Example: You manage a pension fund that will provide retired workers with lifeti
ID: 2757976 • Letter: E
Question
Example:
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $1.9 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.) Market Value Five-year million Twenty-year million b. What must be the face value of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.) Face Value Five-year smillion Twenty-year millionExplanation / Answer
The duration of the perpetuity is : 1.10/0.10 = 11 Years [(1+i)/i]
The present value of the payments is: $1.9 million/0.10 = $19 million
Let w be the weight of the 5-year zero coupon bond and therefore the weight of 20-Year zero coupon bond will be 1 – w.
(w x 5) + [(1 – w) x 20] = 11
W = 9/15 = 60%
So, the weight of 5 year zero coupon bond is 60% and 20 year zero coupon bond is 40%.
Therefore the market value of 5 year zero coupon bond is:
$19 million x 60% = $11.4 million
Similarly, the market value of 20 year zero coupon bond is:
$19 million x 40% = $7.6 million
Face value of the 5 year zero coupon bond:
$11.4 million x (1.10)5 = $18,359,814
Face value of the 20 year zero coupon bond:
$7.6 million x (1.10)20 = $51,128,999.61
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.