Question

Costly Corporation plans a new issue of bonds with a par value of $1000, a maturity of 28 years, and an annual coupon rate of 10.0%. Flotation costs associated with a new debt issue would equal 8.0% of the market value of the bonds. Currently, the appropriate discount rate for bonds of firms similar to Costly is 6.0%. The firm's marginal tax rate is 50%. What will the firm's true cost of debt be for this new bond issue?

Answer 1

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =28

Bond Price =∑ [(10*1000/100)/(1 + 6/100)^k]     +   1000/(1 + 6/100)^28

k=1

Bond Price = 1536.25

Price after flotation cost = current price*(1-flotation cost %) = 1536.25*(1-0.08)=1413.35

cost of debt considering floatation cost

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =28

1413.35 =∑ [(10*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^28

k=1

YTM = 6.69%

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

After tax cost of debt = 6.69*(1-0.5)

= 3.345 = true cost of debt