Question

A company's 8% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $743.61. The company's federal-plus-state tax rate is 35%. What is the firm's after-tax component cost of debt for purposes of calculating the WACC? (Hint: Base your answer on the nominal rate.) Round your answer to two decimal places.

Answer 1

The component cost of debt used in the WACC will be the After Tax Yield To Maturity [YTM] of the Bond

Par Value = $1,000

Semiannual Coupon Amount = $40 [$1,000 x 8% x ½]

Bond Price = $743.61

Maturity Years = 60 Years [30 Years x 2]

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

= [$40 + {($1,000 – $743.61) / 60 Years)] / [($1,000 + $743.61) / 2}] x 100

= [($40 + $4.27) / $871.81] x 100

= 5.46%

Semiannual Yield to Maturity = 5.46%

The Annual Yield to Maturity of the Bond = 10.92% [5.46% x 2]

After Tax Cost of Debt

After Tax Cost of Debt = Bond’s YTM x [ 1 – Tax Rate]

= 10.92% x (1 – 0.35)

= 10.92% x 0.65

= 7.10%

“Therefore, the firm's after-tax component cost of debt for purposes of calculating the WACC would be 7.10%”