Explanation of Solution The computation of the proportion of portfolio must be allocated towards the perpetuities and zero coupon bonds are shown below: Duration of perpetuity =) = (8) = 11 years Let the zero coupon bond's weight is w. therefore computation of the weight is shown below: (wx 1) + (1-w) x 11] = 2.6019 w = (8.31) = 0.8398 Perpetuity = (1-8398) = 0.1620 Conclusion Thus, it can be concluded that 16.02% of the portfolio should be invested in perpetuity and rest 83.89% in the zero coupon bond.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question

Where does the 2.6019 in the solution some from????

Explanation of Solution
The computation of the proportion of portfolio must be allocated towards the perpetuities and zero coupon
bonds are shown below:
Duration of perpetuity = ()
= ()
= I1 years
Let the zero coupon bond's weight is w. therefore computation of the weight is shown below:
(w x 1) + |(1 – w) x II] = 2.6019
8.3981
= 0.8398
Perpetuity = (1 – 8398)
= 0.1620
Conclusion
Thus, it can be concluded that 16.02% of the portfolio should be invested in perpetuity and rest 83.89% in
the zero coupon bond.
Transcribed Image Text:Explanation of Solution The computation of the proportion of portfolio must be allocated towards the perpetuities and zero coupon bonds are shown below: Duration of perpetuity = () = () = I1 years Let the zero coupon bond's weight is w. therefore computation of the weight is shown below: (w x 1) + |(1 – w) x II] = 2.6019 8.3981 = 0.8398 Perpetuity = (1 – 8398) = 0.1620 Conclusion Thus, it can be concluded that 16.02% of the portfolio should be invested in perpetuity and rest 83.89% in the zero coupon bond.
10. A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next
three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually. (@ LO 11-2)
11. If the plan in the previous problem 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? (
O LO 11-4)
Transcribed Image Text:10. A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 10% annually. (@ LO 11-2) 11. If the plan in the previous problem 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? ( O LO 11-4)
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