Evaluate 9.1 Page 330 Problem 33

Venture Limited is a company with net sales of $30 million. The company currently must decide whether to enter one of two risky ventures or invest in a sure thing. The gain from the latter is a sure $125,000. The possible outcomes for the less risky venture are a $0.5 million loss, a $0.1 million gain, and a $1 million gain. The probabilities of these outcomes are 0.25, 0.50, and 0.25, respectively. The possible outcomes of the more risky venture are a $1 million loss, a $1 million gain, and a $3 million gain. The probabilities of these outcomes are 0.35, 0.60, and 0.05, respectively. If Venture Limited must decide on exactly one of these alternatives, what should it do?
Objective: To see how the company’s risk averseness, determined by its risk tolerance in an exponential utility function, affects its decision. Create a line chart that includes three series— that is, three lines (or curves). Each line should show the expected utility of a particular decision for a sequence of possible risk tolerance values. This chart should make it clear when the more risky option becomes optimal and whether the less risky option is ever optimal.