Question

Racquet Centers, Inc. (RCI) is a small investment company. The company is considering building a new racquet center. If the demand for the center is high (i.e., there is a favorable market for the racquet center), RCI could realize a net profit of $100,000. If the market is not favorable, RCI could lose $40,000. Of course, they don’t have to proceed at all; in which case, there is no cost. In the absence of any market data, the best RCI can guess is that there is a 50–50 chance the center will be successful. Construct a decision tree to help analyze this problem. What should RCI do? Please show your decision tree, Excel computations, and fully explain your answer.

Answer 1

Decision Tree

Let us find the expected value of the decision.

EV (Build the plant) = Probability of Favourable Market * Profit + Probability of Unfavourable Market * Loss

= 0.5 * 100000 + 0.5 * (-40000) = 50,000 - 20,000 = $30,000

EV (Do Nothing) = 0

This is calculated in excel as below -

EV = Probability * Profit/Loss EV of Decision = EV (Build Center/Favourable) + EV (Build Center/Unfavourable) Hence, the optimal decision will be to go ahead and build the center since the Expected value of building the center is 30,000 which is greated than the decision of not building the center (