Question

Dinklage Corp. has 6 million shares of common stock outstanding. The current share price is $72, and the book value per share is $9. The company also has two bond issues outstanding. The first bond issue has a face value of $85 million, a coupon rate of 5 percent, and sells for 97 percent of par. The second issue has a face value of $70 million, a coupon rate of 4 percent, and sells for 109 percent of par. The first issue matures in 21 years, the second in 8 years.

Suppose the most recent dividend was $4.40 and the dividend growth rate is 4.7 percent. 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 23 percent. What is the company’s WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Debt:

1^st Issue of Bonds:

Face Value = $85,000,000

Market Value = 97% * $85,000,000
Market Value = $82,450,000

Annual Coupon Rate = 5.00%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $85,000,000
Semiannual Coupon = $2,125,000

Time to Maturity = 21 years
Semiannual Period to Maturity = 42

Let semiannual YTM be i%

$82,450,000 = $2,125,000 * PVIFA(i%, 42) + $85,000,000 * PVIF(i%, 42)

Using financial calculator:
N = 42
PV = -82450000
PMT = 2125000
FV = 85000000

I = 2.619%

Semiannual YTM = 2.619%
Annual YTM = 2 * 2.619%
Annual YTM = 5.238%

Before-tax Cost of Debt = 5.238%
After-tax Cost of Debt = 5.238% * (1 - 0.23)
After-tax Cost of Debt = 4.033%

2^nd Issue of Bonds:

Face Value = $70,000,000

Market Value = 109% * $70,000,000
Market Value = $76,300,000

Annual Coupon Rate = 4.00%
Semiannual Coupon Rate = 2.00%
Semiannual Coupon = 2.00% * $70,000,000
Semiannual Coupon = $1,400,000

Time to Maturity = 8 years
Semiannual Period to Maturity = 16

Let semiannual YTM be i%

$76,300,000 = $1,400,000 * PVIFA(i%, 16) + $70,000,000 * PVIF(i%, 16)

Using financial calculator:
N = 16
PV = -76300000
PMT = 1400000
FV = 70000000

I = 1.370%

Semiannual YTM = 1.370%
Annual YTM = 2 * 1.370%
Annual YTM = 2.740%

Before-tax Cost of Debt = 2.740%
After-tax Cost of Debt = 2.740% * (1 - 0.23)
After-tax Cost of Debt = 2.110%

Total Market Value of Debt = Market Value of 1^st Issue of Bond + Market Value of 2^nd Issue of Bond
Total Market Value of Debt = $82,450,000 + $76,300,000
Total Market Value of Debt = $158,750,000

Weight of 1^st Issue of Debt = $82,450,000 / $158,750,000
Weight of 1^st Issue of Debt = 0.51937

Weight of 2^nd Issue of Debt = $76,300,000 / $158,750,000
Weight of 2^nd Issue of Debt = 0.48063

Estimated After-tax Cost of Debt = 0.51937 * 4.033% + 0.48063 * 2.110%
Estimated After-tax Cost of Debt = 3.109%

Common Stock:

Number of shares outstanding = 6,000,000
Current Price = $72

Market Value of Common Stock = 6,000,000 * $72
Market Value of Common Stock = $432,000,000

Expected Dividend = Current Dividend * (1 + Growth Rate)
Expected Dividend = $4.40 * 1.0470
Expected Dividend = $4.6068

Cost of Common Stock = Expected Dividend / Current Price + Growth Rate
Cost of Common Stock = $4.6068 / $72.00 + 0.0470
Cost of Common Stock = 11.098%

Market Value of Firm = Market Value of Debt + Market Value of Common Stock
Market Value of Firm = $158,750,000 + $432,000,000
Market Value of Firm = $590,750,000

Weight of Debt = $158,750,000 / $590,750,000
Weight of Debt = 0.26873

Weight of Common Stock = $432,000,000 / $590,750,000
Weight of Common Stock = 0.73127

WACC = Weight of Debt * After-tax Cost of Debt + Weight of Common Stock * Cost of Common Stock
WACC = 0.26873 * 3.109% + 0.73127 * 11.098%
WACC = 8.95%