Fundamentals Level – Skills Module, Paper F9

　　Financial Management

　　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

　　––––– –––––

　　(19·59) 4·71

　　––––– –––––

　　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 therefore

　　its shares are more difficult to buy and sell than those of a listed company such as KFP Co. If we reduce the applied

　　price/earnings ratio by 10% (other similar percentage reductions would be acceptable), it becomes 7·2 times and the

　　value 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 dividend

　　growth, i.e. 4·5%. Assuming that this dividend growth continues in the future, the future dividend growth rate will be

　　4·5%.

　　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 relative

　　risk of the two sources of finance. Equity is riskier than debt and so equity is more expensive than debt. This does not depend

　　on the tax efficiency of debt, since we can assume that no taxes exist. We can also assume that as a company gears up, it

　　replaces equity with debt. This means that the company’s capital base remains constant and its weighted average cost of

　　capital (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 a

　　company gears up, there is initially very little increase in the cost of equity and the WACC decreases because the cost of debt

　　is less than the cost of equity. A point is reached, however, where the cost of equity rises at a rate that exceeds the reduction

　　effect of cheaper debt and the WACC starts to increase. In the traditional view, therefore, a minimum WACC exists and, as a

　　result, 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 reduction

　　effect of cheaper debt. WACC was therefore constant at all levels of gearing and no optimal capital structure, where the value

　　of 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 interest