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Suppose an oil company is thinking of buying some land for $11,000,000. 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 11 % . 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 80 % .What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations.

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Answer:

The expected value of the investment is $15,104,760.

Step-by-step explanation:

The investment made is of amount, X = $11,000,000.

The probability of economic growth is, P (G) = 0.60.

The probability of recession is, P (R) = 0.40.

The probability of discovering oil if there is economic growth is,

P (O|G) = 0.46.

The probability of not discovering oil if there is economic growth is,

P (O'|G) = 1 - P (O|G) = 1 - 0.46 = 0.54.

The probability of discovering oil if there is recession is,

P (O|R) = 0.34.

The probability of not discovering oil if there is economic growth is,

P (O'|R) = 1 - P (O|R) = 1 - 0.34 = 0.66.

If they discover oil when there is economic growth, the value of the land will be tripled .

Value of land (O|G) = 3 × 11000000 = 33,000,000.

And if they do not discover oil, the value of the land will decrease by 11% .

Value of land (O'|G) = (1 - 0.11) × 11000000 = 9,790,000.

If there is a recession and the company discovers oil, the value of the land will increase by 50 %.

Value of land (O|R) = (1 + 0.50) × 11000000 = 16,500,000.

If they do not discover oil, the land will decrease in value by 80 % .

Value of land (O'|R) = (1 - 0.80) × 11000000 = 2,200,000.

Computed the expected value of the investment as follows:

E (investment) = [P (O|G) × P(G) × Value of land (O|G)]

                             + [P (O'|G) × P(G) × Value of land (O'|G)]

                                 + [P (O|R) × P(R) × Value of land (O|R)]

                                     + [P (O'|R) × P(R) × Value of land (O'|R)]

                        [tex]=[0.46\times0.60\times33,000,000]+[0.54\times0.60\times9,790,000]\\+[0.34\times0.40\times16,500,000]+[0.66\times0.40\times2,200,000]\\=9108000+3171960+2244000+580800\\=15104760[/tex]

Thus, the expected value of the investment is $15,104,760.

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