Question

Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10%. 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 10%. The face value of the issue is $25 million, and the issue sells for 94% of par value. The firm’s tax rate is 35%.

a. What is the before-tax cost of debt for Olympic? 


b. What is Olympic’s after-tax cost of debt?

Not in Excel Please, explain with formulas and calculator. Thanks

Answer 1

(a)-The before-tax cost of debt for Olympic

Calculation of the Market Price of the First Bond Issue

Par Value = $2,00,00,000

Coupon Amount = $18,00,000 [$200,00,000 x 9%]

YTM = 10%

Maturity Years = 10 Years

The Price of the Bond = Present Value of the Coupon payments + Present Value of Face Value

= $18,00,000[PVIFA 10%, 10 Years] + $2,00,00,000[PVIF 10%, 10 Years]

= [$18,00,000 x 6.14457] + [$2,00,00,000 x 0.38554]

= $ 1,10,60,221 + $ 77,10,866

= $ 1,87,71,087

Calculation of Yield to Maturity of Second Bond Issue

Par Value = $1,000

Bond Price = $940 [$1,000 x 94%]

Coupon Amount = $100 [$1,000 x 10%]

Maturity Period = 15 Years

Therefore, Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

= [$100 + {($1,000 – $940) / 15 Years)] / [($1,000 + $940) / 2}]

= [($100 - $4.00) / $970]

= 0.1083

= 10.83%

Weight of the Capital Structure

Market Value of First Bond = $ 1,87,71,087

Market Value of Second Bond = $ 2,35,00,000 [$250,00,000 x 94%]

Total market Value = $ 4,22,71,087

Weight of Frist Bond = 0.4441 [$1,87,71,087 / $ 4,22,71,087]

Weight of Frist Bond = 0.5559 [$2,35,00,000 / $ 4,22,71,087]

Therefore, The before-tax cost of debt for Olympic = [10% x 0.4441] + [10.83% x 0.5559]

= 4.44% + 6.02%

= 10.46%

“The before-tax cost of debt for Olympic = 10.46%”

(b)- Olympic's after-tax cost of debt

Olympic's after-tax cost of debt = Pre-tax Cost of Debt x (1 – Tax Rate)

= 10.46% x (1 – 0.35)

= 10.46% x 0.65

= 6.80%

“Olympic's after-tax cost of debt = 6.80%”