Question

Cost of debt using both methods​ (YTM and the approximation​ formula) Currently, Warren Industries can sell 20-year​, ​$1,000​-par-value bonds paying annual interest at a 11% coupon rate. Because current market rates for similar bonds are just under 14​%, Warren can sell its bonds for ​$960 each; Warren will incur flotation costs of ​$35 per bond. The firm is in the 28% tax bracket.

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

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.

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A. The net proceeds from the sale of the​ bond, Upper Nd​, is ​$____. (Round to the nearest​ dollar.)

B. Using the​ bond's YTM, the​ before-tax cost of debt is ____%. ​(Round to two decimal​ places.)

Using the​ bond's YTM, the​ after-tax cost of debt is _____​%. ​(Round to two decimal​ places.)

C. Using the approximation​ formula, the before-tax cost of debt is ______​%. ​(Round to two decimal​ places.)

Using the approximation​ formula, the after-tax cost of debt is _____%​(Round to two decimal​ places.)

Answer 1

(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 * 11% = 110

pv is the current market price i.e 925

fv is the face value i.e 1000

=RATE(20,110,-925,1000)

Before tax yield to maturity is 12.00%

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

= 12.00% * (1 - 0.28)

= 8.64%

(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]

= {110 + [(1000 - 925) / 20] } / [(1000 + 925) / 2 ]

= 113.75 / 962.5

= 0.11818181 or 11.82%

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

= 11.82% * (1 - 0.28)

= 8.51%