Question

 ​Currently, Warren Industries can sell 15-year​, ​$1000​-par-value bonds paying annual interest at a 11​% coupon rate. Because current market rates for similar bonds are just under 11​%, Warren can sell its bonds for ​$960​each; Warren will incur flotation costs of ​$30per bond. The firm is in the 29​% tax bracket.

a.  Find the net proceeds from the sale of the​ bond,Upper N Subscript 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.

Answer 1

Answer a.

Current Price = $960
Flotation Cost = $30

Net Proceeds = Current Price - Flotation Cost
Net Proceeds = $960 - $30
Net Proceeds = $930

Answer b.

Par Value = $1,000
Net Proceeds = $930

Annual Coupon Rate = 11.00%
Annual Coupon = 11.00% * $1,000
Annual Coupon = $110

Time to Maturity = 15 years

Let Annual YTM be i%

$930 = $110 * PVIFA(i%, 15) + $1,000 * PVIF(i%, 15)

Using financial calculator:
N = 15
PV = -930
PMT = 110
FV = 1000

I = 12.03%

Annual YTM = 12.03%

Before-tax Cost of Debt = 12.03%

After-tax Cost of Debt = 12.03% * (1 - 0.29)
After-tax Cost of Debt = 8.54%

Answer c.

Par Value, F = $1,000
Net Proceeds, P = $930
Annual Coupon, C = $110
Time to Maturity, N = 15 years

Approximate YTM = [C + (F - P) / N] / [(F + P) / 2]
Approximate YTM = [$110 + ($1,000 - $930)/ 15] / [($1,000 + $930) / 2]
Approximate YTM = $114.6667 / $965.00
Approximate YTM = 0.1188 or 11.88%

Before-tax Cost of Debt = 11.88%

After-tax Cost of Debt = 11.88% * (1 - 0.29)
After-tax Cost of Debt = 8.43%