Bond A Bond B Coupon Rate 5% 14% Years-to-Maturity 10 10 Yield-to-Maturity 7% 7%
ID: 2622840 • Letter: B
Question
Bond A Bond B
Coupon Rate 5% 14%
Years-to-Maturity 10 10
Yield-to-Maturity 7% 7%
Interest Payments Semi- Semi-
Annual Annual
A] What is the current price of these bonds?
B] If the interest rates rise by 2%, what is the percentage price change of these bonds?
C] If the interest rates fall by 2%, what is the percentage price change of these bonds?
D] What does this problem tell you about the interest rate risk of lower-coupon bonds?
Explanation / Answer
A)
For calculating the price i have used the "=pv" function in excel. The inputs are rate which here is 7%/2, nper which in this case is 10*2, pmt which is the annuity cash flow and so 25 (5% of 1000) for bond A and 70 for bond B. Put a - sign for pmt. and lastly fv which is -1000 for both the bonds and you will get the price of the bonds as 857.88 and 1497.43 respectively.
Alternatively you can do it manually by discounting each years cash flow. For eg i will show the calcualtions for Bond A
B) If the interest rates rise by 2% just increase the YTM in the above formula by 2 percentage points and the respective prices of the bonds will be 739.84 for Bond A which means a % change of 13.75% and 1325.2 for Bond B which is a % change of 11.5% ofcourse both on the negative side as the interest rate is inversly related to bond price.
C) If the interest rates fall by 2% just decrease the YTM in the above formula by 2 percentage points and the respective prices of the bonds will be 1000 for Bond A which means a % change of 16.56% and 1701.51 for Bond B which is a % change of 13.62% both on the positive side as the interest rate is falling here
D) From the above two we can easily state that the price of lower coupon bonds are affected more by a change in the interest rates. in other words they are more susceptible to interest rate changes.
Bond A Bond B Coupon 25 70 years 10 10 YTM 7 7 Interest Pmt 2 2 Price 857.88 1497.43