Question

In: Finance

Bond J has a coupon rate of 4 percent.


Interest Rate Risk. 

Bond J has a coupon rate of 4 percent. Bond S has a coupon rate of 14 percent. Both bonds have 13 years to maturity, make semiannual payments, a par value of $1,000, and have a YTM of 8 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Solutions

Expert Solution

BOND J
Par/Face value 1000
Annual Coupon rate 0.04
Annual coupon 40
semi-annual coupon 20
Present Value = Future value/[(1+(r/m))^mt]
r is the yield to maturity that is 8%.
m is the compounding period that is 2
mt is the time period.
price of the bond = sum of present values of future cash flows
r/2 0.04
mt 1 2 3 4 5 6 13
future cash flow 20 20 20 20 20 20 20
present value 19.23077 18.49112 17.77993 17.09608 16.43854 15.80629 12.01148
mt 14 15 16 17 18 19 26
future cash flow 20 20 20 20 20 20 1020
present value 11.5495 11.10529 10.67816 10.26746 9.872562 9.492848 367.903
sum of present values 680.3446
b) The price of BOND J is $680.34.
Do the same analysis for Bond J when YTM increases by 2% and decreases by 2%.
Then calculate the % change in price.
r/2 0.05
mt 1 2 3 4 5 6 13
future cash flow 20 20 20 20 20 20 20
present value 19.04762 18.14059 17.27675 16.45405 15.67052 14.92431 10.60643
mt 14 15 16 17 18 19 26
future cash flow 20 20 20 20 20 20 1020
present value 10.10136 9.620342 9.16223 8.725934 8.310413 7.914679 286.8655
sum of present values 568.7444
When the yield to maturity rises by 2%, the price of BOND J is $568.74.
% change in price when interest rates rise by 2% is (568.74-680.34)/680.34
% change in price when interest rates rise by 2% is -16.40%.
r/2 0.03
mt 1 2 3 4 5 6 13
future cash flow 20 20 20 20 20 20 20
present value 19.41748 18.85192 18.30283 17.76974 17.25218 16.74969 13.61903
mt 14 15 16 17 18 19 26
future cash flow 20 20 20 20 20 20 1020
present value 13.22236 12.83724 12.46334 12.10033 11.74789 11.40572 472.9686
sum of present values 821.2316
When the yield to maturity falls by 2%, the price of BOND J is $821.23.
% change in price when interest rates fall by 2% is (821.23-680.34)/680.34
% change in price when interest rates fall by 2% is 20.71%.
SAME ANALYSIS FOR BOND S AS WAS FOR BOND J
Par/Face value 1000
Annual Coupon rate 0.14
Annual coupon 140
semi-annual coupon 70
b) The price of BOND S is $1479.48.
Do the same analysis for Bond S when YTM increases by 2% and decreases by 2%.
Then calculate the % change in price.
When the yield to maturity rises by 2%, the price of BOND S is $1287.50
% change in price when interest rates rise by 2% is (1287.50-1479.48)/1479.48
% change in price when interest rates rise by 2% is -12.98%.
When the yield to maturity falls by 2%, the price of BOND S is $1715.074.
% change in price when interest rates fall by 2% is (1715.07-1479.48)/1479.48
% change in price when interest rates fall by 2% is 15.92%.
This problem tells us that lower coupon bonds have higher interest rate risk.

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