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 ​$1000​, and a yield to maturity of 9.20 %.   The first bond is issued by Crabbe Waste Disposal and has a coupon interest rate of 6.319​% 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 ​$21000 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 11​%. 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 9.20​%. ​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

1) Price of Bond = Coupon1/(1+YTM)1 + Coupon2/(1+YTM)2 + ........ + (Couponn + Face Value)/(1+YTM)n

2) Total Amount to be invested = 21000
No. of Bonds of Crabbe Waste Disposal that can be purchased = Total Amount to be invested / Price of Crabbe Waste Disposal
= 21000 / 871.53
= 24.1 ~ 24 bonds

No. of Bonds of Malfoy Enterprises that can be purchased = Total Amount to be invested / Price of Malfoy Enterprise
= 21000 / 986.62
= 21.28 ~ 21 bonds

3) Crabbe Waste Disposal
Total Interest Income earned per year per bond = Coupon Rate * Face Value
= 6.319% * 1000
= $63.19
  Total Interest Income earned per year per for 24 bonds = 24 * 63.19
= $1516.56

Malfoy Enterprises
Total Interest Income earned per year per bond = Coupon Rate * Face Value
= 8.9% * 1000
= $89.00
  Total Interest Income earned per year per for 21 bonds = 21 * 89
= $1,869.00

4) Total Dollar Accumulated = Amount received from reinvestment of coupon + Principal Received

Total Dollar Accumulated from Crabbe Waste Disposal = 500.01 + 1000
= $1,500.01

Total Dollar Accumulated from Malfoy Enterprises = 704.24 + 1000
= $1,704.24