Vandelay Industries has two issues of debt.Issue A has a maturity value of 8 million dollars, a coupon rate of 8%, paid annually, and is selling at par.Issue B was issued as a 15-year bond five years ago.Its coupon rate is 9%, paid annually.Investors demand a pre-tax return of 9.3% on this bond.The maturity value of Issue B is 6 million dollars.The Vandelay company has a marginal tax rate of 35%.What is the company's after tax cost of debt?

Question

Quizplus · Accepted Answer

First, we need to calculate the before-tax cost of debt for both Issue A and Issue B.

For Issue A: 
Coupon rate = 8%
Maturity value = $8,000,000
Selling price = par (100% of maturity value)
Therefore, the before-tax cost of debt = coupon rate = 8%

For Issue B: 
Coupon rate = 9%
Maturity value = $6,000,000
Selling price is not given, but we know that investors demand a pre-tax return of 9.3%. This means that the bond must be selling at a discount, because the coupon rate of 9% is less than the required return of 9.3%. We can use the bond pricing formula to calculate the selling price:

PV = C*(1 - (1 + r)^-n)/r + FV*(1 + r)^-n
PV = present value
C = coupon payment
r = required return
n = number of periods
FV = maturity value

PV = $90,000*(1 - (1 + 0.093)^-10)/0.093 + $6,000,000*(1 + 0.093)^-10 = $5,254,734

So, the before-tax cost of debt for Issue B is:

Coupon rate = 9%
Selling price = $5,254,734
Maturity value = $6,000,000
Therefore, the before-tax cost of debt = (coupon payment + (maturity value - selling price)/n)/(maturity value + selling price)/2 = (9% + (6,000,000 - 5,254,734)/10)/(6,000,000 + 5,254,734)/2 = 9.23%

Next, we need to calculate the after-tax cost of debt for both issues. We know that Vandelay's marginal tax rate is 35%, so we can use the following formula:

After-tax cost of debt = before-tax cost of debt*(1 - marginal tax rate)

For Issue A: 
Before-tax cost of debt = 8%
Marginal tax rate = 35%
After-tax cost of debt = 8%*(1 - 35%) = 5.2%

For Issue B: 
Before-tax cost of debt = 9.23%
Marginal tax rate = 35%
After-tax cost of debt = 9.23%*(1 - 35%) = 6.01%

Finally, we need to take a weighted average of the after-tax costs of debt for both issues to find the overall after-tax cost of debt for Vandelay Industries. The weights are based on the relative proportions of each issue in the company's total debt.

Total debt = Issue A + Issue B = $8,000,000 + $5,254,734 = $13,254,734
Weight of Issue A = $8,000,000/$13,254,734 = 60.37%
Weight of Issue B = $5,254,734/$13,254,734 = 39.63%

Overall after-tax cost of debt = Weight of Issue A*After-tax cost of debt for Issue A + Weight of Issue B*After-tax cost of debt for Issue B
= 0.6037*5.2% + 0.3963*6.01% = 5.56%

Therefore, the best answer is B.

Vandelay Industries Has Two Issues of Debt