13. Jack purchases a corporate bond with par-value 30000 on January 15, 2000. Th
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Question
13. Jack purchases a corporate bond with par-value 30000 on January 15, 2000. The bond matures at par-value on January 15, 2030 and pays semiannual coupons at an annual nominal rate of 5% compounded semiannually every January 15 and July 15. The first coupon payment comes on July 15, 2000, and Jack immediately begins investing his coupon payments into a Money Market account which earns an annual interest rate of 2% compounded semiannually. The bond is originally priced to yield an annual rate of 6% compounded semiannually. On June 15, 2020, Jack sells the bond at a price that ?s 8% higher than the stated market price (i.e. clean price) at that time. Factoring in the sale of the bond and the coupon investments, what is Jack?s overall yield on his original investment at the time that he sells the bond? Give your answer as an annual interest rate compounded semiannually. Round your percentage answer to two decimal places. Note: Between January 15, 2020 and June 15, 2020 a period of five months has passed. And, between January 15, 2020 and July 15, 2020 a period of six months has passed. Hint: Find the price at which the bond was purchased and the price at which the bond was sold, and use these along with the invested coupons to determine the rate that needs to be applied to the original purchase price in order to have it equal the value of the invested coupons and the selling price.Explanation / Answer
Price at which the bond is bought: 750 * PVIFA(3%,60) + 30000 * PVIF (3%,60) = 25848
Price at the time if selling the bond: 750 * PVIA(3%, 20) + 30000 * PVIF (3%, 20) = 27769
Actaul price at which the nond is sold: 27769 * 1.08) = 29991
Coupon payment reinvestment value: 750 * FVIFA (1%, 40) = 36665
Total Investment made: 25848
Total Return received while selling te bond: 29991 + 36665 = 66655
Total Return on investment = (66655-25848) / 25848 = 57.88%
57.88% return is over a period of 20 years
Therefore, annualized return is 57.88%/20 = 2.89%
Therefore, semiannual return is (1.0289)^(1/2)-1 = 1.44%
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