Question

S. Claus & Company is planning a zero coupon bond issue. The bond has a par value of $1,000, matures in 2 years, and will be sold at a price of $826.45. The firm's marginal tax rate is 40 percent. What is the annual after-tax cost of debt to the company on this issue?

please show work in written form (not excel) thank you.

Answer 1

Solution: Answer = 6%

Given that,

Face value (F) = $1,000

Price (P) =$ 826.45

Time (t) = 2years

r = cost of debt

For calculating the price of the zero coupon bond,

We know that, price (p) = Face value / (1 + r)^t

(1+r)^t = Face value / price

1+r = (Face value / price)^1/t

r = {(Face value / price)^1/t} - 1

So, cost of debt (r) = {(Face value / price)^1/t} - 1

r = {($1,000 / $826.45)^1/2} -1

r = {(1.21)^1/2} -1

r = (1.10) - 1

r = 0.10 or 10%

So, Cost of debt (r) = 10%

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

After tax cost of debt = 10% ( 1 - 0.40)

After tax cost of debt = 10% (0.60)

After tax cost of debt = 6%