Question

The city of​ Belgrade, Serbia, is contemplating building a second airport to relieve congestion at the main airport and is considering two potential​ sites, X and Y. Hard Rock Hotels would like to purchase land to build a hotel at the new airport. The value of land has been rising in anticipation and is expected to skyrocket once the city decides between sites X and Y.​ Consequently, Hard Rock would like to purchase land now. Hard Rock will sell the land if the city chooses not to locate the airport nearby. Hard Rock has four​ choices: (1) buy land at​ X, (2) buy land at​ Y, (3) buy land at both X and​ Y, or​ (4) do nothing. Hard Rock has collected the following data​ (which are in millions of​ euros):
Site X Site Y
Current purchase price 29 18
Profits if airport & hotel built at this site 35 30
Sale price if airport not built at this site 8 4

Hard Rock determines there is a 55% chance the airport will be built at X (hence, a 45% chance it will be built at Y)

Set up a decision table (in millions of Euros) (enter as a whole number and include minus sign if necessary)


State of Nature
Alternatives Airport at X Airport at Y
buy land at X
buy land at Y
buy land at both X & Y
Do nothing
Probability 0.55 0.45

Answer 1

Answer:

Alternatives                                          Airport at X Airport at Y

Buy land at X                                                 6             -14

Buy land at Y                                               -21             12

Buy land at X and Y                               -15                 -2      

Do nothing                                                 0              0

probability                                                   0.55              0.45

Payoff if you buy land at X = (0.55 x 6) + (0.45 x -) = -3

Payoff if you buy land at Y = (0.55 x -21) + (0.45 x 12) = -6.15

Payoff if you buy land at X and Y = (0.55 x -15) + (0.45 x -2) = -9.15

Payoff for doing nothing = 0

The best option is simply doing nothing. The risks are too high, the potential losses are very large and the benefits are really low.