Assume an investor wants to build a hotel in an area where hurricanes occasional

Question

Assume an investor wants to build a hotel in an area where hurricanes occasionally hit. Suppose that hurricanes could be strong, medium or weak. The investor has to decide how much to reinforce the buildings at the hotel complex. Hotel can be reinforced to withstand a strong, medium or weak hurricane. Probabilities of having a strong, medium, and weak hurricane in the area are 5%, 30%, and 65%. If hotel is built to withstand a strong hurricane, it will cost 30 million dollars and it will not be damaged in any kind of hurricane. If hotel is built to withstand a medium hurricane, it will cost 20 million dollars and it will not be damaged in a medium and weak hurricane, but it will take 5 million dollars damage in a strong hurricane If hotel is built to withstand a weak hurricane, it will cost 15 million dollars, it will take 10 and 15 million dollars damage in a medium and strong hurricane, but it will not be damaged in a weak hurricane. * · » The investor can buy a hurricane forecast service from National Hurricane Center (NHC) that predicts hurricane strength If the hurricane is strong: » NHC predicts a strong hurricane correctly in 80% of the time NHC predicts a medium hurricane incorrectly in 10% of the time NHC predicts a weak hurricane incorrectly in 10% of the time o o If the hurricane is medium: » o o NHC predicts a strong hurricane incorrectly in 20% of the time NHC predicts a medium hurricane correctly in 70% of the time NHC predicts a weak hurricane incorrectly in 10% of the time » If the hurricane is weak: o o o NHC predicts a strong hurricane incorrectly in 10% of the time NHC predicts a medium hurricane incorrectly in 20% of the time NHC predicts a weak hurricane correctly in 70% of the time a) Calculate all the required probabilities b) Draw the decision tree (optional) c) Calculate the EMV without information. d) Calculate the EMV with perfect information. e) Calculate the EMV with imperfect information f) Calculate the EVI. g) Calculate the EVII.

Explanation / Answer

Answer:

Let ES, EM and EW be an event of a strong, medium and weak hurricanes respectively and

AS, AM, AW be events that NHC predicts strong, medium and weak hurricanes respectively.

From the given data

P(AS|EM)=0.2, P(EM)=0.3, P(ES)=0.05, P(AS|ES)=0.8, P(AM|ES)=0.1, P(EW)=0.65,P(AW|ES)=0.1,

P(AW|EW)=0.7,P(AW|EM)=0.1, P(AS|EW)=0.1,P(AM|EM)=0.7, P(AM|EW)=0.2.

P(AS)=P(AS|ES)XP(ES)+P(AS|EW)XP(EW)+P(AS|EM)XP(EM)=0.165

P(AW)=P(AW|ES)XP(ES)++P(AW|EW)XP(EW)P(AW|EM)XP(EM)=0.49

P(AM)=P(AM|ES)XP(ES)+P(AM|EW)XP(EW)+P(AM|EM)XP(EM)=0.345

P(ES|AS)=(P(AS|ES)XP(ES))/P(AS)=0.24, P(ES|AM)=0.01, P(ES|AW)= 0.01,

P(EM|AS)=0.36, P(EW|AS)=0.40, P(EM|AW)=0.06, P(EW|AW)=0.93, P(EM|AM)=0.61,P(EW|AM)=0.38.

c) EMV Calculation without any information:

Expected monetary is, money you can expect to make from a certain decision.

there is no damage till now in any kind of hurricane when hotel is build to withstand a strong hurricane, then

EMV for this type of hotel = 30 mill doll,

there is no damagetill now in a medium and weak hurricane when hotel is build to withstand a medium hurricane, then

EMV for this type of hotel =(20-5xP(ES)) mill doll

=(20+5x0.05) mill doll

=20.25 mill doll

there is no damage till now in a weak hurricane when hotel is build to withstand a weak hurricane, then

EMV for this type of hotel =(15-(10xP(EM)+15xP(ES))) mill doll

=(15-(10x0.3+15x0.05)) mill doll

=18.75 mill doll

EMV without information =(30+20.25+18.75) mill doll

=69 mill doll

d) EMV Calculation with information:

Since there is no damaged in any kind of hurricane when hotel is build to withstand a strong hurricane, then

EMV for this type of hotel=30 mill doll.

Since there is no damaged in a medium and weak hurricane when hotel is build to withstand a medium hurricane,

then EMV for this type of hotel=(20+5x(P(ES|AM)+P(ES|AW))) mill doll

=(20-5x0.02) mill doll

=20.1 mill doll

Since there is no damaged in a weak hurricane when hotel is build to withstand a weak hurricane, then

EMV for this type of hotel =(15+(10xP(EM|AW)+15x(P(ES|AM)+P(ES|AW)))) mill doll

=(15+(10x0.06+15x0.02)) mill doll

=15.9 mill doll

EMV without information =(30+20.1+15.9) mill doll

=66 mill doll

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