Question

Mark​ Goldsmith's broker has shown him two bonds issued by different companies. Each has a maturity of 6 ​years, a par value of ​$1,000​, and a yield to maturity of 6.90%. The first bond is issued by Crabbe Waste Disposal and has a coupon interest rate of 6.322% paid annually. The second ​ bond, issued by Malfoy​ Enterprises, has a coupon interest rate of 8.90​% paid annually.

a. Calculate the selling price for each of the bonds.
b. Mark has ​$19,000 to invest. If he wants to invest only in bonds issued by Crabbe Waste​ Disposal, how many of those bonds could he​ buy? What if he wants to invest only in bonds issued by Malfoy​ Enterprises?
c. What is the total interest income that Mark could earn each year if he invested only in Crabbe​ bonds? How much interest would he earn each year if he invested only in Malfoy​ bonds?
d. Assume that Mark will reinvest all the interest he receives as it is paid and that his rate of return on the reinvested interest will be 9​%. Calculate the total dollars that Mark will accumulate over 6 years if he invests in Crabbe bonds or Malfoy bonds. Your total calculation will include the interest Mark​ gets, the principal he receives when the bonds​ mature, and all the additional interest he earns from reinvesting the coupon payments he receives.
e.The bonds issued by Crabbe and Malfoy might appear to be equally good investments because they offer the same yield to maturity of 6.90​%. Notice, however, that your answers to part d are not the same for each​ bond, suggesting that one bond is a better investment than the other. Why is that the​ case?

Answer 1

A) CRABBE WASTE DISPOSAL

Given, FV= 1000, I/Y=6.9%, N=6, PMT= 0.06322*1000= 63.22

To find selling price, Use financial calculator BA II plus and put FV=1000, I/Y=6.9, PMT= 63.22 and N= 6 . Then Press CPT and PV. PV will be -972.3641. This is the selling price this.

MALFOY ENTERPRISES

Given, FV= 1000, I/Y=6.9%, N=6, PMT= 0.089*1000= 89

To find selling price, Use financial calculator BA II plus and put FV=1000, I/Y=6.9, PMT= 89 and N= 6 . Then Press CPT and PV. PV will be -1095.6258. This is the selling price this.

B) Mark has only 19000 to invest. If he invests in Crabbe, he will be able to buy 19000/972.3641= 19.54 i.e. 19 bonds. Further, if he wants to invest in Malfoy, he will be able to buy 19000/1095.6258= 17.34 i.e. 17 bonds.

c) Total Interest income if he invests in Crabbe is 0.06322*1000= 63.22 as the interest rate is 6.322%

Total Interest income if he invests in Malfoy is 0.089*1000= 89 as the interest rate is 8.90%

d) If he invests in Crabbe, the principal amount he will get is 1000. Each year he will receive coupon payment of 63.22 as calculated above. Further, if he reinvests the coupon payment he will get the following total amount which is coupon plus amount after reinvestment. Put PMT=63.22, I/Y= 9, N=6, PV=0 Then Press CPT and FV. FV will be 475.6252. Out of this, coupon payment of 6 years is 63.22*6= 379.32.

Thus, reinvested = 475.6252-379.32= 96.3052

Thus, total amount he will get after 6 years = 1000+379.32+96.3052= 1475.6252

If he invests in Malfoy, the principal amount he will get is 1000. Each year he will receive coupon payment of 89 as calculated above. Further, if he reinvests the coupon payment he will get the following total amount which is coupon plus amount after reinvestment. Put PMT=89, I/Y= 9, N=6, PV=0 Then Press CPT and FV. FV will be 669.5768. Out of this, coupon payment of 6 years is 89*6= 534.

Thus, reinvested = 669.5768-534= 135.5768

Thus, total amount he will get after 6 years = 1000+534+135.5768= 1669.5768

e) The bonds issues by Crabbe and Malfoy have same "market interest rate" and not "coupon rate". Market interest rate is the rate prevailing in the market for similar kind of bonds. That means if you dont invest in crabbe or malfoy, you will get 6.9% interest rate from anyone in the market.

However, crabbe offers coupon rate of 6.322% which is less than what is being offered in the market. Thus, its selling price is less than the face value.

Simalrly, malfoy offers coupon rate of 8.9% which is more than what is being offered in the market. Thus, its selling pice is more than the face value.

This means investment in malfoy is better than investment in crabbe.