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Sensitivity Analysis

A base-case valuation hides a fragile truth. The net present value rests on assumptions about sales growth, margins, costs and the discount rate, and any of them can be wrong. Sensitivity analysis flexes one input at a time, holding the rest at their expected values, and watches how NPV\mathrm{NPV} responds. The output ranks the drivers by impact, so the analyst learns which few assumptions actually decide whether the project lives or dies. The classic visual is the tornado diagram, a horizontal bar chart sorted from the most influential driver at the top to the least at the bottom.

Try it yourself

Sensitivity & scenario analysis

A project's NPV is the present value of five years of free cash flow, FCFₜ = Sales₀(1 + g)ᵗ · margin, discounted at r. A tornado flexes one driver at a time to rank impact; a scenario moves correlated drivers together.

Base-case NPV$80.6m
base $80.6m▸ Base-year sales$72.6m$88.7mOperating margin$72.6m$88.7mDiscount rate$78.5m$82.8mSales growth$79.3m$82.0mdownsideupside
Base-case NPV $80.6mMost-sensitive driver Base-year salesValue range (top driver) $72.6m → $88.7m
Base-year sales$100m
Sales growth g6.0%
Operating margin18.0%
Discount rate r10.0%
Swing per driver (± of value)±10%
Flexing each driver by ±10% one at a time, Base-year sales moves NPV the most: $72.6m → $88.7m (a $16.1m span). The widest bar sits on top, so the diagram ranks impact, not likelihood.
Try this

Which driver tops the tornado? Then switch to scenarios: the optimistic-to-pessimistic spread dwarfs any one bar because the moves stack.

Reflect: a tornado shows how much NPV moves if one assumption is wrong, holding the rest fixed. A scenario asks what happens when assumptions go wrong together. Neither attaches a probability. What would you add to turn impact into expected value?

Why it matters

Think of the valuation as a machine with many dials. Sensitivity analysis turns one dial up and down while every other dial stays put, then records how far the NPV needle swings. A dial that barely moves the needle does not deserve much worry. A dial that swings it from clearly positive to clearly negative is where the real risk lives, and where you should spend effort tightening the forecast or hedging. In the Earthilizer case the wide-swinging drivers turn out to be gross profit margin, operating expenses and base-year sales.

Formulas

One-at-a-time sensitivity
Sensitivityi=ΔNPVΔxiwith all xj≠i fixed\text{Sensitivity}_i = \frac{\Delta \mathrm{NPV}}{\Delta x_i} \quad \text{with all } x_{j \ne i} \text{ fixed}
Input xix_i is varied while every other input stays at its expected value. A steep slope means the project value is highly sensitive to that one assumption.
Tornado bar half-width
Swingi=NPV(xihigh)−NPV(xilow)\text{Swing}_i = \mathrm{NPV}(x_i^{high}) - \mathrm{NPV}(x_i^{low})
Each driver is shifted to a low and a high value. The width of its bar is the resulting NPV range, and the bars are sorted widest-first to form the tornado shape.

Worked examples

Scenario

CSM’s Earthilizer project has a base-case NPV near A$43,000. Holding all else fixed, raising base-year 2016 sales from A$1.0m to A$1.1m lifts NPV by about A$56,000, while a one percentage point cut in the discount rate lifts it by only a few thousand. Which driver dominates the tornado?

Solution

Base-year sales produce the far larger NPV swing, so its bar sits at the top of the tornado and the discount rate sits well below it. The lesson is to direct scarce forecasting effort at the sales estimate, since a small error there moves the verdict far more than an equal-sized error in the rate. Numbers here are illustrative and meant only to show the ranking logic.

NoteThe tornado diagram is just a sorted bar chart. It needs no special software, only a base case and a high or low value for each driver.

Common mistakes

  • ✗Sensitivity analysis tells you how likely a bad outcome is. It does not. It shows how much NPV moves if a driver changes, never the probability that the driver actually changes.
  • ✗Every input matters equally, so all deserve equal scrutiny. The whole point is the opposite. A handful of drivers usually dominate, and the rest can be left at their base case.
  • ✗Moving inputs one at a time captures the real risk. Because drivers can move together, one-at-a-time analysis misses correlation, which scenario and simulation analysis are built to address.
  • ✗A flat sensitivity line means the input is unimportant to the business. It only means NPV is robust to that input over the range tested, not that the input is irrelevant operationally.

Revision bullets

  • •Flex one input at a time, holding all others at their expected values
  • •Measures how far NPV moves, not how likely a change is
  • •Ranks drivers so effort targets the few that decide the project
  • •Tornado diagram sorts driver bars widest-first, no special software needed
  • •In the Earthilizer case, margin, operating expenses and base-year sales dominate
  • •Blind to correlation between drivers, a gap scenario and simulation fill

Quick check

In one-at-a-time sensitivity analysis, while one input is varied the other inputs are

A tornado diagram is most useful for showing

Connected topics

NPV & AdditivityScenario AnalysisBreak-EvenMonte Carlo

Sources

  1. Titman & Martin, Ch. 3
    Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
    Develops sensitivity analysis and the tornado diagram as tools for learning more about a project’s risk.
How to cite this page
Dr. Phil's Quant Lab. (2026). Sensitivity Analysis. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-sensitivity-analysis
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