Value Measure 0.5 Head 5 Coin flip -1 -1 0.5 Tail -7 0.167 1 spot -7 0.5 0.5 0.167 2 spot -4 0.167 3 spot -1 >>> Die roll 0.5 0.5 0.167 4 spot 2 0.167 5 spot 5 0.167 6 spot 8 U-Value 5 -7 -7 -4 -1 2 5 8 Note that I have accounted for cash paid ($10) to enter the game in Column M, by reducing each "Value Measure" amount by $10. ount by $10. 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-SmartArtgraphic-FAC94C93-500B-4A0A-97AF-124040594842 Learn more about SmartArt graphics. (n.d.). Retrieved from https://support.office.com/en-US/article/Learn-more-aboutSmartArt-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/AboutSmartArt-graphics-in-Office-2016-for-Mac-607b1b23-435a-4bac98b6-0c9ad0f4ef85 Download the Excel Add-in called SimpleDecisionTree_V1.4.xla and add it into your Excel. Watch this video showing how to include an Addin: http://permalink.fliqz.com/aspx/permalink.aspx?at=62469fea72a 2420dae1ea19682bb9372&a=5fae3cf0f1624f39b0341263a6541ea0 Watch this video showing how to use the Simple Decision Tree tool: http://permalink.fliqz.com/aspx/permalink.aspx?at=38aa3b814 00343c9bc2b78461f884789&a=5fae3cf0f1624f39b0341263a6541e a0 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. 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.
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