13. 10.00 points The YTM on a bond is the interest rate you earn on your investm

Question

13. 10.00 points The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is known as the hoiding period yield (HPY) a. Suppose that today you buy a bond with an annual coupon of 9 percent for $1,110. The bopd has 16 years to maturity What rate of return do you expect to earn on your investment? Assume a-par value of $1,000. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected rate of return T 7780 b1. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places,e.g., 32.16.) Bond price b2. What is the HPY on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g. 32.16.) HPY I 24.030%

Explanation / Answer

a. Price of bond=Present value of interest discounted at rate of return for 16 years+Present value of principal repayment discounted at rate of return for the 16th year Let rate of return=r 1110=90*(PVIAF @r,16)+1000*(PVIF @r,16) Use trial and error method, At 7%,Price of bond=(90*9.447)+(1000*0.339)=1189.23 At 8%,Price of bond=(90*8.851)+(1000*0.292)=1088.59 Using interpolation, r=7%+[(1189.23-1110)/(1189.23-1088.59)]*(8%-7%)=7.78% b1. Revised rate of return=7.78-1=6.78% Price of bond=Present value of interest discounted at 6.78% for 14 years+Present value of bond repayment discounted at 6.78% for the 14th year Price of bond=(90*8.8620)+(1000*0.3992)=1196.74 b2. Issue price=Present value of interest discounted at HPY for 2 years+Present value of bond selling price discounted at HPY for 2nd year 1110=(90*PVIAF @ HPY,2)+(1196.74*PVIF @ HPY,2) Use trial and error method, At 11%,Issue price=(90*1.7125)+(1196.74*0.8116)=1125 At 12%,Issue price=(90*1.6901)+(1196.74*0.7972)=1106 Using interpolation, HPY=11%+[(1125-1110)/(1125-1106)]*(12%-11%)=11.79%

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