You are considering an investment in a tree farm. Trees grow each year by the following factor:
year 1 2 3 4 5 6 7 8 9 10
Growth 1.6 1.5 1.4 1.3 1.2 1.15 1.1 1.05 1.02 1.01
The price of lumber follows a binomial lattice with u = 1.2 and d = 0.9. The interest rate is constant at 10%. It costs $2m each year, payable at the beginning of the year, to lease the forest land. The initial value of the tress is $5m. You can cut the trees at the end of any year and then not pay rent after that.
(1) Argue that if the rent were zero, you would never cut the trees as long as they were growing.
(2) With rent of $2m per year,find the best cutting policy and the value of the investment opportunity.