Break-even answers one question: at what volume does contribution cover fixed cost? It is the right tool when the decision is “is there enough demand to pay for this machine, shift, or plant.” It is the wrong tool when cash arrives in uneven years, when capital is scarce versus other projects, or when the interviewer is really asking for a profitability diagnosis.
Say the equation out loud before you multiply. Interviewers grade the setup more than the last digit.
The only formula you need (with units)
Contribution per unit ($/unit) = price − variable cost per unit
Break-even volume (units / period) = fixed cost ($ / period) ÷ contribution per unit ($/unit)
Fixed cost must be in the same period as the volume. Annual lease with monthly scans is how people invent a 12× error. If there is an upfront machine, either amortize it into annual fixed cost (with a stated life) or treat the first year as “cash break-even including capex” and say which one you are doing.
| Piece | Unit | What goes in |
|---|---|---|
| Price | $ / unit | What the payer actually remits, not list |
| Variable cost | $ / unit | Costs that move with that unit |
| Fixed cost | $ / year | Costs that do not move in the relevant range |
| Break-even | units / year | Fixed ÷ contribution |
If contribution is negative, stop. No volume saves a unit that loses cash every time you sell it.
Worked example: district hospital MRI
Prompt. Lakeshore District Hospital wants a second MRI so neurology stop referring 18 patients a week to a private imaging center 40 minutes away. Magnet quote: $2.4m. Annual service contract $180k. One salaried tech team $310k. Space is already owned. Variable cost per scan $70. Blended reimbursement $410 per scan. The CFO asks how many scans until this is not a toy.
Pick the break-even you mean. Partners care about ongoing break-even after the magnet is sunk, and sometimes about year-1 cash including capex. Do both. Do not mix them.
Ongoing (magnet sunk). Fixed = 180k + 310k = $490k / year. Contribution = 410 − 70 = $340 / scan. Break-even = 490,000 / 340 ≈ 1,440 scans / year ≈ 28 per week.
Year-1 cash including capex. Add $2.4m. Total to recover in twelve months: $2.89m. Volume = 2,890,000 / 340 ≈ 8,500 scans. That is 163 a week — a fantasy for a district hospital. Name that standard and reject it unless the board explicitly wants cash payback in year 1.
Capacity check. One magnet, 12 hours a day, 5.5 days a week, 45 minutes per slot: 16 slots/day × 5.5 × 52 ≈ 4,580 slots / year. Ongoing break-even of 1,440 is 31% utilization. Physically fine.
Demand check. Leakage is 18 referrals a week = 936 scans a year. The first magnet runs 3,100 scans and is 12% overbooked. Overflow plus repatriated leakage ≈ 1,310 scans. That is 130 scans short of 1,440 if the second magnet only gets overflow plus leakage.
Recommendation. Do not approve $2.4m on leakage alone. Lock ~300 incremental scans from rural clinic contracts, or keep Saturdays on the existing magnet (cheaper capacity). Risk: neurologists still prefer the private center’s 48-hour report SLA. Next step: SLA and rural volume in writing.
When break-even is the wrong tool
Uneven multi-year cash. A plant with a two-year ramp, a PE hold, or anything with a terminal value is NPV or ROI / payback. Break-even ignores timing and discounting.
The question is which driver moved. Break-even will not tell you that mix shifted to Medicaid. That is a profitability bridge.
Negative contribution. If reimbursement is $410 and variable cost is $430, the intercept does not exist. Say that.
Shared fixed costs. Allocating the hospital CEO to the MRI and then declaring it unviable is a spreadsheet trick. Only include fixed costs that arrive with the decision.
The mistake that is unique to break-even
Mixing list price with collected price. Hospitals bill $1,800 and collect $410. Using $1,800 produces a toy break-even of ~283 scans — “we will smash this” — and a wrong buy. Always ask what you actually receive per unit.
A close second: forgetting that break-even volume must fit on the asset. 8,500 scans on a 4,580-slot magnet is not a stretch goal. It is physically false.
What to say out loud
“I will use contribution of collected price minus variable cost. Fixed costs are only those that come with the MRI. I will quote ongoing break-even in scans per year, then check demand and slot capacity.”
Then run the division. Then interpret.
Drill the setup, not the last digit
Timed quick-math: contribution, divide, then a one-line so-what. Units stay on every line.