Consider an annual coupon bond with a face value of $100, exactly four years to
ID: 2810445 • Letter: C
Question
Consider an annual coupon bond with a face value of $100, exactly four years to maturity and a 4% annual coupon. The bond is priced to yield 3.25% per year (annually compounded rate) a) Calculate the price of the bond. b) Calculate the bond's duration. c) Calculate the bond's modified duration. Make sure your answer accounts for the fact that the bond is an annual pay bond (not semiannual) d) Calculate the proportional change in the bond price if the bond yield changes from 3.25% to 3.5%. e) Compare the answer that you get in d) to the estimate of this proportional change that you can derive from the bond's modified duration.Explanation / Answer
3.25% YTM@ 0.0325 Year Cash flow PV factor PV-Cash flow Time * PV 1 4.00 0.969 3.87 3.874 2 4.00 0.938 3.75 7.504 3 4.00 0.909 3.63 10.902 3 100.00 0.909 90.85 272.553 Total 102.11 294.83 Bond Price= 102.11 Duration= 294.83/102.11 2.89 Modified duration= =Macauley duration/ (1 + (yield-to-maturity / number of coupon periods per year)) Modified duration= =2.89/ (1 + (3.25%/1)) 2.80 Relationship between Duration and Yield Change in Yield * Duration Percentage change in Price= (3.50%-3.25%) * 2.80 Percentage change in Price= 0.700% Price of bond will go down by 0.70% 3.50% YTM@ 0.035 Year Cash flow PV factor PV-Cash flow Time * PV 1 4.00 0.966 3.86 3.865 2 4.00 0.934 3.73 7.468 3 4.00 0.902 3.61 10.823 3 100.00 0.902 90.19 270.583 Total 101.40 292.74 New Price 101.40 Old Price 102.11 Change (0.71) % age change= -0.71/102.11 % age change= -0.70%