Question

The Imaginary Products Co. currently has debt with a market value of $300 million outstanding.
The debt consists of 10 percent coupon bonds (semiannual coupon payments) which have a
maturity of 15 years and are currently priced at $1,440.03 per bond. The firm also has an issue
of 4 million preferred shares outstanding with a market price of $14.00 per share. The preferred
shares pay an annual dividend of $1.20. Imaginary also has 12 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 5 percent per year
forever. Imaginary is subject to a 40 percent marginal tax rate.

What is the after-tax cost of debt? And what is WACC?

Answer 1

Debt:

Face Value = $1,000
Current Price = $1,440.03

Market Value of Debt = $300,000,000

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $1,000
Semiannual Coupon = $50

Time to Maturity = 15 years
Semiannual Period to Maturity = 30

Let Semiannual YTM be i%

$1,440.03 = $50 * PVIFA(i%, 30) + $1,000 * PVIF(i%, 30)

Using financial calculator:
N = 30
PV = -1440.03
PMT = 50
FV = 1000

I = 2.81%

Semiannual YTM = 2.81%
Annual YTM = 2 * 2.81%
Annual YTM = 5.62%

Before-tax Cost of Debt = 5.62%
After-tax Cost of Debt = 5.62% * (1 - 0.40)
After-tax Cost of Debt = 3.372%

Preferred Stock:

Number of shares outstanding = 4,000,000
Current Price = $14.00

Annual Dividend = $1.20

Market Value of Preferred Stock = 4,000,000 * $14
Market Value of Preferred Stock = $56,000,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $1.20 / $14.00
Cost of Preferred Stock = 8.571%

Common Stock:

Number of shares outstanding = 12,000,000
Current Price = $20.00

Market Value of Common Stock = 12,000,000 * $20
Market Value of Common Stock = $240,000,000

Cost of Common Stock = Expected Dividend / Current Price + Growth Rate
Cost of Common Stock = $2.20 / $20.00 + 0.05
Cost of Common Stock = 16.000%

Market Value of Firm = Market Value of Debt + Market Value of Preferred Stock + Market Value of Common Stock
Market Value of Firm = $300,000,000 + $56,000,000 + $240,000,000
Market Value of Firm = $596,000,000

Weight of Debt = $300,000,000 / $596,000,000
Weight of Debt = 0.50336

Weight of Preferred Stock = $56,000,000 / $596,000,000
Weight of Preferred Stock = 0.09396

Weight of Common Stock = $240,000,000 / $596,000,000
Weight of Common Stock = 0.40268

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Common Stock * Cost of Common Stock
WACC = 0.50336 * 3.372% + 0.09396 * 8.571% + 0.40268 * 16.000%
WACC = 8.95%