Question 1

Capaldi plc has the following investment opportunities, none of which is divisible, i.e.
each project must be undertaken in its entirety, or not at all, it isn’t possible to carry
out a fraction of a project:

Initial
Profitability Investment
Project Index £000
A 1.42 700
B 1.75 1,000
C 1.75 800
D 1.50 1,600
E 1.90 900

Funding a portfolio of these projects would not require a change to the company’s
financial structure and each project has the same risk as the company’s existing
business. Each project has a conventional cash flow profile with a single initial
investment outlay. Projects B and C are mutually exclusive. The company has
investment funds that are limited to a total of £4m. Any surplus funds can be used to
reduce the company’s bank overdraft, on which interest is currently payable at 6%
p.a.

Required:

(a) Define the Internal Rate of Return (IRR) concept and explain how it may
be used in project appraisal;

The internal rate of return on an investment is the discount rate at which the cash
flows from the investment have a net present value of zero. The definition in terms of
a zero NPV can be recast into the equivalent: The internal rate of return on an
investment is the discount rate at which the present value of the cash outflows from
an investment is equal to the present value of the investment cash inflows. The IRR
is used in corporate strategic decision-making as part of the process of appraising
potential investment projects.
The higher the IRR the more profitable the project is expected to be, however, the
IRR should not be used in isolation for project appraisal, the risk associated with the
project should be taken into account together with the IRR. In corporate investment
decision-making, only projects with an IRR exceeding the cost of capital for financing
the project should be considered, because only those projects will have a positive
NPV and therefore be wealth-creating and it is manifest that the overriding corporate
objective is the maximisation of shareholder wealth. The IRR is a relative measure,
as a rate of return it measures the return relative to the investment, as such, it is a
measure of the efficiency of the project in using investment funds to generate
returns; however, it doesn’t measure the magnitude of the returns obtained, unlike
NPV which is an absolute measure. An important consequence in project appraisal
of IRR being a relative, not an absolute measure, is that it cannot be used to
discriminate between projects of identical efficiency but different magnitudes. Since
maximisation of the value of the company is the underlying objective,

NPV would have to be the criterion used for choosing between projects with the
same IRR. This consideration applies where there are competing projects that are
mutually exclusive and where limited investment funds constrain the projects that
can be undertaken.

Finally, IRR may be calculated retrospectively for completed projects.

Such calculations may yield insight into the accuracy of past forecasts and the
assumptions on which they were based, enabling improvements in future forecasting
where possible.
Taken in conjunction with an appraisal of the risk of the past project, it may also be
used to inform the appraisal of future potential undertakings.
(20%)

(b) Explain what is meant by “a conventional cash flow profile” and explain
its significance in relation to IRR;

Conventional cash flow is a series of inward and outward cash flows over time in
which there is only one change in the cash flow direction. A conventional cash flow
for a project or investment is typically structured as an initial outlay or outflow,
followed by a number of inflows over a period of time. A conventional cash flow
profile is one where the sign of the cash flow changes once and only once during the
life of the project. The significance of this in relation to IRR is that the project will
have a single positive IRR, whereas with unconventional cash flow profiles there can
be multiple IRRs or even no IRR at all.

(15%)
(c) Using a discount rate of 8%, identify the projects that should be selected
to maximise net present value (NPV) and calculate the NPV figure that
results from your selected portfolio of projects;

Discount Rate = 8%

Investment = 4,000,000 (4 million)

Project that should be selected by NPV E, C, D, A

Total investment funds = (900,000+ 800,000 + 1,600,000 + 700,000)

= 4,000,000

With no surplus funds remaining

Ranking by PI Project E, B, D could require total investment fund of

= (900,000 + 1,000,000 + 1,600,000)
= 3.5 million or 3.5,000,000 – remaining 500,000 which could be used to reduce the
overdraft.

To compare NPV for each project

NPV = (PI – 1) i

Project A (1.42-1) 700,000 = 294,000

Project B (1.75-1) 1,000,000 = 750,000
Project C (1.75-1) 800,000 = 600,000
Project D (1.50-1) 1,600,000 = 800,000
Project E (1.90-1) 900,000 = 810,000

Portfolio comprising E, C, D, A
(i) NPV= 810,000 + 600,000 + 800,000 + 294,000
= 2.504 million / 2.504,000,000
 (ii) Portfolio E, B, D + Possible overdraft reduction (500,000)

Annual interest saved would be = 6% x (remaining fund)

= 6% x 500,000
= 30,000

Discount as perpetuity

PV = Cash inflow / Discount Rate

= 30,000 / 8%
= 375,000

BUT investment required 500,000.

PI of reducing the overdraft is 375,000/ 500,000 = 0.75

0.75 < 1

This is not worthwhile at inly 6% overdraft is a cheaper form of finance than 8% cost
of capital.

Portfolio E, B, D total NPV

= 810,000 + 750,000 + 800,000
= 2.36 million / 2.36,000,000

Portfolio (i) more preferable (Project E, C , D, & A) Should be selected

Comment

In rejecting the option of reducing the overdraft, there is an assumption that either
project with an IRR exceeding the cost of capital will soon become available, or that
existing sources of finance can be replaced through the company using its surplus
funds of £500,000

(40%)
(d) Again using a discount rate of 8%, identify the projects that should be
selected to maximise NPV and calculate the NPV figure that results from your
selected portfolio of projects if the projects were divisible, i.e. fractions of a
project could be undertaken;

Since the mutually exclusive projects B and C have identical PIs,

the one with the higher (= better) utilisation of the scarce funds should be selected.
We select projects E, B, D and use the remaining cash of £500,000 to undertake a
fraction (5/7) of project A to yield NPV of:

£810,000 + £750,000 + £800,000 + (5/7) £294,000

= £2.57million
Question 2

Hume plc and Hegel plc are two companies operating in the maritime transport
industry. The companies enjoy the same business risk and are identical in all
material respects except for their capital structures. Both companies anticipate
earnings before interest of £35m, and both companies have a policy of paying out
residual income by way of dividend. The companies’ capital structures are as
follows:

Hume plc
£m
Ordinary shares of £1 each 80
Profit & Loss account 110
190
10% Debentures 60
250
Hegel plc
£m
Ordinary shares of 50p each 40
Profit & Loss account 160
250

Shares in Hegel plc and Hume plc are currently trading at 200p and 175p each,
respectively, whilst the debentures are trading at par.

Required:

(a) Calculate the weighted average cost of capital for both companies;

In the case of Hegel, WACC = Ke and the annual dividend pay-out to shareholders is
35 million / £35,000,000.

For this, the company receives funding in the form of 80m shares – their nominal
value is 50p, so 80,000000 x 50p = £40,000,000 on the balance sheet –
worth 200p each, so their total market value is
80,000,000 x £ 2,000,000 = £160,000,000
Ke = WACC = £35m/£160m = 21.875%.

For Hume investors, the annual dividend pay-out is (35,000,000 less the debenture
interest of 10% x £60,000,000) = £29,000,000.
For this, the company receives funding in the form of 80m shares worth 175p each,
so their total market value is
80,000,000 x £1.75,000,000 = £140,000,000,
Ke = £29,000,000/£140,000,000 = 20.71% (2 d.p.).
Hume’s debentures are trading at par so the cost of debt is the same as the stated
nominal coupon rate of 10%.
Equity has a market value weighting of 140,000,000.
debt has a weighting of 60,000,00.
WACC = (20.71% x 140,000,000 + 10% x 60,000,000) / 200
= 17.5% (2 d.p.).
Shortcut: We could just have added the payments to the financiers and divided by
the total market value of the company – an idea that we’ve met before.

(b) Showing the steps in an arbitrage strategy, calculate the maximum capital
gain that, in the absence of corporate taxes, could be gained by an
investor who holds 1% of the equity in Hume plc without any reduction in
net income or change in risk;

Sell Hume
1% x 80,000,000 x 175p = £1.4,000,000

Borrow
1% x £60,000,000 = £600,000.
Available funds = £.1.4,000,000+ £600,000 = £2,000,000.

Buy Hegel
1% x £160,000,000 = £1.6,000,000

Capital Gain
£2,000,000 - £1.6,000,000 = £400,000.

We have a check available: the capital gain should be 1% of the difference in the
market values of the shares

1% x (£200,000,000 - £160,000,000) = £400,000:

Checks having a 1% investor simplifies the arithmetic, very often, we’re just moving
the decimal point.
 (c) Show that your scheme in (a) maintains the investor’s net income;

Before
1% x (£35,000,000 – 10% x £60,000,000) = £290,000.

After
1% x £35,000,000 – (1% x 10% x £60,000,000) = £290,000.

(d) By considering the impact of a 10% reduction in earnings before interest

on the investor’s net income, demonstrate that the investor’s risk position
would not change as a result of your scheme;

We consider whether the change in net income would be different if the company’s
earnings decreased:

Income from Hume would be:

1% x (900,000 x £35,000,000m– 10% x £60,000,000) = £255,000.

Income from Hegel would be:

1% x 900,000 x £35,000,000 – (1% x 10% x £60,000,000) = £255,000.

The investor is in no riskier a position after arbitraging than s/he was before.

(e) Suppose that an equilibrium position were to be reached whereby, as a

result of changes in the price of ordinary shares, the market values of both
companies stabilised at £180m. Calculate the following:

(i) the market value of an ordinary share in each company;

MVs of equity at equilibrium

Hegel
£180,000,000/80,000,000 = 2.25 each.

Hume
Assume that the value of the debentures is unaffected:
(£180,000,000 - £60,000,000)/80,000,000 = 1.50 each.

(ii) the weighted average cost of capital of each company;

Both
£35,000,000/£180,000,000 x 100% = 19.44% (2 d.p.)

(f) Compare the results of your calculations in part (a) with those of part (e) (ii)
and comment on their implications in the context of the Modigliani and Miller
capital structure irrelevance principle.

From part (a)

The WACCs are different:
For Hegel, the ungeared company, 21.88% (2 d.p.)
For Hume, 17.5%.
These results are consistent with the ‘traditional’ view that introducing debt into a
previously all-equity company will lower the WACC.

From part (e)

The WACCs are the same, which is consistent with the pre-tax MM model
and the view that corporate structure is irrelevant
- in the absence of taxation.

A key assumption of the ‘traditional’ view is that the introduction of debt will have no
effect on the cost of equity. Let’s see – at equilibrium:
For Hegel, Ke = £35,000,000/£180,000,000 x 100%= 19.44%.

For Hume, Ke = (£35,000,000 - £6,000,000)/£120,000,000 = 24.17%.

This result contradicts the traditional view and confirms the MM contention that
introducing debt will require that returns to equity holders will have to increase to
compensate for the additional financial risk attached to the investment.
Modigliani and Miller capital structure irrelevance principle

 There are no corporate taxes

 Investors are rational
 There are no transaction costs
 Capital markets are efficient
 There are equivalent firms
 Individuals can achieve corporate gearing.
 Interest rates are independent of the level of gearing
 There are no costs associated with financial distress

Comment:

There was no requirement to address the realism of the assumptions, merely to

identify them. However, it does no harm to write, if you have time, a brief comment
on the matter.

For example:

The assumption of the absence of corporate taxes holds in only a very few
jurisdictions. However, the ‘heroic assumption’ is relaxed in M & M’s 1963 paper.
The only remaining serious weaknesses are the last two in the list above.
Furthermore, it appears that the weaknesses are only significant at high levels of
gearing.

We might hypothesise that the tax advantages of loan capital cause the cost of
capital to fall steadily from low to moderate levels of gearing.
Above these moderate levels
the increase in return to providers of debt capital caused by the erosion of their
security, and the increase in return to holders of equity occasioned by the increased
risk of bankruptcy costs cause the cost of capital to increase. The problem then
becomes the identification of a ‘moderate’ level of gearing.
Of course, there will not be a single point representing moderate gearing — there will
be a range, or, rather, there will be a set of ranges, since the range will vary from
industrial sector to industrial sector.
Question 3

Both academic and empirical research suggest that the senior managers of listed
companies should, and do, have as their sole corporate objective the maximisation
of shareholder wealth.

Chapter one

Required:

(a) Explain the concept of the time value of money in relation to shareholder
wealth;

In the absence of a better metric, present value as a measure of monetary value that
incorporates the concept of the time value of money is taken as the proxy for
shareholder wealth in the academic literature and appears from empirical research
to be the criterion used for investment appraisal in practice.

(25%)

(b) Discuss the relative merits of the maximisation of profit and the maximisation
of shareholder wealth as corporate objectives;

In addition to the example given whereby the level of profit is increased whereas the
profit per share and therefore the profit per shareholder is decreased, there is the
wider issue that the aggressive pursuit of profit in the short term may damage a
firm’s prospects in the long-term through, for example, reputational damage.

(25%)

(c) Explain how Cyert & March’s concept of satisficing relates to the objective of
the maximisation of shareholder wealth;

Cyert & March assert that the firm is best seen as a coalition of stakeholder groups.
Each group must be respected and be given a fair return for their contribution to the
firm. If a stakeholder does not receive a return that is both sufficient and satisfactory,
they will act in a way that protects their interests, but damages the firm
and so decreases its value and hence the wealth of its owners,
the shareholders.

(25%)

(d) Discuss the relevance of the satisficing concept to a company professing both
sustainability and social responsibility objectives.
Essentially, the discussion hinges on the costs and benefits of ‘satisficing’
sustainability and social responsibility pressure groups
or not. How powerful is the Green lobby?
With both groups, it’s probably best to maintain awareness of,
and react to, any issues that could have an affect on ‘our’ company, its reputation,
and its sales and profit.