Homework SourseConsider the following a What is the duration of a fouryear
Consider the following. a. What is the duration of a four-year Treasury bond with a 9.5 percent semiannual coupon selling at par? b. What is the duration of a three-year Treasury bond with a 9.5 percent semiannual coupon selling at par? c. What is the duration of a two-year Treasury bond with a 9.5 percent semiannual coupon selling at par? (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
Solution
When bond sell at par then, Discount rate = Coupon rate ; hence Discount rate = 9.5%
a.
Duration = 3.51 Years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+9.5%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
95
0.9132
86.7580
95
86.7580
2
95
0.8340
79.2310
190
158.4621
3
95
0.7617
72.3571
285
217.0713
4
1095
0.6956
761.6539
4380
3046.6154
Total
1000.0000
Total
3508.9068
Price of the Bond = P =
1000.0000
Weighted Price = WP =
3508.9068
Duration = WP/P = 3.51
b.
Duration = 2.75 Years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+9.5%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
95
0.9132
86.7580
95
86.7580
2
95
0.8340
79.2310
190
158.4621
3
1095
0.7617
834.0110
3285
2502.0329
Total
1000.0000
Total
2747.2530
Price of the Bond = P =
1000.0000
Weighted Price = WP =
2747.2530
Duration = WP/P =
2.75
c.
Duration = 1.91 Years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+9.5%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
95
0.9132
86.7580
95
86.7580
2
1095
0.8340
913.2420
2190
1826.4840
Total
1000.0000
Total
1913.2420
Price of the Bond = P =
1000.0000
Weighted Price = WP =
1913.2420
Duration = WP/P =
1.91
| Period | Cash Flow | Discounting factor = 1/(1+R)^Y | PV of the cash flows = Cash flow x Df | Weighted cash flow = Period x Cash flow | Present value of weighted cash flow = Weighted Cash flow x Df |
| Y | CF | Df = 1/(1+9.5%)^Y | PV = CF x Df | WCF = CF x Y | WPV = WCF x Df |
| 1 | 95 | 0.9132 | 86.7580 | 95 | 86.7580 |
| 2 | 95 | 0.8340 | 79.2310 | 190 | 158.4621 |
| 3 | 95 | 0.7617 | 72.3571 | 285 | 217.0713 |
| 4 | 1095 | 0.6956 | 761.6539 | 4380 | 3046.6154 |
| Total | 1000.0000 | Total | 3508.9068 | ||
| Price of the Bond = P = | 1000.0000 | Weighted Price = WP = | 3508.9068 |
