5. (20 points) Consider the following list of projects (data in millions): PW (1

Question

5. (20 points) Consider the following list of projects (data in millions): PW (15%) $716 $757 $179 oPW $544 $616 $40 Alternative Payback Investment $471 $465 $405 2 4 2 Assume that all three projects are mutually exclusive. a. Are any projects dominated? Explain. b. Use threshold analysis with a minimum present-worth standard of maximum standard deviation of $600 million, and a maximum payback of 4 (assume that the payback period for a portfolio is the maximum payback period of any project in the portfolio). What projects should be considered? Assume that the criteria of present worth, standard deviation, and payback period are ordered as listed, with ideal values of $1 billion, $20 million, and 2 respectively. Provide a score for each portfolio and select the best one. c. d. Using only the PW and standard deviation, apply the Freund utility model with B = 0.05 described in Problem 3 to the portfolios to identify the best one.

Explanation / Answer

a. Out of the 3 projects, Project 2 has the highest net present worth of $757 million, hence it is the project that should be selected for investing. In other words, Alternative 1 and 3 are dominated by Alternative 2. [Note: All 3 projects are good for investment since they all have positive net present worth, but since they are mutually exclusive, the firm cannot invest in say, Project 1 if it chooses to invest in Project 2].

b. We can only consider project 1 and project 3 . If we have a threshold constraints of maximum standard devation of $600 million and a maximum payback of 4, we see that Alternative 2 does not meet the first threshold of a maximum SD of $600 million, so we cannot include it in our decision rule. Hence we can only consider project 1 and project 3 and between the best project (with the highest present worth) is selected, which is project 1.

c. The ideal value of a project is a project with a present worth of $1billion, standard deviation of $20 million and a payback period of 2 periods (or years). To develop a scoring model, we have to understand that we prefer projects with higher present worth but lower standard deviation (high SD = high risk) and lower payback period. Let us score the project on these parameters on a scale of 1 to 10.

For the purpose of analysis. Its best to consider returns per unit of risk, i.e. the present worth / standard deviation. This gives us a better view of the projects. for e.g. if a project has an PW of $25 and an SD of $2, the score is 25/2 = 12.5. The higher the number, the better it is. So we can rank our Alternatives as:

We also see that in terms of payback period, best payback is of Alternative 3. Thus a scoring system would rank Alternative 3 as the best project, both in terms of returns per unit of risk and the payback period.

Alternative Present Worth Standard Deviation Score (PW / SD) 1 $716 $544 1.32 2 $757 $616 1.23 3 $179 $40 4.48

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