Generally speaking, risk can be defined as the chance that the actual outcome will differ from the expected outcome. In investment appraisal, we are concerned with evaluating the riskiness of a project’s future cash flows. In other words, we wish to evaluate the chance that actual cash flows will differ from expected cash flows, that the NPV will be negative or the IRR will be less than the cost of capital, that is, that the project will prove unacceptable because of the potential variability of future cash flows.

Some techniques of risk analysis that may be used in investment appraisal are sensitivity analysis; scenario analysis; simulation analysis; and risk-adjusted discount rate (RADR). Sensitivity analysis involves testing how the overall expected outcome of the project (measured in terms of its NPV, or possibly IRR in some cases) is likely to alter in response to changes in any of the input variables (e.g., the initial outlay, selling prices, sales volumes, project lifespan, asset residual values and so forth); and identifying the key or critical variables in the base case appraisal. The objective of sensitivity analysis is to determine how sensitive the NPV is to changes in any of the key variables and to identify which variable has the most significant impact on NPV.

If a small change in a key variable, such as sales volume, produces a substantial change in the NPV, perhaps even turning it negative, then this would probably be deemed a very risky project. Conversely, if with a large change in a key variable, such as sales volume or sales price, the NPV remains positive, then the project may be viewed as low risk. Scenario analysis, also known as “the best, middle, and worst (BMW) approach,” involves examining a range of possible outcomes under differing sets of assumptions about future business conditions. Simulation analysis is a sophisticated, statistical, usually computer-based approach, which can analyze the effects on outcomes of changing multiple variables simultaneously. A risk-adjusted discount rate (RADR) involves a direct adjustment to the discount rate to compensate for the risk. The higher a project’s perceived level of risk, the higher will be the risk premium added.

Dynamic DCF analysis, decision analysis, and real option pricing are other techniques of including risk in investment appraisals. Dynamic DCF analysis uses the opportunity cost of capital as the (risk-adjusted) discount rate to determine the project’s expected net present value. Estimates of the discount rate are typically based on market data about projects with similar risk profiles and, ideally, with identical risks. However, there is no single risk-adjusted discount rate that is appropriate for all cash flows to and from a project. Hence, a correct application of dynamic DCF may require the use of a number of discount rates within the project analysis.

Decision analysis differs from a dynamic DCF analysis in that discounting is used only to reflect time preference and hence is done appropriately at the risk-free rate. Decision analysts focus most on how the decision-maker values the project. Real Option pricing focuses on market value and uses the standard deviation of the rate of return on an underlying (or twin) asset. The underlying asset is an asset with the same risks as the project if the investment were made and the project completed. Risk or uncertainty is characterized by the range of possible future values for the underlying asset.

Option pricing requires only six basic input parameters: the current value of the underlying asset, the rate of foregone earnings, the variance of the rate of return on the underlying asset, the cost of pursuing the opportunity under consideration, the riskless interest rate, and the time remaining until the opportunity disappears. The variance of the rate of return on the underlying asset represents the amount of uncertainty about the future value of the underlying asset. The method to be used depends on the nature of risks involved in the capital investment project.