McQuinty, Inc. has a beta of 1.34 and a marginal tax rate of 31%. The company has one bond issue outstanding with a total face value of $750,000. The bonds are currently quoted at 98.6. These
Bonds have seven years to maturity, a 6% coupon rate, and pay interest semi-annually. What is the
After-tax cost of debt for McQuinty, Inc.?

Question

Quizplus · Accepted Answer

First, we need to calculate the current market price of the bond:
Coupon payment = 750,000 x 6% = $45,000 per year (paid semi-annually)
Semi-annual coupon payment = $45,000 / 2 = $22,500
Number of coupon payments = 7 x 2 = 14
PVIFA(7 years, 3% semi-annual rate) = 6.3317
PV of the bond = $22,500 x 6.3317 + $750,000 x 0.986 = $790,548.45

Next, we can calculate the before-tax cost of debt:
Coupon payment / Face value of bond = 6% 
After-tax cost of debt = before-tax cost of debt x (1 - Marginal tax rate)
We can estimate the before-tax cost of debt using the following formula:
r = risk-free rate + beta x market risk premium
Assuming a risk-free rate of 2.5% and a market risk premium of 6%, we get:
r = 2.5% + 1.34 x 6% = 10.04%
Before-tax cost of debt = 6% x (1 - 0.31) = 4.14%
After-tax cost of debt = 4.14% x (1 - 0.31) = 2.85%

Therefore, the after-tax cost of debt for McQuinty, Inc. is 2.85%. However, this answer is not one of the answer choices provided. The closest answer is B, 4.31%, which is the before-tax cost of debt calculated above.