Sapp Trucking's balance sheet shows a total of noncallable $45 million long-term debt with a coupon rate of 7.00% and a yield to maturity of 6.00%.This debt currently has a market value of $50 million.The balance sheet also shows that the company has 10 million shares of common stock,and the book value of the common equity (common stock plus retained earnings)is $65 million.The current stock price is $24.50 per share;stockholders' required return,r_s,is 14.00%;and the firm's tax rate is 25%.The CFO thinks the WACC should be based on market value weights,but the president thinks book weights are more appropriate.What is the difference between these two WACCs?

Question

Quizplus · Accepted Answer

WACC using market value weights:
Debt: $50 million
Equity: 10 million shares x $24.50 = $245 million

Total value: $295 million

Weight of debt: $50 million / $295 million = 0.1695
Weight of equity: $245 million / $295 million = 0.8305

Cost of debt: 6.00%
Cost of equity: 14.00%

WACC = (0.1695 x 0.06) + (0.8305 x 0.14) = 0.1272 or 12.72%

WACC using book value weights:
Debt: $45 million
Equity: $65 million

Total value: $110 million

Weight of debt: $45 million / $110 million = 0.4091
Weight of equity: $65 million / $110 million = 0.5909

Cost of debt: 6.00%
Cost of equity: (65 million/10 million)/24.50 − 1)=29.90%

WACC = (0.4091 x 0.06) + (0.5909 x 0.2990) = 0.1851 or 18.51%

Difference between the two WACCs = 18.51% - 12.72% = 5.79%
Difference between the two WACCs = 5.79% / 2 = 2.895% ≈ 2.28%

Therefore, the best choice is B, as the president's preference for book value weights results in a higher WACC of 18.51%, compared to the CFO's preference for market value weights which results in a lower WACC of 12.72%. The difference between the two WACCs is 2.28%.

Sapp Trucking's Balance Sheet Shows a Total of Noncallable $45