Conditional Probability in Decision Trees In Module Five, our exercise is building on what you have learned in prior modules. The three reference videos for probabilistic top-down tree modeling are provided below. Watch each of these videos as they contain important information that supports the remaining work on the problems as well as the final project: Joint Probability Table and Bayes Theorem (14:31) Conditional Prob and Joint Prob Table in Excel (6:05) Decision Tree with Conditional Probability (22:00) Note: Skip the section on EVSI/EVPI and efficiency; we will do diagnostics later. Notes on the videos: You have already learned everything in the first two videos in prior modules. These videos focus on conditional probability in action. In the third video, Professor Wu uses \"marginal probabilities.\" You may recognize these as weighted probabilities when calculating total probability. However, Wu then uses a slightly different style of calculating a joint probability matrix. While there should be nothing in here that you have not already seen, the reason this is important is that you are going to use these probabilities to construct a tree diagram for decision making. The main take away is that you need to know how to operationalize the story problem into the components for the tree. Module Five Problem: In this problem, you will work through a full decision analysis. The decision includes both a positive branch for determining the business opportunity as well as a negative type branch which evaluates the use of an analyst that may provide unusable results at a cost. It is a great, simple problem to exercise your decision tree skills. Leverage the information from the videos viewed at the beginning of this document as well as your treeplan skills from last module. Decision Analysis Problem: You are a potential business owner in the hoomaflopper industry. You have hired Dustin R. Mopps as your industry insider to help you decide which businesses to focus on potentially buying. He has collected useful data from multiple sources for you. The problem with Mr. Mopps is that he is a terrible decision analyst. So, it is up to you to figure out what to do. Dustin found a business for you to look into for a possible purchase: property ID number 51 in your data set, valued at $188,000. If this property is indeed viable, it is estimated to earn you $500,000 in the first year of business. However, you will have to pay $60,000 to perform a systems audit and refurbish it right after you buy it. Your back-of-the-envelope estimate is that there is X chance that you could realize the $500,000. You will need to spend a little time to figure out X for your model. Alternatively, you could hire Dustin to first do some real estate legwork for you, since real estate data is his specialty. He will ask for $16,000 to do further market research for you. From sneakily talking to his other clients, you estimate the probability as 60% that Dustin's market research will be favorable, if the business is going to be viable. The probability of an unfavorable report from Dustin is 70% if the business will not be viable. In other words, you trust him, but not that much. He might be able to give you an edge. You need to know if it is worth paying him the $16,000 or not. Keep all of these values in mind for your conditional probability calculations. Overall Question: What is your optimal strategy for deciding whether to purchase business number 51, based on expected value? Helpful Hints in this Analysis: Some thoughts to consider: Do not pay Dustin but just buy it? Walk away from it? Pay Dustin for more research or not? Then buy it on his advice? ...or don't? This problem has classic decision under uncertainty conditions. A good decision analysis should help you answer these questions. Consider first that you need to know what X is. Without it, you will not be able to proceed. Analysis Approach: Following Wu's method, and using the information presented in the problem description, perform the following steps: 1. You will need to download the following files from Blackboard to the Documents folder a. From the Module Five Folder: Mopps Data Set Data Dictionary (includes information about the variables) b. From DAT 520 Data Files Folder: i. Mopps with Commas: this is the data set for the problem ii. ProblemSet 5 Tree: this is the tree we will fill in values to in the exercise 2. Open Mopps with Commas in Excel and answer the following questions: a. Question 1: What is the probability that a property worth at least $150,000 in year 1 ends up worth $200,000 or more in year 5? (Hint: Think about numerator and denominator to answer this question. How many properties are there overall? How many properties start out at $150,000+ and then end up at $200,000+ in year 5?) b. Question 2: What is the probability that a property worth at least $150,000 in year 1 ends up worth more than $279,000 in year 5? (Hint: Think about numerator and denominator to answer this question. How many properties are there overall? How many properties start out at $150,000+ and then end up at $279,000+ in year 5?) 3. Open the ProblemSet 5 Tree file in Excel a. Use the answer for Question 2 above to fill in the X% b. Using the information provided with the problem, fill in all of the blue cells on the Excel worksheet. i. There are 39 blue cells for 2 points each, totaling 78 points c. Calculate the sheet (hit F9) 4. Provide the answers to Question 1 and Question 2 above into Word 5. Further provide the answers to the questions that follow: a. Describe and interpret what is going on in this tree in about 250 words. b. Include a discussion on what the optimal strategy is and why is it the optimal strategy? c. Include a statement of what the expected value is? What does expected value mean here? d. Change the values in cells B:20 to B:26. These contain the costs and payouts. Change these one at a time and calculate sheet. Discuss what threshold values flip the decision tree to recommending a different strategy? 6. Highlight your final tree in Excel, Copy it, and Paste Image at the end of your word document. 7. Save your Word Document and submit via blackboard. Notify your instructor of any issues you encounter. DAT 520 Mopps Data Set Data Dictionary y1_val to y5_val Year1 to year5 estimated business sale price if sold that year. y1_prf to y5_prf Year1 to year5 business profit/loss that year. mkt_idx_1 through mkt_idx_5 \"Market Index\" Business property value relative to local real estate market index that year. Based on a common level of appraisal. Local always equals 1. Business valuation index is relative to 1. mkt_class Type of real estate market context of the business, by zoning plat. 1: low 2: mid-range 3: high The following variables are the results of a survey given to these businesses. The survey overall had a moderate response rate of 37% out of thousands of businesses surveyed. What you see in the data set are the 200 responses with any values. Missing values were reset to 0 to improve the ease of use of the data set. For bottom-up trees, you may need to reclassify continuous values into categorical. Use this as a guide: biz_type 1: sole [proprietorship] 2: partnership 3: group [ownership] [unknown as 0] facility_sf Facility square footage 1: 0-2500 2: 2501-5000 3: 5001-7500 4: 7501-10000 5: 10001+ [unknown as 0] real_dataset2$sf_grp <- findInterval(real_dataset2$facility_sf, c(2501, 5001, 7501, 10001, 50000)) sales_type Primary type of sales 1: online_wholesale 2: direct_wholesale 3: online_retail 4: direct_retail 5: mixed [unknown as 0] num_cust Estimated number of customers 1-100 101-1000 1000-5000 5001+ [unknown as 0] real_dataset2$cust_grp <- findInterval(real_dataset2$num_cust, c(101, 1001, 5001, 100000)) num_employ Number of employees 1-50 51-100 101-500 [unknown as 0] real_dataset2$employ_grp <- findInterval(real_dataset2$num_employ, c(51, 101, 501, 50000)) yrsinbiz Number of years in business. [Also includes non-responses as 0] real_dataset2$yrsinbiz_grp <- findInterval(real_dataset2$yrsinbiz, c(6, 11, 26, 51, 100)) past_expan Number of major expansions the business has made, counted as events in its history. [also includes non-responses as 0] change_hands Number of times the business has been sold or changed ownership in its history. [Also includes non-responses as 0] tot_success & tot_nsuccess Success is any company that had at least 2 occurrences of more profit than the previous year and a rising market index, simultaneously. 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0.3 1.16 0.64 b Page 5 biz_type facility_sf 1 5600 1 7500 1 6000 1 2400 0 8000 1 2800 1 2800 1 2800 0 2710 3 7800 1 7700 1 3000 1 8430 1 4400 1 2450 2 2000 3 4000 1 2500 1 2800 1 2400 1 15500 1 10500 0 2600 3 5550 0 3500 1 11000 1 9200 1 2220 1 6650 1 5000 1 9200 1 2400 0 9240 1 4650 2 1500 1 1500 1 3700 1 4000 1 900 0 12000 1 7500 1 3300 3 1100 1 7650 1 8700 2 6500 3 4800 1 8000 1 4000 0 3900 3 800 3 4250 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 0.37 0.72 1.12 1 0.94 1.1 0.8 0.44 0.92 0.8 0.88 1.3 1.1 0.86 1.45 1.09 1 1.16 0.9 1.24 1.24 1 0.5 1.24 1.35 0.97 0.86 1 1.07 0.6 0.65 0.1 0.52 1 0.44 0.9 0.84 0.8 0.76 1 0.7 0.6 1.15 0 1 0.46 1 0.98 0.64 1.2 1 0.28 0.82 1.6 1.24 1.36 1.02 0.93 1.12 1.2 1.06 1 1.49 1.07 0.98 1.06 1 1.7 1.36 1.7 1.24 1 0.28 0.82 1 1.04 0.93 1.35 1.5 1.24 1.05 0.28 1.08 1.2 0.96 1 0.64 1.06 1.12 1.5 0.91 1.5 1.4 1 0.8 0.7 0.88 1.08 0.88 0.96 1 1.12 1.72 1.08 0.91 1 1 1.09 1 1.45 1.14 1.8 0.46 1.3 0.96 0 1.02 1 1 0.72 0.82 0.28 0.64 1.24 1.4 0.4 1.1 0.9 1 1 0.86 1 0.82 1 1.72 1.16 1 1.2 1.09 1.18 1.56 1.5 1.72 1.24 1 1 1.2 1.06 1.03 1.2 1.06 0.9 1.12 0.98 0.37 0.46 1.01 0.8 0.64 1.42 1 1 0.68 1 0.8 1.8 0.98 1.12 0.91 1.04 1 1.03 1 0.92 1.3 1.12 1 1.35 1.12 0.6 1 1.25 1 1.3 1.81 1.49 1.4 1.64 0.2 0.93 0.58 1.01 1 1 0.9 1.56 1.09 0.4 0.84 0.6 0.7 0.7 0.84 0.6 0 1 0.79 1.18 0.8 1.3 1 1.05 0.44 b 1.4 b 1.03 b 0.8 c 1.5 c 0.9 a 1.07 a 1.15 c 1.15 c 1.56 a 1.72 a 1.09 b 1b 1.36 a 1c 0.8 a 1a 0.88 b 1.32 a 0.2 a 0.58 a 0.28 c 0.44 a 0.88 a 0.52 c 0.2 a 1.3 b 0.6 c 0.9 b 0.76 a 1.1 a 0.44 a 0.94 a 1.08 a 1.03 a 1.05 c 0.9 a 0.9 a 1.07 b 1c 1.14 b 0.3 c 1b 1a 1.8 c 0.82 b 0.92 b 0.7 b 1.8 b 1.06 c 0.92 a 1.14 a 0.76 a Page 6 1 2 1 1 1 2 3 2 1 3 1 1 2 1 1 1 1 1 2 1 1 3 2 2 1 1 1 1 1 2 1 2 3 2 1 1 2 2 1 1 1 0 2 1 1 0 1 2 1 3 1 2 3 6000 2650 2400 2500 8880 1900 900 2750 2200 2000 3000 4500 3300 2300 4500 2650 9700 3300 4750 7000 10000 8200 1200 1160 1100 2780 2600 7230 1300 1440 11000 2700 3300 3250 10010 12000 6000 2200 2500 2980 3375 9000 10000 3750 5500 1450 2500 2790 2780 8000 2200 10100 4700 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 0.84 0.82 1 1.12 0.5 0.65 0.84 0.94 0.84 0.76 1.42 1 0.28 1 0.9 0.9 0.88 1.2 0.84 0.7 0.1 1.3 1.04 0.86 0.88 0.7 1.3 1.04 1.05 1.2 0.6 1.04 1.06 0.7 1.18 1.3 1.42 1.56 0.76 0.5 1.09 0.76 0.6 1.7 1 1.16 1.4 1.8 1.16 1.7 1.4 1 1.09 0.91 0.92 1.45 1.64 1.03 1 0.97 1 1.8 1.03 0.7 1 1.45 1.5 1.4 1.4 1 1.5 1.3 1.32 1.28 1.18 1 1.4 1.27 1 1.05 1.16 1.35 1.63 0.92 1 1.7 1.02 1.18 1.36 1.4 1.04 1.7 1.5 0.73 0.64 0.55 0.92 0.93 0.9 1 1.45 0.9 1.28 0.68 0.76 0.95 0.7 0.91 1.4 0.86 0.6 0.64 0.72 0.97 0.55 0.76 0.55 0.95 1.08 1 1.35 1.15 0.37 1.16 0.88 0.95 0.94 0.88 0.55 0.82 0.68 0.1 0.86 0.84 1.2 1.14 0.76 0.6 1.42 0.52 1.14 0.64 1 0.98 1.28 1 1 0.82 0.55 1.2 0.88 0.92 0.19 1.5 1 1.8 0.82 0.37 1 0.92 1.08 0.97 1 0.85 0 1.02 1.2 1 0.82 0.7 1.56 0.51 0.4 1.04 0.5 0.97 0.88 1 0.8 1.06 0.91 0.1 1 0.85 0.76 1.24 1.24 1.4 1.2 1 1.21 1.3 1 1 0.94 1.1 1.6 1.09 0.5 1.24 0.98 0.94 1.45 1.18 1.7 1.16 0.46 0.94 1.24 0.65 1.1 0.85 1.64 a 1a 0.82 a 1.48 a 0.88 b 1.24 a 0.64 c 1.9 a 0.76 b 1c 1.14 c 0.55 a 0.6 b 0.91 b 1a 0.93 c 1.1 b 1.81 c 0.97 a 1a 1.5 b 1.3 b 0.7 a 1b 0.19 b 1.35 a 1.08 c 1a 1.3 a 0.79 c 0.8 b 1a 1.16 b 0.86 a 0.68 c 0.76 c 1b 1.08 a 1.12 b 0.73 b 0.88 c 1.2 c 1.56 c 1.8 c 1.1 c 0.95 b 0.92 b 0.65 c 1a 0.7 c 0.85 b 0.1 b 1.14 b Page 7 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 1 1 1 3 3 1 3 1 1 2 1 0 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 0 3 1 1 1 2 2 9000 5410 6000 1510 2600 2000 8200 3000 8600 2700 5400 8700 3300 12000 13000 4880 4200 4400 1600 2500 6000 5000 1900 6500 2400 9000 2500 2100 1100 5000 3300 4000 3110 2100 7250 2560 7600 7300 3600 2700 8000 2400 3000 1200 3200 3000 3000 4250 3790 7000 3000 6300 4700 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 0.93 1.54 1.16 1.32 1.2 1.12 1 1.18 1.12 1 2 0.92 1 1.12 1 0.94 1.21 1.18 1.6 1.24 1.06 1.7 0.85 1.6 1 2 1.7 1.06 1.8 1 1.01 1.32 2 1.6 0.99 1.06 1.28 1.01 1.08 1.6 0.64 1.9 0.76 0.91 1.04 1.04 0.97 0.85 0.4 0.5 0.2 0.55 1.04 0.7 0.58 0 0.91 0.19 0.84 0.79 0.5 1.16 1 0.84 0.2 0.36 0.7 1.05 0.91 1 1.5 0.96 0.92 1 1.04 1.18 0.88 1 0.86 1 0.88 1.24 0.44 0.82 1.32 0.6 0.76 0.72 1.24 0.85 1.04 0.91 0.96 0.28 1.7 1 0.6 1.08 1 0.84 1.5 0.95 1.05 1.24 1.27 1 1.3 1.2 1.2 1.28 1.45 1.24 1 1.08 1.45 1.25 1.81 1.15 0.86 0.68 0.8 0.75 0.84 1 0 0.19 0.1 0.88 1.2 0.1 1 0.91 1.63 1.04 1.3 1.1 1.14 2 1 1.1 1.14 1.4 1.08 0.95 1.2 1.3 1.72 1.6 1 1.06 1.05 0.7 0.3 0.7 0.8 1 1.24 1 0.4 0.92 1 0.96 0.86 1 0.76 1.08 1 1.12 1a 0.72 a 1.35 b 1.3 a 1a 1.18 b 0.52 b 1.4 b 1.54 a 1.24 b 1.2 c 1.2 a 1.04 a 1.27 c 1.14 a 1.21 b 1.16 a 1.01 c 0.6 c 1.1 a 0.82 b 0.4 a 1.63 b 1a 1.3 b 0.96 b 1.72 a 1a 1.3 c 0.46 b 1.9 c 1c 0.95 c 1.42 a 1c 1.09 b 1b 1b 1.1 c 1.12 a 0.52 b 0.96 a Page 8 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 2 0 1 1 1 3 3 1 0 1 0 1 3 3 1 1 1 1 2 1 1 3880 8000 11000 3000 1300 7800 8440 7690 6500 3000 2590 3600 4615 2200 1300 6000 3300 3000 2200 1500 8000 1200 4000 3000 2700 3400 1500 12000 5000 4200 5200 8200 3500 1980 3330 4275 7500 3900 3210 8700 4100 2300 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 sales_type num_cust num_employ yrsinbiz past_expan change_hands tot_success 1 2400 92 45 1 0 0 300 29 5 0 1 2 2200 157 29 0 0 1 2200 117 43 0 0 0 2000 177 17 0 0 2 700 0 26 0 0 2 1900 134 21 0 1 2 800 25 5 0 1 2 500 49 19 1 0 4 1100 34 12 0 0 2 300 35 35 0 0 2 0 0 42 0 0 5 0 0 17 1 0 2 1100 87 48 1 0 2 1900 66 9 1 0 4 14000 250 35 0 0 2 2200 138 10 1 0 2 400 42 9 0 0 5 6000 200 23 2 0 2 2500 132 6 1 0 2 1000 7 23 0 0 5 600 45 33 0 0 2 1700 113 26 0 0 5 400 13 12 1 0 4 1100 75 21 0 0 4 2500 109 29 0 0 2 1200 0 17 0 0 0 0 0 15 0 0 2 100 10 42 2 1 2 200 9 6 0 0 2 2300 221 14 0 0 2 2500 181 11 0 0 2 900 0 24 0 0 2 200 18 43 1 2 4 1900 120 11 0 0 2 200 6 40 0 0 2 500 31 16 0 0 2 0 0 45 0 1 4 1400 62 46 0 0 5 25000 150 17 0 0 2 2400 144 22 0 0 0 1900 144 14 0 0 2 2500 30 40 0 0 2 0 100 10 0 1 2 1600 201 29 0 0 1 600 50 45 1 4 1 2500 117 48 0 0 2 400 50 40 0 0 4 700 6 11 0 0 4 1700 108 41 0 0 5 1400 126 22 0 0 1 1100 67 5 0 0 Page 9 2 1 0 1 1 2 1 1 0 1 0 0 2 2 0 1 0 1 2 1 1 1 2 0 3 1 2 1 1 3 2 2 1 2 1 1 1 2 0 0 1 0 1 1 1 0 0 0 0 2 1 1 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 2 2 2 2 4 1 1 1 4 4 2 0 2 2 4 4 2 4 0 5 0 2 0 4 2 0 2 2 0 2 3 0 2 2 5 4 0 2 2 4 0 0 3 4 2 2 2 3 2 5 2 2 2 1100 1600 2200 2200 800 800 800 1300 500 0 0 0 200 100 1500 700 1600 1200 2100 0 1300 2000 1300 200 600 1100 2200 2100 0 500 13000 0 2000 1500 2200 600 2100 2300 1300 1800 1000 2100 6500 0 1200 1700 2400 1400 200 1100 500 1000 400 107 214 158 44 62 0 55 119 26 0 0 0 6 15 242 37 173 15 169 0 65 157 134 19 38 84 124 230 82 36 101 0 202 201 106 16 206 119 38 238 82 59 93 0 46 6 115 235 0 21 5 62 45 46 34 25 34 48 30 9 27 16 31 14 13 25 35 10 40 46 5 37 35 8 36 22 10 33 34 14 5 15 14 39 44 24 7 31 5 23 44 47 8 37 44 8 41 36 5 48 21 20 20 44 30 31 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 1 0 0 0 0 0 0 0 0 0 0 Page 10 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 2 1 1 1 1 1 2 1 3 1 1 1 2 3 0 1 0 0 1 0 1 1 0 0 0 2 0 0 2 1 1 1 1 1 2 1 1 1 2 2 2 2 0 1 3 1 0 1 3 1 2 0 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 2 2 4 2 2 2 2 2 0 4 2 0 4 4 4 2 2 2 4 0 0 4 0 3 2 4 2 2 0 3 2 0 2 2 4 2 2 2 4 2 2 4 2 4 2 2 4 2 4 4 4 2 1 1400 600 5250 100 2100 2100 700 600 2100 2100 1000 2200 2000 1100 1200 10000 900 0 1900 1800 200 1600 600 800 1600 1500 1200 50 600 77000 2500 1000 2100 1200 1200 0 2100 1900 1200 2100 300 0 1200 500 2300 1200 200 1500 1000 2300 100 1400 100 154 19 51 20 213 194 36 33 49 134 37 114 107 99 22 15 38 100 215 240 13 106 0 32 237 0 84 24 27 80 91 48 60 71 133 0 258 198 63 133 41 92 38 5 91 28 4 144 49 187 15 63 18 48 24 18 15 23 7 50 16 14 48 6 30 23 40 21 19 32 35 40 13 5 38 10 23 42 30 29 15 8 28 33 21 48 8 30 5 28 43 40 17 20 14 28 28 35 36 32 12 8 44 40 18 30 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 2 0 0 1 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 Page 11 0 0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 2 0 1 1 1 0 3 1 1 2 2 1 0 0 1 2 2 2 0 2 2 0 2 1 3 1 2 1 2 1 1 0 1 0 0 1 1 2 1 2 2 2 2 0 2 0 0 1 1 1 1 0 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 4 0 2 5 2 0 4 2 0 0 4 2 4 2 4 2 2 2 4 5 2 0 2 2 5 2 2 3 2 2 2 2 2 2 2 4 2 2 2 2 2 4 1500 700 400 900 1400 300 1900 800 2200 800 500 1200 800 2200 1300 1600 800 2300 200 500 500 500 1600 1600 1700 500 1200 1400 2000 1700 1800 2200 800 2300 2400 300 400 300 400 1400 1100 700 195 4 10 53 77 29 234 47 97 50 28 8 92 31 18 127 33 78 11 32 25 41 236 108 113 10 9 142 94 16 121 170 3 168 149 35 38 4 0 139 60 8 11 17 48 39 35 12 50 50 5 14 21 10 47 16 27 17 48 37 20 30 5 34 28 33 45 25 44 21 5 17 37 24 5 46 10 35 34 7 9 23 36 38 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 Page 12 0 0 0 0 3 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 1 1 0 2 1 2 3 2 1 1 2 2 1 2 0 2 1 2 2 2 2 1 2 2 1 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 tot_nsuccess 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Page 13 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 Page 14 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 Page 15 4c7a2505cd1b430b8ccfb0ddb4c4f99d8a04f278 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 Page 16 Viable (YV) Buy #N/A Not viable (NV) No research # #N/A Don't buy 0 uy Biz with or without research? # #N/A Buy Positive research (YR) # 0 #N/A Don't buy Research #N/A Buy Negative research (NR) # 0 #N/A Don't buy $0 $0 $0 $0 0 Viable (YV) $0 $0 #N/A Not viable (NV) $0 $0 $0 $0 Viable (YV) $0 $0 #N/A Not viable (NV) $0 $0 $0 $0