每日一练F9 答案回复可见

following, ordinary, average, capital, company

1 Burse Co wishes to calculate its weighted average cost of capital and the following information relates to the company
at the current time:
Number of ordinary shares 20 million
Book value of 7% convertible debt $29 million
Book value of 8% bank loan $2 million
Market price of ordinary shares $5·50 per share
Market value of convertible debt $107·11 per $100 bond
Equity beta of Burse Co 1·2
Risk-free rate of return 4·7%
Equity risk premium 6·5%
Rate of taxation 30%
Burse Co expects share prices to rise in the future at an average rate of 6% per year. The convertible debt can be
redeemed at par in eight years’ time, or converted in six years’ time into 15 shares of Burse Co per $100 bond.
Required:
(a) Calculate the market value weighted average cost of capital of Burse Co. State clearly any assumptions that
you make. (12 marks)
(b) Discuss the circumstances under which the weighted average cost of capital can be used in investment
appraisal. (6 marks)
(c) Discuss whether the dividend growth model or the capital asset pricing model offers the better estimate of
the cost of equity of a company. (7 marks)
(25 marks)

1 (a) Calculation of weighted average cost of capital (WACC)
Cost of equity
Cost of equity using capital asset pricing model = 4·7 + (1·2 x 6·5) = 12·5%
Cost of convertible debt
Annual after-tax interest payment = 7 x (1 – 0·3) = $4·90 per bond
Share price in six years’ time = 5·50 x 1·066 = $7·80
Conversion value = 7·80 x 15 = $117·00 per bond
Conversion appears likely, since the conversion value is much greater than par value.
The future cash flows to be discounted are therefore six years of after-tax interest payments and the conversion value received
in year 6:
Year Cash flow $ 10% DF PV ($) 5% DF PV ($)
0 market value (107·11) 1·000 (107·11) 1·000 (107·11)
1–6 interest 4·9 4·355 21·34 5·076 24·87
6 conversion 117·00 0·564 66·00 0·746 87·28
––––––– ––––––––
(19·77) 5·04
––––––– ––––––––
Using linear interpolation, after-tax cost of debt = 5 + [(5 x 5·04)/(5·04 + 19·77)] = 6·0%.
(Note that other after-tax costs of debt will arise if different discount rates are used in the linear interpolation calculation.)
We can confirm that conversion is likely and implied by the current market price of $107·11 by noting that the floor value of
the convertible debt at an after-tax cost of debt of 6% is $93·13 (4·9 x 6·210 + 100 x 0·627).
Cost of bank loan
After-tax interest rate = 8 x (1 – 0·3) = 5·6%
This can be used as the cost of debt for the bank loan.
An alternative would be to use the after-tax cost of debt of ordinary (e.g. not convertible) traded debt, but that is not available
here.
Market values
Market value of equity = 20m x 5·50 = $110 million
Market value of convertible debt = 29m x 107·11/100 = $31·06 million
Book value of bank loan = $2m
Total market value = 110 + 31·06 + 2 = $143·06 million
WACC = [(12·5 x 110) + (6·0 x 31·06) + (5·6 x 2)]/143·06 = 11·0%
(b) The weighted average cost of capital (WACC) can be used as a discount rate in investment appraisal provided that the risks
of the investment project being evaluated are similar to the current risks of the investing company. The WACC would then
reflect these risks and represent the average return required as compensation for these risks.
WACC can be used in investment appraisal provided that the business risk of the proposed investment is similar to the
business risk of existing operations. Essentially this means that WACC can be used to evaluate an expansion of existing
business. If the business risk of the investment project is different from the business risk of existing operations, a projectspecific
discount rate that reflects the business risk of the investment project should be considered. The capital asset pricing
model (CAPM) can be used to derive such a project-specific discount rate.
WACC can be used in investment appraisal provided that the financial risk of the proposed investment is similar to the
financial risk of existing operations. This means that financing for the project should be raised in proportions that broadly
preserve the capital structure of the investing company. If this is not the case, an investment appraisal method called adjusted
present value (APV) should be used. Alternatively, the CAPM-derived project-specific cost of capital can be adjusted to reflect
the financial risk of the project financing.
A third constraint on using WACC in investment appraisal is that the proposed investment should be small in comparison with
the size of the company. If this were not the case, the scale of the investment project could cause a change to occur in the
perceived risk of the investing company, making the existing WACC an inappropriate discount rate.
(c) The dividend growth model has several difficulties attendant on its use as a way of estimating the cost of equity. For example,
the model assumes that the future dividend growth rate is constant in perpetuity, an assumption that is not supported by the
way that dividends change in practice. Each dividend paid by a company is the result of a dividend decision by managers,
who will consider, but not be bound by, the dividends paid in previous periods. Estimating the future dividend growth rate is
also very difficult. Historical dividend trends are usually analysed and on the somewhat risky assumption that the future will
repeat the past, the historic dividend growth rate is used as a substitute for the future dividend growth rate. The model also
assumes that business risk, and hence business operations and the cost of equity, are constant in future periods, but reality
shows us that companies, their business operations and their economic environment are subject to constant change. Perhaps
the one certain thing about the future is its uncertainty.

It is sometimes said that the dividend growth model does not consider risk, but risk is implicit in the share price used by the
model to calculate the cost of equity. A moment’s thought will indicate that share prices fall as risk increases, indicating that
increasing risk will lead to an increasing cost of equity. What is certainly true is that the dividend growth model does not
consider risk explicitly in the same way as the capital asset pricing model (CAPM). Here, all investors are assumed to hold
diversified portfolios and as a result only seek compensation (return) for the systematic risk of an investment. The CAPM
represent the required rate of return (i.e. the cost of equity) as the sum of the risk-free rate of return and a risk premium
reflecting the systematic risk of an individual company relative to the systematic risk of the stock market as a whole. This risk
premium is the product of the company’s equity beta and the equity risk premium. The CAPM therefore tells us what the cost
of equity should be, given an individual company’s level of systematic risk.
The individual components of the CAPM (the risk-free rate of return, the equity risk premium and the equity beta) are found
by empirical research and so the CAPM gives rise to a much smaller degree of uncertainty than that attached to the future
dividend growth rate in the dividend growth model. For this reason, it is usually suggested that the CAPM offers a better
estimate of the cost of equity than the dividend growth model.