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The Imaginary Products Co. currently has debt with a market value of $250 million outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon payments) which have a maturity of 15 years and are currently priced at $931.90 per bond. The firm also has an issue of 2 million preferred shares outstanding with a market price of $22. The preferred shares pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 7 percent per year forever. If Imaginary is subject to a 40 percent marginal tax rate, then what is the firm’s weighted average cost of capital?

Explanation / Answer

1)

Market value of debt = 250,000,000

Market value of preferred stock = 2,000,000 * 22 = 44,000,000

Market value of common stock = 14,000,000 * 20 = 280,000,000

Total market value =  250,000,000 + 44,000,000 + 280,000,000 = 574,000,000

Weight of debt = 250,000,000 / 574,000,000 = 0.4355 or 43.55%

Weight of preferred stock = 44,000,000 / 574,000,000 = 0.0767 or 7.67%  

Weight of common stock = 280,000,000 / 574,000,000 = 0.4878 or 48.78%

2)

Face value = 1,000

Coupon payment = 0.09 * 1000 = 90 / 2 = 45

Number of periods = 15 * 2 = 30

Before tax cost of debt using a financial calculator = 9.8799%

Keys to use in a financial calculator = 2nd I/Y 2, FV 1000, PV -931.9, PMT 45, N 30, CPT I/Y

After tax cost of debt = 0.098799 ( 1 - 0.4)

After tax cost of debt = 5.93%

3)

Cost of preferred equity = Annual dividend / Preferred share price

Cost of preferred equity = 1.2 / 22

Cost of preferred equity = 0.054545 or 5.45%

4)

Cost of common equity = ( D1 / share price ) + growth rate

Cost of common equity = ( 2.2 / 20 ) + 0.07

Cost of common equity = 0.18 or 18%

5)

Weighted average cost of capital = Weight of debt * cost of debt + weight of preferred stock * cost of preferred stock + weight of common stock * cost of common stock

Weighted average cost of capital = 0.4355 * 0.0593 + 0.0767 * 0.0545 + 0.4878 * 0.18

Weighted average cost of capital = 0.025825 + 0.00418 + 0.087804

Weighted average cost of capital = 0.1178 or 11.78%

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