Question

Norfolk Southerns' (NS) balance sheet shows a total of $50 million long-term debt with a coupon rate of 8.00%. The yield to maturity on this debt is 7.00%, and the debt has a total current market value of $40 million. The balance sheet also shows that the company has 10 million shares of stock, and the stock has a book value per share of $6.00. The current stock price is $25.00 per share, and stockholders' required rate of return, rs, is 14.00%. The company recently decided that its target capital structure should have 30% debt, with the balance being common equity. The tax rate is 40%. Calculate WACCs based on book, market, and target capital structures, and then find the average of these three WACCs.

Answer 1

Calculating WACC on the basis of book value

Book value of debt = $50 million = D, Book value of Equity = E = no of shares x book value per share = 10 million x 6 = $60 million

Total book value of capital =T = D + E = 50 + 60 = $110 million

Pre tax cost of debt = r_d = yield to to maturity of debt = 7%, Cost of equity = stockholder's required rate of return = r_s = 14%

WACC based on book value = r_d(D/T)(1-tax rate) + r_s(E/T) = 7%(50/110)(1-40%) + 14%(60/110)

= 7% x 0.454545 x 60% + 14% x 0.545454 = 0.019090 + 0.076363 = 0.0954543 = 9.54543%

Calculating WACC on the basis of market value

market value of debt = $40 million = D, Market value of Equity = E = no of shares x current stock price per share = 10 million x 25 = $250 million

Total market value of capital =T = D + E = 40 + 250 = $290 million

Pre tax cost of debt = r_d = yield to to maturity of debt = 7%, Cost of equity = stockholder's required rate of return = r_s = 14%

WACC based on market value = r_d(D/T)(1-tax rate) + r_s(E/T) = 7%(40/290)(1-40%) + 14%(250/290)

= 7% x 0.137931 x 60% + 0.862069 x 14% = 0.005793 + 0.120689 = 0.126482 = 12.6482%

Calculating WACC on the basis of target capital structure

Weight of debt = D/T = 30% , Weight of equity = E/T = 1 - (D/T) = 1 - 30% = 70%

Pre tax cost of debt = r_d = yield to to maturity of debt = 7%, Cost of equity = stockholder's required rate of return = r_s = 14%

WACC based on market value = r_d(D/T)(1-tax rate) + r_s(E/T) = 7%(30%)(1-40%) + 14%(70%) = 7% x 30% x 60% + 14% x 70% = 1.26% + 9.8% = 11.06%

Calculating average of three WACCs = (WACC on basis of book value + WACC on basis of market value + WACC on basis of target capital structure) / 3 = ( 9.5454% + 12.6482% + 11.06%) / 3 =33.2536% / 3 = 11.08453 % = 11.08% (rounded to two decimal places)