Can you build a decision tree for the following info and create the Expected Monetary Value (EMV) for the following question. There are 2 parts

Problem 1 Decision Tree Bill owns a limited liability company, but the company is in finance trouble now: owe $600,000 in debt. The debt maturity will be in one week. To pay off the debt, Bill has hired a sales agent to sell a small office building of the company at the selling price $750,000, which is a normal price in the current market. A potential buyer has provided an offer at the price $680,000. Bill has two choices: either accept the offer or reject it. If Bill accepts the offer, he has to pay 5% of the final price as the service fee to the sales agent. If Bill rejects the offer, he cannot find out another potential buyer before the debt maturity, but he can sign a loan contract with a finance company to borrow $600,000, and repay $624,000 in two months. Then, he still has chance to sell the building in the coming two months. The final price as shown in Table 1 depends on the future demand and whether potential buyers know that Bill's company has been in finance trouble. Suppose that potential buyers know that Bill's company has been in finance trouble with probability 30%. Percentage of the normal price in the current market Market High Demand Low Demand Table 1 Bill can sell it Buyers know 90% 70% Buyers do not know 120% 90% Probability that Bill cannot sell 0.05 0.10 For example, if the future demand is high and potential buyers know his finance trouble, the final price will be $675,000, which is 90% of the normal price (i.e. $750,000). Of course, he also has to pay 5% of the final price to the sales agent. In two months, if Bill could not repay the loan, the office building would be auctioned. He also has to pay 5% of the final price as the service fee. In auctions, the final price depends on the future demand, and the distribution of final prices is estimated as follows: + Probabilities Percentage of the normal price in the current market 50% 60% 80% 100% 120% 0.3 0.5 0.2 0.4 0.3 Market High Demand Low Demand 0.3 Table 2 Finally, after selling the office building, if the net income (Le revenue-cost) is at least $30,000 less than the loan repayment, Bill will have to sell his company at a discounted price such that he will lose $100,000. Bill estimates the demand will be high with probability 60%, and will be low with probability 40%. Now, Bill can consider whether to hire one of the following two consultants in order to better predict the future demand: (1) Consultant A: consulting fee is $3,500; the historical data of forecasting performance is in the excel file consultant-A.xlsx. (2) Consultant B: consulting fee is $2,000; the historical data of forecasting performance is in the excel file consultant-B.xlsx. Note that these two consultants provided service in many projects. Each consultant recorded data with the project number as the index independently. In other words, if you see the same project number in two excel files, the two projects do not have relationship. The excel data file has four columns: (1) if a number in column "Project # is larger, the time is closer to now; (2) there are two possible types of buildings: house and office building. Number 1 means house, and number 2 means office building; (3) The real demand is the realized demand after forecasting. Number 1 means low demand, and number 2 means high demand. If the demand prediction is the same as the real demand, the prediction is right. If Bill hires a consultant, he will make decisions after getting the demand prediction report. Part 1 (16 marks) Perform an analysis of Bill's problem. Be sure to include the following items: data analysis; a decision tree; the whole optimal decision strategy and the corresponding EMV. Part 2_(8 marks) Suppose that Consultant A and Consultant B are unavailable, but Consultant C can provide forecasting service. The consulting fee of Consultant C is only $1000, but the quality is very poor: according to historical data, when the demand was high, Consultant C correctly forecasted with probability 20%; when the demand was low, Consultant C correctly forecasted with probability 35%. It is a good deal to get so poor-quality information? Problem 1 Decision Tree Bill owns a limited liability company, but the company is in finance trouble now: owe $600,000 in debt. The debt maturity will be in one week. To pay off the debt, Bill has hired a sales agent to sell a small office building of the company at the selling price $750,000, which is a normal price in the current market. A potential buyer has provided an offer at the price $680,000. Bill has two choices: either accept the offer or reject it. If Bill accepts the offer, he has to pay 5% of the final price as the service fee to the sales agent. If Bill rejects the offer, he cannot find out another potential buyer before the debt maturity, but he can sign a loan contract with a finance company to borrow $600,000, and repay $624,000 in two months. Then, he still has chance to sell the building in the coming two months. The final price as shown in Table 1 depends on the future demand and whether potential buyers know that Bill's company has been in finance trouble. Suppose that potential buyers know that Bill's company has been in finance trouble with probability 30%. Percentage of the normal price in the current market Market High Demand Low Demand Table 1 Bill can sell it Buyers know 90% 70% Buyers do not know 120% 90% Probability that Bill cannot sell 0.05 0.10 For example, if the future demand is high and potential buyers know his finance trouble, the final price will be $675,000, which is 90% of the normal price (i.e. $750,000). Of course, he also has to pay 5% of the final price to the sales agent. In two months, if Bill could not repay the loan, the office building would be auctioned. He also has to pay 5% of the final price as the service fee. In auctions, the final price depends on the future demand, and the distribution of final prices is estimated as follows: + Probabilities Percentage of the normal price in the current market 50% 60% 80% 100% 120% 0.3 0.5 0.2 0.4 0.3 Market High Demand Low Demand 0.3 Table 2 Finally, after selling the office building, if the net income (Le revenue-cost) is at least $30,000 less than the loan repayment, Bill will have to sell his company at a discounted price such that he will lose $100,000. Bill estimates the demand will be high with probability 60%, and will be low with probability 40%. Now, Bill can consider whether to hire one of the following two consultants in order to better predict the future demand: (1) Consultant A: consulting fee is $3,500; the historical data of forecasting performance is in the excel file consultant-A.xlsx. (2) Consultant B: consulting fee is $2,000; the historical data of forecasting performance is in the excel file consultant-B.xlsx. Note that these two consultants provided service in many projects. Each consultant recorded data with the project number as the index independently. In other words, if you see the same project number in two excel files, the two projects do not have relationship. The excel data file has four columns: (1) if a number in column "Project # is larger, the time is closer to now; (2) there are two possible types of buildings: house and office building. Number 1 means house, and number 2 means office building; (3) The real demand is the realized demand after forecasting. Number 1 means low demand, and number 2 means high demand. If the demand prediction is the same as the real demand, the prediction is right. If Bill hires a consultant, he will make decisions after getting the demand prediction report. Part 1 (16 marks) Perform an analysis of Bill's problem. Be sure to include the following items: data analysis; a decision tree; the whole optimal decision strategy and the corresponding EMV. Part 2_(8 marks) Suppose that Consultant A and Consultant B are unavailable, but Consultant C can provide forecasting service. The consulting fee of Consultant C is only $1000, but the quality is very poor: according to historical data, when the demand was high, Consultant C correctly forecasted with probability 20%; when the demand was low, Consultant C correctly forecasted with probability 35%. It is a good deal to get so poor-quality information