sensitivity and scenario analysis

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What is the Problem?

When a business decides to take on a new project (like building a new factory or launching a new product), it uses financial models to estimate how profitable the project will be. The main result of this is often the Net Present Value (NPV). However, the NPV is based on a lot of assumptions—what if those assumptions are wrong?

For example, what if:

* Sales are lower than expected?

* The cost of raw materials goes up?

* The cost of borrowing money increases?

Sensitivity and Scenario Analysis are two tools used to handle this uncertainty and understand the project's risk.

1. Sensitivity Analysis

* Core Idea: This method looks at how the project's NPV changes when one variable at a time changes.

* How it works: You hold all other variables constant and then test a range of values for a single variable. For example, you would ask:

* "If sales decrease by 10%, what happens to the NPV?"

* Then, "If the cost of capital increases by 1%, what happens to the NPV?"

* What it tells you: It helps you identify the most critical variables. If a small change in one variable (like sales price) causes a huge swing in the NPV, then that variable is highly "sensitive." This means you need to be very careful with your assumptions for that variable.

* The document's point: The document mentions that the range of the optimistic NPV minus the pessimistic NPV gives a sense of the project's risk. A wider range means the project's outcome is very sensitive to that variable, and therefore riskier.

2. Scenario Analysis

* Core Idea: This is a more comprehensive approach. Instead of changing just one variable, it evaluates the impact of multiple variables changing at the same time to create a complete "scenario."

* How it works: You create a few possible future situations, or "scenarios," for the project. The document gives an example:

* Scenario 1 (High Inflation): You would set a pessimistic value for cash inflows, a high value for cash outflows, and a high value for the cost of capital. You would then calculate the NPV for this specific situation. This gives you a Pessimistic NPV.

* Scenario 2 (Low Inflation): You would set an optimistic value for cash inflows, a low value for cash outflows, and a low value for the cost of capital. You would then calculate the NPV for this situation. This gives you an Optimistic NPV.

* You could also calculate a "most likely" or "base case" scenario.

* What it tells you: It gives you a much better picture of the project's overall risk profile. Instead of just seeing what happens if one number changes, you see the outcome of a complete, realistic situation. It helps the decision-maker understand the potential range of outcomes, from a worst-case disaster to a best-case success.

Summary Table

| Feature | Sensitivity Analysis | Scenario Analysis |

|---|---|---|

| Variables | Changes one variable at a time. | Changes multiple variables simultaneously. |

| Purpose | To identify the most critical variables that have the biggest impact on the outcome. | To assess the outcome of a complete, realistic situation (a scenario). |

| Output | A graph or table showing how the NPV changes for each variable. | A few key NPV values (Optimistic, Pessimistic, Base Case). |