Question

1. A bond is paying $60 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 8.5% due to a credit rating upgrade? (Provide your answer in percent rounded to two decimals, omitting the % sign.)

Please be sure of answer and show explanations.

Answer 1

The price of the bond can be calculated by discounting the coupon payments and face value received from the bond at the current YTM of 10% and new YTM of 8.5%. The coupon payments are received semi-annually thus; the number of periods will be 10 (5 years multiplied with 2). Calculate the price of the bond using excel as follows: 5 1 Number of years 2 Coupon payment per 6-month 3 Face value 4 Number of compounding per year 5 Number of periods 60 1000 =B1*B4 Current 0.1 =B7/B4 New 0.085 =C7/B4 7 YTM 8 YTM per period 9 Calculate price of bond: 10 Price of bond --PV(B8, B5,B2,B3) --PV(C8,B5,B2,B3) The answers are as follows:

The answers are as follows: A 1 Number of years 2 Coupon payment per 6-month 3 Face value 4 Number of compounding per year 5 Number of periods $60.00 $1,000.00 10 Current New 5% 8.50% 4.25% 7 YTM 8 YTM per period 9 Calculate price of bond: 10 Price of bond $1,077.22 $1,140.19 The percentage change in the price of the bond can be calculated as follows: Price of bond at New YTM-Price of bond at Current YTM % change in price = Price of bond at Current YTM $1,140.19-$1,077.22 $1,077.22 $62.97 $1,077.22 = 0.05845603 or 5.84560257 Hence, the price of the bond will increase by 5.85 when the YTM falls from 10% to 8.5%.