Decision Tree and Value of Information

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Scenario: You are deciding among three investments, as you do for Case 4. You have heard of an expert who has a highly reliable “track record” in the correct identification of favorable vs. unfavorable market conditions. You are now considering whether to consult this “expert.” Therefore, you need to determine whether it would be worth paying the expert’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.

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 “Favorable” .9 .3
Predicts “Unfavorable” .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
Favorable (F)
Unfavorable (U)
0.45 says "F/F"
Real Estate(F)0.75 (U)0.25
Just Hats(F)0.90 (U)0.10
0.15 says "F/U"
Real Estate(F)0.75 (U)0.25
Just Hats(F)0.30 (U)0.70
0.30 says "U/F"
Real Estate(F)0.125 (U)0.875
Just Hats(F)0.90 (U)0.10
0.10 says "U/U"
Real Estate(F)0.125 (U)0.875
Just Hats(F)0.30 (U)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 won’t, and also a 90% chance that the Hat market will be Favorable and 10% chance it won’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 expert’s information. You need to enter the probabilities into this tree to see if the expert’s information will increase the overall expected value of your decision. Download the Excel file with the incomplete Decision Tree: (See attached file: SLP Assignment_incomplete Decision Tree Excel.xlsx)

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?

Develop a PowerPoint presentation to your private investment company and explain your analysis and your recommendation. Provide clear rationale/ justification for your decision. Use audio/video feature in PowerPoint to present each slide. Be sure to check the Oral Communication Rubric (See attached file: Oral rubric) to understand the requirements for the PowerPoint presentation.

SLP Assignment Expectations
Analysis: Conduct accurate and complete analysis in Excel. Check the following link on PowerPoint presentation:
https://support.office.com/en-US/article/PowerPoint-training-40e8c930-cb0b-40d8-
82c4-bd53d3398787

Required:
Meet Length requirements: 10-15 slides (not including Cover and Reference pages).
Provide a brief introduction to/background of the problem.
Show analysis that supports Excel analysis and provides thorough discussion of
assumptions, rationale, and logic used.
Offer meaningful and accurate recommendation(s).
Oral presentation of each slide should use video/audio feature in PowerPoint.

Unformatted Attachment Preview

Criteria Central Message & Language Choices Organizational Pattern (specific introduction and conclusion, sequenced material within the body, and transitions) Supporting Materials (explanations, examples, illustrations, statistics, analogies, quotations from relevant authorities) Delivery Techniques (manner of delivery, vocal expressiveness, and how spoken information fits with visual media) Timeliness Level 4 - Excellent Level 3 - Proficient Level 2 - Developing Level 1 - Emerging 15 points 11 points 9 points 7 points Central message is Central message is Central message is compelling (precisely clear and consistent basically stated, appropriately with the supporting understandable but is repeated, memorable, material. Language not often repeated and and strongly choices are thoughtful is not memorable. supported). Language and generally support Language choices are choices are the effectiveness of the mundane and partially imaginative, presentation. Language support the memorable, and in presentation is effectiveness of the compelling, and appropriate to presentation. Language enhance the audience. in presentation is effectiveness of the appropriate to presentation. Language audience. in presentation is appropriate to audience. 5 points 4 points 2 points Central message can be deduced but is not explicitly stated in the presentation. Language choices are unclear and minimally support the effectiveness of the presentation. Language in presentation is not appropriate to audience. 1 point Demonstrates Demonstrates adequate Demonstrates some Demonstrates very significant attention to attention to attention to minimal or no attention organizational pattern organizational pattern organizational pattern to organizational within the within the within the pattern within the presentation. presentation. presentation. presentation. 4 points Supporting materials are varied and make appropriate reference to information or analysis that significantly supports the presentation or establishes the presenter's credibility and authority on the topic. 3 points 3 points 1 point Supporting materials Supporting materials Supporting materials make appropriate make appropriate are inefficient and reference to reference to make reference to information or analysis information or analysis information or analysis that generally supports that partially supports that minimally supports the presentation or the presentation or the presentation or establishes the establishes the establishes the presenter's credibility presenter's credibility presenter's credibility and authority on the and authority on the and authority on the topic. topic. topic. 2 points Delivery techniques Delivery techniques make the presentation make the presentation compelling, and interesting, and speaker appears speaker appears polished and confident. comfortable. 3 points 2 points 2 points 1 point 0 points Delivery techniques make the presentation understandable, and speaker appears tentative. Delivery techniques detract from the understandability of the presentation, and speaker appears uncomfortable. 1 point 0 points Value Measure U-Value 0.5 High/Favorable 7.5 7.5 2 2 4.5 4.5 2.5 2.5 2.25 2.25 >>> A-Real Estate 4.75 4.75 0.5 UNFAVORABLE 0.75 High/Favorable B-Just Hats 4.75 4.75 4 4 0.25 UNFAVORABLE 10 year Bond 0.5 Favorable >>> A-Real Estate 4.75 4.75 0.5 Unfavorable 0.75 Favorable B-Just Hats 4 4 0.25 Unfavorable 10 year Bond 0 Exp says "F/F" 2.25 2.25 4.75 4.75 >>> 0 Exp says "U/U" 2.25 2.25 >>> Consult Expert 0 0 0 Exp says "F/U" 2.25 2.25 >>> 0 Exp says "U/F" 2.25 2.25 >>> Value Measure U-Value 7.5 7.5 2 2 4.5 4.5 2.5 2.5 Use the probabilities from the Table tree. The cells that need probability 2.25 2.25 Once you have correctly updated the you will be able to see the Expected Expert's predictions. 0 Favorable 7.5 7.5 Real Estate 0 0 0 Unfav 2 2 0 Favorable 4.5 4.5 2.5 2.5 Keep in mind that you have not cons simply performing an analysis based prior estimates of the probabilities o markets. You want to see if consultin additional value to your decision. Be sure to write your report and incl Upload your report and this Excel file Just Hats 0 0 0 Unfav. Bond 2.25 2.25 Expert's Prediction Prob. 0.45 0.15 0.30 0 Fav 0.10 7.5 7.5 2 2 4.5 4.5 2.5 2.5 2.25 2.25 7.5 7.5 2 2 4.5 4.5 2.5 2.5 2.25 2.25 7.5 7.5 2 2 Real Estate 0 0 0 Unf 0 Fav Just Hats 0 0 0 Unf Bond 0 Fav Real Estate 0 0 0 Unf 0 Fav Just Hats 0 0 0 Unf Bond 0 Fav Real Estate 0 0 0 Unf 0 Fav 4.5 4.5 2.5 2.5 2.25 2.25 Just Hats 0 0 0 Unf Bond e probabilities from the Table below and fill in this decision he cells that need probability values are highlighted in green. you have correctly updated the d-tree with the probabilities, ll be able to see the Expected NPV of this analysis with the 's predictions. n mind that you have not consulted the Expert yet, you are performing an analysis based on his track record and your stimates of the probabilities of Favorable or Unfavorable ts. You want to see if consulting this expert will provide onal value to your decision. e to write your report and include the results of this analysis. d your report and this Excel file to SLP4 Dropbox. pert's Prediction Prediction says "F/F" says "F/U" says "U/F" Posterior Probabilities of Market States Real Estate Just Hats F U F U 0.750 0.250 0.900 0.100 0.750 0.250 0.300 0.700 0.125 0.875 0.900 0.100 says "U/U" 0.125 0.875 0.300 0.700 DECISION TREE AND VALUE OF INFORMATION Scenario: You are deciding among three investments, as you do for Case 4. You have heard of an expert who has a highly reliable “track record” in the correct identification of favorable vs. unfavorable market conditions. You are now considering whether to consult this “expert.” Therefore, you need to determine whether it would be worth paying the expert’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. 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: 1/4 True State of the Market Expert Prediction Favorable Unfavorable Predicts “Favorable” .9 .3 Predicts “Unfavorable” .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 0.45 0.15 0.30 says "F/F" says "F/U" says Just Hats F U F U 0.75 0.25 0.90 0.10 0.75 0.25 0.30 0.70 0.125 0.875 0.90 0.10 2/4 "U/F" 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 won’t, and also a 90% chance that the Hat market will be Favorable and 10% chance it won’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 expert’s information. You need to enter the probabilities into this tree to see if the expert’s information will increase the overall expected value of your decision. Download the Excel file with the incomplete Decision Tree: Decision Tree for 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? Develop a PowerPoint presentation to your private investment company and explain your analysis and your recommendation. Provide clear rationale/ justification for your decision. Use audio/video feature in PowerPoint to present each slide. Be sure to check the Oral Communication Rubric (under Assessments>Rubrics) to understand the requirements for the PowerPoint presentation. Upload both your PowerPoint presentation and Excel file with the Decision Tree analysis to the SLP 4 Dropbox. SLP Assignment Expectations Analysis Conduct accurate and complete analysis in Excel. Check the following link on PowerPoint presentation: https://support.office.com/en-US/article/PowerPoint-training-40e8c930-cb0b-40d882c4-bd53d3398787 Required: Meet Length requirements: 10-15 slides (not including Cover and Reference pages). Provide a brief introduction to/background of the problem. 3/4 Show analysis that supports Excel analysis and provides thorough discussion of assumptions, rationale, and logic used. Offer meaningful and accurate recommendation(s). Oral presentation of each slide should use video/audio feature in PowerPoint. 4/4 Value Measure U-Value Market Behavior Product choices 0.4 Want high value 50 50 10 10 8 8 35 35 0 0 >>> High V, High C 26 26 0.6 Want avg value 0.4 Want high value Avg V, avg C 26 26 24.2 24.2 0.6 Want avg value Consult the expert Expert Says "wants high value" Says "wants avg value" Market behavior High value Avg Value 0.85 0.08 0.15 0.92 Market Behavior Product choices 0.4 Want high value High V, High C 26 26 0.6 Want avg value 0.4 Want high value Avg V, avg C 24.2 24.2 0.6 Want avg value 37.27617 37.27617 >>> High V, High C 45.04 0.388 Says "want High V 45.04 45.04 Avg V, avg C 11.348 Consider >>> Consult Expert 37.2762 37.2762 High V, High C 13.92 0.612 Says "wants Avg V 32.354 32.354 >>> Avg V, avg C 32.354 Value Measure U-Value 50 50 10 10 38.8% 61.2% 100.0% 8 8 35 35 50 50 10 10 8 8 35 35 50 50 10 10 8 8 0.876 Want high value High V, High C 45.04 0.124 Want avg value 0.876 Want high value Avg V, avg C 11.348 0.124 Want avg value 0.098 Want high value High V, High C 13.92 0.902 Want avg value 0.098 Want high value Avg V, avg C 32.354 0.902 Want avg value 35 35 Expert Says "wants high value" Says "wants avg value" Expert Says "wants high value" Says "wants avg value" Expert Says "wants high value" Says "wants avg value" 0.4 0.6 Market behavior High value Avg Value 85% 8% 15% 92% 34.0% 6.0% 4.8% 55.2% Conditiional Market behavior High value Avg Value 87.6% 12.4% 9.8% 90.2% 100% 100% Value Measure U-Value 0.7 Left 25 25 20 20 20 20 35 35 Alternative 1 23.5 23.5 24.5 24.5 0.3 Right 0.7 Left >>> Alternative 2 24.5 24.5 0.3 Right Expert Says "Left" Says "Right" Future Behavior Left Right 0.92 0.12 0.08 0.88 Consult the Expert??? You do it. Then check your results. 0.7 Left Alternative 1 23.5 23.5 0.3 Right 0.7 Left Alternative 2 24.5 24.5 0.3 Right 27.1798 27.1798 >>> Alternative 1 24.735 24.735 0.68 Says "Left" 24.735 24.735 Alternative 2 20.795 20.795 >>> Consult Expert 27.1798 27.1798 Alternative 1 20.875 20.875 0.32 Says "Right" 32.375 32.375 >>> Alternative 2 32.375 32.375 Value Measure U-Value 25 25 20 20 68.0% 32.0% 100.0% 20 20 35 35 25 25 20 20 20 20 35 35 25 25 20 20 20 20 0.947 Outcome 1 0.053 Outcome 2 0.947 Outcome 1 0.053 Outcome 2 0.175 Outcome 1 0.825 Outcome 2 0.175 Outcome 1 0.825 Outcome 2 35 35 Expert Says "Left" Says "Right" Expert Says "Left" Says "Right" 0.7 0.3 Future Behavior Left Right 0.92 0.12 0.08 0.88 0.644 0.056 0.036 0.264 94.7% 17.5% 5.3% 82.5% 100.0% 100.0% EV with Expert info is $27.18 EV w/o Expert info is $24.50 Increased value. Is it worth consulting him?
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