Contemporary Engineering Economics 6th Edition by Chan Park

تمرين 13

You are considering an investment in a Christmas tree farm over three 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 it 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 less attractive, so a three-year rotation appears to be a typical lifecycle 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 forestland. 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 1) of any year and then nor pay rent after that.
(a) It costs $400,000 each year, payable at the beginning of the year, to lease the forest land. You can cut the trees at the beginning of Christmas season (Say, December 1) of any year and then not pay rent after that. Find the best cutting policy with this rent.
(b) Suppose there is no rent. Find the best cutting policy without rent.