Final answer:
The student's question is about computing the expected value of different venture capital investments. The expected value is calculated by multiplying the potential outcomes of an investment by their respective probabilities and summing them up. For the provided investment options, a step-by-step calculation would yield the expected profit for each, aiding the venture capitalist's decision-making process.
Step-by-step explanation:
Calculating Expected Value in Venture Capital Investments
The concept of expected value is a crucial aspect in venture capital and business investments. Expected value is a calculation that combines the possible outcomes of an investment with the probabilities of their occurrence. This computation gives investors an idea of the average monetary outcome they can expect over many trials of the investment scenario, allowing them to compare the profitability of different ventures.
In the given scenario, we want to calculate the expected profit for three different companies in which a venture capitalist might invest $1,000,000. To find the expected value for each investment, we multiply each potential outcome by its probability and sum these products.
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- For the software company, the expected value is (0.10 * $5,000,000) + (0.30 * $1,000,000) - (0.60 * $1,000,000).
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- For the hardware company, the expected value is (0.20 * $3,000,000) + (0.40 * $1,000,000) - (0.40 * $1,000,000).
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- For the biotech firm, the expected value is (0.10 * $6,000,000) + (0.70 * $0) - (0.20 * $1,000,000).
By computing these values, the venture capitalist can determine which investment has the highest expected profit and make an informed decision.
Lastly, we'll use the provided example to construct a probability density function (PDF) for each investment, which visually represents the probabilities of various returns on investment.