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Using a Decision Tree and finding expected value

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Rob Johnson is a product manager at Diamond Chemicals, which is considering whether to launch a new product line that will require it to build 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 Chemicals will realize a profit of $650,000. If the process does not succeed, the company will lose $800,000. Rob estimates that there is 60% probability that the process will succeed.

Rob can also decide to build a pilot plant for $50,000 to test the new process before deciding to build the full-scale facility. If the pilot plant succeeds, Rob feels there is 85% chance of the success of the full-scale facility. If the pilot plant fails, Rob feels there is only 20% chance of the success of the full-scale facility. The probability that the pilot plant will succeed is approximately 60%. Structure this problem using a decision tree and advise Rob what to do.

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Option 1

Success (.6)(650,000) = 390,000
Failure (.4)(-800,000) = -320,000 Combining these results gives an expected value of 70,000

Option 2 with pilot plant

Pilot Success and product success (-50,000) + (.60)(.85)(650,000) = 281,500
Pilot Success and product failure ...

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Financial advisor using Decision Tree

A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:
Investment Good Economy Fair economy Poor Economy
Fund A $10.000 $2,000 -$5,000
Fund B $6,000 $4,000 0
Probability .2 .3 .5

a) Draw the decision tree to represent this situation.
b) Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?
c) Suppose there is question about the return of Fund A in a good economy. It could be higher or lower that $ 10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (I.E., the EMV's would be the same)?

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