The comptroller of the macrosoft corporation has 100$ million of excess funds to invest. She has been instructed to invest the entire amount for one year in either stocks or bonds and then to reinvest the entire fund in either stocks or bonds for one year more. The objective is to maximize the expected monetary value of the fund at the end of the second year.

The annual rates of return on these investments depend on the economic environment, as shown in the following table:

Rate of return
Economic environment Stocks Bonds
Growth 20% 5
Recession -10 10
Depression -50 20

The probabilities of growth, recession and depression for the first year are 0.7, 0.3 and 0, respectively. If growth occurs in the first year these probabilities remain the same for the second year. However, if a recession occurs in the first year, these probabilities change to 0.2,0.7 and 0.1, respectively, for the second year.

a) Constructed by hand the decision tree for this problem and then analyzes the decision tree to identify the optimal policy.
b) Use TreePlan to construct and solve the decision tree.