Question

Suppose an oil company is thinking of buying some land for $950,000. There is a 60% chance of economic growth and a 40% chance of recession. The probability of discovering oil is 46% when there is economic growth and 34% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%. If they do not discover oil, the land will decrease in value by 75%. What is the expected value of the investment

Answer 1

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.