# Quantitative Analysis: Retail development probabilities

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### Question Description

Must attach excel document and fill out chart

A real estate developer is assessing an area for future retail development. She believes it is only profitably to develop a retail outlet in this area if a medical facility or industrial facility is built in the general vicinity within the next 5 years. Typically industrial facilities precede the development of medical facilities. Using this knowledge and some market research, she has arrived at the following probabilities. The overall probability that an industrial facility will be built in the area in the next 5 years is 30%. If the industrial facility is built, she believe the probability that the medical facility is built is 40%. If the industrial facility is not built, she believes the probability that the medical facility will be built goes down to 20%. What is the probability of the following events?

a) neither am industrial facility or medical facility is built

b) only an industrial facility is built

c) only a medical facility is built

d) both an industrial facility and a medical facility is built

e) She also has arrived at the following net present values for her retail development project based on the 4 events above. Given these outcomes and the probabilities you calculated above, what is her expected NPV? Should she do the project?

 EVENT NPV neither a industrial facility or medical facility is built -10 Million only an industrial facility is built 5 million only a medical facility is built 3 million both an industrial facility and a medical facility is built 20 million

f. Our real estate developer has learned that the probability that an industrial facility is built in the next 5 years has risen from 30% to 90%. Based on this, rework the problem and provide the new expected NPV of the project. Should she do the project?

 # 1 What is the probability of the following events a) neither am industrial facility or medical facility is built b) only an industrial facility is built c) only a medical facility is built d) both an industrial facility and a medical facility is built e) what is her expected NPV? Should she do the project? f) scenario 2: what is her expected NPV? Should she do the project?

pallveechem123
School: UC Berkeley

here is solution.Kindly ask if any doubt.

Quantitative Analysis
a) Neither an industrial facility nor medical facility is built
Probability of an industrial facility will not be built in the area in the next 5 years = 0.70
Probability that the medical facility will not be built = 0.80
Prob. that neither an industrial facility nor medical facility is built = 0.8  0.7 = 0.56
b) Only an industrial facility is built

(

Prob. that only an industrial facility is built= P I  M
Prob. that there is Industrial facility = P(I ) = 0.30

)

Prob. that medical facility is not built when there is Industrial facility = P( M / I ) = 0.60

(

)

M 
P I  M = P   P(I ) = 0.60  0.30 = 0.18
 I 
c) Only a medical facility is built
Prob. that medical facility is built when there is not Industrial facility = P( M / I ) = 0.20
Prob. that there is not Industrial facility = P(I ) = 0.70

(

)

()

M 
P I  M = P   P I = 0.20  0.70 = 0.14
 I 

d) Both an industrial facility and a medical facility is built
M 
P(I  M ) = P   P(I ) = 0.40  0.30 = 0.12
 I 
e) She also has arrived at the following net present values for her retail development
project based on the 4 events above. Given these outcomes and the probabilities you
calculated above, what is her expected NPV? Should she do the project?

Net Present Value (NPV)
= −10  P I  M + 5  P M  I + 3  P M  I + 20  P(M  I )

(

)

(

)

(

= −10  0.56 + 5  0.18 + 3  0.14 + 20  0.12
= −1.88 million
As NPV is negative, she should not do this project.

)

f) Our real estate developer has learned that the probability that an industrial
facility is built in the next 5 years has risen from 30% to 90%. Based on this,
rework th...

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Anonymous
Good stuff. Would use again.

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