4. Demand for electric power in a region appears to be growing at a rate of 6 percent per year, and a new generating plant is being designed to serve this demand. The company feels that there is 0.70 probability that the demand will continue to grow at this rate and a probability of 0.30 that the demand growth may slow to about 5 percent. A smaller plant costing $290 million and a larger plant costing $340 million are being considered. If the smaller plant is built and demand remains high, the generating ca- pacity can be expanded. The net present worth of all future annual operating revenues minus disbursements other than those for recovery of the plant investment is $485 million if the larger plant is built and demand is high. If demand is low, the company will have used valuable cap- ital in excess capacity and will have to follow uneconomical alternatives in other operat- ing decisions within the company, so that the PW will be only $375 million. Should the company elect to build a smaller plant and the demand be low, the PW will be $410 million. If the demand is high under this condition, the company has the option of purchasing power so that the PW will be $370 million, or it can expand the plant's generating capacity for $90 million. With expansion programs there will be some inefficiencies and lost revenues so that the PW will be $480 million.

a. Draw the decision tree for this analysis.

b. Which decision should the company make to maximize the expected present worth after the cost of the plant is deducted?