Respuesta :
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.
