You are considering an investment in a Christmas tree farm over two years. The farm already has trees planted a year ago, and these trees grow each year by the following factors.

The price of the trees follows a binomial lattice with w = 1.25 and d = 0.80. As the trees grow older, the value of the investment in general will increase. However, if the trees get too big, they are less attractive, so a three-year rotation appears to be a typical life-cycle for this type of Christmas tree. The interest rate (risk-free) is constant at continuous 6%. It costs $400,000 each year-payable at the beginning of the year-to lease the forest land. The initial value of the one-year old trees is $1 million (assuming they were harvested immediately). You can cut the trees at the beginning of the Christmas season (say, December 1st) of any year and then not pay rent after that. With rent of $400,000 per year, find the best cutting policy (when to cut) and the value of the investment opportunity with the best cutting policy.

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Year 1.6 1.5 Growth