Final answer:
The profitability index is a financial metric used to rank projects by comparing the present value of future cash flows to the initial investment, with a higher index indicating a more desirable project. Calculations cannot be provided without cash flow data. Investments' expected values, safety, and risk depend on the variance in possible outcomes and probabilities.
Step-by-step explanation:
The question pertains to calculating the profitability index of investment projects when the opportunity cost of capital is 11 percent. To determine the profitability index for each project, we need the present value of the project's future cash flows and the initial investment. Unfortunately, without specific cash flow data, we cannot calculate the exact profitability index. However, the concept can be explained: it is the ratio of the present value of future expected cash flows of a project and the initial amount invested. To answer if the profitability index ranks investments correctly, yes, it generally does, as it reflects both the return and the scale of investment. A higher profitability index indicates a more desirable investment.
GIVEN: If an investment with a 6% return for the Gizmo Company provides an 11% return to society, applying this additional 5% social benefit, the criteria for project selection may change compared to focusing solely on financial returns.
For the expected value of an investment, you would multiply possible outcomes by their probabilities and sum these. The safest investment typically has the smallest range of possible outcomes (lower variance), while the riskiest has the greatest range of outcomes. The investment with the highest expected return offers the greatest potential profit, but also usually comes with higher risk.