A bond fund manager has a five-year time horizon, and is considering two bonds.
ID: 2750905 • Letter: A
Question
A bond fund manager has a five-year time horizon, and is considering two bonds. The first is a 15-year to maturity bond with a 5.75% coupon rate, paid annually. The price of this bond today is 100% of face value. The second bond is a 20-year to maturity bond with a 7% coupon rate, paid annually. The price of this bond is 102% of face value.
The bond fund manager forecasts that, in five years, the 15-year bond (which will have 10 years remaining until maturity) will sell at a yield to maturity of 5.45% and the 20-year bond (which will have 15 years remaining until maturity) will sell at a yield to maturity of 6.50%. The bond fund manager also expects that the coupons can be reinvested at an annual rate of 5% over the period. Calculate the expected annualized compound rate of return over the five years for each bond. Which bond offers the higher expected compound rate of return?
Explanation / Answer
Bond 1:
Coupon earned each year = 5.75% * 100 = 5.75
Future value at the end od year 5 =FV(5%,5,-5.75,0,0) = 31.77
Price at the end of year 5 =PRICE(A1,A2,5.75%,5.45%,100,1) = 102.27
Here cells A1 and A2 contain today's date and date of maturity which is 10 years from today
Capital gain = 102.27 - 100 = 2.27
Total return = 31.77 + 2.27 = 34.04
Annualized compounded rate of return = (134.04/100)(1/5) - 1 = 6.03%
Bond 2:
Coupon earned each year = 7% * 100 = 7
Future value at the end od year 5 =FV(7%,5,-7,0,0) = 40.26
Price at the end of year 5 =PRICE(A1,A2,7%,6.5%,100,1) = 104.70
Here cells A1 and A2 contain today's date and date of maturity which is 15 years from today
Capital gain = 104.70 - 102 = 2.70
Total return = 40.26 + 2.70 = 42.96
Annualized compounded rate of return = (144.96/102)(1/5) - 1 = 7.28%
2nd bond gives higher expected rate of return
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