Question

3.     Kruger Industrial Smoothing has a target capital structure consisting of 30% debt, 5% preferred stock, and 65% common equity. Kruger has 20-year, 7.25% semiannual coupon bonds that are selling for $875. Kruger’s preferred stock sells for $95 and pays a 9% dividend on a $100 par value. Kruger is a constant growth firm with a growth rate of 4% and just paid a dividend of $2.35 on its common stock that is currently selling for $30.00 per share. The beta is 1.25 and the risk free rate is 5.25%. The required return on the stock market is 11.50%. The firm’s marginal tax rate is 40%.   

        a.   What is Kruger’s component after-tax component cost of debt?

        b.   What is Kruger’s component cost of preferred stock?

        c.   What is Kruger’s component cost of common equity based on the CAPM?

        d.   What is Kruger’s component cost of common equity based on the DCF model?

        e.   What is the WACC for Kruger assuming the firm use an average component cost of equity given the two       methods used?

Answer 1

Answer a.

Face Value = $1,000
Current Price = $875

Annual Coupon Rate = 7.25%
Semiannual Coupon Rate = 3.625%
Semiannual Coupon = 3.625% * $1,000
Semiannual Coupon = $36.25

Time to Maturity = 20 years
Semiannual Period to Maturity = 40

Let semiannual YTM be i%

$875 = $36.25 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -875
PMT = 36.25
FV = 1000

I = 4.283%

Semiannual YTM = 4.283%
Annual YTM = 2 * 4.283%
Annual YTM = 8.566%

Before-tax Cost of Debt = 8.566%
After-tax Cost of Debt = 8.566% * (1 - 0.40)
After-tax Cost of Debt = 5.14%

Answer b.

Par Value = $100
Current Price = $95

Annual Dividend = 9.00% * $100
Annual Dividend = $9

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $9 / $95
Cost of Preferred Stock = 9.47%

Answer c.

Cost of Equity = Risk-free Rate + Beta * (Return on Market - Risk-free Rate)
Cost of Equity = 5.25% + 1.25 * (11.50% - 5.25%)
Cost of Equity = 13.06%

Answer d.

Last Dividend = $2.35
Growth Rate = 4%
Current Price = $30

Expected Dividend = Last Dividend * (1 + Growth Rate)
Expected Dividend = $2.35 * 1.04
Expected Dividend = $2.444

Cost of Equity = Expected Dividend / Current Price + Growth Rate
Cost of Equity = $2.444 / $30 + 0.04
Cost of Equity = 12.15%

Answer e.

Average Cost of Equity = (Cost of Equity using CAPM + Cost of Equity using DDM) / 2
Average Cost of Equity = (13.06% + 12.15%) / 2
Average Cost of Equity = 12.61%

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Equity * Cost of Equity
WACC = 0.30 * 5.14% + 0.05 * 9.47% + 0.65 * 12.61%
WACC = 10.21%