Homework Sourse1 Compute the Macaulay duration for a 5year bond paying annu
1) Compute the Macaulay duration for a 5-year bond paying annual coupons of 9% and having a yield to maturity of 9.5%.
a. 3.86 Answers: a. 3.86 b. 4.57 c. 5.00 d. 3.78 e. 4.23
2) Which of the following bonds would be cheapest to deliver given a T-note futures price of 90.4697? (Assume that all bonds have semiannual coupon payments based on a par value of $100.)
Answers: a. 9.5-year bond with 4.5% coupons and a yield of 3.5% b. 7.5-year bond with 6.5% coupons and a yield of 7.5% c. 6.5-year bond with 8.5% coupons and a yield of 8%
Please explain with steps, thank you!
Solution
ANS 1 e) 4.23
| Year | Project Cash Flows (i) | DF@ 9.5% (ii) | PV of Project A ( (i) * (ii) ) | DURATION= PRESENT VALUE* TIME |
| 0 | 0 | 1 | - | - |
| 1 | 90 | 0.913 | 82.19 | 82.19 |
| 2 | 90 | 0.834 | 75.06 | 150.12 |
| 3 | 90 | 0.762 | 68.55 | 205.65 |
| 4 | 90 | 0.696 | 62.60 | 250.41 |
| 5 | 1090 | 0.635 | 692.40 | 3,461.99 |
| TOTAL | 980.80 | 4,150.36 | ||
| DURATION = | (PRESENT VALUE*TIME)/ TOTAL PRESENT VALUE | |||
| 4150.36 / 980.80 | ||||
| 4.23 | ||||
