Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.50 percent, a par value of $1,000 per bond, matures in 8 years, has a total face value of $3.6 million, and is quoted at 109 percent of face value. The second issue has a coupon rate of 5.94 percent, a par value of $2,000 per bond, matures in 21 years, has a total face value of $7.9 million, and is quoted at 95 percent of face value. Both bonds pay interest semiannually. The company's tax rate is 40 percent. What is the firm's weighted average aftertax cost of debt

2.9652%

Explanation:

to determine the cost of debt we must use the FMV of the bonds plus the YTM:

first bond:

FMV = 1.09 x $1,000 = $1,090 x 3,600 bonds = $3,924,000

YTM = {C + [ (F - P) / n]} / [ (F + P) / 2] = {17.5 + [ (1000 - 1090) / 16]} / [ (1000 + 1090) / 2] = (17.5 - 5.625) / 1045 = 1.136% x 2 = 2.27% annual

second bond:

FMV = 0.95 x $2,000 = $1,900 x 3,950 bonds = $7,505,000

YTM = {C + [ (F - P) / n]} / [ (F + P) / 2] = {59.4 + [ (2000 - 1900) / 42]} / [ (2000 + 1900) / 2] = (59.4 + 2.38) / 1950 = 3.168% x 2 = 6.34% annual

total debt = $3,924,000 + $7,505,000 = $11,429,000

weighted average after tax cost of debt:

{ ($3,924,000/$11,429,000 x 2.27%) + ($7,505,000/$11,429,000 x 6.34%) } x (1 - 0.40) = (0.779% + 4.163%) x 0.6 = 4.942% x 0.6 = 2.9652%