Question

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff (profit in thousands of dollars) table based on whether a business will be brisk, medium, or slow.   

                                           Business Level

Decision               Brisk           Medium                Slow

────────────────────────────────────────

Buy                          90                 50                       30                                         

Rent                         50                 60                       45                                         

Lease                       40                55                       50

Assume that the probability of a brisk business level is 0.4, the probability of a medium business level is 0.4 and the probability of a slow business level is 0.2.

(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

(c) Calculate and interpret the value of perfect information for this problem.

Answer 1

Please upvote if you find it helpful. Each step is explained in detail.

The answer to Q a)

	Business Level
Decision	Brisk	Medium	Slow	Expected Value	Expected Value
Probability	0.4	0.4	0.2
Buy	90	50	30	(0.4*90)+(0.4*50)+(0.2*30)	62
Rent	50	60	45	(0.4*50)+(0.4*60)+(0.2*45)	53
Lease	40	55	50	(0.4*40)+(0.4*55)+(0.2*50)	48

From the expected value, the best alternative is Buy.

The answer to Q b)

Expected opportunity loss value

Step 1: Calculate regret.

Regret = Best pay off – pay off received

	Business Level
Decision	Brisk	Medium	Slow
Probability	0.4	0.4	0.2
Buy	90-90	60-50	50-30
Rent	90-50	60-60	50-45
Lease	90-40	60-55	50-50

Step 2: Calculate the expected value

	Business Level
Decision	Brisk	Medium	Slow	Expected Value	Expected Value
Probability	0.4	0.4	0.2
Buy	0	10	20	(0.4*0)+(0.4*10)+(0.2*20)	8
Rent	40	0	5	(0.4*40)+(0.4*0)+(0.2*5)	17
Lease	50	5	0	(0.4*50)+(0.4*5)+(0.2*0)	22

The minimum expected value is selected for the decision. The best decision is to buy.

The answer to Q c)

Value of perfect information = Expected value with Perfect information – Expected value without perfect information

Expected value with perfect information = sum of (maximum value of each column*probability) = (90*0.4)+(60*0.4)+(50*0.2) =36+24+10=70

Value of perfect information = 70-62 = 8

Interpretation: The perfect information worth $ 8000.