Question

Monica Britt has enjoyed sailing small boats since she was 7 years old, when her mother started sailing with her. Today, Monica is considering the possibility of starting a company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between the ages of 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems of capsizing. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favorable market, Monica can expect to make $90,000 from the large facility or $60,000 from the smaller facility. If the market is unfavorable, however, Monica estimates that she would lose $30,000 with a large facility, and she would lose only $20,000 with the small facility. Because of the expense involved in developing the initial molds and acquiring the necessary equipment to produce fiberglass sailboats for young children, Monica has decided to conduct a pilot study to make sure that the market for the sailboats will be adequate. She estimates that the pilot study will cost her $10,000. Furthermore, the pilot study can be either favorable or unfavorable. Monica estimates that the probability of a favorable market given a favorable pilot study is .8. The probability of an unfavorable market given an unfavorable pilot study result is estimated to be .9. Monica feels that there is a .65 chance that the pilot study will be favorable. Of course, Monica could bypass the pilot study and simply make the decision as to whether to build a large plant, small plant, or no facility at all. Without doing any testing in a pilot study, she estimates that the probability of a favorable market is .6. What do you recommend? compute EVSI

Answer 1

Survey\Market	Unfavourable (0.4)	Favorable (0.6)
Unfavorable (0.35)	0.9	0.1
Favorable (0.65)	0.2	0.8

E(S_f) = 0.4*0.2 + 0.8*0.6 =0.56

E(S_u) = 0.4*0.9 + 0.1*0.6 =0.42

E(M_f) = 0.35*0.1 + 0.8*0.65 =0.555

E(M_u) = 0.35*0.9 + 0.2*0.65 =0.445

So the expectation of the survey to be favourable is 0.56 Thus we had to go for the pilot survey.

Market\ facility	Large	Small
Favourable (0.6)	90,000	60,000
Unfavorable (0.4)	-30,000	-20,000

E(L) = 0.6*90,000+ 0.4*-30,000 = 42,000

E(S) =0.6*60,000 + 0.4*-20,000 = 28,000

So E(profit) = Max{E(L), E(S)} = 42,000 for large facility.

Market\ facility	Large	Small
Favourable (0.8)	90,000	60,000
Unfavorable (0.2)	-30,000	-20,000

E(L/SI) = 0.8*90,000+ 0.2*-30,000 = 66,000

E(S/Si) = 0.8*60,000+ 0.2*-20,000 = 44,000

with proper sample information, we would have chose to setup large facility with E(profit/SI) = Max{E(L/SI), E(S/SI)} = 66,000

EVSI = E(profit/SI) - E(profit) = 66,000-42,000 = $24,000 {>10,000}

Since EVSI > the survey cost and since the chances to the survey to be favourable is also high, thus Monica should opt for the survey.