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

Annual rates of return on these investments depend on economic environment, as given in the following table:

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

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

a) Create by hand decision tree for this problem and then examine decision tree to recognize optimal policy.
b) Use TreePlan to create and solve decision tree.