Question

Samuel Knight is considering opening a print shop on Johnson Street, two blocks away from a local college. He has found a good location that attracts possible business. His options are to open a small shop, a medium shop, or no shop at all. The market for a print shop can be positive, average, negative compared to the area business climate. The probabilities for these three are 0.20 for a positive market, 0.50 for an average market, and 0.30 for a negative market. The net profit or loss figures for the medium, small, and no shops for the various market conditions are given in the table. Building no shop at all yields no loss and no gain.

Alternative	Positive Market	Average Market	Negative Market
Small Shop	75,000	25,000	-40,000
Medium Shop	100,000	35,000	-60,000
No shop	0	0	0

(Question A:) Report the expected value outcomes. Based upon the expected value outcomes, what decision would you recommend for Samuel?

(Question B:) What is the EVPI?

(Question C:) Create a regret table for this case. What decision would you recommend Samuel based upon the minimax regret approach?

Answer 1

A)

Expected value of Small shop = 75000*0.2+25000*0.5+(-40000)*0.3 = $ 15,500

Expected value of Medium shop = 100000*0.2+35000*0.5+(-60000)*0.3 = $ 19,500

Expected value of No shop = 0

Based on the expected value outcomes, Medium shop is recommended, because it has the highest expected value (=19500).

B) Expected Value with Perfect Information (EVwPI) = MAX(75000,100000,0)*0.2+MAX(25000,35000,0)*0.5+MAX(-40000,-60000,0)*0.3 = $ 37,500

EVPI = EVwPI - EV(w/o)PI

= 37500 - 19500

= $ 18,000

C)

Formula used for creating minimax regret

B11 =MAX(B$3:B$5)-B3 copy to B11:D13

E11 =MAX(B11:D11) copy to E11:E13

E15 =MIN(E11:E13)  

Maximum regret of Small shop is the minimum of all. Therefore, Small shop is recommended.