In a city there is a plan to build an airport. There are two alternate locations
ID: 325619 • Letter: I
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
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
Explanation / Answer
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.
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Part B
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
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
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
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.
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-
Among these minimize the maximum regret, which means the target will be to build hotels at both locations with regret of -3 MUSD
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.
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