1. (50 points) The president of Chem-Tech is trying to decide whether to start a new product line or purchase a small company. It is not nancially possible to do both. To make the product for a 3-year period will require an initial investment of $250,000. The expected annual cash ows with probabilities in parentheses are: $75,000 (0.5}, $90,000 (0.4, and $150,000 (0.1). To purchase the small company will cost $450,000 now. Market surveys indicate a 55% chance of increased sales for the company and 45% chance of severe decreases with an annual cash ow of +$25,000. If decreases are experienced in the rst year, the company will be sold immediately (during year 1} at a price of $200,000. Increased sales would result in an annual cash ow of $100,000 for the rst two years. If this occurs, a decision to expand aer 2 years at an additional investment of $100,000 will be considered. This expansion could generate cash ows with indicated probabilities as follows: $120,000 (0.3), $140,000 (0.3), and $175,000 (0.4). If expansion is not chosen, the current size will be maintained with anticipated sales to continue. Assume there are no salvage values on investments. Use the description above and a 15%-per year return to do the following: a) Construct a decision tree with all values and probabilities shown. b) Determine the expected PW values at the \"expansionr'no expansion\" decision node after 2 years provided sales are up. 0) Determine what decision should be made now to offer the greatest return possible for ChemTech. d) Explain in words what happen to expected values at each node if the planning horizon were extended beyond 3 years and all cash ow values continued as forecasted in the description