# Sensitivity Analysis, Scenario Analysis and Simulation Analysis

Simulation analysis, scenario analysis and sensitivity analysis are all stand-alone risk measures that depend on the variation of the project’s cash flows.

## Sensitivity Analysis

Sensitivity analysis involves assessing the effect of changes in one input variable at a time on NPV. These inputs may include sales, fixed costs, and variable costs which all affect the NPV and IRR of a project. Sensitivity analysis is used to identify the most influential variable. For example, NPV is usually most sensitive to changes in the unit sales and unit prices than changes in cost per unit, tax rates, and salvage values. The required rate of return also influences NPV and IRR but not as substantially as changes in unit sales or unit prices. Managers are at liberty to choose which variable to change and by how much.

## Scenario Analysis

Scenario analysis creates different scenarios that can be labeled as (1) pessimistic, (2) optimistic, and (3) most likely scenario. It then changes of the input variables and calculates the NPV for each scenario. For the pessimistic scenario managers assume a higher required rate of return, lower revenues, and high cost which results to a negative NPV. In the case of the optimistic scenario, the variables are adjusted to reflect higher revenues, lower costs, and a favorable rate of return resulting in a positive NPV and an IRR above the required rate of return (RRR).

## Simulation Analysis

Simulation analysis involves examining the effect on NPV when all uncertain input variables follow their corresponding probability distributions. An analyst can assume several input variables to be stochastic and not point estimates. She/he can come up with a good estimate of the distributions of the NPV or IRR by iterating the results hundreds of times with the help of a computer.

## Question

Which of the following are the most likely effects of changes in unit prices on NPV when carrying out a sensitivity analysis?

A. No effect on NPV.

B. Increase in after-tax cash flows resulting in a higher NPV.

C. Increases in salvage value leading to higher NPV.

#### Solution

Unit sales, fixed cost and variable costs all have a significant impact on NPV.

A is incorrect. Unit sales has a significant impact on NPV.

C is incorrect. Unit price has no relationship with salvage value.

LOS 19 (d) Explain how sensitivity analysis, scenario analysis and Monte Carlo simulation can be used to assess the stand-alone risk of a capital project.

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