Answer:
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%
