1 (a) Weighted average cost of capital (WACC) calculation
Cost of equity of KFP Co = 4·0 + (1·2 x (10·5 – 4·0)) = 4·0 + 7·8 = 11·8% using the capital asset pricing model
To calculate the after-tax cost of debt, linear interpolation is needed
After-tax interest payment = 100 x 0·07 x (1 – 0·3) = $4·90
Year Cash flow $ 10% discount PV ($) 5% discount PV ($)
0 Market value (94·74) 1·000 (94·74) 1·000 (94·74)
1 to 7 Interest 4·9 4·868 23·85 5·786 28·35
7 Redemption 100 0·513 51·30 0·711 71·10
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(19·59) 4·71
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After-tax cost of debt = 5 + ((10 – 5) x 4·71)/(4·71 + 19·59) = 5 + 1·0 = 6·0%
Number of shares issued by KFP Co = $15m/0·5 = 30 million shares
Market value of equity = 30m x 4·2 = $126 million
Market value of bonds issued by KFP Co = 15m x 94·74/100 = $14·211 million
Total value of company = 126 + 14·211 = $140·211 million
WACC = ((11·8 x 126) + (6·0 x 14·211))/140·211 = 11·2%
(b) (i) Price/earnings ratio method
Earnings per share of NGN = 80c per share
Price/earnings ratio of KFP Co = 8
Share price of NGN = 80 x 8 = 640c or $6·40
Number of ordinary shares of NGN = 5/0·5 = 10 million shares
Value of NGN = 6·40 x 10m = $64 million
However, it can be argued that a reduction in the applied price/earnings ratio is needed as NGN is unlisted and thereforeits shares are more difficult to buy and sell than those of a listed company such as KFP Co. If we reduce the appliedprice/earnings ratio by 10% (other similar percentage reductions would be acceptable), it becomes 7·2 times and thevalue of NGN would be (80/100) x 7·2 x 10m = $57·6 million
(ii) Dividend growth model
Dividend per share of NGN = 80c x 0·45 = 36c per share
Since the payout ratio has been maintained for several years, recent earnings growth is the same as recent dividendgrowth, i.e. 4·5%. Assuming that this dividend growth continues in the future, the future dividend growth rate will be4·5%.Share price from dividend growth model = (36 x 1·045)/ (0·12 – 0·045) = 502c or $5·02
Value of NGN = 5·02 x 10m = $50·2 million
(c) A discussion of capital structure could start from recognising that equity is more expensive than debt because of the relativerisk of the two sources of finance. Equity is riskier than debt and so equity is more expensive than debt. This does not dependon the tax efficiency of debt, since we can assume that no taxes exist. We can also assume that as a company gears up, itreplaces equity with debt. This means that the company’s capital base remains constant and its weighted average cost ofcapital (WACC) is not affected by increasing investment.
The traditional view of capital structure assumes a non-linear relationship between the cost of equity and financial risk. As acompany gears up, there is initially very little increase in the cost of equity and the WACC decreases because the cost of debtis less than the cost of equity. A point is reached, however, where the cost of equity rises at a rate that exceeds the reductioneffect of cheaper debt and the WACC starts to increase. In the traditional view, therefore, a minimum WACC exists and, as aresult, a maximum value of the company arises.
Modigliani and Miller assumed a perfect capital market and a linear relationship between the cost of equity and financial risk.
They argued that, as a company geared up, the cost of equity increased at a rate that exactly cancelled out the reductioneffect of cheaper debt. WACC was therefore constant at all levels of gearing and no optimal capital structure, where the valueof the company was at a maximum, could be found.
It was argued that the no-tax assumption made by Modigliani and Miller was unrealistic, since in the real world interestpayments were an allowable expense in calculating taxable profit and so the effective cost of debt was reduced by its taxefficiency. They revised their model to include this tax effect and showed that, as a result, the WACC decreased in a linearfashion as a company geared up. The value of the company increased by the value of the ‘tax shield’ and an optimal capitalstructure would result by gearing up as much as possible.
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