OPTIMAL PLANT INVESTMENT PLAN (Part 3)
UTILITY AND DECISION ANALYSIS

Last edit:  Sept. 2003

GOAL: Combine utility with decision analysis to evaluate a risky project.

GENERAL PROBLEM DESCRIPTION:

Thanks to your hard work, your company is closer to deciding on a plant investment plan.  Clearly, dollar
return has been an important issue: up to this point you have been using discounted cash flows (NPV)
to evaluate the alternatives.  As you have learned from the CAPM, the discount rate should account for
the time value of money, given the market risk of the project.  Utility theory provides another means for
evaluating risky outcomes, but makes no assumptions regarding risk preferences.  In this case, your boss
owns the company, and you have approximated his utility for money.   Re-evaluate the plant alternatives,
using his utility function as the decision criterion.

PROBLEM OUTLINE:

Same details as Part 2 (demand growth uncertainty).
Evaluate ten years of sales, using cash flows discounted at 10 percent.
Your boss has a utility for money that fits the following form:
U(\$) = [(x+5)/(30)]^c
for outcomes between -\$5 million and \$25 million;
where x = actual outcome (in millions of dollars);
and c = exponent that describes risk preference.

ACTIONS:

Plot utility functions for x values between -\$5 to 25 (million) and c values of 0.5, 1, and 2.
Refer to the 2nd decision tree developed in Part 2 (this is the one with the decision to expand at Year 3).
Use the provided function and c values of 0.5 and 2 to convert the cash outcomes to utility values.
Build two new decision trees (one each for c= 0.5 and c= 2) and use the utility values calculated above
to identify the preferred alternative.
In your report, include the two decision trees, and provide a brief summary with recommendation
and discussion of issues.
Also, describe briefly the role of c in the utility function provided (e.g. what does a c value of 0.5 or 2 imply).
How does the risk characteristic affect the preferred alternative?

NOTE FOR TREEAGE USERS:

(see TreeAge Manual or Instructions Summary for more detail)

You can use the same tree as developed in Part 2 and keep the links with the spreadsheet by just modifying
the outcome expression (using the formula given to you above).    If you enter the exponent c as a variable,
you will be able to use the same base tree for your analysis, and you will be in a perfect position to perform
a sensitivity analysis on that coefficient.