Question

(Cost of debt) Gillian Stationery Corporation needs to raise $579,000 to improve its manufacturing plant. It has decided to issue a $1,000 par value bond with an annual coupon rate of 7.2 percent with interest paid semiannually and a 10-year maturity. Investors require a rate of return of 11.1 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? a. The market value of the bonds is $ 767.93 (Round to the nearest cent.) b. The number of bonds that the company needs to sell is 754 bonds. (Round up to the nearest integer.) c. The firm's after-tax cost of debt is 7.33%. (Round to two decimal places.)

Answer 1

a). Bond's Market Value = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(7.2%/2)*$1,000} * {(1 - (1 + 0.111/2)^-(10*2)) / (0.111/2)}] + [$1,000 / {1 + (0.111/2)}^(10*2)]

= [$36 * {0.6605 / 0.0555}] + [$1,000 / 2.9455]

= [$36 * 11.9010] + $339.50

= $428.43 + $339.50 = $767.93

b). No. of bonds to sell = Amount to be raised / Current Bond Price

= $579,000 / $767.93 = 753.97, or 754 bonds

c). After-tax cost of debt = Before-tax cost of debt * (1 - t) = 11.1% * (1 - 0.34) = 7.33%