Question

In a city there is a plan to build an airport. There are two alternate locations for the airport. An investor is planning to build a hotel at one of these locations. Depending on the selected location of the airport the present value (PV) of the hotel will vary. The investor would like to evaluate the 4 options of buying location 1 only, location 2 only, buying both locations 1 and 2 or not investing in any of these locations at all. The following table provides the total cost and the PV for each location.

	Location 1	Location 2
Total Cost of Land, Construction, etc..	$18*	$12
PV of Hotel if airport is built here	$31	$23
PV of Hotel if airport is built at the other location	$6	$4

*Millions of Dollars

a) Construct the payoff table based on the data given above and

b) Apply the following decision rules to come up with a recommendation:

i. The Pessimistic Rule

ii. The Optimistic Rule

iii. A Compromise Rule • Do a sensitivity analysis on your decision for varying ?.

iv. The Average Rule

v. The Regret Avoidance Rule

Answer 1

Payoff table

Choices	Airport At Location-1	Airport at Location2
Build Hotel at Location 1	-18+31=13	-18+6=-12
Build Hotel at Location 2	-12+4= -8	-12+23=11
Build Hotel at both Locations	-18-12+31+4=2	-18-12+23+6=-1
Do not invest in any location.	-	-

Part B

1. Pessimistic rule

Choices	Airport At Location-1	Airport at Location2	Worst payoffs	Best worst payoff
Build Hotel at Location 1	13	-12	-12
Build Hotel at Location 2	-8	11	-8
Build Hotel at both Locations	2	-1	-1	-1
Do not invest in any location.	-	-

So, the investor should build hotel at both the locations

1. Optimistic

Choices	Airport At Location-1	Airport at Location2	Best Payoffs	Better of Best payoff
Build Hotel at Location 1	13	-12	13	13
Build Hotel at Location 2	-8	11	11
Build Hotel at both Locations	2	-1	2
Do not invest in any location.	-	-

So, according to this rule investor should build hotel Location-1

1. Average rule

Considering probabilities of airport coming at location 1 or location 2 is 0.5 each

Choices	Airport At Location-1	Airport at Location2	Average	Best payoff
Build Hotel at Location 1	13	-12	0.5
Build Hotel at Location 2	-8	11	1.5	1.5
Build Hotel at both Locations	2	-1	0.5
Do not invest in any location.	-	-

With Average rule, hotel should be built at location 2

1. Regret Avoidance rule

Size of the regret/ loss of opportunity needs to be made. The biggest pay-off for each demand row is to be subtracted from all other numbers in this row.

Choices	Airport At Location-1	Airport at Location2
Build Hotel at Location 1	13-13=0	-12-13= -25
Build Hotel at Location 2	-8-11= -19	11-11=0
Build Hotel at both Locations	2-2=0	-1-2= -3
Do not invest in any location.	-	-

Among these minimize the maximum regret, which means the target will be to build hotels at both locations with regret of -3 MUSD