Question

An investor is deciding whether to build a retail store. If she invests in the store and it is successful, she expects a return of $100,000 in the first year. If the store is not successful, she will suffer a loss of $80,000. She guesses that the probability that the store will be a success is 0.6. To remove some of the uncertainty from this decision, the investor tries to establish more information, but this market research will cost $20,000. If she spends this money, she will have more confidence in her investment. There is a 0.6 probability that this information will be favorable; if it is, the likelihood that the store will be a success increases to 0.9. If the information is not favorable, the likelihood that the store will be a success reduces to only 0.2. Of course, she can elect to do nothing.

A) Draw the associated decision tree.
B) What do you recommend?
C) How much is the information worth?
Replace all the monetary values with the following utilities
Monetary Value Utility
$100,000 1.00
$80,000 0.40
$0 0.20
-$20,000 0.10
-$80,000 0.05
-$100,000 0.00
A) What do you recommend, based on expected utility?
B) Is the investor a risk soeker or a risk avoider?

Answer 1

Step-by-step explanation:

Given that,

expects a return of $100,000 in the first year

loss of $80,000

probability that the store will be a success is 0.6

research will cost $20,000

0.6 probability that this information will be favorable

store will be a success increases to 0.9

store will be a success reduces to only 0.2

a) Decision tree is attached

EMV= (payoff of first outcome) * (probability of first outcome) + (payoff of second outcome) * (probability of second outcome) + (payoff of third outcome) * (probability of third outcome)

EMV(node 1) = EMV(new store)

= ($100,000 * 0.6) + (-80,000 * 0.4)

=$28,000

EMV (node 2) = EMV (no store)

= $0

EMV (node 3) = EMV ( new store and favourable research)

= ($100,000 * 0.9) + (-80,000 * 0.1)

=$82,000

EMV (node 4) = EMV ( no store and favourable research)

= $0

EMV (node 5) = EMV ( new store and unfavourable research)

= ($100,000 * 0.2) + (-80,000 * 0.8)

= -$44,000

EMV (node 6) = EMV ( no new store and unfavourable research)

= $0

B) Here we compare EMV of not conducting the market research ans EMV of conducting the market research and the maximum EMV shall be taken for decision making

• Here the EMV of conducting the market research is higher than not conducting

Hence, the investor can go to market research test. If result is positive, she can invest in the store, if negative she can stop the proposal.