# Decision tree and expected value

Decision tree and expected value.

Scenario: Using the same situation from the Module 3 SLP, recall that you are deciding among three investments. You have heard of an expert who has a highly reliable â€śtrack recordâ€ť in the correct identification of favorable vs. unfavorable market conditions. You are now considering whether to consult this â€śexpert.â€ť Therefore, you need to determine whether it would be worth paying the expertâ€™s fee to get his prediction. You recognize that you need to do further analysis to determine the value of the information that the expert might provide.

In order to simplify the analysis, you have decided to look at two possible outcomes for each alternative (instead of three). You are interested in whether the market will be Favorable or Unfavorable, so you have collapsed the Medium and Low outcomes. Here are the three alternatives with their respective payoffs and probabilities.

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Option A: Real estate development. This is a risky opportunity with the possibility of a high payoff, but also with no payoff at all. You have reviewed all of the possible data for the outcomes in the next 10 years and these are your estimates of the Net Present Value (NPV) of the payoffs and probabilities:

High/Favorable NPV: \$7.5 million, Pr = 0.5

Unfavorable NPV: \$2.0 million, Pr = 0.5

Option B: Retail franchise for Just Hats, a boutique-type store selling fashion hats for men and women. This also is a risky opportunity but less so than Option A. It has the potential for less risk of failure, but also a lower payoff. You have reviewed all of the possible data for the outcomes in the next 10 years and these are your estimates of the NPV of the payoffs and probabilities.

High/Favorable NPV: \$4.5 million, Pr = 0.75

Unfavorable NPV: \$2.5 million, Pr = 0.25

Option C: High Yield Municipal Bonds. This option has low risk and is assumed to be a Certainty. So there is only one outcome with probability of 1.0:

NPV: \$2.25 million, Pr = 1.0

You have contacted the expert and received a letter stating his track record which you have checked out using several resources. Here is his stated track record:

 True State of the Market Expert Prediction Favorable Unfavorable Predicts â€śFavorableâ€ť .9 .3 Predicts â€śUnfavorableâ€ť .1 .7

You realize that this situation is a bit complicated since it requires the expert to analyze and predict the state of two different markets: the real estate market and the retail hat market. You think through the issues of probabilities and how to calculate the joint probabilities of both markets going up, both going down, or one up and the other down. Based on your original estimates of success, here are your calculations of the single probabilities and joint probabilities of the markets.

 Probabilities Favorable Unfavorable A: Real Estate 0.50 0.50 B: Just Hats 0.75 0.25
 Joint Probabilities A Fav, B Fav (A+, B+) 0.375 A Unf, B Unf (A-, B-) 0.125 A Fav, B Unf (A+, B-) 0.125 A Unf, B Fav (A-, B+) 0.375

Finally, after a great deal of analysis and calculation, you have determined the Posterior probabilities of Favorable and Unfavorable Markets for the Real Estate business and the boutique hat business.

 Real Estate Just Hats F U F U 0.45 says “F/F” 0.75 0.25 0.90 0.10 0.15 says “F/U” 0.75 0.25 0.30 0.70 0.30 says “U/F” 0.125 0.875 0.90 0.10 0.10 says “U/U” 0.125 0.875 0.30 0.70

For example, this table says that there is 45% chance that the expert will predict Favorable for both markets (F/F), and when he makes this prediction, there is a 75% chance that the Real Estate market will be favorable and 25% chance that it wonâ€™t, and also a 90% chance that the Hat market will be Favorable and 10% chance it wonâ€™t.

You have developed a Decision Tree showing the original collapsed solution and also showing an expanded Decision Tree for evaluating the value of the expertâ€™s information. You need to enter the probabilities into this tree to see if the expertâ€™s information will increase the overall expected value of your decision. Download the Excel file with the incomplete Decision Tree: Decision Tree for BUS520 SLP 4

Assignment

Complete the information in the Decision Tree in the Excel file. Determine the Expected NPV of the decision if you were to consult the Expert. Does use of the Expert increase the value of your analysis? If so, by how much?

Analysis

• Accurate and complete analysis in Excel.

Required:

• Length requirements: 2â€“3 pages minimum (not including Cover and Reference pages). NOTE: You must submit 2â€“3 pages of written discussion and analysis. This means that you should avoid use of tables and charts as â€śspace fillers.â€ť
• Provide a brief introduction to/background of the problem.
• Written analysis that supports Excel analysis and provides thorough discussion of assumptions, rationale, and logic used.

Decision tree and expected value