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Bond valuation and yield to maturity Personal Finance Problem Mark Goldsmith's broker has shown him two bonds issued by different companies. Each has a maturity of 5 years, a par value of $1,000, and a yield to maturity of 5.80%. The first bond is issued by Crabbe Waste Disposal and has a coupon interest rate of 6.317% paid annually. The second bond, issued by Malfoy Enterprises, has a coupon interest rate of 8.90% paid annually. Calculate the selling price for each of the bonds.

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Final answer:

Crabbe Waste Disposal and Malfoy Enterprises Bonds can be valued using the present value calculation, discounting the annual coupon payments and face value at maturity by the yield to maturity of 5.80%. Higher coupon rates lead to selling prices above par, while lower coupon rates result in selling prices below par value.

Step-by-step explanation:

To calculate the selling prices of two bonds with a par value of $1,000 and a yield to maturity of 5.80%, we will use the bond valuation formula, which is based on discounting the future cash flows to the present based on the yield to maturity. The cash flows consist of the annual coupon payments and the par value of the bond that is repaid at maturity.

For Crabbe Waste Disposal’s bond with a 6.317% coupon rate paid annually, the annual coupon payment is $1,000 x 6.317% = $63.17. For Malfoy Enterprises Bond with an 8.90% coupon rate, the annual payment is $1,000 x 8.90% = $89. Using the present value formula for each payment and the face value repaid at maturity, discounted at the yield to maturity of 5.80%, we can find the selling price of each bond:

Crabbe Waste Disposal Bond Valuation: PV = $63.17 x (1 - (1 + .058)^-5)/.058 + $1,000 x (1 + .058)^-5

Malfoy Enterprises Bond Valuation: PV = $89 x (1 - (1 + .058)^-5)/.058 + $1,000 x (1 + .058)^-5

The resulting present values will give us the selling prices of the bonds. This is due to the inverse relationship between bond prices and yields; for bonds with a coupon rate higher than the yield to maturity, their selling price will be above par, while bonds with a coupon rate below the yield to maturity will sell for less than par value.

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