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 **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).

and discussion of issues.

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.