COLLEGE OF ARTS SOCIAL AND MANAGEMENT SCIENCES (CASMAS)

DEPARTMENT OF ACCOUNTING, FINANCE & TAXATION

COURSE: ACC 301 – CORPORATE FINANCE / FIN 301 – FINANCIAL MGT 1

LECTURES FOUR – SIX

4. CAPITAL BUDGETING/INVESTMENT APPRAISAL

4.1 Introduction
One of the major decisions confronting a financial manager is investment decision. Investment
decision is the decision making as to what project should be invested in. It involves the
identification and evaluating of available opportunities to select the most viable of them. The
financial manager should select the most profitable investment portfolio that will reduce to the
barest minimum the risk of the organisation and maximising the wealth of the shareholders. In
doing this, the risk and return factor on the identified investments opportunities must be given
adequate consideration through capital budgeting technique.
Capital budgeting is the process whereby decisions are taken on how capital funds shall be
deployed to capital projects. It includes the appraisal of proposed investment projects by reference
to their future cash flows, expected returns and to the cost of capital. The relationship between
investment projects can be in any of these forms:
i. Independent projects – These are investments which do not compete with each other and
they can be selected individually without affecting the other. They can be carried out
together.
ii. Mutually Exclusive projects – These are investments which compete with each other.
Investment projects that are mutually exclusive cannot be embarked upon together at a
time.
iii. Mutually Dependent or Contingent projects – These are investment projects that are
depending on each other. It means the choice of one investment will necessitate
undertaking the other in such a way that they must be done or otherwise together. It is
either the mutually dependent projects are accepted for executed together or they are
rejected. Because of this fact that execution of one investment is contingent to the other,
mutually dependent projects are usually bundled together as one.

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4.1.1 Steps Involved In Capital Budgeting Decisions
The steps involved in capital budgeting decisions can be summarised as follows:
i. Identification of possible investment opportunities/projects
ii. Gather relevant information about the investment opportunities including the cashflows
iii. Evaluate the investment opportunities using the most desire methods/techniques
iv. Select the most feasible and profitable projects considering all limitations.
v. Seek for management authorisation and approval
vi. Execute project in line with the approval and timeline.
vii. Monitor and control project implementation to track unfavourable deviation
viii. Carry out post-implementation audit
4.1.2 Features of Capital Budgeting
Capital budgeting have the following characteristics which made it differ from revenue
expenditure investments.
i. They involve large capital outlay
ii. They involve exchange of current fund for future benefits
iii. The future benefits accrued over a long period of time of over one year
iv. They are not reversible once initiated or reversible at a huge cost
v. They are very risky as outcome cannot be precisely determined

4.2 Methods/Techniques of Capital Budgeting Evaluation

There are several capital budgeting techniques that are used in practice. These can be classified
under two categories:
a. Non-Discounted Cashflow or Traditional Methods
i. Payback Period - PBP
ii. Accounting Rate of Return – ARR

b. Discounted Cashflow or Modern Methods (Considers Time Value of Money)

i. Net Present Value - NPV
ii. Profitability Index – PI
iii. Internal Rate of Return – IRR
iv. Discounted Payback Period - DPBP
4.2.1 Payback Period
This is a method where the emphasis is on how long it will takes to recover the initial capital outlay
of a project from the cashflows generated. It is the measure of number years it will take to recoup
the capital outlay. The method focus on liquidity consideration of a project rather than profitability.
Where the project generates constant annual cashflow, the payback period can be computed by
dividing the initial capital outlay by the annual cash inflow.

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 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑂𝑢𝑡𝑙𝑎𝑦
𝑃𝐵𝑃 = 𝐴𝑛𝑛𝑢𝑎𝑙 𝐶𝑎𝑠ℎ 𝑖𝑛𝑓𝑙𝑜𝑤

Where the annual cash inflows are not constant, the PBP can be obtained by adding up the cash
inflows until the cumulative amount is equal to the initial capital outlay. The basic assumption
here is that all cask inflows accrued evenly over the years.
Decision/Acceptance rule - The shorter the payback period (in years), the better a project i.e.
Accept a project with shorter PBP or PBP shorter than (or equals to) the firm’s PBP cut-off rate.
Illustration 4.1
Early Birds Ltd have two investment projects to evaluate. The details are stated below:
Project I Project II
Initial Outlay (N’000) 500,000 750,000
Cash inflows 180,000 annually Yr 1= 140,000; Yr 2= 200,000; Yr 3= 350,000;
for 5 years Yr 4= 480,000; Yr 5= 320,000

a) Determine the PBP for the two projects

b) If the projects are mutually exclusive, advise on which to accept
c) If the risk cut-off PBP for the company is 2 years, advise on which to accept

Advantages of Payback Period

i. It is simple, easy to estimate and understand
ii. The emphasis is on early recovery of the investment, thus it gives an insight to the liquidity
of the project.
iii. It is cost effective compare with other sophisticated techniques which require more data.
iv. It is more appropriate to use in an unstable and risky economic environment.
Disadvantages of Payback Period
i. It disregards the time value of money
ii. It disregards all the cash inflows after the payback period
iii. It disregards the profit maximisation objectives by focusing on liquidity only
iv. It is not an objective technique as there is subjectivity in determining the acceptable PBP

4.2.2 Accounting Rate of Return - ARR

The accounting rate of return, also called return on investment (ROI) uses the accounting
information from the financial statements to measure the profitability of investment projects. It is
the average return expressed as a percentage of the average investment outlay. It is calculated as:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑐𝑐𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑃𝑟𝑜𝑓𝑖𝑡
𝐴𝑅𝑅 = × 100
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

(Accounting profit is the PBIT (1-t) i.e. Profit before interest and after tax. “t” is the tax rate.)

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Where
𝑇𝑜𝑡𝑎𝑙 𝑃𝑟𝑜𝑓𝑖𝑡 𝑜𝑣𝑒𝑟 𝑦𝑒𝑎𝑟𝑠
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑟𝑜𝑓𝑖𝑡 =
𝑁𝑜. 𝑜𝑓 𝑌𝑒𝑎𝑟𝑠

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡/𝑂𝑢𝑡𝑙𝑎𝑦

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 = 2

Another variation in the definition of ARR is the expression of average profit to the Initial capital
outlay. This version is deemed to be less consistent as the profit is average while the capital outlay
is used in total.
Decision/Acceptance rule - The higher the ARR (in percentage), the better a project i.e. Accept a
project with higher ARR or ARR higher than (or equals to) the firm’s ARR cut-off rate.
Illustration 4.2
Freaky Business Ltd is to invest the sum of N10m in a project which is expected to have a scrap
value of N2m after 5 years. Estimated profit before charging depreciation for the five years are as
follows:
Yr 1 N3.6m
Yr 2 N4.5m
Yr 3 N5.0m
Yr 4 N5.4m
Yr 5 N6.0m
Calculate the ARR of the project and advise the management if the desire cut-off (minimum) ARR
is 40%.

Illustration 4.3
Obinna All Spare & Co. is planning an investment of N3,000,000 in a certain investment, with
life span of 4 years, that will yield the following profit after tax:
Year 1: 1,000,000
Year 2: 2,000,000
Year 3: 500,000
Year 4: 400,000
Calculate the ARR of the project

Advantages of ARR
i. It is simple, easy to calculate and understand
ii. It uses readily available accounting data
iii. It consider the profits/cashflows over the entire life of the project
iv. It could be used for performance comparison of companies

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Disadvantages of ARR
i. It ignores the risk associated with the investment and the management attitude to risk
ii. It ignores the time value of money
iii. It uses accounting profit rather than the superior cash profit in measuring benefit
iv. It ignores working capital
v. It suffers problem of definition

4.2.3 The Net Present Value (NPV)

This is a method that takes cognisance of the time value of money. The concept of the time value
of money is that an amount of money today will not be the same in a year’s time due to depreciation
in real value of money. Thus, a Naira invested today is expected to yield an amount above the
Naira invested. The extra amount is assumed to be the compensation for the loss in value amount
of Naira invested, hence the interest rate is often used for discounting.
The NPV method postulates that cashflows arising at different time period will differ in value and
can only be comparable when their equivalents of their present values are determined. The NPV
of a project is the net of the cost of the project and the present values of the future cashflows of
the project over the life of the project.
NPV is calculated as
C1(1+r)-1 + C2(1+r)-2 + C3(1+r)-3 + C4(1+r)-4 +…………+ Cn(1+r)-n - IO
Where
C1, C2, C3, C4,………Cn is the cashflows in years 1 to year n
R is the discount rate
IO is the Initial Capital Outlay
Decision/Acceptance rule – Project with positive NPV, i.e. NPV ≥ 0 should be accepted and the
higher the NPV, the better a project is. This is valid for independent projects and there may be
variation in dependent and exclusive projects.

Illustration 4.4
ABC Ltd wishes to invest N4,000,000 in a coal project which has a life span of 6 years. The net
cashflow of the project for the 6 years is as follows:
Yr 1 N1,000,000
Yr 2 2,000,000
Yr 3 500,000

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Yr 4 1,000,000
Yr 5 500,000
Yr 6 500,000
The cost of capital is 10%. Calculate the NPV of the project and advise if the project should be
undertaken.
Illustration 4.5
ABC Ltd, as in illustration 4.4, has a water project with a life span of 5 years on which it can invest
the same amount. The project, which has a scrap value of N250,000.00, have a net inflow of
N1,120,000 for each of years 1 to 5.
Calculate the NPV of the project.
4.2.4 Profitability Index (PI)
The Profitability Index is a technique where the benefit of an investment project in term of its
present value is compared with the cost of the project. PI is the ratio of the PV of an investment
project at the required cost of capital, to the initial capital outlay of the investment project. It is
also called Benefit-Cost Ratio.
PI can be calculated either on a net (NPI) or gross (GPI) basis.
Net Profitability Index is calculated as:

𝑁𝑃𝑉𝑜𝑓 𝐶𝑎𝑠ℎ 𝑖𝑛𝑓𝑙𝑜𝑤𝑠

𝑁𝑃𝐼 =
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑜𝑢𝑡𝑙𝑎𝑦
On the gross basis, it is calculated as:

𝑃𝑉𝑜𝑓 𝐶𝑎𝑠ℎ 𝑖𝑛𝑓𝑙𝑜𝑤𝑠

𝐺𝑃𝐼 =
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑜𝑢𝑡𝑙𝑎𝑦
Decision/Acceptance rule under the net approach (NPI)
Accept a project when the PI is positive i.e. NPI > 0, and reject when NPI is negative i.e. < 0. A
project with NPI of “0” may be accepted but it is obvious that it does not quantitatively increase
the value of the firm.
Decision/Acceptance rule under the gross approach (GPI)
Accept a project when the GPI is greater than one i.e.GPI > 1, and reject when GPI < 1. A project
with GPI of “1” may be accepted but it is obvious that it does no quantitatively increase the value
of the firm.

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PI is a relative measure of profitability that recognised the time value of money and it is consistent
with firm value maximisation objective. It is a variation of the NPV method, the same computation
is required and the same decision outcome is arrived at.
Illustration 4.6
Compute the PI of the projects in illustrations 5.4 and 5.5 above. Comment on your result in
relation to the result obtained with the NPV method.

4.2.5 Internal Rate of Return (IRR)

Internal rate of return is the rate of return (cost of capital) which will equate the Initial capital
outlay of a project with the PV of all the future cash inflows. It is the rate of return or discount rate
at which the NPV of a project will equals to zero. IRR is the maximum rate at which the cashflows
of an investment will be discounted to be profitable.
IRR can be computed by trial and error and the two trial rates are interpolated with the resulting
NPVs

+𝑣𝑒𝑁𝑃𝑉
𝐼𝑅𝑅 = 𝐿𝑅 + { + (𝐻𝑅 − 𝐿𝑅)}
+𝑣𝑒𝑁𝑃𝑉 − −𝑣𝑒𝑁𝑃𝑉

Decision/Acceptance rule – Accept a project with IRR higher than the firm’s cost of capital or the
cut-off rate (hurdle rate) and vice versa. For mutual exclusive project, the higher the IRR the better
the project.
Illustration 4.7
Refer to illustrations 4.4 and 4.5 above. Compute the IRR of the two projects and rank them in
order of priority.

4.3 Capital Budgeting Under Risk And Uncertainty

Capital budgeting requires the projection of cash inflow and outflow of the future and the future
is always uncertain. Risk and uncertainty are integral part of capital budgeting decisions where the
future is uncertain with risk involved.
Risk is a situation where the probabilities of an event occurring are known and can be ascertained
or estimated objectively. Uncertainty is a subjective phenomenon in which no observation can be
drawn from the frequency distribution, i.e. the probabilities of an event occurring are unknown
and cannot be ascertained or estimated with any objectivity.

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Uncertainty occurs due to a lack of sufficient information about what is likely to happen. It is
possible to assess the uncertainty in a project, but with less mathematical precision than for the
assessment of risk. Therefore investment decisions should consider the risk and uncertainty in
investment projects, as well as the expected returns and the NPV.
There are various methods for accounting and handling risk in capital budgeting, common among
them are:
a) Risk adjusted cut-off rate
i. Shorter payback period
ii. Higher Internal Rate of Return Conservative Methods
iii. Higher Cost of capital
b) Certainty equivalent method

c) Sensitivity analysis
d) Probability technique
e) Standard deviation method Modern Methods
f) Co-efficient of variation method
g) Decision tree analysis method

a) Risk adjusted cut-off rate - This is one of the simplest method while calculating the risk in
capital budgeting. It involves adjusting the cut-off rate (shorter PBP, higher IRR) or the
discount factor (COC) by certain percentage to compensate for the inherent risk. This
adjustment difference in the rate is called risk premium.

Illustration 4.8
Priority Ltd is considering a new investment. Two alternative investments are available (X and Y)
each costing N1,500,000. Cash inflows are expected to be as follows:
Cash Inflows
Year Investment X Investment Y
N N
1 600,000 850,000
2 450,000 550,000
3 350,000 400,000
4 300,000 400,000

The company has a target return on capital of 10%. Risk premium rate are 2% and 8% respectively
for investment X and Y. Which investment should be preferred?

b) Certainty equivalent method - The risk level of a project under this method is taken into account
by adjusting the expected cash inflows. Thus the expected cash inflows are reduced to a
conservative level by a risk-adjustment factor (also called correction factor). This factor is

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 expressed in terms of Certainty Equivalent Co-efficient which is the ratio of riskless cash flows
to risky cash flows. The certainty equivalent is obtained by multiplying the expected cash
inflows by certainly equivalent co-efficient.

Illustration 4.9
ABC Ltd has two projects A and B of which it intends to invest in one. Each involves an investment
of N500,000

Project A Project B
Year Cash inflows Certainty Cash inflows Certainty
co-efficient co-efficient
1 350,000 0.8 250,000 0.9
2 300,000 0.7 350,000 0.8
3 200,000 0.9 200,000 0.7

Risk-free cutoff rate is 10%. Suggest which of the two projects should be preferred.
c) Sensitivity analysis – Sensitivity analysis is a method of handling risk in capital budgeting that
takes the form of how the benefit/NPV of a project will respond to changes to relevant
cashflows, initial capital outlay and cost of capital due to uncertainty in the estimates. This
approach looks at the “tolerable level” of change that can occur in each of the estimates to
make the project not viable. It means that forecasts of many calculated NPVs under various
alternative functions are compared to see how sensitive the NPV is to changing conditions. It
may be found that a certain variable or group of variables, once their assumptions are changed
or relaxed, drastically alters the NPV. This results in a much riskier asset/project than was
originally forecast.
𝑁𝑃𝑉 𝑜𝑓 𝑃𝑟𝑜𝑗𝑒𝑐𝑡
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 = × 100
𝑃𝑣 𝑜𝑓 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝐼𝑅𝑅 − 𝐶𝑂𝐶
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑡𝑜 𝐶𝑂𝐶 = × 100
𝐶𝑂𝐶

𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝐿𝑖𝑓𝑒 − 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝑃𝐵𝑃 (𝐵𝐸𝑃)

𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑡𝑜 𝑃𝑜𝑗𝑒𝑐𝑡 𝐿𝑖𝑓𝑒 = × 100
𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝐿𝑖𝑓𝑒

The higher the margin of sensitivity of a variable, the less risky a project is and vice versa.
Illustration 4.10
A company is considering a project with the following estimated cashflows (All in N’m).

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Year Equipment Income Total cost Net cashflow DCF@10% PV
0 (55,000) 1.000 (55,000)
1 50,000 35,000 15,000 0.909 13,635
2 80,000 55,000 25,000 0.826 20,650
3 100,000 70,000 30,000 0.751 22,530
4 40,000 30,000 10,000 0.683 6,830
NPV + 8,645
Required
Estimate the sensitivity of the project to:
i. Income
ii. Total Cost
iii. Equipment cost
iv. Cost of capital.

d) Probability technique – Also called expected value method. This is the assessment of the
chance that a particular event will occur as predicted or forecasted with a distribution indicating
the chances or probability of all possible occurrences or outcomes. The future cashflows are
assigned with relative frequency probability (p). The certainty of occurrence is = 1 and as such
p>0 and p<1; i.e. (0<p<1). The sum of probability of all possible occurrences is 1. i.e. ∑p
=1.
Illustration 4.11
Two mutually exclusive investment proposals are being considered. The following information is
available.
Project A Project B
Cost 10,000 10,000
Cash inflows
Year N Probability N. Probability
1 10,000 0.2 12,000 0 .2
2 18,000 0.6 14,000 0.6
3 8,000 0.2 14,000 0.2

Cost of capital is 10%. Advise on the selection of the project.

Solution

Project A
Year Inv. Cost Cash Inflow Probability EV DF@10% PV
0 (10,000) (10,000) 1.000 (10,000)
1 10,000 0.2 2,000 0.909 1,818
2 18,000 0.6 10,800 0.826 8,821

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3 8,000 0.2 1,600 0.751 1,202
NPV 1.941

Project B
Year Inv. Cost Cash Inflow Probability EV DF@10% PV
0 (10,000) (10,000) 1.000 (10,000)
1 12,000 0.2 2,400 0.909 2,182
2 14,000 0.6 8,400 0.826 6,938
3 14,000 0.2 2,800 0.751 2,103
NPV 1.223

Decision: As the NPV of project A is more than that of project B after taking into consideration
the probabilities of cash inflows project A is more profitable one.

Illustration 4.12
A company is considering an investment in a project. The project would be a five year project, and
would cost N2,000,000. The actual returns from the investment are subject to uncertainty, but the
following estimates have been prepared for the different possible outcomes:
Probability NPV
0.10 (80,000)
0.30 40,000
0.40 120,000
0.20 200,000
The EV of the NPV is calculated as follows:
Probability NPV EV
p x Px
0.10 (80,000) (8,000)
0.30 40,000 12,000
0.40 120,000 48,000
0.20 200,000 40,000
EV of NPV 92,000
The EV of the NPV is positive, +N92,000. The decision should therefore be to undertake the
investment, provided that the risk does not seem too great. In this example there is a 10%

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probability that the NPV will be negative, –N80,000. Management might therefore consider
whether the investment is worth undertaking, in view of this risk.

Illustration 4.13
HAYBEECEE Ltd is considering an investment project which would involve an investment of
N1,000,000. The expected returns will depend on economic conditions over the next four years.
The following estimates have been prepared. The cost of capital is 10%.
Year Strong economy Weak economy
0 (1,000,000) (1,000,000)
1 400,000 100,000
2 600,000 300,000
3 400,000 200,000
4 300,000 50,000
Probability 0.75 0.25

Required
Calculate the EV of the NPV of the project, and recommend whether the project should or should
not be undertaken.
e) Standard Deviation method – This is an extension of the expected value or probability method.
Standard deviation is the measure of dispersion of a set of data from its mean (expected value).
It is a statistical measures that captures the difference between the average and the outliers in
a set of data. It is a measure of volatility and in turn, a measure of risk. The higher the deviation
of the outliers from the mean, the riskier the data; and a project having a higher SD is said to
be more risky.

Standard deviation denoted by 𝜎 , is calculated as:

𝜎 = √∑𝑝(𝑦 − ӯ)2
P = Probability value

y = Individual data
ӯ = Mean or Average of the data set. = ∑y⁄𝑁 ; N= Number of data in the set or observation

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f) Co-efficient of variation method – Co-efficient of variation is a relative measure of dispersion.
It is calculated as:
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝜎
=
𝑀𝑒𝑎𝑛 𝑉𝑎𝑙𝑢𝑒 ӯ

Illustration 4.14
From the following information relating to BEEHAY Ltd, ascertain which of the two mutually
project should be selected on the basis of:
a) Standard deviation
b) Co-efficient of variation

Project HAY Project BEE

Cash inflow Probability Cash inflow Probability
Nm Nm
3,200 0.2 32,000 0.1
5,500 0.3 5,500 0.4
7,400 0.3 7,400 0.4
8,900 0.2 8,900 0.1

g) Decision tree method - A decision tree is a graphical method of showing the sequence of
possible outcomes. The approach is a useful analytical technique in capital budgeting to
evaluate risky investment involving sequential decision.

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