# Sensitivity Analysis

## What is a 'Sensitivity Analysis'

A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions. This technique is used within specific boundaries that depend on one or more input variables, such as the effect that changes in interest rates have on bond prices.

## BREAKING DOWN 'Sensitivity Analysis'

Sensitivity analysis, also referred to as what-if or simulation analysis, is a way to predict the outcome of a decision given a certain range of variables. By creating a given set of variables, the analyst can determine how changes in one variable impact the outcome.

## Sensitivity Analysis Example

Assume Sue, a sales manager, wants to understand the impact of customer traffic on total sales. She determines that sales are a function of price and transaction volume. The price of a widget is \$1,000 and Sue sold 100 last year for total sales of \$100,000. Sue also determines that a 10% increase in customer traffic increases transaction volume by 5%, which allows her to build a financial model and sensitivity analysis around this equation based on what-if statements. It can tell her what happens to sales if customer traffic increases by 10%, 50% or 100%. Based on 100 transactions today, a 10%, 50% or 100% increase in customer traffic equates to an increase in transactions by 5, 25 or 50. The sensitivity analysis demonstrates that sales are highly sensitive to changes in customer traffic.

## Sensitivity vs. Scenario Analysis

In finance, a sensitivity analysis is created to understand the impact a range of variables has on a given outcome. It is important to note that a sensitivity analysis is not the same as a scenario analysis. As an example, assume an equity analyst wants to do a sensitivity analysis and a scenario analysis around the impact of earnings per share (EPS) on the company's relative valuation by using the price-to-earnings (P/E) multiple.

The sensitivity analysis is based on the variables impacting valuation, which a financial model can depict using the variables' price and EPS. The sensitivity analysis isolates these variables and then records the range of possible outcomes. A scenario analysis, on the other hand, is based on a scenario. The analyst determines a certain scenario such as a market crash or change in industry regulation. He then changes the variables within the model to align with that scenario. Put together, the analyst has a comprehensive picture. He knows the full range of outcomes, given all extremes, and has an understanding for what the outcomes would be given a specific set of variables defined by real-life scenarios.