Answer:
$619,210
Explanation:
As we know that:
Expected Value = ∑P1V1 + ∑P2V2 + ∑P3V3 + ............... + ∑PnVn
Individual Expected Value for (n=1) = ∑P1V1
Here
Case Scenario 1:
P1 is the joint probability under Economic Growth & oil discovery positions
= 60% * 46% = 27.6%
V1 is the Value of investment under case scenario 1 which is three times: Value = 300% * $950,000 = 2,850,000
Expected Value of land = 27.6% * 2,850,000 = $786,600
Case Scenario 2:
P2 is the joint probability under Economic Growth & No oil discovery positions = 60% * 52% = 31.2%
V2 is the Value of investment in this case would be:
Value = (1 - 10%) * 950,000 = 855000
Expected Value of land = 31.2% * 855,000 = $266,760
Case Scenario 3:
P3 is the joint probability under Recession and Oil Discovery ) = 46%*34%
= 0.1564
V3 is the Value of investment here:
Value = 950,000 * 150% = 1,425,000
Expected Value of land = 31.2% * 1,425,000 = $444,600
Case Scenario 4:
P4 is the joint probability under Recession and no oil Discovery = 40%*75%
= 30%
V4 is the Value of investment here:
Value = (1 - 75%) * $950,000 = $237,500
Expected Value of land = 30% * $237,500 = $71,250
Now,
Expected Value = ∑P1V1 + ∑P2V2 + ∑P3V3 + ∑P4V4
By putting the above values, we have:
Expected Value of Land = $786,600 + $266,760 + $444,600 + $71,250
Expected Value of Land = $1,569,210
The above expected value is of land. Now we want the expected value of the investment. For this reason we will deduct the cost of the land from the expected value of the land.
Now we have:
Expected value of Investment = $1,569,210 - $950,000 = $619,210
The expected value of Investment is a positive value, which means that the investment will generate average value of $619,210 for the oil company. Thus the company must invest in it.
