Price Sensitivity of Fixed Income Securities A 6% coupon bond pays interest annually, matures in 7...

Price Sensitivity of Fixed Income Securities

A 6% coupon bond pays interest annually, matures in 7 years, and has a principal of $1000.

(a) Assuming a discount rate of 8%, what is the price of this bond?

(b) Assuming a discount rate of 8.5%, what is the price of this bond?

(c) Assuming a discount rate of 7.5%, what is the price of this bond?

(d) What is the duration of this bond, assuming that the price is the one you calculated in part (a)?

(e) If the yield changes by 100 basis points, from 8% to 7%, what would be the approximate % price

change using the calculated duration from part (d)?

(f) What is the actual % price change given the yield change in (e)?

Expert Solution

1-
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =8%
1	60	55.55555556
2	60	51.44032922
3	60	47.62993446
4	60	44.10179117
5	60	40.83499182
6	60	37.81017761
7	1060	618.499819
price of bond when discount rate is 8%	sum of present value of cash flow	895.8725988

2-
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =8.5%
1	60	55.29953917
2	60	50.96731721
3	60	46.97448591
4	60	43.29445706
5	60	39.9027254
6	60	36.77670544
7	1060	598.8219318
price of bond when discount rate is 8.5%	sum of present value of cash flow	872.037162

3-
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =7.5%
1	60	55.81395349
2	60	51.91995673
3	60	48.29763417
4	60	44.92803179
5	60	41.79351794
6	60	38.87769111
7	1060	638.920195
price of bond when discount rate is 8%	sum of present value of cash flow	920.5509802
4-
Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =8%	year *present value
1	60	55.55555556	55.55555556
2	60	51.44032922	102.8806584
3	60	47.62993446	142.8898034
4	60	44.10179117	176.4071647
5	60	40.83499182	204.1749591
6	60	37.81017761	226.8610657
7	1060	618.499819	4329.498733
price of bond when discount rate is 8%	sum of present value of cash flow	895.8725988
sum of year*present value			5238.26794
duration of bond	sum of year*present value/ price of bond	5238.26794/895.872	5.85
% change in price	duration*change in rate	-5.85*-1%	5.85%
actual change in price	(895.87)*(1+change in rate in price)	(895.87)*(1+.0585))	948.278395

jeff jeffy answered 2 years ago

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