Question

An Institute issued a 30 year , 8 percent semi-annual bond 3 years ago. The bond currently sells for 93 percent of its face value. The Company's tax rate is 35%,

a. What is the pre-taxed cost of debt?

b. What is the after tax cost of debt?

Answer 1

A.) the pre-taxed cost of debt is its yield to maturity (YTM)

Assume that Face value or par value of debt is M= $1000

Therefore price P0 = 93% of $1000 = $930

Coupon semiannual C = 1,000*8%*0.5 = $40

Time n = (30 -3) *2 = 54

And i is YTM=?

Formula for calculation of YTM of bond is

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Therefore we have,

$ 930 = $40 * [1 – 1 / (1+i) ^54] /i + 1000 / (1+i) ^54

Now we have to use trial and error method to find out the value of i

If i= 4.34% semiannual

Therefore annual YTM = 4.34% *2 = 8.68%

B.)The after tax cost of debt = 8.68% *(1 – T)

Where T is the tax rate =35%

Therefore

After tax cost of debt = 8.68% *(1 – 0.35) = 5.64%

Therefore pre-tax cost is 8.68%