Verified against ChatGPT · 2026-08-13
Calculate the break-even point for a new product or offering and show exactly how sensitive it is to price
Computes the break-even unit volume and revenue for a new product line from fixed costs, variable costs, and price, then shows how the break-even point shifts if price or cost assumptions change, instead of handing over a single static number.
The prompt
Ready to copy — highlighted parts are example details you can swap.
Calculate the break-even point for the offering described below, and show how sensitive that number is to the assumptions behind it — a single break-even figure without sensitivity context is easy to misread as more certain than it is. FIXED COSTS $45,000 for initial tooling, setup, and the first year's fixed licensing fee. VARIABLE COST PER UNIT $18 per unit (materials, packaging, and per-unit shipping). PLANNED SELLING PRICE $42 per unit. UNCERTAIN COST OR PRICE ASSUMPTIONS Not fully sure the $18 per-unit cost will hold if a key supplier raises prices, which they've hinted at. STEP 1 — BASE CALCULATION Show the contribution margin per unit (price minus variable cost), then the break-even unit volume (fixed costs divided by contribution margin) and break-even revenue, with the formula and inputs shown at each step so the math can be checked line by line. STEP 2 — SENSITIVITY Recalculate break-even volume for a 10% and 20% swing in the selling price (both up and down) and, separately, for the same swings in variable cost per unit, holding the other variable constant in each case. Present this as a small table so the requester can see at a glance how much the break-even point moves for a given change in either lever, rather than just describing the sensitivity in prose. STEP 3 — CONTEXT CHECK If any uncertain assumptions were listed, state plainly which one, if it turned out wrong, would move the break-even point the most — the single input worth double-checking before relying on this number. Do not state a specific timeframe for reaching break-even volume (e.g. "you'll hit this in 4 months") unless the requester has provided an expected sales rate; if no sales rate was given, say the timeframe isn't calculable from what's provided rather than guessing one. OUTPUT FORMAT 1. Base case: contribution margin, break-even units, break-even revenue, with formulas shown. 2. Sensitivity table: price/cost change | new break-even units | % change from base. 3. The single most consequential uncertain assumption, named directly. 4. Explicit note on timeframe-to-break-even being uncalculable if no sales rate was given.
Customize
Optional — swap in your own details for the highlighted parts above.
Why this works
Requiring the sensitivity table as a mandatory second step, not an optional add-on, is what stops the output from being a single static number that looks more certain than it is — a break-even figure on its own invites the reader to treat it as fixed, when in reality a 10% price cut (a common early-stage pricing adjustment) might move the break-even volume by a much larger percentage than 10%, and that nonlinearity is exactly the kind of thing that's invisible until it's shown side by side in a table. Holding one variable constant while varying the other in each sensitivity pass, rather than varying both simultaneously, is a deliberate simplification that keeps the table readable and interpretable — varying both price and cost together would produce a matrix of scenarios that's more mathematically complete but harder to read at a glance, and for a first-pass break-even sensitivity check, isolating one lever at a time is the more useful default. The refusal to state a break-even timeframe without a given sales rate addresses a specific pattern where GPT-5.1, asked for a break-even analysis, will often helpfully add "at this rate you should break even in about 6 months" by silently assuming a sales velocity that was never actually provided — that fabricated assumption can be more consequential to a business decision than the break-even unit count itself, since it implies a specific runway need, so refusing to guess it and instead flagging the missing input keeps the output honest about what it can and can't calculate from what was given.
What you get back
Contribution margin: $42 - $18 = $24/unit. Break-even units: $45,000 / $24 = 1,875 units. Break-even revenue: 1,875 x $42 = $78,750. Sensitivity: a 10% price cut to $37.80 raises break-even units to roughly 2,273 (+21%) — the break-even point is more sensitive to price than the percentage price change itself. Most consequential uncertain assumption: the per-unit cost holding at $18 if the supplier raises prices as hinted.
Verified against
ChatGPT GPT-5.1 · 2026-08-13
Changelog
- 2026-08-13 — Initial publish, verified against ChatGPT GPT-5.1.
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