Olympic Sports has two issues of debt outstanding. One is a 8% coupon bond with

Question

Olympic Sports has two issues of debt outstanding. One is a 8% coupon bond with a face value of $21 million, a maturity of 10 years, and a yield to maturity of 9%. 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 9%. The face value of the issue is $25 million, and the issue sells for 93% 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.)

Explanation / Answer

Present value of a bond equals the present value (PV) of its future cash flows, i.e. sum of PV of future coupon payments and redemption price (face value).

Annual coupon, bond 1 = $21 million x 8% = $1.68 million

PV, bond 1 ($ million) = 1.68 x PVIFA(9%, 10) + 21 x PVIF(9%, 10)

= 1.68 x 6.4177 + 21 x 0.4224

= 10.78 + 8.87

= 19.65

Present value of bond 2, P = $25 million x 0.93 = $23.25 million

Annual coupon, C = $25 million x 9% = $2.25 million

Face value, F = $25 million

N: Years to maturity = 15

So, approximate YTM is:

YTM = [C + (F - P) / N] / [(F + P) / 2] = [2.25 + (25 - 23.25) / 15] / [(25 + 23.25) / 2]

= [2.25 + (1.75 / 15)] / [48.25 / 2]

= [2.25 + 0.12] / 24.125

= 2.37 / 24.125

= 0.0982, or 9.82%

Proportion of bond 1 = 19.65 / (19.65 + 23.25) = 19.65 / 42.9 = 0.458

Proportion of bond 2 = 1 - 0.458 = 0.542

So,

(a)

before tax cost of debt, kd = Proportion of bond 1 x YTM of bond 1 + Prportion of bond 2 x YTM of bond 2

= 0.458 x 9% + 0.542 x 9.82%

= 4.12% + 5.32%

= 9.44%

(b)

After tax cost of debt = kd x (1 - tax rate) = 9.44% x (1 - 0.3) = 9.44% x 0.7

= 6.61%

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