Final answer:
To find each investment's expected rate of return, one must multiply the probability of each outcome by its respective payoff and sum these values. The biotech firm is likely the safest investment due to its high probability of no loss or profit, offering stability. The investment with the highest expected return can be ascertained by comparing the calculated expectations for each company.
Step-by-step explanation:
To calculate the expected rate of return for each investment, we will use the probabilities of the different outcomes and the respective returns. For the software company, the expected return is calculated as follows: (10% × $5,000,000) + (30% × $1,000,000) - (60% × $1,000,000). For the hardware company: (20% × $3,000,000) + (40% × $1,000,000) - (40% × $1,000,000). For the biotech firm: (10% × $6,000,000) + (70% × $0) - (20% × $1,000,000).
The safest investment is typically the one with the smallest range of potential outcomes and the closest actual returns to the expected rate of return year after year. Based on the provided scenarios, the biotech firm appears to be the safest, with a 70% chance of no loss or profit, indicating more stability. In contrast, the riskiest investment would be the one with a wide range of potential payoffs and a high probability of significant loss, which could be the software company with a 60% chance of losing the entire investment.
The investment with the highest expected return, on average, can be determined by calculating the expected return for each option and comparing the results. Calculation of the expected return will take into account the probability of each outcome and the corresponding payoff