Olympic Sports has two issues of debt outstanding. One is a 6% coupon bond with
ID: 2790123 • Letter: O
Question
Olympic Sports has two issues of debt outstanding. One is a 6% coupon bond with a face value of $35 million, a maturity of 10 years, and a yield to maturity of 7%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 7%. The face value of the issue is $40 million, and the issue sells for 94% of par value. The firm's tax rate is 40%.
a. What is the before-tax cost of debt for Olympic? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
b. What is Olympic's after-tax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Explanation / Answer
a) The cost of debt for the first issue is 7% (Yield to Maturity).But we need to estimate the market value of debt of the first issue. We are given the following information:
Future Value (FV) =$ 35 Mn
Coupon=6% of FV=0.06*35= $ 2.10
Time to Maturity (n) = 10 years
Yield to Maturity=7%
We need to estimate the Present Value (PV). To do so we will use the excel function of PV. The syntax for PV is:
PV= (rate, nper, pmt,[FV],[type])
rate= Discount rate or the opportunity cost=7%
nper= number of periods=10
pmt= Dollar value of the coupon payments=2.10
FV= The principal that we will receive at maturity. 35
Type=0 or 1. 0 means payments made at the end of the period while 1 means payment made at the beginning of the period. The default setting in excel is 0.
PV= (0.07,10,2.10,35,0)
=$ 32.54
We need to find the cost of debt for the second issue. For the second issue we are given the following information:
Future Value (FV) =$ 40 Mn
Coupon=7% of FV=0.07*40= $ 2.80
Time to Maturity (n) = 15 years
Present Value (PV) =94 % of FV=0.94*40=$ 37.60
We can use the excel rate function to calculate YTM. The syntax for the rate function is:
=rate (nper,pmt,pv,[fv],[type],[guess])
nper= number of periods= 15 years
pmt= Dollar value of the coupon payment=$ 2.80
PV=Present Value=$ 37.60
FV= Future Value=$ 40
Type=0 or 1. 0 means payments made at the end of the period while 1 means payment made at the beginning of the period. The default setting in excel is 0.
Guess= Your guess on the rate. Default is 10%. Both type and guess are option commands.
=rate(15,2.80,-37.60,40)
-=7.688%
Note: In the formula the PMT and FV amount is positive as we will be receiving them while PV is negative as that is the market price and thus what we need to pay for the bond.
Total Debt issued by Olympic=Market Value of Debt of both issue=32.54+37.60=$70.14
Therefore, before cost of debt for Olympic= (32.54/70.14)×7+(37.60/70.14)×7.688
=3.2475+4.1213
=7.3688%=7.37%.
b) The after tax cost of debt is:
Before Tax cost of Debt×(1-Tax Rate)
=7.37×(1-0.40)
=7.37×0.60
=4.42%.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.