Question

Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 2 years to maturity, whereas Bond Dave has 14 years to maturity.

If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Sam?

1. -8.47%
2. -9.25%
3. 8.69%
4. -8.45%
5. 9.54%

If interest rates suddenly rise by 5 percent, what is the percentage change in the price of Bond Dave?

1. -30.34%
2. -43.56%
3. 34.73%
4. -30.32%
5. 53.22%

If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Sam be then?

1. 9.52%
2. 8.69%
3. 9.50%
4. -8.42%
5. 9.57%

If rates were to suddenly fall by 5 percent instead, what would the percentage change in the price of Bond Dave be then?

1. 53.20%
2. 34.73%
3. 53.18%
4. -30.29%
5. 53.25%

Answer 1

1)	Lets assume that the par value is 1000.
	If the bond is priced at par/face value then the yield to maturity is equal to the coupon rate.
	BOND SAM has two years to maturity.
	If interest rates rise by 5%, the yield to maturity will become 14%.
	Calculate the price when the yield to maturity is 14%. Then calculate the percentage
	change in price.
	price of the bond = sum of present values of future cash flows
	r/2	0.07
	mt	1	2	3	4
	future cash flow	45	45	45	1045
	present value	42.05607	39.30474	36.7334	797.2255
	sum of present values	915.32
	The bond is priced at par value that is 1000.
	When interest rates increase by 5% the price changes to 915.32.
	% change in price	(915.32 -1000)/1000
	% change in price	-0.08468
	a) -8.47%.
2)	BOND DAVE has fourteen years to maturity.
	If interest rates rise by 5%, the yield to maturity will become 14%.
	Calculate the price when the yield to maturity is 14%. Then calculate the percentage
	change in price.
	price of the bond = sum of present values of future cash flows
	r/2	0.07
	mt	1	2	3	4	5	6	7	26	27	28
	future cash flow	45	45	45	45	45	45	45	45	45	1045
	present value	42.05607	39.30474	36.7334	34.33028	32.08438	29.9854	28.02374	7.748797	7.241867	157.1703
	sum of present values	696.57
	The bond is priced at par value that is 1000.
	When interest rates increase by 5% the price changes to 696.57
	% change in price	(696.57 -1000)/1000
	% change in price	-0.30343
	a) -30.34%.
3)	Present Value = Future value/[(1+(r/m))^mt]
	FOR BOND SAM, when interest rates fall by 5% the yield to maturity will become 4%.
	r is the interest rate that is 4%.
	price of the bond = sum of present values of future cash flows
	r/2	0.02
	mt	1	2	3	4
	future cash flow	45	45	45	1045
	present value	44.11765	43.2526	42.40451	965.4185
	sum of present values	1095.19
	The bond is priced at par value that is 1000.
	When interest rates decrease by 5% the price changes to 1095.19.
	% change in price	(1095.19 -1000)/1000
	% change in price	0.09519
	a) 9.52%.
4)	Present Value = Future value/[(1+(r/m))^mt]
	FOR BOND DAVE, when interest rates fall by 5% the yield to maturity will become 4%.
	r is the interest rate that is 4%.
	price of the bond = sum of present values of future cash flows
	r/2	0.02
	mt	1	2	3	4	5	6	7	26	27	28
	future cash flow	45	45	45	45	45	45	45	45	45	1045
	present value	44.11765	43.2526	42.40451	41.57304	40.75789	39.95871	39.17521	26.89107	26.36379	600.2214
	sum of present values	1532.03
	The bond is priced at par value that is 1000.
	When interest rates decrease by 5% the price changes to 1532.03
	% change in price	(1532.03 -1000)/1000
	% change in price	0.53203
	a) 53.20%.