Solve Exercise 16 in Chapter 14 assuming that the annual storage cost of cut lumber is \(5 \%\) of its value.

Data from Exercises 16 chapter 14

You are considering an investment in a tree farm. Trees grow each year by the following factors:

The price of lumber follows a binomial lattice with \(u=1.20\) and \(d=9\). The interest rate is constant at \(10 \%\). It costs \(\$ 2\) million each year, payable at the beginning of the year, to lease the forest land. The initial value of the trees is \(\$ 5\) million (assuming they were harvested immediately). You can cut the trees at the end of any year and then not pay rent after that. (For those readers who care, we assume that cut lumber can be stored at no cost.)

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Year 1 2 3 4 5 6 78 9 10 Growth 1.6 1.5 1.4 1.3 1.2 1.15 1.1 1.05 1.02 1.01