Question

Before-tax cost of debt and? after-tax cost of debt??Personal Finance Problem???David Abbot is interested in purchasing a bond issued by Sony. He has obtained the following information on the? security: Sony Bond Par value ? $1000 Coupon interest rate Corporate tax rate 5.5?% 35?% Cost????????? Years to maturity 10?? ?$910 Answer the following? questions: a.??Calculate the ?before-tax cost of the Sony bond using the? bond's yield to maturity? (YTM). b.??Calculate the ?after-tax cost of the Sony bond given the corporate tax rate. a.?? The ?before-tax cost of the Sony bond using the? bond's yield to maturity? (YTM) is nothing ?%. ?(Round to two decimal? places.)

Answer 1

a) Annual interest payment = $1000 x 5.5% = $55

Years till maturity = 10

First, compute approximate YTM using the following formula -

where, I = interest payment, RV = redeemable value, MV = market value, n = no. of time periods

or, Approx YTM = 6.7%

Now, YTM is close to this rate. We need to choose two rates close to approximate YTM and compute the market value of the bond at those rates. The rate at which market value is equal to the market price will be the YTM. Remember, the closer the rates to YTM, the closer will be your answer.

Lets try 6.5% and 7%.

At 6.5%, Bond Price = $55 x PVIFA (6.5%, 10) + $1000 x PVIF (6.5%, 10) = $55 x 7.18883022252 + $1000 x 0.53272603548 = $928.111697718

At 7%, Bond Price = $55 x PVIFA (7%, 10) + $1000 x PVIF (7%, 10) = $55 x 7.02358154071 + $1000 x 0.5083492921 = $894.646276839

Now, we need to interpolate -

Difference required = $928.111697718 - $910 = $18.111697718

Total difference = $928.111697718 - $894.646276839 = $33.465420879

YTM = Lower rate + Difference in rates x (Difference required / Total difference)

or, YTM = 6.50% + 0.50% x (18.111697718 / $33.465420879) = 6.7706032% or 6.77%

Therefore, Before Tax cost of Debt = 6.77%

b) After tax cost of debt = Before tax cost of debt x (1 - tax rate) = 6.77% x (1 - 0.35) = 4.4005% or 4.40%