If a bond\'s yield to maturity does not change, the return on the bond each year

Question

If a bond's yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this for both a premium and a discount bond using a 4-year 3.3 percent coupon bond with annual coupon payments and a face value of $1,000. a. Assume the yield to maturity is 2.3 percent. What is the current value of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price today What will the bond value be in one year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price in one year What is the rate of return for the first year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) Rate of return b. Assume the yield to maturity is 4.3 percent. What is the current value of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price today What will the bond value be in one year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Bond price in one year What is the rate of return for the first year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) Rate of return

Explanation / Answer

a Year Cash flow Discount factor @ 2.3% =1/(1+r)^n 1 33 0.977517 32.258 2 33 0.95554 31.533 3 33 0.934056 30.824 4 1033 0.913056 943.187 1037.802 Current Value of Bond - $ 1037.80 Price of Bond after one year Year Cash flow Discount factor @ 2.3% =1/(1+r)^n 1 33 0.977517 32.258 2 33 0.95554 31.533 3 1033 0.934056 964.880 1028.671 Bond Value after one year - $ 1028.67 Rate of Return - (1028.67-1037.80)/1037.80 -0.88% b Year Cash flow Discount factor @ 4.3% =1/(1+r)^n 1 33 0.958773 31.640 2 33 0.919245 30.335 3 33 0.881347 29.084 4 1033 0.845012 872.897 963.956 Current Value of Bond - $ 963.96 b Price of Bond after one year Year Cash flow Discount factor @ 4.3% =1/(1+r)^n 1 33 0.958773 31.640 2 33 0.919245 30.335 3 1033 0.881347 910.432 972.406 Bond Value after one year - $ 1028.67 c Rate of Return - (972.41-963.96)/963.96 0.88%

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