An investor is considering an investment in a start-up company. She estimates that she has probability 0.38 of a $22,000 loss, probability 0.29 of a $95000 profit, probability 0.15 of a $42,000 profit, and probability 0.18 of breaking even (a profit of $0). What is the expected value of the profit?

Answer 1

To calculate the expected value of the profit from the investment, we will multiply each outcome by its probability and then sum these values.

Let’s define the outcomes and their probabilities:

• Probability of a $22,000 loss: 0.38
• Probability of a $95,000 profit: 0.29
• Probability of a $42,000 profit: 0.15
• Probability of breaking even ($0 profit): 0.18

Now, we can calculate the expected value:

1. For the loss of $22,000: \[ E(Loss) = 0.38 \times (-22000) = -8356 \]

2. For the profit of $95,000: \[ E(Profit) = 0.29 \times 95000 = 27550 \]

3. For the profit of $42,000: \[ E(Profit) = 0.15 \times 42000 = 6300 \]

4. For breaking even ($0): \[ E(BreakEven) = 0.18 \times 0 = 0 \]

Now, we can sum these contributions to get the expected value of the profit: \[ E(Expected\ Value) = E(Loss) + E(Profit_{95000}) + E(Profit_{42000}) + E(BreakEven) \] \[ E(Expected\ Value) = -8356 + 27550 + 6300 + 0 \] \[ E(Expected\ Value) = -8356 + 27550 + 6300 = 27494 \]

Therefore, the expected value of the profit from the investment is $27,494.

Answer 2

Based on this, should the investor make the investment?

Answer 3

To decide whether the investor should make the investment, we can consider the expected value of the investment. The expected value we calculated is $27,494, which indicates that, on average, the investor can expect to gain this amount from the investment over the long run.

However, the decision to invest should also take into account several factors:

1. Risk Tolerance: The investor should consider her tolerance for risk, especially given that there is a probability of a significant loss ($22,000) with a relatively high likelihood (0.38). If she is risk-averse, she might be uncomfortable with the potential for loss even if the expected value is positive.

2. Investment Horizon: The time frame for the investment may also influence the decision. If the investor is looking for quick returns, the risks associated with a start-up might be too high compared to other investment options.

3. Alternative Investments: The investor should compare the expected return and risk of this investment with other possible investments. If there are safer investments with a similar or better return, she may prefer those instead.

4. Due Diligence: It’s also essential for the investor to conduct due diligence on the start-up – understanding its business model, market potential, team, and financial health can be crucial in making an informed decision.

5. Emotional and Psychological Factors: Sometimes, investments are also influenced by emotional and psychological factors. The investor should reflect on how much uncertainty she’s willing and able to handle.

In summary, while the expected value of $27,494 suggests a potentially favorable investment, the final decision should involve a careful consideration of the investor's risk tolerance, investment strategy, and other personal financial goals. If she feels comfortable with the associated risks and believes in the potential of the start-up, investing might be a reasonable choice. If not, it could be wise to pass on this opportunity.