Question

Business projection: An investor is considering a $10,000 investment in a start-up company. She estimates that she has a probability 0.39 of a $14,000 loss, probability 0.22 of a $7200 profit, probability 0.19 of a $38,000 profit, and probability 0.2 of breaking even (a profit of $0). What is the expected value of the profit? Would you advise the investor to make the investment?

a) $0
b) -$2,360
c) $6,760
d) $17,800

Answer 1

To find the expected value of the profit, we multiply each outcome by its probability and sum the results. The expected value here is $3,344, indicating a favorable average outcome for the investment.

Step-by-step explanation:

The question asks to calculate the expected value of the profit for an investment into a start-up company with varying outcomes and probabilities.

To calculate the expected value (EV), we multiply each potential profit or loss by its probability and sum these products. The calculation is as follows:

• EV from a $14,000 loss: 0.39 * (-$14,000) = -$5,460
• EV from a $7,200 profit: 0.22 * $7,200 = $1,584
• EV from a $38,000 profit: 0.19 * $38,000 = $7,220
• EV from breaking even: 0.2 * $0 = $0

Summing these values gives the expected value of the investment:

EV = -$5,460 + $1,584 + $7,220 + $0 = $3,344

Since the expected value of the profit is positive, it suggests the investment has a favorable outcome on average. However, one must also consider the individual's risk tolerance and other investment opportunities before making a decision.