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##### Subject 4. Risk Analysis of Capital Investments - Stand-Alone Methods
Risk is measured as a dispersion of outcomes. In the case of stand-alone risk, we typically measure the riskiness of project by the dispersion of its NPVs or the dispersion of its IRRs.

Sensitivity Analysis

It is a technique which shows how much a project's NPV or IRR will change in response to a given change in an input variable such as sales, other things held constant.

• It begins with a base-case situation, which is developed using the expected values for each input.
• A base-case NPV is thus calculated.
• Then each variable is changed by several percentage points above and below the expected value, holding other things constant. A new NPV is calculated using each of these values.
• Finally, the set of NPVs is plotted against the variable that was changed.
• The slopes of the lines show how sensitive NPV is to changes in each of the inputs. The steeper the slope, the more sensitive the NPV is to a change in each of the variable.
• The project with the steeper sensitivity lines would be riskier.

In general, a project's stand-alone risk depends on (1) the sensitivity of NPV to changes in key variables and (2) the range of likely values of these variables as reflected in their probability distributions. The sensitivity analysis considers the first factor only and is incomplete. It only examines the base-case scenario.

Scenario Analysis

It is a risk analysis technique in which the best- and worst-case NPVs are compared with the project's expected NPV. It considers both the sensitivity of NPV to changes in key variables and the likely range of variable values. The least "reasonable" set of circumstances (low unit sales, high construction cost, etc) and the most "reasonable" set are specified first. The NPVs under the bad and good conditions are then calculated and compared to the expected, or base-case, NPV. Even though there are an infinite number of possibilities, scenario analysis only considers a few discrete outcomes (NPVs).

Monte Carlo Simulation

It is a risk analysis technique in which a computer is used to simulate probable future events and thus to estimate the profitability and risk of a project. Random values of input variables are generated on a computer. The mean of the target variable is computed to measure the expected value. Standard deviation (or coefficient of variation) is computed to measure risks.

Learning Outcome Statements

d. explain how sensitivity analysis, scenario analysis, and Monte Carlo simulation can be used to assess the stand-alone risk of a capital project;

CFA® 2023 Level I Curriculum, Volume 3, Module 19

User Comment
kalps Sensitivity - changes one variable and looks at NPV Scenario - NPV's under extremem good and bad conditions calc and compared to base case Monte carlo - simulates probably future events - ext. profit/risk - computer generated
SueLiu Simulation analysis = sensitivity AND scenario analysis 