Suggested answers to selected problem questions(a) Personal borrowingLee’s dividend after the issue (12,500 ×£0.304) £3,800
Less: Interest (10% ×£3,000) £300
Lee’s income £3,500(b) The business borrowingProfit (pre-interest) £15.2m
Less: Interest (10% ×£12.0m) £1.2m
£14.0m
Earnings and dividend per share (£14.0m/40m) £0.35
Lee’s income (10,000 ×£0.35) £3,500Thus Lee’s income is identical for identical risk. Since homemade gearing is a perfect
substitute for corporate gearing, logically investors will not pay a premium to invest in
geared equities. Thus the cost of capital will be independent of the level of gearing, subject
to the MM assumptions.12.1 Distributors plcThe dividend will need to be such that its present value, discounted at the shareholders’
opportunity cost of capital, is £25m. That is:
£25m ×(1 +0.2)^3 =£43.2m
Together with the normal dividend of £25m, this makes a total of £68.2m.
If the payoff were to be more than £43.2m the shareholders would, in theory, prefer the
investment to be made. If the payoff were to be less than this amount the shareholders
would prefer the immediate dividend of £25m.12.3 HLM plcThe equity cost of capital is (1.5/10) ×100% =15% p.a.
In effect, the investment amounts to two outlays of £1.0m, the first after one year and the
second after two years, and an annual inflow of £0.4m in perpetuity starting after three years.
The NPV (in £m) of this investment is:−− + =−0.870 −0.756 +2.016which is equivalent to a £0.39m increase in the value of the business or a 3.9p increase in
the value of each share.12.6 Images plc
The NPVs of the projects are:
I −2.00 +(0.75 ×2.283) =−0.288
II −2.00 +(0.65 ×3.352) =+0.179
III −3.00 +(0.80 ×3.352) =−0.318
IV −1.00 +(0.50 ×2.283) =+0.142
Thus, logically, the cash generated from profits should be invested in Projects II and IV, a
total investment of £3m. This would leave £2m to be distributed as a dividend, since the0.4/0.15
(1 +0.15)^21.0
(1 +0.15)^21.0
(1 +0.15)Chapter 12
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