Module 4 – Case

DECISION TREE AND VALUE OF INFORMATION

Assignment Overview

Scenario: You are a consultant who works for the Diligent Consulting Group. You have learned about three different investment opportunities and need to decide which one is most lucrative. Following are the three investment options and their 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 cash payoff and probabilities:

Required initial investment: $0.75 million

High NPV: $5 million, Pr = 0.5

Medium NPV: $2 million, Pr = 0.3

Low NPV: $0, Pr = 0.2

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 payoffs and probabilities:

Required initial investment: $0.55 million

High NPV: $3 million, Pr = 0.75

Medium NPV: $2 million, Pr = 0.15

Low NPV: $1 million, Pr = 0.1

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:

Required initial investment: $0.75 million

NPV: $1.5 million, Pr = 1.0

Case Assignment

Develop an analysis of these three investments, and determine which of them you should choose. Be sure to account for cash paid for each of the three alternatives. If you do not recall how to do this, review the practice exercises in the Background page. Do your analysis in Excel using the Decision Tree add-in or SmartArt graphic, as suggested in the Background page.

Write a report to your private investment company and explain your analysis and your recommendations. Provide a rationale for your decision.

Upload both your written report and Excel file with the decision tree analysis to the case 4 Dropbox.

Assignment Expectations

Excel Analysis

Conduct accurate and complete Excel analysis using decision tree add-in.

Written Report

• Length requirements: 2–3 pages minimum (not including Cover and Reference pages)
• 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.
• Complete, meaningful, and accurate recommendation(s).
• Write clearly, simply, and logically. Use double-spaced, black Verdana or Times Roman font in 12 pt. type size.
• Have an introduction at the beginning to introduce the topics and use keywords as headings to organize the report.
• Avoid redundancy and general statements such as “All organizations exist to make a profit.” Make every sentence count.
• Paraphrase the facts using your own words and ideas, employing quotes sparingly. Quotes, if absolutely necessary, should rarely exceed five words.

Module 4 – Background

DECISION TREE AND VALUE OF INFORMATION

Required Reading

Introduction to Decision Trees

Consider the decision to choose between two different alternatives. Imagine that you have a decision where there are three, four or more choices. Then consider that you may have to estimate the probabilities of two or more future states for choice. How do you model this decision in such a way so that you can visualize it easily, analyze the data, get results, and then even make changes for sensitivity analysis? The answer is to use a Decision Tree (D-tree) model.

Let’s take a very simple, generic problem. You have two options to choose from, A and B. let’s say two different stocks choices. You determine that there are three basic outcomes: the market goes high, the market goes medium, and the market goes low. Given the research that you have done, here are the two possible investments and outcomes for a specific period of time, say a year:

Table 1: Possible investments and outcomes

	Option A			Option B
Market level	High	Medium	Low	High	Medium	Low
Probability	0.4	0.3	0.3	0.6	0.25	0.15
Payoff	10	6	2	8	4	3

You can do the calculations in Excel, like you did in module 2. But consider that you may have more complex problems. So using a D-tree is the best way to go. Here is the way this problem looks using a D-tree in Excel using the Simple Decision Tree tool.

The blue square denotes a decision node. A node is a place in the tree where this branches. You see two branches from the blue decision node. These represent the two choices. The choice on the top is labeled Option A and the bottom is Option B (keeping it generic). You could label these with specific names of the stocks. Each option shows the future states. In this example, we have determined that there are two completely separate futures, indicated by the fact that the probabilities are different. But each future has three possible states: high, medium, and low, which are based on the possible behavior of the market, depending on which stock you might buy. The green circle denotes an Uncertainty node. You see the three branches coming off each of these nodes. We have labeled these High, Medium, and Low for each uncertainty node corresponding to each choice of stock. We have entered the probabilities on each branch coming off the uncertainty node. For Option A you see the probabilities 0.4, 0.3, and 0.3 and the corresponding payoffs at the end of the branches, 10, 6, and 2. For Option B you see the probabilities 0.6, 0.25, and 0.15 and the corresponding payoffs at the end of the branches, 8, 4, and 3.

Once we have created the d-tree and entered the labels, the probabilities and the payoffs, the d-tree automatically calculates the best choice. Note that on the top branch you see the Expected Value of this choice is 6.4. The bottom branch shows the Expected Value of 6.25. You also see that on the top branch, there is this symbol >>> next to Option A, which means it is the preferred choice. Then next to the blue square, you see the value of 6.4 which is the value of the best choice, Option A.

You can change the numbers and do sensitivity analysis and play “what-if” games to test out different theories and scenarios. You can add branches to any node or delete branches from any node. Note that there are few “rules” when creating D-tree models, mostly which conform to probability theory. First, at the Choice node, you need to include all of the relevant choices, including the one, do nothing. We have done so here, but for a complete analysis, there is always the status quo or do nothing. Then each chance node must have branches that correspond to a set of mutually exclusive and collectively exhaustive outcomes. Mutually exclusive means that only one of the outcomes can happen. In our example, for either stock, the market can only do one thing, go high, medium or low. Collectively exhaustive means that no other possibilities exist and one of the specified outcomes has to occur. While not a hard and fast rule, usually time is represented from Left to Right. First the Decision Maker chooses an option, then action takes place over time and ultimately one of the future states occurs. Of course in our model we represent all possible future states.

The following instructions on Decision Tree apply to Windows users. If you are a Mac user and do not have any access to a Windows PC, you may try one of the options below (please note that the first two options would incur additional costs):

1. Install Excel and third party add-in in Mac such as http://treeplan.com/trial/.
2. Install Parallels software (http://www.parallels.com/) to create a Windows virtual desktop in Mac;
3. Create the decision tree manually. You may use SmartArt Graphics in Office applications (Word, Excel and PowerPoint) to do decision trees. Refer to the following links on SmartArt Graphics:

Create a SmartArt graphic. (n.d.). Retrieved from https://support.office.com/en-US/article/Create-a-SmartArt-graphic-FAC94C93-500B-4A0A-97AF-124040594842

Learn more about SmartArt graphics. (n.d.). Retrieved from https://support.office.com/en-US/article/Learn-more-about-SmartArt-Graphics-6ea4fdb0-aa40-4fa9-9348-662d8af6ca2c

About SmartArt graphics in Office 2016 for Mac. (n.d.). Retrieved from https://support.office.com/en-US/article/About-SmartArt-graphics-in-Office-2016-for-Mac-607b1b23-435a-4bac-98b6-0c9ad0f4ef85

Download the Excel Add-in called SimpleDecisionTree_V1.4.xla and add it into your Excel.

Watch this video showing how to include an Add-in: http://permalink.fliqz.com/aspx/permalink.aspx?at=…

Watch this video showing how to use the Simple Decision Tree tool: http://permalink.fliqz.com/aspx/permalink.aspx?at=…

Practice creating a decision tree by using this example problem:

You have a choice of which game to play: flipping a coin or rolling a single die. It costs you $10 to play the game. If you choose the coin flip, you will win $15 for a heads, but will win only $3 for a tails. If you choose the die roll, you will win 3 times the amount showing on the die. For example, a 4 pays $12 and a 6 pays $18, while a 1 pays only $3.

Once you have created your d-tree for this problem, download this Excel file to check it: Decision Tree-Which Game to Play. Then you are ready for Case 4.

Deciding to use an Expert: the Value of Information

Wouldn’t it be nice if you could find an expert that could predict the future with 100% accuracy? (Imagine how rich this expert would be.) All you would have to do is pay this expert and he would tell you whether the future will go one way or the other, and then you would know what to do. Your decision would be easy. But that is a fantasy. Some experts are good at predicting the future and we can find out what their track record is.

For example, suppose you are in the last stages of product development of two similar product designs, a new smart phone. One smart phone has many new advanced features but will be very costly to produce and sell with a high price. The other smart phone has only a few new features and would be considered to be only average in its value and have only an average price on the market. We need to decide which one of these two smart phone options we are going to finish and take to market, but only one. We estimate the two possible future states of the market demand: the market will generally want a High Value, High Price smart phone (Pr = 0.4), or an Average Value, Average Price smart phone (Pr = 0.6). This is the decision tree for this decision including the payoffs.

You know an Expert that you can consult who has a good track record of predicting the future in these situations. This is the track record:

	Market behavior
Expert	High value	Avg Value
Says “wants high value”	0.85	0.08
Says “wants avg value”	0.15	0.92

When the Market actually is demanding High Value, the expert is correct (predicts “High value”) 85% of the time, and is wrong (predicts “Avg. value) 15% of the time. When the Market is actually demanding Avg. value, the expert is correct (predicts “Avg. value) 92% of the time, and is wrong (predicts “High value”) 15% of the time. We can also state these using conditional probability statements:

Pr( Expert Says “wants high value” | Market demand is High value) = 85%

Pr( Expert Says “wants avg value” | Market demand is High value) = 15%

Pr( Expert Says “wants high value” | Market demand is Avg value) = 8%

Pr( Expert Says “wants avg value” | Market demand is Avg value) = 92%

We are showing these probability statements because in a moment you will be asked to read an article that explains Bayes’ Theorem, which uses this kind of probability statements. Here is the modified decision tree if you were to consider consulting an Expert. Note that you have not yet consulted the expert, but are only considering it.

Aggregating multiple probability distributions: when using several experts, combine their distribution assessments into one for use by

In this scenario, with the consideration of consulting an expert, you do not know what he/she will say, and therefore these are unknown future states. He could say the market “wants High V” or “wants Avg V”. We need to determine these probabilities. And note that the probabilities of which actual future market will occur will be different depending on the expert’s prediction.

We need to use Bayes’ theorem to help us determine these new probabilities. Go to this website page which provides an easy to understand explanation of Bayes’ theorem using a medical example, testing for cancer: http://betterexplained.com/articles/an-intuitive-and-short-explanation-of-bayes-theorem/

Now that you have an understanding of Bayes’ Theorem and “flipping” the probabilities, here are the calculations for the smart phone example.

	0.4	0.6
	Market behavior
Expert	High value	Avg Value
Says “wants high value”	85%	8%
Says “wants avg value”	15%	92%

This is the expert’s track record. Multiply the probabilities (your estimates) of actual market behavior (0.4, and 0.6) down the column to get conditional probabilities.

	Expert
38.8%	Says “wants high value”	34.0%	4.8%
61.2%	Says “wants avg value”	6.0%	55.2%
100.0%

Then you add across to get the probabilities of what the expert might say:

Pr(Expert Says “wants high value”) = 38.8%

Pr( Expert Says “wants avg value”) = 61.2%

And added together these equal 100%, since the expert must say one or the other. Now calculate the conditional probabilities of the future states given what the expert says:

	Conditional
	Market behavior
Expert	High value	Avg Value
Says “wants high value”	87.6%	12.4%	100%
Says “wants avg value”	9.8%	90.2%	100%

For example, in the top row: 0.34 / 0.388 = 0.876, and 0.048 / 0.388 = 0.124. Now we can enter these probabilities into the decision tree and determine what the EVM payoff is for consulting the expert. If this EVM is higher than the EVM for not consulting the expert, then there is value in the information provided by the expert.

Finally, we need to decide if the value of this information is enough for us to pay for it. If this value is more than what the expert charges, then we should consult the expert.

Download the Excel file BUS520 Module 4 SLP Examples-Practice.xlsx that provides examples and a Practice Exercise.

Watch this video showing how to determine the value of information: http://permalink.fliqz.com/aspx/permalink.aspx?at=…

Practice determining the Value of Information; do the Practice Exercise in the Excel file.

You are ready for SLP 4.

Optional Reading

Charlesworth, D. (2013). Decision analysis for managers: A guide for making better personal and business decisions. New York, NY: Business Expert Press. Available in the Trident Online Library.

Rubric Name: MBA/MSHRM/MSL Case Grading Rubric -Timeliness v1

Criteria Level 4 – Excellent Level 3 – Proficient Level 2 – Developing Level 1 – Emerging Assignment-Driven Criteria 23 points Demonstrates mastery covering all key elements of the assignment in a substantive way. 20 points Demonstrates considerable proficiency covering all key elements of the assignment in a substantive way. 18 points Demonstrates partial proficiency covering all key elements of the assignment in a substantive way. 14 points Demonstrates limited or poor proficiency covering all key elements of the assignment in a substantive way. Critical Thinking 9 points Demonstrates mastery conceptualizing the problem. Multiple information sources, expert opinion, and assumptions are analyzed, synthesized, and critically evaluated. Logically consistent conclusions are presented with appropriate rationale. 8 points Demonstrates considerable proficiency conceptualizing the problem. Information sources and viewpoints of experts are proficiently analyzed and evaluated. Assumptions are clearly stated and supported, but may not be questioned. Conclusions are logical, but may be somewhat disconnected from the analysis. 7 points Demonstrates partial proficiency conceptualizing the problem. Information sources and viewpoints of experts are stated, but not necessarily synthesized, or critically evaluated. Assumptions are stated but not supported. Conclusions may be logical, but are not connected to or supported by the preceding analysis. 6 points Demonstrates limited or poor proficiency conceptualizing the problem. Information sources and viewpoints of experts are either absent or poorly analyzed, synthesized, and evaluated. Assumptions are implied, but not clearly stated. Conclusions are either absent or poorly conceived and unsupported. Business Writing 4 points Demonstrates mastery in written communication and a skilled, knowledgeable, and error-free presentation to an appropriately specialized audience. 3 points Demonstrates considerable proficiency in written communication with a well-organized presentation to an appropriately specialized audience. 2 points Demonstrate partial proficiency in written communication with few grammatical or syntax errors, but may lack headings or be pitched at the wrong audience. 1 point Demonstrates limited or poor ability to write clearly, and uses poor grammar and syntax. Text may be disorganized and rambling. Effective Use of Information 6 points Demonstrates mastery in locating relevant and quality sources of information, using strong and compelling content to support ideas, convey understanding of the topic, and shape the whole work. 5 points Demonstrates considerable proficiency in retrieving information, and in using appropriate and relevant content to support ideas, and convey understanding of the topic. Few arguments left unsupported. 4 points Demonstrates partial proficiency to retrieve information, but may not be able to discriminate quality. Uses relevant content to partially support ideas, but leaves many arguments unsupported. May use immaterial or disparate content in an attempt to support arguments. 3 points Demonstrates inability to retrieve information, or use appropriate or relevant content to support ideas, convey understanding of the topic and shape the whole work. Makes unsupported arguments and assertions. Citing Sources 3 points Demonstrates mastery using in-text citations of sources, proper format for quotations, and correctly format full source information in the reference list using APA style (bibliography). 2 points Demonstrates considerable proficiency using of in-text citations of sources, proper format for quotations, and provides sufficient source information in the reference list, though not in APA format (bibliography). 1 point Demonstrates occasional use of in-text citations of sources and provides partial reference information, such as a URL or web link (bibliography). 0 points Demonstrates inability to cite sources or provide a reference list (bibliography). Timeliness 5 points Assignment submitted on time or collaborated with professor for an approved extension on due date. 3 points Assignment submitted 1-2 days after module due date. 2 points Assignment submitted 3-4 days after module due date. 0 points Assignment submitted 5 or more days after module due date. Overall Score Level 4 45 or more Level 3 40 or more Level 2 35 or more Level 1 0 or more

Module 4 – SLP

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:

	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
		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 favorabl

 

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