Question

A bond is paying $40 coupon every six month. The bond's face value is $1000 and it has 5 years to maturity. By what percentage will the price of the bond change, if the current YTM of 10% decreases to 9% due to a credit rating upgrade? (Provide your answer in percent rounded to two decimals, omitting the % sign.)

Answer 1

Given coupon Face Value Maturity YTM 1 YTM 2 40 1000 5 years 10% 9% Solution Step 1: Calculate Bond Value (Presnet Value of future cash inflow) 40 4 Year Interest PVF @ 10% LPV PVF @ 9% PV 1 0.909 36.36 0.917 36.70 2 40 0.826 33.06 0.842 33.67 3 40 0.751 30.05 0.772 30.89 40 0.683 27.32 0.708 28.34 1.5 1040 0.621 645.76 0.650 675.93 Present Value 772.55 805.52 where, PVF (Present Value Factor) = 1/(1-r)^n where r is YTM and n is Number of year PV (Present Value) = Cashflow X PVF Change in Price = Change in Price = New Price - Old Price Old Price 805.52 - 772.55 772.55 32.96 772.55 4.27 Change in Price = Change in Price = Hence, Change in price is 4.27