10. A pension plan is obligated to make disbursements of $3.3 million. $4.0 mill

Question

10. A pension plan is obligated to make disbursements of $3.3 million. $4.0 million, and $3.3 million at the end of each of the next three years. respectively. The annual interest rate is 10%. If the plan wants to fully fund and immunize its position. how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities. respectively, if these are the only two assets funding the plan? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Portfolio Investment in one-year zero-coupon bonds Investment in perpetuity A bond currently sells for $1.050. which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to $1.025. What is the duration of this bond? (Do not round intermediate calculations. Round your answer to 4 decimal places.) Duration

Explanation / Answer

Answer

Computation of duration , interest rate =10%

Duration :- 3.65 years

The duration of the perpetuity is: (1 + y)/y = 1.10/0.10 = 11 years

Let w be the weight of the zero-coupon bond. Then we find w by solving:

(w × 1) + [(1 – w) × 11] = 3.6492 w = 7.350792/10 = 0.73508

Therefore, your portfolio should be 75.51% invested in the zero and 9.26% in the perpetuity.

1 2 3 4 5 Years PMT PV of PMT Wt of PMT 1*4 1 3.3 .9091 .274379 0.905451 2 4.0 1.6529 0.498868 1.995473 3 3.3 0.7513 0.226753 0.748284 Column sum 3.31 1 3.65

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.