Question

A firm has the following capital structure: £240 million of equity (market value), trading at £2.4 per share, and £160 million of debt. The beta of the firm’s stock is 1.5. The firm’s cost of equity is 10 percent, and the expected return on the market portfolio is 7 percent. There is no tax. Assuming that the firm can borrow at the risk free rate and that both CAPM (Capital Asset Pricing Model) and the Modigliani-Miller theorem hold, answer the following questions. i) How many shares of the firm are outstanding? ii) What should be the risk free rate?What is the WACC of the firm? iii) What is the WACC of the firm? iv) Suppose the firm changes its capital structure so that its debt increases to £200 million, and the equity decreases by £40 million. What should be the firm’s cost of equity after the change?

Answer 1

(i) Market Value of Equity Capital = MV(E) = 240 million pound, Price of each equity share = 2.4 pound

Therefore, Number of Shares Outstanding = MV(E) / Price of each equity share = 100 million shares

(ii) Beta of firm's stock = , cost of equity of the firm = % , expected return on market portfolio = % and let the risk free rate be .

NOTE: CAPM states that the expected return of a portfolio or a security is proportional to the market risk premium (market portfolio return Less risk free rate) with the porportionality factor being equal to the portfolio's beta with respect to the benchmark index (the market portfolio in this case).

Therefore, by CAPM , where the values of each variable is given above.

Therefore, 10 = + 1.5 x (7 - )

= 1%

(iii) Let the cost of debt of the firm be denoted by . As the firms can borrow at the risk free rate (calculated in part (ii) above) the same should be its cost of debt

Therefore, = = 1%

Value of Equity = = 240 million pounds , Value of Debt = = 160 million pounds and

Total Value of Company = 160 + 240 = 400 million pounds

Corporate Tax Rate = 0 (as the question states that there is no tax)

Cost of Equity = %

Therefore, company WACC = = 10 x (240/400) + 1 x (160/400) = 6.4 %

(iv) The Modigliani Miller Theory states that in a perfect market the Capital Structure is irrelevant to a firm's WACC and consquently to its cost of equity. Hence, with changes in capital structures the firm's cost of equity remains constant.

NOTE: In practice however, the risk of default of the firm increases on taking up more debt (as in this case) and hence its equity beta increases thereby propping up the firm's cost of equity. The same can be calculated as given below

Let the Asset Beta be , Equity Beta : Before = =1.5 (given) and After =

Initial Capital Structure: Debt = D1 = 160 million pounds and Equity = E1 = 240 million pounds

Therefore, Initial DE Ratio = D1 / E1 = 160 / 240 = 2/3

Final Capital Structure: Debt = D2 = 200 million pounds (given) and Equity = E2 = 200 million pounds

Therefore Final DE Ratio = D2 / E2 = 1

Therefore, = [ / {1 + (D1/E1) } ] = [1.5 / {1 + (2/3)}] =0.9

Equity Beta post change in capital structure = x [1+(D2/E2)] = 0.9 x [1+1] = 0.9 x 2 =1.8

Risk Free Rate = =1 %, Market Return Rate = = 7% and new equity beta = 1.8

Therefore, utilizing CAPM: New Cost of Equity = = + x ( - )

= 1 + 1.8 x (7-1) = 11.8%