Currently, the term structure is as follows: One-year bonds yield 7.75%, two-yea

Question

Currently, the term structure is as follows: One-year bonds yield 7.75%, two-year bonds yield 8.75%, three-year bonds and greater maturity bonds all yield 9.75%. You are choosing between one-, two-, and three-year maturity bonds all paying annual coupons of 8.75%, once a year. You strongly believe that at year-end the yield curve will be flat at 9.75%.

a. Calculate the one year total rate of return for the three bonds. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

One Year%

Two Years%

Three Years%

b. Which bond you would buy?

Explanation / Answer

a) RATE OF RETURN OBTAINED: The price paid for the bond at t0 is what is given under (1) above and the price realized at t1 is what is given under (2). Besides, interest for 1 year amounts to $87.5 for all the bonds. Hence, return in one year = (interest+price at t1-price at t0)/price at t0. Substituting values in the above equation we get the total rate of return as below: One year = (87.5+1000-1009.28)/1009.28 = 7.75% Two year = (87.5+990.89-1000)/1000 = 7.84% Three year = (87.5+982.59-975.02)/975.02 = 9.75% b) I would buy the three year bond as it has higher rate of return, if held for 1 year. WORK SHEET: 1) CURRENT PRICE OF THE BONDS: The price of the bonds is the PV of the expected cash flows from the bonds if they are held to maturity, the discount rate being the expected yield of 9.75% for all the bonds. Price of the one year bond = 1087.5/1.0775 = $      1,009.28 Price of the two year bond = 87.5/1.0875+1087.5/1.0875^2 = $      1,000.00 Price of the three year bond = 87.5/1.0975+87.5/1.0975^2+1087.5/1.0975^3 = $          975.02 2) PRICE OF THE BONDS AT THE END OF THE 1ST YEAR: Price of the one year bond need not be found out as it will be the maturity value of $1000. Price of the two year bond = 1087.5/1.0975 = $          990.89 Price of the three year bond = 87.5/1.0975+1087.5/1.0975^2 = $          982.59

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