Question

Cost of debt using both methods (YTM and the approximation formula) Currently, Warren Industries can sell 15-year, $1,000-par-value bonds paying annual interest at a 7% coupon rate. Because current market rates for similar bonds are just under 7%, Warren can sell its bonds for $1,010 each; Warren will incur flotation costs of $30 per bond. The firm is in the 21% tax bracket. 

a. Find the net proceeds from the sale of the bond, N_d. 

b. Calculate the bond's yield to maturity (YTM) to estimate the before-tax and after-tax costs of debt. 

c. Use the approximation formula to estimate the before-tax and after-tax costs of debt. 

a. The net proceeds from the sale of the bond, N_d, is$. (Round to the nearest dollar.)

Answer 1

Answer a.

Net Proceeds = Current Price - Flotation Cost
Net Proceeds = $1,010 - $30
Net Proceeds = $980

Answer b.

Face Value = $1,000
Net Proceeds = $980

Annual Coupon Rate = 7%
Annual Coupon = 7% * $1,000
Annual Coupon = $70

Time to Maturity = 15 years

Let Annual YTM be i%

$980 = $70 * PVIFA(i%, 15) + $1,000 * PVIF(i%, 15)

Using financial calculator:
N = 15
PV = -980
PMT = 70
FV = 1000

I = 7.22%

Annual YTM = 7.22%

Before-tax Cost of Debt = 7.22%

After-tax Cost of Debt = 7.22% * (1 - 0.21)
After-tax Cost of Debt = 5.70%

Answer c.

Face Value, F = $1,000
Net Proceeds, P = $980
Annual Coupon, C = $70
Time to Maturity, n = 15 years

Approximate YTM = [C + (F - P) / n] / [(F + P) / 2]
Approximate YTM = [$70 + ($1,000 - $980) / 15] / [($1,000 + $980) / 2]
Approximate YTM = $71.333 / $990
Approximate YTM = 0.0721 or 7.21%

Before-tax Cost of Debt = 7.21%

After-tax Cost of Debt = 7.21% * (1 - 0.21)
After-tax Cost of Debt = 5.70%