An investor is deciding between two investments: A and B. Each can be purchased now for $10. There is a 40% chance that investment A will grow rapidly in value and a 60% chance that it will grow slowly. If A grows rapidly the investor can cash it in for a net gain of $80 or trade it for investment C which has a 25% chance of growing to $110 and a 75% chance of reaching $90. If A grows slowly it is sold for $60. There is a 70% chance that investment B will grow rapidly in value and a 30% chance that it will grow slowly. If B grows rapidly the investor can cash it in for a net gain of $100 or trade it for investment D which has a 20% chance of growing to $105 and an 80% chance of reaching $90. If B grows slowly it is sold for $55. Draw the decision tree for this problem. a) Draw a decision tree for this problem. b) What is the optimal decision for this investor and what is the EMV for this decision? Rob Johnson is a product manager for Diamond Chemical. The firm is considering whether to launch a new product line that will require building a new facility. The technology required to produce the new product is yet untested. If Rob decides to build the new facility and the process is successful Diamond Chemical will realize a profit of 675000. If the process does not succeed the company will lose $825000. Rob estimates that there is a 0.6 probability that the process will succeed. Rob can also decide to build a pilot plant for $60000 to test the new process before deciding to build the full-scale facility. If the pilot plant succeeds Rob feels the chance of the full-scale facility succeeding is 85%. If the pilot plant fails Rob feels the chance of the full-scale facility succeeding is only 20%. The probability that the pilot plan will succeed is estimated at 0.6. a) Draw a decision tree for this problem. b) What is the optimal decision you would recommend to Rob and what is the EMV for this decision?

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# An investor is deciding between two investments: A and

Monday July 18, 2022

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