Question

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.76 percent, a par value of $2,000 per bond, matures in 3 years, has a total face value of $4.9 million, and is quoted at 108 percent of face value. The second issue has a coupon rate of 6.53 percent, a par value of $1,000 per bond, matures in 17 years, has a total face value of $9.2 million, and is quoted at 105 percent of face value. Both bonds pay interest semiannually. The company's tax rate is 35 percent. What is the firm's weighted average aftertax cost of debt?

Answer 1

1st Issue of Bonds:

Face Value = $4,900,000

Market Value = 108% * $4,900,000
Market Value = $5,292,000

Annual Coupon Rate = 3.76%
Semiannual Coupon Rate = 1.88%
Semiannual Coupon = 1.88% * $4,900,000
Semiannual Coupon = $92,120

Time to Maturity = 3 years
Semiannual Period to Maturity = 6

Let semiannual YTM be i%

$5,292,000 = $92,120 * PVIFA(i%, 6) + $4,900,000 * PVIF(i%, 6)

Using financial calculator:
N = 6
PV = -5292000
PMT = 92120
FV = 4900000

I = 0.522%

Semiannual YTM = 0.522%
Annual YTM = 2 * 0.522%
Annual YTM = 1.044%

Before-tax Cost of Debt = 1.044%
After-tax Cost of Debt = 1.044% * (1 - 0.35)
After-tax Cost of Debt = 0.679%

2nd Issue of Bonds:

Face Value = $9,200,000

Market Value = 105% * $9,200,000
Market Value = $9,660,000

Annual Coupon Rate = 6.53%
Semiannual Coupon Rate = 3.265%
Semiannual Coupon = 3.265% * $9,200,000
Semiannual Coupon = $300,380

Time to Maturity = 17 years
Semiannual Period to Maturity = 34

Let semiannual YTM be i%

$9,660,000 = $300,380 * PVIFA(i%, 34) + $9,200,000 * PVIF(i%, 34)

Using financial calculator:
N = 34
PV = -9660000
PMT = 300380
FV = 9200000

I = 0.522%

Semiannual YTM = 3.027%
Annual YTM = 2 * 3.027%
Annual YTM = 6.054%

Before-tax Cost of Debt = 6.054%
After-tax Cost of Debt = 6.054% * (1 - 0.35)
After-tax Cost of Debt = 3.935%

Total Market Value of Debt = $5,292,000 + $9,660,000
Total Market Value of Debt = $14,952,000

Weight of 1st Issue of Debt = $5,292,000 / $14,952,000
Weight of 1st Issue of Debt = 0.35393

Weight of 2nd Issue of Debt = $9,660,000 / $14,952,000
Weight of 2nd Issue of Debt = 0.64607

Estimated After-tax Cost of Debt = 0.35393 * 0.679% + 0.64607 * 3.935%
Estimated After-tax Cost of Debt = 2.78%