Question

My pension plan will pay me $17,000 once a year for a 10-year period. The first payment will come in exactly five years. The pension fund wants to immunize its position. a. What is the duration of its obligation to me? The current interest rate is 11.0% per year. (Do not round intermediate calculations. Round your answer to 4 decimal places.) b. If the plan uses 5-year and 20-year zero-coupon bonds to construct the immunized position, how much money ought to be placed in each bond? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.) c. What will be the face value of the holdings in each zero? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)

Answer 1

Solution share of Puration of obligation of lension Teal Calculation IPlon Cash Year) flow 85000 85000 170,000 x 17000 X 5 & Discounting Present facher allt Value (w won 0.59345132 50,443,3629 262,216.81425 0.3521 8447 29,135,607 299,35 6.80621 80,379.0426 551,573.62.1352 Duration - zwx a 531,573.621352 80,379,0436 EN 6.8622 yas Note:- Intermediate calculations have not been rounded off to calculate the final answer However, for the purpose of presentchon, it is shown as rounded off to u docimal places. (6 question in the Since both the bonds given ZOBs, Dulghen - Mohurity, Syes bond to ke x and to yes bond to be y. Let

Money to be placed in Bond x = $80.379.8436 * 0.87585 = $70 400.2532495 a $70.40 Ans Money to be placed in Bond Y= $80,374,0436X0, 12415 = $ 9979 same as cursaat co Assuming Yoeld on the bond is interest rate of 11%. her Bond X na sya, y fru = 11% a fya 70400 x Coll) x = $1, 18, 628 Aus For Bond Y no 2o yes cy yfy all% a7a 1, 20 = $80,454 Ang

Durahon of x= 5 Puahua of Y = 20. Money should be demotion of both the of pension Plan. placed bonds such that is equal to dual - 5x next Loxwy = 6.8622 here, cox is the weight of money to be placed in Bond X and simplicwly toe Bondy. 5x byx +20x (1-x) = 6.8622 SX Wu tho Lonki - 6-8622 I nx = 0.87585 My = 0.12415 I Mone to be placed in Bond x s 170.000 X0,87585