Pension funds pay lifetime annuities to recipients. Firm expects to be in business indefinitely, its pension obligation perpetuity. Suppose that your pension fund must make perpetual payments of $2 million/year. The yield to maturity on all bonds is 16%. Duration of 5-year bonds with coupon rates of 12% (paid annually) is 4 years. Duration of 20-year bonds with coupon rates of 6% (paid annually) is 11 years.

How much of each of these coupon bonds (in market value) should you hold to both fully fund (i.e. value of bonds = PV of obligation) and immunize your obligation?

Note that this problem requires you to use two useful properties of duration:

Duration of a perpetuity = (1 + ytm) / ytm

Duration of a portfolio = weighted average of the durations of the components of the portfolio

*********NO EXCEL SOLUTION PLEASE, HANDWRITTEN