Question

Susan's Lemonade, Inc. has a single issue of bonds. The bonds have a face value of $1000, a coupon rate of 5.25% with coupons paid semi-annually, a time to maturity of 2 years, and a current market price of $985.04. The firm is financed with 35% debt and 65% common stock. The firm's common stock has a beta of 1.3. The risk-free rate is 1.56%. The expected return on the market portfolio is 9.6%. The corporate tax rate is 30%. a. What is the firm’s cost of debt (i.e., the yield to maturity on the bond)? b. What is the firm’s cost of equity? c. What is the firm’s after-tax weighted average cost of capital (WACC)?

Answer 1

Answer a.

Face Value = $1,000
Current Price = $985.04

Annual Coupon Rate = 5.25%
Semiannual Coupon Rate = 2.625%
Semiannual Coupon = 2.625%*$1,000 = $26.25

Time to Maturity = 2 years
Semiannual Period to Maturity = 4

Let semiannual YTM be i%

$985.04 = $26.25 * PVIFA(i%, 4) + $1,000 * PVIF(i%, 4)

Using financial calculator:
N = 4
PV = -985.04
PMT = 26.25
FV = 1000

I = 3.03%

Semiannual YTM = 3.03%
Annual YTM = 2 * 3.03%
Annual YTM = 6.06%

Cost of Debt = 6.06%

Answer b.

Cost of Equity = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Cost of Equity = 1.56% + 1.30 * (9.60% - 1.56%)
Cost of Equity = 12.01%

Answer c.

WACC = Weight of Debt * Cost of Debt * (1 - Tax Rate) + Weight of Equity * Cost of Equity
WACC = 0.35 * 6.06% * (1 - 0.30) + 0.65 * 12.01%
WACC = 9.29%