Question

Jiminy’s Cricket Farm issued a 15-year, 6 percent semiannual coupon bond 4 years ago. The bond currently sells for 93 percent of its face value. The company’s tax rate is 23 percent.

a.	What is the company’s pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	What is the company’s aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. Time to Maturity = 15 years - 4 years

= 11 years

Since it is a semi annual coupon time = 22

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 30+ ( $ 1,000- $ 930) /22] /[( $ 1,000+ $ 930)/2] *100

= 33.18/965*100

= 3.44%

Annual Yield to Maturity = 3.44% *2

= 6.88%

Note : Coupon = Rate /2 * Face Value

= 6% /2 * $ 1,000

= $ 30

Since this formula gives an approximate value, the financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $  930

Annual rate = 6% /2

= 3 %

Maturity in Years = 11 *2 Years

= 22

Hence the yield to maturity = 3.46%

Annual yield to maturity = 3.46% *2

= 6.92%

Hence the correct answer is 6.92%

b. Now, the after tax cost of debt = Yield to Maturity * (1- tax Rate)

= 6.92% * ( 1-23%)

= 5.3284%

Hence the correct answer is 5.33%