Question

Mojo Mining has a bond outstanding that sells for $1,058 and matures in 24 years. The bond pays semiannual coupons and has a coupon rate of 6.02 percent. The par value is $1,000. If the company's tax rate is 35 percent, what is the aftertax cost of debt? Multiple Choice 5.29% 3.63% 5.67% 3.40% 3.90%

Answer 1

After tax cost of debt = YTM * (1 - Tax rate)

Here, YTM = Yield to maturity

i) Tax rate = 35% or 0.35

ii) YTM = (Coupon + ((F - P)/n)) / ((F + P)/2)

Here,

F (Face value) = $1,000

P (Market price) = $1,058

n (semi annual period) = 24 years * 2 = 48

Coupon = Face value * Coupon rate * 6/12 months

Coupon (semi annual) = $1,000 * 6.02% * 6/12 month

Coupon (semi annual) = $30.10

Now put the values into YTM,

YTM = ($30.10 + (($1,000 - $1058) / 48)) / (($1,000 + $1058) / 2)

YTM = ($30.10 - $1.20) / $1,029

YTM = $28.90 / $1,029

YTM (semi annual) = 0.0280

YTM (annual) = (1 + Semi annual YTM)^n - 1

n (compounding per year) = 2 (semi annual)

YTM (annual) = (1 + 0.0280)^2 - 1

YTM = 0.0567

Now use the value of annual YTM & tax rate for after tax cost of debt :

After tax cost of debt = 0.0567 * (1 - 0.35)

After tax cost of debt = 0.0567 * 0.65

After tax cost of debt = 0.0368 or 3.68%

Answer : 3.63%

Note : Nominal amount of difference in answer due to decimal workings.