Suppose that you are managing a pension fund with obligations to make perpetual payments of $4.2 million per year to beneficiaries. The required rate of return is 20%.
a. If the duration of 5-year maturity bonds with coupon rates of 16% (paid annually) is 3.7 years and the duration of 20-year maturity bonds with coupon rates of 10% (paid annually) is 6.2 years, how much of each of these coupon bonds (in $ market value) will you want to hold to fully fund and immunize your obligation? The yield to maturity on both bonds is 20%.
[Hint: compute the present value and duration of liabilities first. This provides the dollar amount and target duration you will need to match with an investment in the two coupon bonds above.]
(Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal place.)
Holdings:
5 Year Bond $ _________ Million
20 Year Bond $ _________ Million
b. What will be the par value of your holdings in the 20-year coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Par Value $ _______ Million