1) Compute the Macaulay duration for a 5-year bond paying annual coupons of 9% a

Question

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!

Explanation / Answer

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

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