Many investment decisions are fraught with risks and uncertainty. In these circumstances, decision makers can estimate the cash flows they expect to receive by assigning probabilities to each. By performing this analysis, the decision maker can determine the cash flows that will allow him to choose between a risk-free project and one with risky cash flows.

## Step 1.

Project the cash flow. Forecast the cash outflow and inflow from beginning to completion of the project under consideration. For example, if a project requires an investment of \$1,000 at the outset and returns \$2,000 the following year, the cash flow would equal negative \$1,000 in year zero and positive \$2,000 in year one.

## Step 2.

Determine the certainty equivalent coefficients. Select a coefficient between zero and one that reflects the riskiness of each cash flow. A coefficient of zero indicates that you do not expect to receive the cash flow at all, and a coefficient of one indicates full confidence that you will receive the cash flow. Unfortunately, there is no precise way of estimating certainty equivalents. The adjustments should reflect your judgment about the project's riskiness. For example, a coefficient of 0.5 would indicate 50 percent confidence in receiving a cash flow.

## Step 3.

Calculate the certainty equivalent cash flows. Multiply each cash flow by its corresponding certainty equivalent coefficient. For example, if you selected a coefficient of 1.0 for the cash outflow of negative \$1,000 in year zero and 0.5 for the cash inflow of positive \$2,000 in year one, the certainty equivalent cash flows would equal negative \$1,000 in year zero and positive \$1,000 in year one.

## Step 4.

Calculate the net present value, or NPV. Discount each the certainty equivalent cash flow by the project's discount rate to estimate the project's NPV. If the NPV is positive and your estimates of the certainty equivalent coefficients are accurate, you should proceed with the investment.