Sensitivity analysis tests how financial results respond to changed inputs, using one-way tests, two-way tables, or broader methods to identify key drivers.
Sensitivity analysis tests how a financial result changes when one or more model inputs change. It helps identify the assumptions that drive a valuation, forecast, or risk measure and the points at which a conclusion reverses.
A one-at-a-time test holds other assumptions fixed, but that is only one form of sensitivity analysis. Two-way tables and broader global methods can examine several inputs and their interactions.
| Method | What varies | Useful for |
|---|---|---|
| One-way test | One input while the others remain fixed | Isolating a particular input’s effect |
| Two-way table | Every tested combination of two inputs | Seeing how two assumptions jointly affect the result |
| Global sensitivity analysis | Inputs over defined ranges or distributions | Assessing broader effects and interactions |
The European Commission’s Joint Research Centre explains the limits of relying exclusively on one-at-a-time analysis in How to Avoid a Perfunctory Sensitivity Analysis. A two-way spreadsheet table is useful, but it is not a complete global analysis of every uncertain input.
Assume a hypothetical project costs USD 100,000 today and generates a single net cash inflow one year later. The base case uses USD 120,000 of inflow and a 10% annual discount rate. Assume no taxes, residual value, or additional cash flows.
Here, C_1 is the year-end net cash inflow, r is the annual discount rate, and I_0 is today’s initial cost. The base-case result is:
Now vary both the inflow and discount rate. Each cell shows NPV in U.S. dollars, rounded to cents:
| Year-end net cash inflow | 5% discount rate | 10% discount rate | 15% discount rate |
|---|---|---|---|
| USD 100,000 | -4,761.90 | -9,090.91 | -13,043.48 |
| USD 110,000 | 4,761.90 | 0.00 | -4,347.83 |
| USD 120,000 | 14,285.71 | 9,090.91 | 4,347.83 |
Reading down the 10% column is a one-way cash-flow sensitivity test. Reading across the USD 120,000 row is a one-way discount-rate test. The full grid is a two-way sensitivity table.
The corner cells also show combined changes, but they do not establish whether those combinations are plausible or likely. There are nine cells because nine combinations were selected, not because each has a one-ninth probability.
Suppose the criterion is NPV greater than zero. At a fixed 10% discount rate, the break-even year-end cash inflow is:
That is USD 10,000, or approximately 8.33%, below the base inflow of USD 120,000. It is a sensitivity of net cash inflow, not necessarily an 8.33% fall in sales: costs and collection timing could change too.
Alternatively, hold the USD 120,000 inflow fixed. The discount rate that makes NPV zero is:
These are separate threshold tests. The 20% rate is not a forecast market rate or an investment recommendation. Other project criteria, including interim liquidity needs, remain outside this simplified example.
HM Treasury’s Green Book discussion of sensitivity analysis and switching values describes a comparable threshold approach for public-sector appraisal. Its public-sector valuation rules are not being imposed on the hypothetical business project here.
Use ranges that reflect uncertainty, contractual limits, or a stated stress rather than selecting values solely to preserve a positive answer.
Keep nominal cash flows with nominal rates and real cash flows with real rates. Hold the currency, time basis, and definition of the output consistent. State what remains fixed, especially taxes, financing, working capital, and terminal assumptions.
When comparing drivers, explain how their ranges were chosen. A large output swing may reflect a very wide tested range, not inherently greater importance. Sensitivity rankings can also change at another starting point.
Use scenario analysis when the question is how a coherent operating environment affects the result. Use simulation when a probability model and repeated sampling are appropriate. These methods complement rather than replace each other.
This article provides general financial education, not a valuation opinion, project approval, or personalized investment recommendation.