The following information is available concerning a firm's capital: Debt : Bonds with a face value of $1000 and an initial 20-year term were issued five years ago with a coupon rate of 8% paying semiannually. Today these bonds are selling for $846.30.
Preferred stock : Preferred stock that pays an annual dividend of $9.50 is trading at $79.16.
Common equity : The stock is selling for $22.50 per share. An annual dividend of $1.70 was just paid and is expected to grow indefinitely at 6%.
Target capital structure : The firm's target capital structure is of 30% debt, 20% preferred stock, and 50% equity.
The firm can issue any type of security without paying floatation costs. The combined federal and state tax rate is 40%. Calculate the firm's WACC based on its target capital structure.

Question

Quizplus · Accepted Answer

1) Cost of debt:

Since the bonds are currently selling for $846.30 whereas they were issued at $1000, it is assumed that the market rate is now different from the coupon rate. Therefore, we need to calculate the current yield-to-maturity as the cost of debt.

PV = -$846.30, FV = $1000, PMT = $40 (8% coupon rate, semi-annual), n = 30-5=25*2 = 50 (semi-annual periods)
Solving for i (yield-to-maturity): 
PV = FV / (1+i)^n + PMT * [(1 - 1 / (1+i)^n ) / i]
i = 4%

After considering the tax deductibility, the after-tax cost of debt is: 
After-tax cost of debt = Yield-to-maturity * (1 - tax rate) 
= 4% * (1 - 0.4) 
= 2.4%

2) Cost of preferred stock:

Cost of preferred stock = Preferred dividend / Net issuing price 
Net issuing price = $79.16 * (1 - 0.4) = $47.50 ($79.16 is before-tax price)
Cost of preferred stock = $9.50 / $47.50 = 20%

3) Cost of equity:

Cost of equity (using dividend growth model) = (Dividend / Current stock price) + Growth rate of dividend 
Growth rate of dividend = 6% 
Cost of equity = ($1.70 * (1+0.06)) / $22.50 + 0.06 
= 13.2%

4) Weighted average cost of capital (WACC):

WACC = (Weight of debt * cost of debt) + (Weight of preferred stock * cost of preferred stock) + (Weight of equity * cost of equity) 
= (0.3 * 2.4%) + (0.2 * 20%) + (0.5 * 13.2%) 
= 11.2%

The Following Information Is Available Concerning a Firm's Capital: Debt