Question

5. 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? 0.40 0.20 6. Replace all the monetary values in Question 5 with the following utilities Monetary Value Utility $100,000 $80,000 SO -$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? Justify your answer?

Answer 1

Solution : Gimn, spected to form = $100,000 in Hirst year loss = $80,000 Probability =0.6 refearch cost = 820,000. Probability 2016 incieele -0.9 seduce = 0.2 Decision tree is: - succeds 828000 $100,000 fails $28,000 New New Hore 8-80,000 no action 2 o 4th cm so Succeeds No market research +$180,000 8 82000 News fails 889 our * - $ 90, and 31 No actin po action market refearch 60.6) Pilett Pust succeeds -$44,000 + 8 100000 - 60 fails perstar Pilot failure (0.4) - 580,000 xo Niacin

2 Explanation: EMV = (payoff of first outcome) +(probability of i stoutware) +(payoff of and outcome) * (proba bility of a ndotene) + payoff of 3rd outcome) * (probability of 3rd astrome) EMV (model) = ENV (New store) =($1001000 *0.6)+(-80,000 $0.4) =1828000 Amucoden) - Emu (postore) Emu (node3 ) -Emv (new store and favourable e research) = 68100000 *019+680000 * 0.1) =$82,000. EMV Choden) - Emu (no store and favourable research) Emu (node 8) = Emu (of new store and unfavou -rable refearch)

- 100000 *0-2) + (-80000 10.8) =7344 000 Emv (node) - Emu (no Store and unfavourable refearch) b) Recommended: conducting the market Here we compare Emu of not research and Emu of Conducting the market research and the maximum Emr shall be taken for decision making the market research is Here the Emu of Conducting higher than not conducting " Hence, the investor can go for market research positive, she can invest in the test. If refultis Store, if negative she can stop the proposal.

© Information worth: --- EVSI = FMV of beft decision with Sample info, (assuming no cost to get it) - (Emy of best decisim without any info) -Emy (Noresearch) - (Emu (conduct research) =($49,200) -"C828,000) = $ 21, 200] Efficiency of survey = Evs llevp) - Evsha EV wpl - Max (Emu) Ev1 = $ 21,200 max (EMU) = 849,200 EV wpl = ($100000 *0.6)+ ($0*0.4) = $60,000 :. Efficiency of survey = $ 21200 Goooo – 049200 =11.96