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Scenario Analysis

Sensitivity analysis flexes one driver in isolation, but the real world moves several at once. Scenario analysis builds a small set of internally coherent stories, usually a base case, an optimistic case and a pessimistic case, and revalues the project under each. Within a scenario, every input is set to a value that fits that narrative, so a recession scenario lowers both sales growth and margins together. The result is a handful of NPV estimates that reveal how the project fares when correlated assumptions shift in the same direction. It answers a sharper question than sensitivity alone, namely what happens when things genuinely go right or wrong.

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

A pessimistic world is not just lower sales with everything else unchanged. Weak demand usually drags margins, pricing and growth down together. Scenario analysis respects that by changing the inputs as a bundle, so each scenario reads like a plausible chapter of the firm’s future rather than a single isolated tweak. Three well-chosen scenarios often teach more than a dozen one-at-a-time slopes, because they capture the way bad news tends to arrive in clusters.

Formulas

NPV under a scenario
NPVs=∑t=0nFCFt,s(1+r)t\mathrm{NPV}_s = \sum_{t=0}^{n} \frac{\mathrm{FCF}_{t,s}}{(1 + r)^{t}}
Each scenario ss supplies its own coherent set of cash flows FCFt,s\mathrm{FCF}_{t,s}. The base, best and worst cases differ because several inputs move together within each story.
Probability-weighted expected NPV
E[NPV]=∑sps NPVsE[\mathrm{NPV}] = \sum_{s} p_s \, \mathrm{NPV}_s
If subjective probabilities psp_s are assigned to the scenarios, their weighted average gives an expected NPV. The weights are judgement calls, so treat the result as indicative.

Worked examples

Scenario

For Earthilizer, the base case assumes 2016 sales of A$1.0m growing at 10 percent. A pessimistic scenario sets initial sales at A$0.5m and growth at 5 percent, lowering both together. How does this differ from sensitivity analysis?

Solution

Scenario analysis changes the two correlated drivers in one coherent move, so the pessimistic NPV reflects a genuinely weak-demand world rather than a single isolated tweak. Sensitivity analysis would instead vary initial sales alone, then growth alone, missing the way the two travel together in a downturn. The base, best and worst NPVs give management a feel for the spread of outcomes under realistic combinations. The figures are illustrative.

Common mistakes

  • ✗Scenario analysis and sensitivity analysis are the same thing. Sensitivity flexes one input at a time. Scenario analysis moves a coherent bundle of inputs together within each story.
  • ✗The worst case is the lowest possible value of every input at once. A sound worst case is a plausible recession narrative, not an unrealistic stacking of every input at its extreme.
  • ✗Three scenarios capture the full range of outcomes. Only a handful of discrete cases are tested, so rare or in-between combinations are missed, which is why simulation extends the idea.
  • ✗Scenario probabilities are objective facts. The weights placed on base, best and worst are subjective judgement, so the expected NPV they produce is indicative rather than precise.

Revision bullets

  • •Builds a few coherent stories, typically base, optimistic and pessimistic
  • •Moves several correlated inputs together within each scenario
  • •Captures how bad news tends to arrive in clusters, unlike sensitivity
  • •Earthilizer pessimistic case lowers both initial sales and growth at once
  • •Optional subjective probabilities give a probability-weighted expected NPV
  • •Tests only a handful of discrete cases, a limit simulation overcomes

Quick check

The key feature that distinguishes scenario analysis from one-at-a-time sensitivity analysis is that scenario analysis

Connected topics

NPV & AdditivitySensitivityBreak-EvenMonte CarloRisk vs Uncertainty

Sources

  1. Titman & Martin, Ch. 3
    Titman, S., & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
    Presents scenario analysis as the revaluation of a project under coherent base, best and worst cases.
How to cite this page
Dr. Phil's Quant Lab. (2026). Scenario Analysis. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-scenario-analysis
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