Question

(Cost of debt) Gillian Stationery Corporation needs to raise $638 comma 000 to improve its manufacturing plant. It has decided to issue a $1 comma 000 par value bond with an annual coupon rate of 8.4 percent with interest paid semiannually and a 15 -year maturity. Investors require a rate of return of 10.6 percent.

a. Compute the market value of the bonds.

b. How many bonds will the firm have to issue to receive the needed funds?

c. What is the firm's after-tax cost of debt if the firm's tax rate is 34 percent?

Answer 1

a)

Coupon = (0.084 * 1000) / 2 = 42

Number of periods = 15 * 2 = 30

Rate = 10.6% / 2 = 5.3%

Market value of bonds = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Market value of bonds = 42 * [1 - 1 / (1 + 0.053)³⁰] / 0.053 + 1000 / (1 + 0.053)³⁰

Market value of bonds = 42 * 14.86043 + 212.39724

Market value of bonds = $836.54

b)

Number of bonds = 638,000 / 836.54

Number of bonds = 763 bonds

c)

After tax cost of debt = 0.106 (1 - 0.34)

After tax cost of debt = 0.07 or 7.00%