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

Question

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Respuesta :

jepessoa jepessoa · Answer 1 · 2020-10-16T03:59:45+02:00

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.