Magnolia, property development company, has liabilities of $10 million dollars, payable at the end of years 2, 4, and 6. The amount of cash they have exactly matches the present value of their liabilities. The current annual effective interest rate is 6%.

a) Calculate the present value of their liabilities, Dmac, and Dmod.

b) The assets available for their portfolio are 2 year and 6 year zero coupon bonds.

i) How much of each should they buy to match the duration of their assets and liabilities.

ii) Is the resulting portfolio Redington immunized?

iii) Is the resulting portfolio fully immunized? (This can be proved (see text), but I will settle for a spreadsheet showing the value of the portfolio for interest rates from 0.1% to, say 20%)

c) Same as b) but the only available assets are 3 year and 5 year zero coupon bonds.