Question

A company has 7,054,129 shares of common stock outstanding. The current share price is $58.26, and the book value per share is $3.77. This company also has two bond issues outstanding. The first bond issue has a face value of $41,975,487, has a 0.05 coupon, matures in 10 years and sells for 83 percent of par. The second issue has a face value of $55,010,588, has a 0.06 coupon, matures in 20 years, and sells for 92 percent of par.

The most recent dividend was $2.67 and the dividend growth rate is 0.05. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 0.38.

What is the company's WACC? answer with 4 decimal

Answer 1

Debt:

1st Issue of Bonds:

Face Value = $41,975,487

Market Value = 83% * $41,975,487
Market Value = $34,839,654.21

Annual Coupon Rate = 0.050
Semiannual Coupon Rate = 0.025
Semiannual Coupon = 0.025 * $41,975,487
Semiannual Coupon = $1,049,387.175

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$34,839,654.21 = $1,049,387.175 * PVIFA(i%, 20) + $41,975,487 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -34839654.21
PMT = 1049387.175
FV = 41975487

I = 3.720%

Semiannual YTM = 3.720%
Annual YTM = 2 * 3.720%
Annual YTM = 7.440%

Before-tax Cost of Debt = 7.440%
After-tax Cost of Debt = 7.440% * (1 - 0.38)
After-tax Cost of Debt = 4.613%

2nd Issue of Bonds:

Face Value = $55,010,588

Market Value = 92% * $55,010,588
Market Value = $50,609,740.96

Annual Coupon Rate = 0.060
Semiannual Coupon Rate = 0.030
Semiannual Coupon = 0.030 * $55,010,588
Semiannual Coupon = $1,650,317.64

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

Let semiannual YTM be i%

$50,609,740.96 = $1,650,317.64 * PVIFA(i%, 40) + $55,010,588 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -50609740.96
PMT = 1650317.64
FV = 55010588

I = 3.367%

Semiannual YTM = 3.367%
Annual YTM = 2 * 3.367%
Annual YTM = 6.734%

Before-tax Cost of Debt = 6.734%
After-tax Cost of Debt = 6.734% * (1 - 0.38)
After-tax Cost of Debt = 4.175%

Total Market Value of Debt = $34,839,654.21 + $50,609,740.96
Total Market Value of Debt = $85,449,395.17

Weight of 1st Issue of Debt = $34,839,654.21 / $85,449,395.17
Weight of 1st Issue of Debt = 0.40772

Weight of 2nd Issue of Debt = $50,609,740.96 / $85,449,395.17
Weight of 2nd Issue of Debt = 0.59228

Estimated After-tax Cost of Debt = 0.40772 * 4.613% + 0.59228 * 4.175%
Estimated After-tax Cost of Debt = 4.354%

Common Stock:

Number of shares outstanding = 7,054,129
Current Price = $58.26

Market Value of Common Stock = 7,054,129 * $58.26
Market Value of Common Stock = $410,973,555.54

Expected Dividend = Current Dividend * (1 + Growth Rate)
Expected Dividend = $2.67 * 1.05
Expected Dividend = $2.8035

Cost of Common Stock = Expected Dividend / Current Price + Growth Rate
Cost of Common Stock = $2.8035 / $58.26 + 0.05
Cost of Common Stock = 0.09812 or 9.812%

Market Value of Firm = Market Value of Debt + Market Value of Common Stock
Market Value of Firm = $85,449,395.17 + $410,973,555.54
Market Value of Firm = $496,422,950.71

Weight of Debt = $85,449,395.17 / $496,422,950.71
Weight of Debt = 0.17213

Weight of Common Stock = $410,973,555.54 / $496,422,950.71
Weight of Common Stock = 0.82787

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Common Stock * Cost of Common Stock
WACC = 0.17213 * 4.354% + 0.82787 * 9.812%
WACC = 8.8725%