Companies will be resistant to deviation from accepted dividend or payment norms within the
industry.
7. Growth Stage
Dividend policy is likely to be influenced by firm’s growth stage e.g a young rapidly growing firm
is likely to have high demand for development finance and therefore may pay low dividend or a
defer dividend payment until company reaches maturity. It will retain high amount.
8. Ownership Structure
A dividend policy may be driven by Time Ownership Structure e.g in small firms where owners
and managers are same, dividend payout are usually low. However in a large quoted public
company dividend payout are significant because the owners are not the managers. However, the
values and preferences of small group of owner managers would exert more direct influence on
dividend policy.
9. Shareholders expectation
Shareholder clientele that have become accustomed to receiving stable and increasing dividend will
expect a similar pattern to continue in the future. Any sudden reduction or reversal of such a policy
is likely to dissatisfy the shareholders and may result in a failure in share prices.
10. Access to capital markets

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Large, well established firms have access to capital markets hence can get funds easily. They pay
high dividends thus, unlike small firms which pay low dividends (high retention) due to limited
borrowing capacity.
11. Contractual obligations on debt covenants
They limit the flexibility and amount of dividends to pay e.g. no payment of dividends from
retained earnings.
11.7. DIVIDEND RATIOS
1. Dividend per shares (DPS) = Earnings to ordinary shareholders
Number of ordinary shares
Indicate cash returns received from every share holder.
2. Dividend yield (DY) = DPS
MPS
Indicate dividend returns for every shilling invested in the firm.
Profit After Tax
3. Dividend cover =Dividend Payable
Show percentage of earning being retained to enhance expansion.
4. Dividend Payout Ratio = DPS
EPS
Shows the proportion of Earnings which was paid out as dividends and how much was retained.
Example
A comparative study of the records of two oil companies, A Ltd and B Ltd., in terms of their asset
composition, capital structure and profitability shows that they have been very similar for the past
five years. The only significant difference between the two firms is their dividend policy. A Ltd.
maintains a constant dividend per share while B Ltd maintains a constant dividend pay-out ratio.
Relevant data is as follows:

Year Earnings Dividend Price range Earnings Dividend Price range

per per share in stock per share per share in stock
share exchange exchange
Shs. Shs. Shs. Shs. Shs. Shs.
2006 1.89 0.45 16 – 18 2.05 0.35 11 – 15
2007 1.50 0.45 12 – 15 1.45 0.25 6 - 14
2008 2.00 0.45 14 – 20 2.07 0.36 7 - 16
2009 2.60 0.45 21 – 26 2.55 0.45 15 – 23
2010 3.90 0.45 26 – 40 4.08 0.69 21 – 44
Required
a) For each company, determine the dividend pay-out ratio and the price earnings ratio for each of
the five years.
b) B Ltd’s management is surprised that the shares of this company have not performed as well as
A Ltd.’s in the stock exchange. What explanation would you offer for this state of affairs?
Comment on the applicability of the Simple Price/Earnings (P/E) ratio to the typical technology
(IT) company with a high valuation and heavy losses.

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 SOLUTION
DPS
a) Dividend payout ratio = x100
EPS
A Ltd. B Ltd
Year
2006 0.45
x100  23.8%
0.35
x100  17.1%
1.89 2.05

2007 0.45 0.35

x100  30.0% x100  17.2%
1.50 1.45

0.45 0.35
2008 x100  22.5% x100  17.4%
2.00 2.08

0.45 0.35
2009 x100  17.30% x100  17.7%
2.60 2.55

0.45 0.35
2010 x100  11.5% x100  16.9%
3.90 4.08

MPS
Price – earning ratio =
EPS
A Ltd. B Ltd
Year
2006 16  18 ½  9.0yrs / times 11  15½  6.34 yrs / times
1.89 2.05

2007 12  15 ½  9.0yrs 6  14 ½  6.9yrs

1.50 1.45

14  20 ½  8.5yrs 7  16 ½  5.56 yrs

2.00 2.08
2008
21  26 ½  9.0yrs 15  23½  7.45yrs
2.60 2.55
2009
26  40 ½  8.46 yrs 21  44 ½  7.97 yrs
3.90 4.08
2010
b) The shares of B Ltd. are not performing well because of uncertainty of DPS compared to
certainty of DPS for A Ltd. This uncertainty leads to higher required rate of return by ordinary
shareholders thus lower market value of a share.
c) If a firm is making heavy losses, the EPS would be negative. With a positive P/E ratio the MPS
would be negative i.e. MPS = -EPS x P/E ratio
A negative MPS cannot be interpreted hence the P/E ratio model collapses.

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TOPIC 10: EMERGING ISSUES IN FINANCIAL MANAGEMENT

1.CORPORATE GOVERNANCE

1. Definition
The corporate governance is the system by which companies are directed and controlled. Good
corporate governance involves the risk management and the internal control, the accountability
to stakeholders and other shareholders and conducting the business in an ethical and effective way.

The ‘purpose of corporate governance is to facilitate effective, entrepreneurial and prudent

management that can deliver the long-term success of the company’.

Corporate governance considers the responsibilities of directors, how the board of directors should
be run and structured, the need for good internal controls and the relationship with external
auditors. It is important for companies to consider good corporate governance principles as often it
is management or those charged with governance who run the company, but the owners are the
shareholders and they are not involved in the running of the business.

For these shareholders their only opportunity to raise concerns is at the annual general meeting,
which only occurs once a year and often attendance is low. Shareholders need to ensure that their
needs are taken into account by management, and that there is a process in place for them to be
informed as to how the business is operating.

Corporate governance represents the set of policies and procedures that determine how an
organisation is directed, administered and controlled.

Most systems of corporate governance are focused on several core principles or values, which
include:
· Accountability
· Transparency
· Fairness
· Responsibility

TCWG: Those “charged with governance” are defined as the persons who are “accountable for
ensuring that the entity achieves its objectives, with regard to reliability of financial reporting,
effectiveness and efficiency of operations, compliance with applicable laws, and reporting to
interested parties.”
Although there is no universal rule, in most instances these persons will either be the board of
directors and/or the audit committee

2.Provisions of international codes of corporate governance

The Principles cover six key areas of corporate governance:

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 1. Ensuring the basis for an effective corporate governance framework (should promote
transparent and efficient markets, be consistent with the rule of law and have a clear
division of responsibilities among different supervisory, regulatory and enforcement
authorities)
2. The rights of shareholders and key ownership functions
3. The equitable treatment of shareholders
4. The role of stakeholders in corporate governance
5. Disclosure and transparency
6. The responsibilities of the board
There are a number of key elements in corporate governance:
(a) The management and reduction of risk is a fundamental issue in all definitions of good
governance; whether explicitly stated or merely implied.
(b) The notion that overall performance enhanced by good supervision and management within
set best practice guidelines underpins most definitions.
(c) Good governance provides a framework for an organisation to pursue its strategy in an ethical
and effective way from the perspective of all stakeholder groups affected, and offers safeguards
against misuse of resources, physical or intellectual.
(d) Good governance is not just about externally established codes, it also requires a willingness to
apply the spirit as well as the letter of the law.
(e) Accountability is generally a major theme in all governance frameworks.

Corporate governance codes of good practice generally cover the following areas:
(a) The board should be responsible for taking major policy and strategic decisions.
(b) Directors should have a mix of skills and their performance should be assessed regularly.
(c) Appointments should be conducted by formal procedures administered by a nomination
committee.
(d) Division of responsibilities at the head of an organisation is most simply achieved by
separating the roles of chairman and chief executive.
(e) Independent non-executive directors have a key role in governance. Their number and status
should mean that their views carry significant weight.
(f) Directors' remuneration should be set by a remuneration committee consisting of independent
non-executive directors.
(g) Remuneration should be dependent upon organisation and individual performance.
(h) Accounts should disclose remuneration policy and (in detail) the packages of individual
directors.
(i) Boards should regularly review risk management and internal control, and carry out a wider
review annually, the results of which should be disclosed in the accounts.
(j) Audit committees of independent non-executive directors should liaise with external audit,
supervise internal audit, and review the annual accounts and internal controls.
(k) The board should maintain a regular dialogue with shareholders, particularly institutional
shareholders. The annual general meeting is the most significant forum for communication.
(l) Annual reports must convey a fair and balanced view of the organisation. They should state
whether the organisation has complied with governance regulations and codes, and give specific
disclosures about the board, internal control reviews, going concern status and relations with
stakeholders.
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3.Important terms in corporate governance
 An executive director: an executive director is a director responsible for the administration of
a company. They are primarily responsible for carrying out the strategic plans and policies as
established by the board of directors.
 A non-executive director (NED): a non-executive director is a director without day-to-day
operational responsibilities of the company.
4. The OECD Principles of Corporate Governance

The OECD Principles of Corporate Governance cover six main areas, which are divided into
chapters. The Principles:
· Request that governments have in place an effective legal, regulatory, and institutional
framework to support good corporate governance practices
· Call for a corporate governance framework that protects the exercise of shareholders’ rights
and supports the equal treatment of all shareholders, including minority and foreign
shareholders
· Address the effect of institutional investors and other intermediaries in stock markets and
the resulting corporate governance implications
· Recognize the importance of the role of stakeholders in corporate governance Examine the
importance of timely, accurate, and transparent disclosure mechanisms
· Address board structures, responsibilities, and procedures

The OECD Principles of Corporate Governance is regarded as one of the hallmark sources of
guidance for corporate governance practices for organizations throughout the world. Broadly, the
Principles state that an entity’s corporate governance framework should:
· Promote transparent and fair markets and the efficient allocation of resources.
· Be consistent with the rule of law.
· Support effective supervision and enforcement.
· Protect and facilitate the exercise of shareholders’ rights.
· Ensure the equitable treatment of all shareholders, including minority and foreign
shareholders.
· Provide all shareholders with the opportunity to obtain effective redress for violation of their
rights.
· Create sound incentives throughout the investment chain.
· Enable stock markets to function in a way that contributes to good corporate governance.
· Recognize the rights of stakeholders established by law or through mutual agreements.
· Encourage active cooperation between corporations and stakeholders in creating wealth,
jobs, and the sustainability of financially sound enterprises.
· Ensure that timely and accurate disclosure is made on all material matters regarding the
corporation, including the company’s financial situation, performance, ownership, and
governance.
· Ensure the strategic guidance of the company, the effective monitoring of management by
the board, and the board’s accountability to the company and the shareholders.
5. Driving forces/factors behind keen interest in corporate governance.
 Increasing corporate fixtures e.g collapse of sugar factories, financial institutions,
manufacturing concerns etc.

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  Increasing fraudulent and corrupt behaviour e.g money laundering bribery, abuse of
corporate power etc. e.g golden berg scandal, bad debt crisis in the banking sector,
fraudulent claims in insurance sector.
 A growing demand by stakeholders for transparency, accountability as the world embraces
wider issues of democratisation and good governance. This has increased shareholders
activism.
 Powerful and dominant BOD that manipulates shareholders and other stakeholders of the
firm. The BOD perceive most shareholders as illiterate to understand fully issues in the
business sector.
 Structures that demand academic and professional gratifications e.g some boards never
demand basic qualifications of the board members. Shareholding and influencing are used
as a benchmark to get a seat in the board.
 The growth of multi-nationals and transnational firms.
 The global governance revolution resulting from globalisation of firms and economic
liberalisation.
 Separation of ownership from control.
6.Advantages of good corporate governance
 Protection of investors rights.
 Enhances corporate performance, capital formation and maximisation of shareholders wealth
(promotes corporate growth).
 Promotes standards of self regulation.
 Greater investor’s confidence and access to capital
 Less risk of costly litigation and substantial compensation payouts.
 Efficient and responsible use of capital by companies
 Greater loyalty from customers and employees
 Creates mechanism that selects, monitor and replaces the managers in a timely manner.
 Enhanced corporate image
7. Arguments for against the introduction of statutory controls on corporate governance
a) Arguments for the introduction of statutory controls on corporate governance
(1) There already exist a raft of statutory controls on corporate governance, mainly in the
Company Law. For example, companies must appoint auditors, directors can be removed
according to standard procedures, and directors may not generally receive loans from their
companies. What we are arguing here is whether the present statutory controls should be
extended. It is fair to say that the existing controls have rather developed on a piecemeal
basis, prohibiting specific acts when they have been observed in practice; thus the statute
has lagged behind the reality. It would be more satisfactory if statutory controls could be
developed at the same pace as developments in practice, though this ideal situation is
impractical.
(2) The board of directors is supposed to act in the best interests of shareholders. However
there may be situations where the interests of shareholders diverge from the managers’ own
interests; this conflict can be so strong that statutory controls are required to ensure that
companies are run in the best interests of the shareholders. An example is directors’
remuneration and service contracts. Directors might want large remuneration and contracts
offering large compensation if they are sacked.

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(3) A further conflict arises where auditors are appointed by the directors, and the directors fix
their remuneration, yet they report to the shareholders. There is a temptation for auditors to
which to please the directors who have appointed them, rather than to act objectively in the
shareholders’ best interests. The independence of mind of auditors is guaranteed by their
professionalism
(4) The best way of ensuring good governance is likely to be the threat of further statutory
controls. When directors see that a government is sincere in wishing to encourage good
governance, the worst practices will be stopped for fear of attracting new legislation.
b) Arguments against the introduction of statutory controls on corporate governance
(1) One cannot legislate against evil. If a bad man is determined to carry out a fraud, whether
or not controls are enshrined in statute will be irrelevant.
(2) Statutory controls may stifle individual entrepreneurship. Many companies have flourished
in recent years because of the existence of one strong individual business person combining
the roles of chairman and chief executive and pushing through their will.
(3) Putting rules into statute encourages companies to obey the letter of the law rather than the
spirit. The whole experience of the Securities and Investments Board in implementing the
Financial Services Act regulations has proved that detailed rule books are an ineffective
means of regulation. Statute should contain broad rules, backed up by self-regulatory
practice notes and points of interpretation. It is this latter approach that has been adopted by
the Accounting Standards Board in drawing up its new accounting standards, an approach
that has proved successful to date.
8.Impact of corporate governance requirements on businesses
 The consequences of failure to obey corporate governance regulations should be considered
along with failure to obey any other sort of legislation.
 Businesses that fail to comply with the law run the risk of financial penalties and the financial
consequences of accompanying bad publicity.
 In regimes where corporate governance rules are guidelines rather than regulations, businesses
will consider what the consequences might be of non-compliance, in particular the impact on
share prices.
 Obedience to requirements or guidelines can also have consequences for businesses.
Compliance may involve extra costs, including extra procedures and investment necessary to
conform.

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