You are evaluating investment alternatives for a ski resort.There are four alternative investments and their payoffs (in $10,000s) are shown in the following table, depending on the snow conditions for the next season. $\begin{array}{r}\text { Snow Conditions }\\\begin{array}{ccc}\text { Investment } & \text { Good } & \text { Bad } \\d_{1} & 3 & 1 \\d_{2} & 8 & 0 \\d_{3} & 12 & -4 \\d_{4} & 18 & -12\end{array}\end{array}$
If you use the EMV criterion, what is the minimum probability that the conditions will be good for you to decide investment d₄?

Question

You are evaluating investment alternatives for a ski resort.There are four alternative investments and their payoffs (in $10,000s) are shown in the following table, depending on the snow conditions for the next season.

\begin{array}{r}\text { Snow Conditions }\\\begin{array}{ccc}\text { Investment } & \text { Good } & \text { Bad } \\d_{1} & 3 & 1 \\d_{2} & 8 & 0 \\d_{3} & 12 & -4 \\d_{4} & 18 & -12\end{array}\end{array}

If you use the EMV criterion, what is the minimum probability that the conditions will be good for you to decide investment d₄?

Quizplus · Accepted Answer

The Expected Monetary Value (EMV) for an investment is calculated as $EMV = p \times \text{Good} + (1-p) \times \text{Bad}$, where $p$ is the probability of good snow conditions. To find the minimum probability ($p$) that makes $d_3$ more attractive than $d_1$, we compare their EMVs. For $d_1$, $EMV = p \times 3 + (1-p) \times 1$. For $d_3$, $EMV = p \times 12 + (1-p) \times (-4)$. Setting $EMV_{d_3} > EMV_{d_1}$, we get $p \times 12 + (1-p) \times (-4) > p \times 3 + (1-p) \times 1$. Solving for $p$ gives $p > 0.57$.

You Are Evaluating Investment Alternatives for a Ski Resort If You Use the EMV Criterion, What Is the Minimum