## Sensitivity Analysis in Finance

# What is Sensitivity Analysis

**Sensitivity Analysis** is a popular way to find out how the NPV of a project changes if sales, labor or material costs, the discount rate, or other factors vary from one case to another. In simple terms it is a “what if” study.

**Sensitivity Analysis** attempts to quantitatively answer questions concerning future outcomes. It is a form of Quantitative Research, which is useful in making Investments decisions. In other words, Sensitivity Analysis is a popular way to find out how the NPV (Net Present value) of a project, where the changes of sales, labor or material costs, the discount rate or the factors are different from one case to another. In simple terms Sensitive Analysis is known as “What-If Study”.

**Few Interesting aspects on NPV of a project:**

- What happens to NPV of a project if cash flow increased by 10%, 20% or 30% each year, Will the NPV still be positive if there is no cash flow the second year?
- Which Project’s NPV will fall more sharply if the discount rate goes up from 8% to 11%?

As, these are the kind of questions arise when financial analysts want to measure the risk of a project through Sensitivity Analysis.

**A worked out example using Sensitivity Analysis: **

**Prob:** Suppose the cash flows Project A are $1000 in a year and $1500 in year 2. Project B has expected cash flows of $1800 in 1year and $700 in second year. The initial investment for each project is $1600. Which project is more risky if the discount rate changes from 10% to 12%?

**Sol:** To answer this first we need to find out NPV of each project at 10%. Using the NPV method of Project A determines at 10% is $548 and the NPV of Project B is at the same rate $614. (We need to multiply the cash flows at present values factors at 10%, add up the answers and then subtract the initial investment $1600.) The changes in the NPVs of these two projects should need to calculate the NPVs of cash flows in the new rate. Using the same method we can find the NPV of Project A at 12% is $489 and the NPV of Project B at the same rate is $546.

We can summarize this as:

Project | NPV at 10% | NPV at 12% | Percentage change in NPV |

A | $548 | $489 | -10.77 |

B | $614 | $546 | -7.98 |

By looking at this table we can easily make out that the NPVs of both Projects decline when the discount rate rises from 10% to 12%.

Sensitivity Analysis for a Mathematical model in its simplest form and works out by adding complications to it one at a time. By this process it is easy to get Sensitivity Analysis method of increasing complexity, which is starting from elementary approaches to more the quantitative ones.

**A simple model portfolio is: **

Y=Cs Ps + Ct Pt + Cj Pj

Where Y is estimated as the risk^1 in €, Cs, Ct, Cj are the quantities per item and Ps, Pt, Pj are hedged portfolios in €^2. This means that each Px, X = (s, t, j) is composed for more than one item, So that the average return Px is zero €.

This is the common use of the term; Y is in fact a return. The negative uncertain value of Y is what constitutes the risk.

This simple model could be well seen as a Synthetic or a composite indicator by aggregating the set of standardized basic indicators with Pj and weights Cj.

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The article is in continuation with our previous articles on Finance which include **Present Value, Net Present Value, Profitability Index, Internal Rate of Return**