Sensitivity Analysis: Definition, Formula & How to Use It

What Is Sensitivity Analysis?

Sensitivity analysis is used in financial modelling and investment appraisal to determine how variation in a single input assumption affects a defined output. It belongs to the broader discipline of corporate finance and valuation, where practitioners build base-case models using projected cash flows, growth rates, margins, and discount rates, then test how dependent the conclusion is on each assumption.

The technique applies wherever a model produces a quantitative result from a set of assumptions. Discounted cash flow (DCF) valuations, capital budgeting decisions, and project finance assessments all rely on sensitivity analysis because they require executives to understand which assumptions deserve the most scrutiny before capital is committed.

How Sensitivity Analysis Works

The process begins with a completed base-case model, typically a DCF or net present value (NPV) calculation that produces a single output from a defined set of inputs. The analyst then identifies the assumptions most likely to influence that output, which often include revenue growth, operating margin, the weighted average cost of capital (WACC), and terminal growth.

For each assumption, the analyst defines a realistic range and recalculates the model at regular intervals while holding other inputs constant. A WACC assumption, for example, might be tested from 8 percent to 12 percent to show how the valuation changes as the required return rises. The resulting table gives decision-makers a clear view of which assumptions produce the largest swing in value, and that directs attention toward the inputs that need stronger evidence, tighter governance, or closer monitoring after approval.

Sensitivity Analysis Example

Consider a manufacturing company evaluating a new production line with a base-case NPV of £4.2 million. The finance team tests two assumptions that matter directly to the investment decision, with WACC ranging from 8 percent to 12 percent and annual revenue growth ranging from 3 percent to 7 percent. The table shows how the project value changes across those ranges.

The table shows that WACC has a large effect on NPV across the tested range. At WACC 12 percent and 3 percent growth, the project produces only £0.6 million of value, while the base case produces £4.2 million. For the board, that difference changes the approval discussion because the cost of capital assumption requires stronger support before the investment can be treated as robust.

Key Considerations and Limitations

Sensitivity analysis is most valuable when it forces a modelling team to rank assumptions by impact. A model may contain dozens of inputs, but only a small number usually determine the decision outcome. By separating high-impact inputs from marginal ones, the technique helps finance teams focus review time on the assumptions that could change whether a project should proceed.

Its main constraint comes from the way it isolates variables. Revenue growth, margins, inflation, and discount rates often move together in response to the same market conditions, so a sensitivity table that treats them independently can understate the true range of outcomes. The technique also reveals exposure to assumptions without assigning probability. A variable may produce a large movement in NPV while still being well evidenced, while a less sensitive input may carry greater uncertainty because management has limited visibility over it.

The most common practical error is treating the outer edges of a sensitivity table as the project's worst and best cases. Those boundaries only show the range the analyst chose to test. If the selected range is too narrow, the table can make a fragile investment appear resilient, which is why the range itself should be challenged as carefully as the base-case assumption.

Sensitivity Analysis vs Scenario Analysis

Sensitivity analysis isolates individual variables, while scenario analysis changes multiple inputs at the same time to represent a coherent future state. A recession case, for example, may combine lower revenue growth, weaker margins, higher funding costs, and delayed customer payments because those conditions often occur together. That makes scenario analysis better suited to testing strategic resilience, while sensitivity analysis is better suited to identifying the assumptions that drive the model most strongly.

Used together, the two methods give a fuller view of model risk. Sensitivity analysis shows which assumptions deserve the most attention, and scenario analysis shows how the investment behaves when those assumptions move in a realistic combination.

In Practice

Sensitivity analysis helps executives move from point estimates to decision quality. A single base-case valuation can create false precision, while a well-built sensitivity table shows where judgement matters most. In a capital allocation meeting, that distinction changes the conversation from whether the model produces a positive result to whether the assumptions behind that result are defensible.

For boards and finance leaders, the technique is most useful when it leads to action. If value is highly sensitive to WACC, the financing plan and discount rate assumptions need closer review. If value is highly sensitive to revenue growth, commercial evidence and downside protection become central to the approval decision. Sensitivity analysis is therefore less a modelling exercise than a governance tool for testing how much confidence management should place in a proposed allocation of capital.