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 4.7 percent coupon bond with annual coupon payments and a face value of $1,000.

a. Assume the yield to maturity is 3.7 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 5.7 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

The price of a bond is the sum total of the PV of the expected cash flows from the bond, if it is held till maturity, the discount rate being the market interest rate. The expected cash flows from the bonds are: *the maturity value of $1000, receivable at EOY 4, and *the annual interest payments of $47. a) Current value of the bond: = 1000/1.037^4+47*(1.037^4-1)/(0.037*1.037^4) = $        1,036.56 Bond price in 1 year: = 1000/1.037^3+47*(1.037^3-1)/(0.037*1.037^3) = $        1,027.91 Rate of return for the 1st year = (Annual interest+Gain in price)/Current price = [(47+(1027.91-1036.56)]/1036.56 = 3.70% c) Current value of the bond: = 1000/1.057^4+47*(1.057^4-1)/(0.057*1.057^4) = $            965.11 Bond price in 1 year: = 1000/1.057^3+47*(1.057^3-1)/(0.057*1.057^3) = $            973.12 Rate of return for the 1st year = (Annual interest+Gain in price)/Current price = [(47+(973.12-965.11)]/965.11 = 5.70%

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