# Calculating expected profit and utility values

An individual is considering two investment projects. Project A will return a zero profit if conditions are poor, a profit of $4 if conditions are good, and a profit of $8 if conditions are excellent. Project B will return a profit of $2 if conditions are poor. a profit of $3 if conditions are good, and a profit of $4 if conditions are excellent. The probability distribution of conditions is as follows:

Conditions: Poor Good Excellent

Probability 40% 50% 10%

a) Using excel, calculate the expected value of each project and identify the preferred project according to this criterion.

b) Assume that the individual's utility function for profit is U(X) = X -0.05X2. Calculate the expected utility of each project and identify the preferred project according to this criterion.

c) Is this individual risk averse, risk neutral, or risk seeking? Why?

#### Solution Preview

Please refer attached file for better clarity of formulas and tables.

a) Using excel, calculate the expected value of each project and identify the preferred project according to this criterion.

Project A

State / Probability Profit

Condition p X p*X

Poor 0.4 $0.00 $0.00

Good 0.5 $4.00 $2.00

Excellent 0.1 $8.00 $0.80

Expected profit $2.80

Project B

State / Probability Profit

Condition p X p*X

Poor ...

#### Solution Summary

Solution depicts the steps to estimate the expected value and expected utility for each of the given projects. It also predicts the nature of the individual based upon the calculated values.