Question

Previous Page Next Page Page 5 of 10 Question 5 (14 points) Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry can open a large store, a small store or no store. The profits will depend on the size of the store and whether the market is favourable or unfavourable. In addition, Jerry is thinking about having a market research study done at a cost of $5,000. The study could be favourable or unfavourable. After analysing all of the available information Jerry has created the following decision tree with the payoffs shown in $1000s: Pavourable Markot (0.99 Large Store Unfavourable Market (01) -55 Favourable Market (0.9) 35 Favourable Survey (0.6) Small Store Uafavourable Mark(1)-2s -5 Favoarable Market (012) Large Store Unisvairable Mark CuNS- Survey 4S Siaali sow Unfavourable Survey (。4) B: ment #4 2:00:00 Kudzaishe Chakabveyo: Attempt 1 Large Store Unfavourable Markt (01)-55 Favourable Mad -35 Favourable Survey (0.6) Small Store Unlavourable Market (0.1) 2 No Store Favourable Market (0.12) Large Store Unfavoarable Market (0.8H) 5s -53 Pavoaralble Market (0.12 ) a all Store UnExvourable Market (0s5)25 No St Large Sto4e Undswoarable Marka (0) 50 Fawarable Mark (0.5) Store Unfavouratde Marekt (os)g0 Round your answers to 1 decimal place as needed. In blank #1 enter the expected value at node 6. * In blank #2 enter the expected value at node 7 In blank #3 enter the expected value at node 8. In blank #4 enter the expected value at node 9 Unfavour able Marekt (05) 20 0 Round your answers to 1 decimal place as needed. In blank #1 enter the expected value at node 6 In blank #2 enter the expected value at node 7. In blank #3 enter the expected value at node 8. In blank #4 enter the expected value at node 9. In blank #5 enter the expected value at node 10. In blank #6 enter the expected value at node 11. In blank #7 enter the expected value at node 3. In blank #8 enter the expected value at node 4. . In blank #9 enter the expected value at node 5. . In blank #10 enter the expected value at node 2. . In blank #11 enter the expected value at node 1 . In blank #12 enter the expected value of sample information. Is the market research study worth the cost? Enter your answer las 'yes" or "no") in blank #13. . In blank #14 enter the efficiency of the sample information (include the percent sign with your answer and round to 0 decimal places. Enter your answers in $1000s without the $ sign (i.e as 12.34, not $12.340). Round your answers to 2 decimal places as needed (if the second decimal place is 0, enter the number as 12.3, not 12.30)

Answer 1

Expected value at node 6 = 0.9*55+0.1*(-55) = 44

Expected value at node 7 = 0.9*35+0.1*(-25) = 29

Expected value at node 8 = 0.12*55+0.88*(-55) = -41.8

Expected value at node 9 = 0.12*35+0.88*(-25) = -17.8

Expected value at node 10 = 0.5*60 + 0.5*(-50)= 5

Expected value at node 11 = 0.5*40 + 0.5*(-20) = 10

Expected value at node 3 = Expected value at node 6 + Expected value at node 7 + Expected value of No store

= 44+29-5 = 68

Expected value at node 4 = Expected value at node 8 + Expected value at node 9 + Expected value of No store

= -41.8 -17.8 - 5 = -64.6

Expected value at node 5 = Expected value at node 10 + Expected value at node 11 + Expected value of No store
=
= 5+10+0 = 15

Expected value at node 2 = Expected value at node 3 + Expected value at node 4

= 68*0.6 - 64.6*0.4
= 14.96

Expected value at node 1 = Expected value at node 2 + Expected value at node 5 = 14.96+15 = 29.96

Expected value of sample information = 5000 as without survey yields higher payoffs than payoffs with survey so if perfect information had been present survey would not be conducted and the cost of the survey would have been saved

Expected value at node 2 = 14.96*1000 = 14960 which is greater than the cost of the study so research study is worth the cost