Question

Currently, Warren Industries can sell 20 dash year​, ​$1000​-par-value bonds paying annual interest at a 13​% coupon rate. Because current market rates for similar bonds are just under 13​%, Warren can sell its bonds for ​$960 ​each; Warren will incur flotation costs of ​$35 per bond. The firm is in the 22​% 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.) Net Proceeds = Sale price of Bond - Flotation cost

= 960 - 35

= 925

(b.) Calculation of Bond's Yield to maturity :

Using Financial calculator Rate function of Excel :

=RATE(nper,pmt,pv,fv)

nper is the number of years of maturity i.e 20

pmt is coupon payment i.e 1000 * 13% = 130

pv is the current market price i.e 925

fv is the face value i.e 1000

=RATE(20,130,-925,1000)

Before tax yield to maturity is 14.1417%

After tax yield to maturity is before tax yield to maturity * (1 - tax rate)

= 14.1417 * (1 - 0.22)

= 11.03%

(c.) Calculation of Yield to maturity using Approximation formula :

YTM = {Coupon + [(Face value - Net Proceeds) / Number of years of maturity] } / [(Face value + Net Proceeds) / 2]

= {130 + [(1000 - 925) / 20] } / [(1000 + 925) / 2 ]

= 133.75 / 962.5

= 0.13896103896 or 13.8961039896% or 13.90%

After tax yield to maturity = Before tax yield to maturity * (1 - tax rate)

= 13.8961039896% * (1 - 0.22)

= 10.84%