Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $3.0 million per year to beneficiaries. The yield to maturity on all bonds 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 7% (paid annually) is 6.5 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 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? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Par value $

You are managing a portfolio of $2.6 million. Your target duration is 13 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 8%.

a. How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Zero-coupon bond	%
Perpetuity bond	%

b. How will these fractions change next year if target duration is now ten years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Zero-coupon bond	%
Perpetuity bond	%