How is the risk-adjusted profitability index calculated?

The risk-adjusted profitability index is calculated by dividing the expected return of an investment project by its risk level. It is a measure used to assess the profitability of an investment while taking into consideration the associated risk.

To calculate the risk-adjusted profitability index, follow these steps:

1. Determine the expected return of the investment project. This can be calculated by multiplying the probability of each possible outcome by its respective return and summing them up. For example, if there are three possible outcomes with probabilities of 0.3, 0.5, and 0.2, and their respective returns are $10,000, $15,000, and $8,000, the expected return would be (0.3 * $10,000) + (0.5 * $15,000) + (0.2 * $8,000) = $12,700.

2. Assess the risk level of the investment project. This can be done by calculating the standard deviation of the returns. The standard deviation measures the dispersion of the returns around the expected return. A higher standard deviation indicates higher risk.

3. Divide the expected return by the risk level to obtain the risk-adjusted profitability index. For example, if the expected return is $12,700 and the risk level is 0.05 (or 5%), the risk-adjusted profitability index would be $12,700 / 0.05 = $254,000.

The risk-adjusted profitability index provides a measure of the return per unit of risk for an investment project. A higher index value indicates a better risk-adjusted profitability, suggesting that the investment is more attractive.