13.16 Growth Options

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

Year1 : growth 1.6, year2 : growth 1.5

The price of the trees follows a binomial lattice with u = 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 les 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 $1million (assuming they were harvested immediately) you can cut the trees at the beginning of the Christmas season (say, December 1^st) 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.