A Company has two issues of debt. Issue A has a maturity value of 6 million doll

Question

A Company has two issues of debt. Issue A has a maturity value of 6 million dollars, a coupon rate of 8.00% paid annually, and is selling at par. Issue B was issued as a subordinate, 15 year bond 5 years ao. Issue B's coupon rate is 8.25%, paid annually. Risk has increased, and investors now demand a pre-tax return of 8.50% on issue B bonds. The maturity value of issue B is 4.5 million dollars. The firm has a marginal tax rate of 35%. What is the company's after tax cost of debt?

0.0821

0.0536

0.0527

0.0534

Please show your work.

Explanation / Answer

Answer is Option D..i.e. 0.0534

For Bond Issue A,

Maturity Value = $6,000,000

Coupon = 8%

The bond is selling at par

Maturity Value = P*(1+r)^n; where P = Principal, r = rate of interest, n = compounding periods

=> P = 6,000,000/(1+8%) = $5,555,556

For Bond Issue B,

Maturity Value = $4,500,000

Coupon = 8.25%

Investor desired rate of return = 8.5% i.e. Yield

Again using the above formula, Principal = 4,500,000/(1+8.5%) = $4,147,465

Hence,

Total Principal = $5,555,556 + $4,147,465 = $9,703,021

Total Maturity Value = $6,000,000 + $4,500,000 = $10,500,000

Again using the above formula, rate of interest i.e. before-tax cost of debt = ((Maturity Value)/(Principal)) - 1

i.e., r = ((10,500,000)/(9,703,021)) - 1

=> r (before tax cost of debt) = 8.214%

Marginal Tax rate of the firm = 35%

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

=> r (after tax cost of debt) = 8.214%*(1-35%)

= 5.34% (or) 0.0534

Hence the correct answer is Option D

* (Here n is irrelevant as we are trying to find the after tax cost of debt from the year in which investors demanded for a pre-tax return of 8.5% for bond issue B)*

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