Question

Zagrot Trucking’s balance sheet shows a total of noncallable $45 million long-term debt with a coupon rate of 8.00% and a yield to maturity of 6.00%. This debt currently has a market value of $100 million. The balance sheet also shows that the company has 20 million shares of common stock, and the book value of the common equity (common stock plus retained earnings) is $650 million. The current stock price is $100 per share; stockholders' required return, r_s, is 13.00%; and the firm's tax rate is 21%. 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?

Answer 1

MV WACC

MV of equity=Price of equity*number of shares outstanding

MV of equity=100*20000000

=2000000000

MV of Bond=Par value*bonds outstanding*%age of par

MV of Bond=1000*45000*2.22222222222222

=100000000

MV of firm = MV of Equity + MV of Bond

=2000000000+100000000

=2100000000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 2000000000/2100000000

W(E)=0.9524

Weight of debt = MV of Bond/MV of firm

Weight of debt = 100000000/2100000000

W(D)=0.0476

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 6*(1-0.21)

= 4.74

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.74*0.0476+13*0.9524

WACC =12.61%

BV WACC

BV of firm = BV of Equity + BV of Bond

=650000000+45000000

=695000000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 650000000/695000000

W(E)=0.9353

Weight of debt = MV of Bond/MV of firm

Weight of debt = 45000000/695000000

W(D)=0.0647

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 6*(1-0.21)

= 4.74

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.74*0.0647+13*0.9353

WACC =12.47%

Difference: 12.61-12.47=0.14%