Question

Olympic Sports has two issues of debt outstanding. One is a 5% coupon bond with a face value of $33 million, a maturity of 10 years, and a yield to maturity of 6%. 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 6%. The face value of the issue is $38 million, and the issue sells for 90% of par value. The firm's tax rate is 30%.

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.)

Answer 1

Answer and Explanation:

The computation is shown below

a. For before tax cost of debt

But before that following calculations need to be determined

For Bond 1:

Face value = $33,000,000

Coupon payment = 0.05 × $33,000,000 = $1,650,000

The Price of the bond is

= Coupon × [ 1 - 1 ÷ ( 1 + r)^n] ÷ r + FV ÷ ( 1 + r)^n

= $1,650,000 × [ 1 - 1 ÷ ( 1 + 0.06)^10] ÷ 0.06 + $33,000,000 ÷ ( 1 + 0.06)^10

= 1,650,000 × 7.360087 + 18,427,027.64

= $30,571,171.196

For Bond 2:

Price = 0.9 × $38,000,000

= $34,200,000

Now

Coupon = 0.06 × $38,000,000

= $2,280,000

Now before tax cost of debt is

Given that

PV -$34,200,000,

FV $38,000,000,

N 15,

PMT $2,280,000

The formula is shown below:

= RATE(NPER,PMT, PV,FV,TYPE)

After applying the above formula, the Before tax cost of debt of bond is 7.1053%

Now

Total market value is

= $34,200,000 + $30,571,171.196

= $64,771,171.19

And,

finally

Before tax cost of debt for olympic is

= ($30,571,171.196 ÷ 64,771,171.19) × 0.06 + ($34,200,000 ÷ 64,771,171.19) × 0.071053

= 0.028319 + 0.037517

= 0.0658 or 6.58%

b)

And,

After tax cost of debt is

= 0.0658× ( 1 - 0.3)

= 0.0461 or 4.61%