WACC and Valuation -Traditional Perspective Cost of capital
Cost of Equity WACC
0.20
Cost of Debt
0.08 Debt / Equity
Value
Optimal Debt/Equity Ratio
Value of Company V0 = X X
1 k
1 = V0 inverse relationship between value and the discount rate k¯
Debt / Equity
2
Optimal Debt/Equity Ratio
The Cost of Equity, the Cost of Debt, and the Weighted Average Cost of Capital: MM Proposition II with No Corporate Taxes Cost of capital:
k e = kU +
kU
W A C C = kO =
BG ´ ( kU - k i ) SG
BG SG ´ ki + ´ ke BG + SG BG + SG ki
ki
Debt-to-equity Ratio 3
BG SG
Question 1: Tartan plc (Introduction of Gearing) Tartan plc has always followed a policy of avoiding any debt financing. But the company needs to raise an additional £26m to finance a major project and is considering the issue of bonds at 9 per cent. Alternatively it could sell 13 million additional shares at the prevailing market price of £2. This would increase the number of shares outstanding to 30 million. The annual earnings following the investment in the new project are expected to be £20m before tax. The company is not expected to be able to generate any other investments that will be worth exploiting and expected earnings are expected to remain constant indefinitely into the future. One of the advantages of employing debt would be the tax savings associated with the interest expense. The tax rate is 40 per cent. But it is also recognised that earnings could fall below the expected level in any one period. No of shares outstanding ( N 0 ) Proposed issue of shares (DN ) Price per share Additional Funding Required
17m 13m £2m £26m
Question 1 a Solution a) Calculate the expected earnings per share for both financing possibilities.
Expected earnings before interest and tax Interest (0.09 x26m) Earnings before tax Tax(40 per cent) Profit after tax Number of shares outstanding Expected earnings per share (EPS)
20 0 20 -8 12 30 0.400
20 -2.34 17.66 -7.064 10.596 17 0.623
Question 1 b Solution
b Calculate the level of earnings at which earnings per share would be the same for both financing possibilities. Let the level of earnings (profit) at which the expected earnings per share would be the same for both financing options be X * .
(
)
X * (1 - tc ) X * - ki BG (1 - tc ) = N 0 + DN N0
(
)
X * (1 - 0.4 ) X * - 0.09 ´ £26m (1 - .4 ) = 30m 17 m Cancel the tax factors and cross multiply 17 X *m = 30 X *m - 70.2m 13 X *m = 70.2m X * = 5.4m
Question 1 b – Check answer Expected earnings before interest and tax Interest (0.09 x26m) Earnings before tax Tax(40 per cent) Profit after tax Number of shares outstanding Expected earnings per share (EPS)
5.4 0 5.4 -2.16 3.24 30 0.108
5.4 -2.34 3.06 -1.224 1.836 17 0.108
The overall capital employed is £60m (30m shares at £2.00) and to produce the same EPS for the two financing options will require the rate of return on the capital to be equal to the interest rate (0.09 x £60m = £5.4m). If the rate of return on capital employed is equal to the interest rate the component of the capital funded by debt does not create a surplus or deficit for the shareholders. This implies that the EPS will be the same whether the financing is by debt or equity.
Question 1c
As the earnings per share are expected to be greater if debt financing is employed does this imply that the new project should necessarily be financed by debt?
In a word – no! The earnings per share for the geared option is riskier than that for the ungeared option, and consequently are not directly comparable. Rather than consider the impact on the earnings per share figure the company should focus on the cost of capital in the assessment of financing options. Lastly, the earnings per share figure for one year might be misleading if we drop the convenient assumption that expected earnings are unchanged indefinitely into the future – the perpetuity assumption is convenient but not always appropriate.
Question 2a
Araf Plc has run into cash flow problems recently as a result of a fall in sales caused by an economic recession and is having difficulty servicing its debts. The company has discussed the possibility of a rights issue with its investment bank and it has been agreed that this is the most appropriate way of dealing with its problems. The investment bank has warned the CEO that the company should anticipate that the announcement of the issue is very likely to produce a negative reaction in the market. When the company’s board of directors is told this some directors oppose the proposed issue on the grounds that it will push down the share price and this will not be in the shareholders’ interest. As the CEO respond to these concerns of the shareholders.
Question 2a Solution
Araf Plc has run into cash flow problems recently as a result of a fall in sales caused by an economic recession and is having difficulty servicing its debts. The company has discussed the possibility of a rights issue with its investment bank and it has been agreed that this is the most appropriate way of dealing with its problems. The investment bank has warned the CEO that the company should anticipate that the announcement of the issue is very likely to produce a negative reaction in the market. When the company’s board of directors is told this some directors oppose the proposed issue on the grounds that it will push down the share price and this will not be in the shareholders’ interest. As the CEO respond to these concerns of the shareholders.
If the company’s shares are overvalued as a result of the market being unaware of the company’s cash flow problems, particularly if these problems are indicative of even more fundamental difficulties, the share price will eventually fall anyway. Any expected fall is not the result of the issue of new shares, but the consequence of the basic problems facing the company. A failure to raise the funds may result in even more problems and an even lower value for the company. Despite the possibility of a fall in the share price the company may need to proceed with the issue and to keep the market informed of its position and intentions.
Question 2b Solution
Explain why information asymmetry may explain the average market response to cash offers to raise funds but are not so likely to explain the average market response to the announcement of a rights issue.
The information asymmetry based on the different information available to managers and investors assumes that the investors believe that managers will exploit their added information. They assume that the managers will only issue shares to outside investors when they are overvalued. If they achieve this it will benefit their existing shareholders. In the case of a rights issue the shares are sold to insiders and consequently there are no external investors to exploit on their behalf.
Question 3
Miller plc is expected to produce earnings next year of £18m and it is anticipated that it will be able to maintain this level of earnings indefinitely into the future. The company is financed entirely by equity and has a market value of £150m. The company’s management is considering the possibility of issuing debt of £50m and it has been established that this can be done at an interest rate of 6 per cent. The proceeds would be used to buy back £50m worth of its equity.
Determine the cost of equity capital and the weighted average cost of capital for the company if its capital structure is restructured to include debt of £50m. Use both the traditional and Modigliani-Miller approaches in answering the question. Assume there are no corporate taxes.
Question 3 Answer (1) VU = £150m BG = £50m
Traditional Approach The cost of geared equity, ke , and the cost of debt, ki , are assumed to be remain constant over limited amounts of debt – assume £50m constitutes a limited amount of debt in this context - where kU = X = X = £18m = 0.12 = ke the cost of equity capital for an SU
VU
£150m
ungeared company with constant expected earnings The cost of equity is assumed to remain constant as debt is substituted for equity financing as there is no perception of any increase in equity risk until the level of debt increases to the point where it is thought to be a good chance of it leading to the firm’s bankruptcy at some stage in the future. The increase in equity risk in the form of the added variability of returns is not recognised
Question 3 Answer (2) Traditional Approach WACC = k e = 0.12 x
SG BG + ki SG + B G SG + B G
100m 50 m + 0.06 x = 0.10 100m + 50 m 100m + 50 m
Modigliani - Miller Approach B 50 m k e = kU + (kU - ki ) G = 0.12 + (0.12 - 0.06) = 0.15 SG 100m WACC = k e = 0.15 x
SG BG + ki SG + B G SG + B G
100m 50 m + 0.06 x = 0.12 = kU 100m + 50 m 100m + 50 m
Question 4 Alban plc and Bruce plc are companies with identical assets and expected cash flow. Alban is financed entirely by equity whereas Bruce employs some debt capital. Alban has 100 million shares outstanding and these are trading at £6.00 per share. Brice employs debt of £150 million and has 75 million shares outstanding. The interest rate on the dent is 8 per cent and the company’s expected earnings are £96 million. a) Based on the analysis developed by Modigliani and Miller (with no taxes) determine the equity cost of capital for both Alban and Bruce. b) Determine the weighted average cost of capital for both companies.
Question 4: Solution Given M - M assumptions VA = VB = PA xN A = 6.00 x100m = 600m VB = SG + BG SG = VB - BG = 600m - 150m = 450m kUA =
X 96m = = 0.16 = WACC A VA 600m
keB =
X - ki BG 96m - 0.08 x150m 84m = = = 0.186 V 450 m 450 m SG B
WACC B = kOB = keB = 0.186
Equity Debt + ki Equity + Debt Equity + Debt
450m 150m + .08 = 0.16 600m 600m
= 0.16 WACC A = WACC B = 0.16
Question 5 In an economy characterised by perfectly competitive markets an un-geared company with expected earnings in perpetuity of £100m is valued in the market at £500m. An equivalent company that employs £200m debt, issued at 10 per cent, is valued at £600m. A shareholder owns 20 per cent of the geared company’s equity. Demonstrate that the shareholder will benefit from selling her shares and borrowing and investing in the un-geared company.
Question 5 Solution Given M - M assumptions VU = 500m
VG = SG + BG = 600m
SG = VB - BG = 600m - 200m = 400m
Shareholder owns 0.20x SG = 0.20x 400m = 80m Shareholder sells shares to realise 80m Shareholder borrows 0.20 BG = 0.20 x 200m = 40m Total shareholder funds to invest in the ungeared equity = 120m Earnings from the initial investment in G YG = 0.20 x EAE (G) = 0.20 (X - k i ) = 0.20 (100 - 0.10 x 200) = 16 Earnings from the investment in U
New ownership of the ungeared firm = 120/500 = 24%
YU = 0.24 x (X) - k i B personal = (0.24 x 100) - ( 40 x 0.10) = 20 YU > YG
and the risk is the same as the personal borrowing produces the same ratio
of debt to equity for the investor as is employed by the geared company. This should lead to the sale of shares in G and the purchase of the shares in U, leading to a fall in the value of the equity of G and an increase in the value of the equity of U. This will continue until VG = VU .
Question 6 Dunbar plc is financed entirely by equity and its expected earnings before interest and tax is £180m and the tax rate is 30 per cent. Its equity is valued at £840m. a) Determine the required rate of return on the ungeared equity. b) Specify Dunbar’s cost of equity using the capital asset pricing model. Assume a risk free rate of 7 per cent and an expected return on the market of 13 per cent. ( The company’s beta is 1.25. c) Now assume that the company restructures its financing to employ £300 of debt. Determine the value of the company and its equity, recognising the tax advantages of debt. d) The interest rate on the debt is 7 per cent as it is risk free. Determine the company’s cost of equity capital and its overall cost of capital – derive both using different approaches (equations).
Question 6 Answers Dunbar plc is financed entirely by equity and its expected earnings before interest and tax is £180m and the tax rate is 30 per cent. Its equity is valued at £840m.
a) Determine the required rate of return on the ungeared equity. Given M - M assumptions VA = VB = PA xN A = 6.00 x100m = 600m VB = SG + BG SG = VB - BG = 600m - 150m = 450m kU =
X (1 - tC ) 180m(1 - 0.30) = = 0.15 = k0 VA 840m
b) Specify Dunbar’s cost of equity using the capital asset pricing model. Assume a risk free rate of 7 per cent and an expected return on the market of 13 per cent. ( The company’s beta is 1.33.) E ( RU ) = RF + bU ( E ( RM ) - RF ) = 0.07 + 1.33(0.13 - 0.07) = 0.15
Question 6 Answers c) Now assume that the company restructures its financing to employ £300 of debt. Determine the value of the company and its equity, recognising the tax advantages of debt. VG = VU + tC BG = 840m + 0.30 x300m = 930m SG = VG - BG = 930
d) The interest rate on the debt is 7 per cent as it is risk free. Determine the company’s cost of equity capital and its overall cost of capital – derive both using different approaches (equations). ke = kU + (kU - ki )(1 - tC ) BG / SG = 0.15 + (0.15 - 0.07)(1 - 0.30)300m / 630m = 0.176 keB =
