Question

McIntire Corp. is considering the issue of $1,000 face value, 20 year, 9 percent coupon bonds. The bonds will make coupon payments on a semi-annual basis. It observes that bonds of Barrett Company are trading at $1079.31, have the same maturity date and pay an annual coupon of 10 percent. If the two bonds are expected to be similar in risk, what price will a bond of McIntire Corp. sell for?

Answer 1

YTM on Barrett Company can be calculated as below

100 * ((1-(1+i)^(-20))/i) + 1000/(1+i)^20 – 1079.31 = 0

Since it’s market price is greater than par value, YTM has to be less than the coupon rate.

For i = 10% value of above equation is -79.31

For i = 9% value of above equation is 11.9755

By interpolation

YTM = 9% + (10% - 9%) * (0-11.9755)/(-79.31-11.9755) = 9.13%

Hence, expected yield on the bonds of McIntire Corp is 9.13%

Therefore price for McIntire Corp bond is

P = 45 * ((1-(1+4.565%)^(-40))/4.565%) + 1000/(1+4.565%)^40 = $988.15

Price for a bond of McIntire Corp. is $988.15.