Drawing a Decision Tree
Dr. Nott is considering investing in a waste treatment plant. Returns depend on the size of plant and the market condition for the facility. From experience, Nott believes that a small size would yield a $500,000 return regardless of the market scenario. However, the success of a medium sized plant would depend on the market. A low market demand for waste treatment would bring a $100,000 return. A medium market demand would yield a $500,000 return, and a high demand would return $800,000. While a large facility is much riskier, the potential return is much greater. With a high market demand, the large facility should return a million dollars. With a medium demand, the large facility will only return $500,000. Also, Nott estimates that the large facility would be a big failure if there is a low demand for waste treatment. He estimates that he would lose approximately $300,000 with a large treatment facility if demand was indeed low.
At present time, Dr. Nott estimates that the probability of a low demand for waste treatment is 0.28, the probabilities of a medium and high demand are 0.27 and 0.45, respectively. An economic survey may be performed to obtain more information and get a better feeling for the probability of a low, medium, or high demand market with the cost of $50,000. The survey could result in only 2 possible indications of High and Low. Regards the historical data, given a high market demand, the probability of High: Low indication from the survey is 14:1. On the other hand, with a medium market demand, the probability of High: Low conclusion from the survey is 7:2. The probability of High: Low indication from the survey is 1:3.
- Draw decision tree and advise Dr. Nott
- What is the value of EVSI and its efficiency?
If Dr. Nott chooses to invest in a medium-sized plant, he should first perform the economic survey, which costs $50,000. Based on the survey result, he can estimate the probability of each market scenario. If the survey result indicates a high demand market, the probability of a high market demand is updated to 0.93, and the probability of a low market demand is updated to 0.07. In this case, Dr. Nott can expect a return of $800,000. If the survey result indicates a low demand market, the probability of a low market demand is updated to 0.64, and the probability of a high market demand is updated to 0.36. In this case, Dr. Nott can expect a return of $100,000.
If Dr. Nott chooses to invest in a large-sized plant, he should also perform the economic survey. Based on the survey result, he can estimate the probability of each market scenario. If the survey result indicates a high demand market, the probability of a high market demand is updated to 0.98, and the probability of a low market demand is updated to 0.02. In this case, Dr. Nott can expect a return of $1,000,000.
