Question

ABC can borrow funds at an interest rate of 7.30% for a period of six years. Its marginal federal-plus-state tax rate is 30%. ABC's after-tax cost of debt is (round to two decimal places). At the present time, ABC has 15-year noncallable bonds with a face value of $1,000 that are outstanding. These bonds have a current market price of $1,555.38 per bond, carry a coupon rate of 11%, and distribute annual coupon payments. The company incurs a federal-plus-state tax rate of 30%. If ABC wants to issue new debt, what would be a reasonable estimate for its after-tax cost of debt (rounded to two decimal places)?

a) 2.57%

b) 3.99%

c) 5.71%

d) 6.84%

Answer 1

Fromula pf approximate YTM will be used to measure cost of debt

Par Value (P) = $1,000

Market Value (F) = $1,555.38

Number of years to maturity (N) = 15

Coupon rate = 11%

Coupon Payment (C) = $110

Tax rate (t) = 30%

\( \begin{align*} \rm\text{Annual YTM} &= \frac{C+\frac{F-P}{N}}{\frac{F+P}{2}}\\ &= \frac{\$110+\frac{\$1,000-\$1,555.38}{15}}{\frac{\$1,000+\$1,555.38}{15}}\\ &=\frac{\$110-\$37.03}{\$1,277.69}\\ &=\frac{\$72.97}{\$1,277.69}\\ &= 0.0571 \rm\text{ or } 5.71\%\\ \rm\text{After tax cost of debt} &= \rm\text{Annual YTM}(1-t)\\ &= 5.71\%(1-0.30)\\ &= 3.99\%\end{align*} \)

So, the after-tax cost of ABC is 3.99%

Hence, option B is correct

The answer is 3.99%

Option B is correct