Question

A power plant is planning construction of a new plant to generate electricity four years hence and must decide now between a small, medium, or large-sized plant. The exact size needed is uncertain because future demands can only be estimated. Forecasters have estimated future demands and their likelihoods as follows:

Level of Demand	Probability
High	0.30
Medium	0.55
Low	0.15

            In the following, all the future costs and earnings have been adjusted to their present worth:

1. The capacity of a small plant would limit its NPV to $60 million regardless of demand. If demand is medium, a small plant can be enlarged a moderate amount at a cost of $20 million. Its NPV would then be $110 million less the cost of $20 million for the expansion. If demand is high, a small plant can be enlarged greatly in size at a cost of $80 million. Its NPV would then be $170 million less the cost of $80 million for the expansion. On the contrary, if demand is high, a small plant can be enlarged a moderate amount to increase its NPV to $140 million less the cost of $40 million for the expansion.
2. A medium-sized plant will have an NPV of $120 million if demand is high or medium and a loss of $5 million if demand is low. If demand is high, a medium-sized plant can be enlarged at a cost of $40 million to generate an additional $80 million in earnings.
3. If a large plant is built and demand is high, the plant’s net present value (NPV) is estimated to be $180 million. If the demand is medium, however, the NPV of a large plant will drop to $100 million. If the demand is low the NPV will be loss of $200 million.

Use decision-tree analysis in MS Excel to determine the size of the power-generating plant the company should build now. (Please show the formulas in the cells)

Questions:

1. What size of the power-generating plant the company should build now?

2. Will the answer be the same if you will change the forecasters estimated demands and their likelihoods to:

Level of Demand	Probability
High	0.25
Medium	0.55
Low	0.20

Answer 1

Decision Tree is following:

Expected NPV of Small plant = 0.15*60+0.55*90+0.30*100 = $ 88.5 million

Expected NPV  of Medium plant = 0.15*(-5)+0.55*120+0.30*(120+40) = $ 113.25 million

Expected NPV of Large plant = 0.15*(-200)+0.55*100+0.30*180 = $ 79 million

Expected NPV  of Medium plant is the highest.

Therefore, the company should build a Medium sized plant now and if the demand is high, then the plant should be expanded .

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The decision tree using the new probabilities is following:

In the above decision tree, we see that Expected NPV of build medium plant is the highest.

Therefore, the company should build a medium sized plant now, and if demand is high, then Expand .

Expected NPV of this decision strategy = $ 105 million