Answer and Explanation:
The computation of each point is shown below:-
But before that we need to do the following calculations
First Issue of Bonds:
Face Value = $45,000,000
Market Value = 95% × $45,000,000
= $42,750,000
Annual Coupon Rate = 6%
Semiannual Coupon Rate = 3%
= 3% × $45,000,000
= $1,350,000
Time to Maturity = 26 years
Semiannual Period to Maturity = 52
Let semiannual YTM be i%
$42,750,000 = $1,350,000 × PVIFA(i%, 52) + $45,000,000 × PVIF(i%, 52)
N = 52
PV = -42750000
PMT = 1350000
FV = 45000000
I = 3.20%
Semiannual YTM = 3.20%
Annual YTM = 2 × 3.20%
Annual YTM = 6.40%
Before-tax Cost of Debt = 6.40%
After-tax Cost of Debt = 6.40% × (1 - 0.40)
= 3.84%
Second Issue of Bonds:
Face Value = $50,000,000
Market Value = 54% × $50,000,000
= $27,000,000
Time to Maturity = 15 years
Semiannual Period to Maturity = 30
Let semiannual YTM be i%
$27,000,000 = $50,000,000 × PVIF(i%, 30)
Using a financial calculator:
N = 30
PV = -27000000
PMT = 0
FV = 50000000
I = 2.075%
Semiannual YTM = 2.075%
Annual YTM = 2 × 2.075%
= 4.15%
Before-tax Cost of Debt = 4.15%
After-tax Cost of Debt = 4.15% × (1 - 0.40)
= 2.49%
a. The total book value of debt is
Total Book Value of Debt = $45,000,000 + $50,000,000
= $95,000,000
b. The total market value of debt is
Total Market Value of Debt = $42,750,000 + $27,000,000
= $69,750,000
c. The estimate of the aftertax cost of debt is
Weight of first Issue of Debt is
= $42,750,000 ÷ $69,750,000
= 0.6129
Weight of second issue of Debt
= $27,000,000 ÷ $69,750,000
= 0.3871
So,
Estimated After-tax Cost of Debt is
= 0.6129 × 3.84% + 0.3871 × 2.49%
= 3.32%
