Sensitivity Analysis

The decision tree ended with an uncomfortable jolt: drag one slider and the whole recommendation flips. That’s the general anxiety of every model — the answer rests on inputs you only guessed at. This lesson is the disciplined cure: a way to find which guess your conclusion actually hangs on, so you can stop fretting over the rest.

Every business plan is a chain of assumptions. Price will hold. Customers will show up. Costs will stay under control. The spreadsheet confidently prints a single answer — $800,000 profit — but that number is only as trustworthy as its weakest assumption. Sensitivity analysis (changing one input at a time to see how much the output moves) tells you exactly which assumption is the weak link. Once you know that, you know where to spend your research budget — and where it is safe to make a quick guess.

The model we will stress-test

We will use a stripped-down profit formula throughout this lesson:

Profit = (Price − Unit Cost) × Volume − Fixed Costs

Base case — the numbers the team agreed on:

Plugging in:

Profit = ($50 − $30) × 100,000 − $1,200,000
       = $20 × 100,000 − $1,200,000
       = $2,000,000 − $1,200,000
       = $800,000

Good. The base case is $800,000. Now the real question: which assumption, if wrong, wipes out that profit?

Varying one assumption at a time

The core mechanic of sensitivity analysis is simple: hold every assumption at its base value, nudge just one up and down over a plausible range, record what happens to profit, then move on to the next assumption. Repeat for every input. The result is a table of swings — how far profit can move if that single assumption is off.

Price ±10 %

Price is often the assumption the team feels most confident about — and most often wrong about. A 10 % range ($45 to $55) is realistic given competitive pressure or discounting.

At $45:  ($45 − $30) × 100,000 − $1,200,000 = $1,500,000 − $1,200,000 = $300,000
At $55:  ($55 − $30) × 100,000 − $1,200,000 = $2,500,000 − $1,200,000 = $1,300,000
Swing:   $300,000 to $1,300,000  →  ±$500,000 from base

A 10 % price miss cuts or adds half a million dollars. That is the biggest swing of any assumption.

Volume ±20 %

Volume (the number of units customers actually buy) is notoriously uncertain for new products. A ±20 % range is conservative.

At 80,000:   $20 × 80,000  − $1,200,000 = $1,600,000 − $1,200,000 = $400,000
At 120,000:  $20 × 120,000 − $1,200,000 = $2,400,000 − $1,200,000 = $1,200,000
Swing:   $400,000 to $1,200,000  →  ±$400,000 from base

Unit cost ±10 %

Unit cost (the variable cost to produce or deliver each unit — materials, labour, fulfilment) moves with supplier prices and operational efficiency.

At $33:  ($50 − $33) × 100,000 − $1,200,000 = $1,700,000 − $1,200,000 = $500,000
At $27:  ($50 − $27) × 100,000 − $1,200,000 = $2,300,000 − $1,200,000 = $1,100,000
Swing:   $500,000 to $1,100,000  →  ±$300,000 from base

Fixed costs ±10 %

Fixed costs (rent, salaries, insurance — the bills you pay regardless of volume) feel like the big scary number at $1.2 M. But watch what happens when they shift.

At $1,320,000:  $2,000,000 − $1,320,000 = $680,000
At $1,080,000:  $2,000,000 − $1,080,000 = $920,000
Swing:   $680,000 to $920,000  →  ±$120,000 from base

The largest cost line in the model produces the smallest swing. Why? Because a 10 % change on $1.2 M is only $120,000 — and fixed costs have no leverage with volume. Price, by contrast, multiplies across every single unit.

The tornado chart

A tornado chart is a horizontal bar chart where each bar represents one assumption’s full swing around the base case, sorted widest-on-top and narrowest-on-bottom. The sorted shape (wide at the top, narrow at the bottom) is why it is called a tornado. The top bars are where to spend your diligence.

The takeaway is stark: price drives five times more swing than fixed costs — even though fixed costs look like the big scary number. If you spend a month negotiating a lease to save 10 % on fixed costs, you save $120,000 in expected profit uncertainty. If you spend the same month stress-testing your pricing strategy, you protect $500,000.

What the tornado tells you to do

Reading the chart top-to-bottom gives a direct prioritisation list:

1. Price — nail down your pricing power. Talk to customers. Run pricing experiments. Understand competitor moves. This is where bad assumptions kill plans.
2. Volume — validate demand. A pilot, a waitlist, a small test market. Getting ±20 % tighter on volume is worth more than any other data-gathering effort.
3. Unit cost — get supplier quotes locked in. Understand your variable cost drivers.
4. Fixed costs — yes, model them, but once they are known (signed lease, headcount plan) they barely move the needle. Don’t over-invest here.

This is the payoff of the analysis: don’t research every assumption equally. The tornado tells you the few inputs that actually move the decision, so you concentrate time and money where it changes the answer.

From sensitivity to scenario analysis

Sensitivity analysis is a one-at-a-time tool. That is its strength for ranking — and its limitation for realism.

Scenario analysis (also called what-if analysis) is the practice of varying several assumptions together into coherent stories: a best case (high price, high volume, low cost), a base case, and a worst case (low price, low volume, high cost). Because in reality assumptions move together — a price war usually comes with volume pressure at the same time — scenarios are more realistic than single-variable swings.

Use both: tornado to rank priorities, scenarios to stress-test the full picture.

Summary

Sensitivity analysis is a one-variable-at-a-time diagnostic that turns a single-point forecast into a ranked priority list. The tornado chart makes the ranking visual and immediate. In our model, a 10 % price miss creates a $500,000 swing; a 10 % fixed-cost miss creates only a $120,000 swing. That gap tells every business analyst exactly where to spend their next week.

In one breath

Sensitivity analysis nudges one input at a time over a plausible range, holding the rest fixed, and records how far the output swings — turning a single confident number into a ranked list of what to worry about. Plotted as a tornado chart (bars sorted widest-on-top), it shows at a glance that in our profit model price swings profit ±$500k while the scary-looking $1.2M fixed costs swing it only ±$120k — because price has leverage, multiplying across every unit, while fixed costs hit profit dollar-for-dollar. So research the top bars (price, volume) and stop over-investigating the bottom ones. Two honest limits: the bar width depends on the range you chose (a wide implausible range fakes importance), and one-at-a-time misses correlated shocks — so pair the tornado with a worst-case scenario that moves several inputs together.

Practice

A question to carry forward

The tornado told us which input to worry about — price, then volume. But notice what it didn’t tell us: how likely each value is. We said price could land anywhere from $45 to $55, and treated both ends as equally worth charting. In reality $50 is far more probable than $45, and the four inputs don’t move one at a time — they wobble all at once, every day.

So the question to carry forward is: instead of nudging one knob at a time between two endpoints, what if you turned all the knobs at random — thousands of times — drawing each from its own probability distribution? You’d get not a swing but a full picture: not “profit could be $300k or $1.3M,” but “there’s a 2.3% chance we actually lose money.” The next lesson is Monte Carlo simulation — sensitivity analysis grown all the way up.