Question

(After tax cost of dept) FitBite, Inc, currently has an outstanding bond that pays interest annually, a coupon rate of 6%, priced at $1,050, and 5 years until maturity. If it is in the 35% marginal tax rate, what is its after tax cost of dept? What is the after tax cost of dept of it pays interest semiannually?

Answer 1

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

= [$ 60 + ( $ 1,000- $ 1050 ) /5] /[( $ 1,000+ $ 1050)/2] *100

= 50/1025*100

= 4.87804878%

Note : Coupon = Rate * Face Value

= 6% * $ 1,000

= $ 60

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

where,

Par Value = $ 1,000

Market Price = $ 1,050

Annual rate = 6% and

Maturity in Years = 5 Years

Hence the yield to maturity = 4.85%

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

= 4.85% * ( 1-35%)

= 3.1525%

Hence the correct answer is 3.1525%

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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- $ 1050 ) /10] /[( $ 1,000+ $ 1050)/2] *100

= 25/1025*100

= 2.43902439%

Hence yield to maturity annual =  2.43902439% * 2

= 4.88%

Note : Coupon = Rate * 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 = $ 1,050

Annual rate = 3% and

Maturity in Years = 10 Years

Compounding = Annual

Hence the yield to maturity = 2.43%

Hence yield to maturity annual = 2.43% *2

= 4.86%

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

= 4.86% * ( 1-35%)

= 3.159%

Hence the correct answer is 3.159%