Personal Finance Problem

P$6-31$

Bond valuation and yield to maturity Mark Goldsmith's broker has shown him two bonds issued by different companies. Each has a maturity of five years, a par value of $$1,000,$ and a yield to maturity of $7\mathrm{.}5\%.$ The first bond is issued by Crabbe Waste Disposal Corporation and has a coupon rate of $6\mathrm{.}324\%$ paid annually.

The second bond, issued by Malfoy Enterprises, has a coupon rate of $8\mathrm{.}8\%$ paid annually.

$($a$)$ Calculate the selling price for each bond.

$($b$)$ Mark has $$20,000$ 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? Round your answers to the nearest integer.

$($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 his rate of return on reinvested interest will be $10\%.$ Calculate the total dollars that Mark will accumulate over five years if he invests in Crabbe bonds or Malfoy bonds. Your total dollar 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 that 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 $7\mathrm{.}5\%.$ 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?