Question

Jiminy’s Cricket Farm issued a 30-year, 6.3 percent semiannual bond eight years ago. The bond currently sells for 110 percent of its face value. The company’s tax rate is 22 percent.

a.	What is the 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 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.)
c.	Which is more relevant, the pretax or the aftertax cost of debt?

Answer 1

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

= [$ 31.5+ ( $ 1,000- $ 1100) /44] /[( $ 1,000+ $ 1100)/2] *100

= 29.22727273/1050*100

=2.783549784%

Annual YTM = 2.783549784% * 2

= 5.57%

Note : Coupon = Rate * Face Value

= 6.3% * $ 1,000

= $ 63

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

where,

Par Value = $ 1,000

Market Price = $ 1100

Annual rate = 6.3% and

Maturity in Years = 22 Years

Hence the yield to maturity = 5.50%

a. pre tax cost of debt = 5.50%

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

= 5.50% * ( 1-22%)

= 4.29%

b. after tax cost of debt = 4.29%

c. after tax cost of debt

Note:

The after tax cost of debt is more relevant because when a company raises money through debt, it incurs interest expense. The interest expense is tax deductible and hence the tax shield saves money for the company.This tax shield lowers the yiled of the debt issued.