Scenario and Sensitivity Analysis
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In short
Every valuation depends on assumptions that might be wrong, and the only responsible thing to do about that is to find out how much it matters.
Canonical data. Figures tie to Wexford Instruments and the DCF article. The market price of $12.00 is an illustrative teaching value.
That is what these two techniques are for. They are frequently confused, they are not interchangeable, and the more common one is the weaker one.
The difference
Sensitivity analysis moves one input at a time and holds everything else fixed. It answers: how much does the answer depend on this? Displayed as a grid or a tornado chart, it ranks the assumptions by influence — which is genuinely useful, because it tells you where to concentrate your thinking.
Scenario analysis moves several inputs together in ways that are internally coherent. It answers: what happens if the world turns out a particular way? A downturn does not politely reduce your growth assumption and leave everything else alone — it lowers growth, compresses margins, and raises the discount rate simultaneously, because the same conditions drive all three.
Which is why sensitivity analysis systematically understates the range. By construction it holds correlated variables still. The worked example measures the understatement.
Designing scenarios that mean something
The common approach — take the base case and flex everything ±20% — produces arithmetic rather than insight, because a 20% reduction in growth alongside an unchanged discount rate describes no world that could actually occur.
A useful scenario starts with a description, not a number. Write the world first — demand weakens, a competitor enters, input costs rise — and then ask what each input becomes in that world. The numbers follow the story, and they hang together because the story does.
Two disciplines follow. Coherence: every input in a scenario must be consistent with every other. And restraint: three or four scenarios is usually the practical limit, since beyond that they stop being distinct worlds and become noise.
The probability-weighting trap
The temptation, having built three scenarios, is to assign probabilities and compute an expected value. This feels rigorous and it defeats the purpose.
It collapses the range back into a single number — the very thing the exercise was performed to avoid — and it does so using probabilities that are themselves guesses, now buried inside a figure that looks like an answer. The output of scenario analysis is the range and the reasoning behind each end of it. A reader who takes away one number has thrown away everything the work produced.
Worked example
Worked example: three ways of measuring the same uncertainty (canonical figures, USD millions). One variable at a time. Holding terminal growth at 2% and varying only the discount rate from 8% to 10%, the DCF value runs from 446.6 to 332.2 — a range of 1.34×. A two-variable grid. Varying the discount rate across 8–10% and terminal growth across 1–3% gives a low of 303.9 and a high of 519.7 — 1.71×. Three coherent scenarios. Now write worlds rather than flex numbers. Downside — demand weakens, so interim growth 3%, terminal 1%, discount rate 10% to reflect higher perceived risk: 247.7. Base — interim 8%, terminal 2%, discount 9%: 381.2. Upside — the investment programme delivers, interim 12%, terminal 3%, discount 8%: 614.9. Range: 2.48×. The finding. The single-variable analysis reported a 1.34× range on the same underlying uncertainty that coherent scenarios show to be 2.48× — it understated the spread by roughly half, purely because it held correlated inputs still. And the trap, demonstrated. Weighting those three scenarios 25/50/25 gives 406.3 — a single, precise-looking figure that has discarded the 247.7-to-614.9 range which was the entire output of the work. (Canonical figures; independently verified. All values use the DCF article's five-year construction from free cash flow of 20.3; the two-variable grid's extremes are the 10% / 1% and 8% / 3% corners.)
Frequently asked
7 questions
What's the difference between sensitivity and scenario analysis?
Sensitivity moves one input at a time with everything else fixed, answering how much the answer depends on that input. Scenario analysis moves several inputs together in coherent combinations, answering what happens if the world turns out a particular way.
Why does sensitivity analysis understate risk?
Because it holds correlated variables still, and real conditions move several at once — a downturn lowers growth, compresses margins, and raises the discount rate together. On the illustration here, single-variable analysis reported a 1.34× range where coherent scenarios showed 2.48×.
How should I build a scenario?
Start with a description rather than a number. Write the world — demand weakens, a competitor enters, costs rise — then ask what each input becomes in that world. The numbers follow the story and hang together because the story does.
What's wrong with flexing everything ±20%?
It produces arithmetic rather than insight, because a 20% growth reduction alongside an unchanged discount rate describes no world that could actually occur.
How many scenarios should I build?
Three or four is usually the practical limit. Beyond that they stop being distinct worlds and become noise.
Should I probability-weight my scenarios?
It feels rigorous and defeats the purpose — it collapses the range back into the single number the exercise existed to avoid, using probabilities that are themselves guesses. On the illustration, weighting 25/50/25 gives 406.3 and discards the 247.7-to-614.9 range that was the whole output.
So what is the output of this work?
The range, and the reasoning behind each end of it. A reader who takes away one number has thrown away what the analysis produced.
References
- Investor.gov (SEC) — How to Read Financial Statements —
- SEC — Beginners' Guide to Financial Statements —
- Investor.gov (SEC) — Investor Bulletin: Performance Claims (projections presented as single figures conceal their assumptions) —
Educational and informational only — not investment advice, a recommendation, or an offer to buy or sell any security. Investing involves risk, including the possible loss of principal. Worked examples use fictional companies and figures.