A firm issues a 10-year debt obligation that bears a 8% coupon rate and gives th
ID: 2664655 • Letter: A
Question
A firm issues a 10-year debt obligation that bears a 8% coupon rate and gives the investor the right to put the bond back to the issuer at the end of the fifth year at 103% of its face amount. The issue has no sinking fund. Interest is paid semiannually.The issuer’s tax rate is 40%.
a. Calculate the after-tax cost of debt, assuming the debt remains outstanding until
maturity.
b. Calculate the after-tax cost of debt, assuming investors put the bond back to the firm at the end of the fifth year. (Note: Any unamortized issuance expenses and any redemption premium can be deducted for tax purposes in the year of redemption.)
Explanation / Answer
Coupon rate = 8%
Semi-annual coupon rate = 8% / 2
Semi-annual Coupon rate = 4%
Face value of the bond = $1,000
Bond’s Call Price = 103% of face amount = [$1,000 * 103%] = $1,030
(a) Calculate the after-tax cost of debt, assuming the debt remains outstanding until maturity:
Calculating Yield to Maturity of the bond (YTM):
(Using Ms-Excel "Rate" Function):
Number of Periods (Nper)
10*2
Semi-annual Coupon payment [$1,000 * 4%]
-40
Present Value of the bond (PV)
1030
Face value (or) Future Value of the bond
-1000
Semi-annual YTM
3.78%
Annual YTM = [3.78% * 2]
Annual YTM = 7.56%
Annual Yield to Maturity of the bond
7.56%
After-tax Cost of Debt = 7.56% * (1-40%)
After-tax Cost of Debt = 0.0756 * (1-0.40)
After-tax Cost of Debt = 0.04536 (or) 4.536%
After-tax Cost of Debt = 4.536%
(b) Calculating the after-tax cost of debt, assuming investors put the bond back to the firm at the end of the fifth year:
Calculating Yield to Maturity of the bond (YTM):
(Using Ms-Excel "Rate" Function):
Number of Periods (Nper)
5*2
Semi-annual Coupon payment [$1,000 * 4%]
-40
Present Value of the bond (PV)
1030
Face value (or) Future Value of the bond
-1000
Semi-annual YTM
3.64%
Annual YTM = [3.64% * 2]
Annual YTM = 7.28%
Annual Yield to Maturity of the bond
7.28%
After-tax Cost of Debt = 7.28% * (1-40%)
After-tax Cost of Debt = 0.0728 * (1-0.40)
After-tax Cost of Debt = 0.04368 (or) 4.368%
After-tax Cost of Debt = 4.368%
Calculating Yield to Maturity of the bond (YTM):
(Using Ms-Excel "Rate" Function):
Number of Periods (Nper)
10*2
Semi-annual Coupon payment [$1,000 * 4%]
-40
Present Value of the bond (PV)
1030
Face value (or) Future Value of the bond
-1000
Semi-annual YTM
3.78%
Annual YTM = [3.78% * 2]
Annual YTM = 7.56%
Annual Yield to Maturity of the bond
7.56%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.