Question

A buyer is deciding where to invest his money. He can purchase either an apartment building, an office building or a warehouse. He considers two states of nature, either economic conditions will be good or poor with respective probabilities of 0.6 and 0.4. The table below summarizes is profit in thousands of dollars:

	State of Economy
Alternative	Good	Poor
Apartment	50	30
Office	100	-40
Warehouse	30	10

1)Draw the decision tree for this problem

2)Conduct a sensitivity analysis on the probabilities

Answer 1

1) Decision tree is as follows

Good Economy 0.6050 Poor Economy 0.40 30 Good Economy 0.60 100 Poor Economy 0.40 -40 Good Economy 0.6030 Poor Economy 0.40 10 artment ? 2 3 4

With the current set of probabilities of Good and Poor economy, Expected Monetary Value calculations are given below:

EMV of node 2 = 0.6*50+0.4*30 = 42

EMV of node 3 = 0.6*100+0.4*(-40) = 44

EMV of node 4 = 0.6*30+0.4*10 = 22

EMV of node 3 is maximum. Therefore, best decision is to construct Office

2) Sensitivity analysis on the probabilities is as follows:

Apartment Office Warehouse 100 -40 Sensitivity Analysis 30 10 Poor 30 120 100 80 60 2 40 20 5 P(Good) Apartment Office Warehouse 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 30 32 -40 26 12 10 12 14 16 18 20 16 30 10 40 42 13 14 46 86 100 28 30 16 17 18 19 0.00 0.40 0.60 0.80 1.00 -20 -40 60 21 P(Good) Probability of Good Economy 23 24 25 Apartment Office Warehouse

Formula to construct the sensitivity table

B6 =$A6*B$2+(1-$A6)*B$3 copy to B6:D16

In the graph, we see that as probability of good economy increases, EMV of Office increases at faster rate than the EMV of other two alternatives. For probability [P(Good)] upto little less than 0.60, Apartment is the best option, and for probabilities greater than that, Office is the best option. Warehouse is never the best option out of the three.