A firm currently has the following capital structure which it intends to maintai

Question

A firm currently has the following capital structure which it intends to maintain. Debt: $3,000,000 par value of 9% bonds outstanding with an annual before-tax yield to maturity of 7.67% on a new issue. The bonds currently sell for $1,150 each for a total market value of $3,450,000. Common stock: 46,000 shares outstanding currently selling for $50 per share. The firm expects to pay a $5.50 dividend per share one year from now and is experiencing a 3.67% growth rate in dividends, which it expects to continue indefinitely. The firm's marginal tax rate is 40%. The company has no plans to issue new securities. The firm's weighted average cost of capital is:

A. 0.0897

B. 0.0863

C. 0.1071

D. 0.1047

Explanation / Answer

Solution: Answer is B. 0.0863 Working Notes: market value Long term debt (Bond) 3,450,000 Given   Equity 2,300,000 [no of shares 46,000 x current price $50] Total market value of capital structure 5,750,000 cost of debt after tax (kd) = Annual before-tax yield to maturity x (1-tax rate) Kd= 7.67% x (1-0.40) Kd= 7.67% x 0.60 Kd= 4.602% Using Gordon growth model : P0 = D1 / (Ke - g), where D1 =$5.50 cost of equity (ke) = Po=current share price = $50 per share g= growth rate= 3.67 % P0 = D1/(Ke -g) Ke= D1/P0 + g Ke= $5.50/$50 + 3.67% Ke= 0.11 + 3.67% Ke= 11% + 3.67% Cost of equity (Ke) = 14.67% long term Debt weight in capital structure = D/V = market Value of debt / Total mkt Value of Company =3,450,000/5,750,000 =0.60 Common stock weight in capital structure = E/V = mkt Value of common stock / Total mkt Value of Company =2,300,000/5,750,000 =0.40 WACC= Ke x E/V + Kd   x D/V E/V =   0.40       from above calculation D/V = 0.60 WACC= Ke x E/V + Kd   x D/V = 14.67% x 0.40 + 4.602% x 0.60 =0.086292 =0.0863 Please feel free to ask if anything about above solution in comment section of the question.

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