Question

Several years ago the Jakob Company sold a $1,000 par value, noncallable bond that now has 22 years to maturity and a 7.00% coupon that is paid semiannually. The bond currently sells for $835, and the company’s tax rate is 40%. What is the AFTER-TAX component cost of debt: ((rd)(1-T))?

Answer 1

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

= [$ 35+ ( $ 1,000- $ 835) /44] /[( $ 1,000+ $ 835)/2] *100

= 38.75/917.5*100

= 4.223433243%

Annual YTM = 4.223433243% * 2

= 8.45%

After Tax cost of debt = 8.45%*(1-40%)

= 5.07%

Note : Semi Annual Coupon = Rate * Face Value

= 7%/2 * $ 1,000

= $ 35

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

where,

Par Value = $ 1,000

Market Price = $  835

Annual rate = 7% and

Maturity in Years = 22 Years

Payments = Semi Annual

Hence the yield to maturity = 8.70%

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

= 8.70% * ( 1-40%)

= 5.22%

Hence the yield to maturity = 5.22%

Answer = 5.22%