In: Finance
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)? |
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 |