Question

The Saunders Investment Bank has the following financing outstanding.

Debt:	10,000 bonds with a coupon rate of 11 percent and a current price quote of 109.5; the bonds have 20 years to maturity. 180,000 zero coupon bonds with a price quote of 20 and 30 years until maturity. Both bonds have a par value of $1,000. Assume semiannual compounding.
Preferred stock:	100,000 shares of 9 percent preferred stock with a current price of $84, and a par value of $100.
Common stock:	2,100,000 shares of common stock; the current price is $70, and the beta of the stock is 1.4.
Market:	The corporate tax rate is 35 percent, the market risk premium is 6 percent, and the risk-free rate is 3 percent.

What is the WACC for the company? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Debt:

Bond 1:

Number of bonds outstanding = 10,000
Face Value = $1,000
Current Price = 109.50% * $1,000 = $1,095

Value of Debt = 10,000 * $1,095
Value of Debt = $10,950,000

Annual Coupon Rate = 11%
Semiannual Coupon Rate = 5.50%
Semiannual Coupon = 5.50%*$1,000 = $55

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

Let semiannual YTM be i%

$1,095 = $55 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -1095
PMT = 55
FV = 1000

I = 4.95%

Semiannual YTM = 4.95%
Annual YTM = 2 * 4.95%
Annual YTM = 9.90%

Before-tax Cost of Debt = 9.90%
After-tax Cost of Debt = 9.90% * (1 - 0.35)
After-tax Cost of Debt = 6.435%

Bond 2:

Number of bonds outstanding = 180,000
Face Value = $1,000
Current Price = 20% * $1,000 = $200

Value of Debt = 180,000 * $200
Value of Debt = $36,000,000

Annual Coupon Rate = 0%
Semiannual Coupon = $0

Time to Maturity = 30 years
Semiannual Period to Maturity = 60

Let semiannual YTM be i%

$200 = $0 * PVIFA(i%, 60) + $1,000 * PVIF(i%, 60)

Using financial calculator:
N = 60
PV = -200
PMT = 0
FV = 1000

I = 4.11%

Semiannual YTM = 4.11%
Annual YTM = 2 * 4.11%
Annual YTM = 8.22%

Before-tax Cost of Debt = 8.22%
After-tax Cost of Debt = 8.22% * (1 - 0.35)
After-tax Cost of Debt = 5.343%

Preferred Stock:

Number of shares outstanding = 100,000
Current Price = $84
Annual Dividend = 9.00%*$100 = $9

Value of Preferred Stock = 100,000 * $84
Value of Preferred Stock = $8,400,000

Cost of Preferred Stock = Annual Dividend / Current Price
Cost of Preferred Stock = $9/ $84
Cost of Preferred Stock = 10.714%

Equity:

Number of shares outstanding = 2,100,000
Current Price = $70

Value of Common Stock = 2,100,000 * $70
Value of Common Stock = $147,000,000

Cost of Common Equity = Risk-free Rate + Beta * Market Risk Premium
Cost of Common Equity = 3% + (1.40 * 6%)
Cost of Common Equity = 11.40%

Value of Firm = Value of Debt + Value of Preferred Stock + Value of Common Stock
Value of Firm = $10,950,000 + $36,000,000 + $8,400,000 + $147,000,000
Value of Firm = $202,350,000

Weight of Bond 1 = $10,950,000 / $202,350,000
Weight of Bond 1 = 0.0541

Weight of Bond 2 = $36,000,000 / $202,350,000
Weight of Bond 2 = 0.1779

Weight of Preferred Stock = $8,400,000 / $202,350,000
Weight of Preferred Stock = 0.0415

Weight of Common Stock = $147,000,000 / $202,350,000
Weight of Common Stock = 0.7265

WACC = Weight of Bond 1 * After-tax Cost of Bond 1 + Weight of Bond 2 * After-tax Cost of Bond 2 + Weight of Preferred Stock * Cost of Preferred Stock + Weight of Common Stock * Cost of Common Stock
WACC = (0.0541 * 0.06435) + (0.1779 * 0.05343) + (0.0415* 0.10714) + (0.7265 * 0.1140)
WACC = 0.1003 or 10.03%