The five-minute factory math every professional runs, MBA Training, MBA Training
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The five-minute factory math every professional runs
# The five-minute factory math every professional runs
A plant manager tells the board that utilization is "up nicely" and margins are "healthy." Nobody asks a follow-up question, and the slide moves on. Thirty seconds of arithmetic would have shown utilization was 61% (below the level most plants need to cover fixed costs) and that "healthy" margins were actually thinner than last year's. This lesson gives you those thirty seconds.
Why this matters before you read a single benchmark
Manufacturing conversations are dense with numbers that sound precise but often aren't checked. Capacity, cost per unit, breakeven, inventory days: these four calculations let you sanity-check almost any factory claim in real time, without a spreadsheet. Investors, plant tours, supplier negotiations, and board decks all lean on them.
The essential vocabulary first
Capacity utilization: the percentage of maximum possible output a plant actually produces. A plant that can make 100,000 units a month but makes 70,000 runs at 70% utilization.
OEE (Overall Equipment Effectiveness): a stricter measure combining availability (uptime), performance (speed vs. ideal), and quality (good units vs. total). World-class OEE is often cited around 85%; most plants run 40 to 60% (estimate, widely cited industry benchmark, see OEE reference from Vorne).
Contribution margin: revenue per unit minus variable cost per unit (materials, direct labor, energy tied to that unit). It's what's left to cover fixed costs and profit.
Breakeven volume
: the number of units where total contribution margin equals fixed costs, profit is zero.
Days of inventory (or DIO, Days Inventory Outstanding): how many days of sales are sitting in inventory. Formula: (average inventory / cost of goods sold) x 365.
BOM (Bill of Materials): the itemized list of raw materials and components needed to build one unit. It's the backbone of variable cost calculations.
Takt time: available production time divided by customer demand, the pace a line must run to match demand, not a cost metric but frequently confused with cycle time (the actual time to produce one unit).
The sample plant
Assume a mid-size auto-parts plant, the kind of numbers you'd see in a real operating review (illustrative, not from a specific company):
Maximum monthly capacity: 100,000 units
Actual monthly output: 61,000 units
Selling price per unit: $40
Variable cost per unit: $26 (materials $18, direct labor $6, energy $2)
Monthly fixed costs: $900,000
Average inventory value: $3.2 million
Monthly COGS: $6.5 million
Calculation 1: Capacity utilization
Formula: actual output / maximum capacity
61,000 / 100,000 = 61%
Context: most discrete manufacturing plants (auto parts, machinery, electronics assembly) target 75 to 85% utilization as healthy; anything below 70% for a sustained period usually signals demand softness, changeover losses, or overbuilt capacity. Utilization below 50% often triggers restructuring conversations. If someone says utilization is "up nicely" without a number, ask: up from what, and up to what percent of max?
Calculation 2: Contribution margin per unit
Formula: price per unit minus variable cost per unit
$40 − $26 = $14 per unit
Contribution margin ratio: $14 / $40 = 35%
This is the number that tells you how much each additional unit sold actually helps the business, before touching fixed costs like rent, salaried staff, or depreciation on machinery. If a sales team offers a 10% discount without recalculating this, margin can evaporate fast: a price cut to $36 drops contribution margin to $10, a 29% hit to profit contribution for the same volume.
Calculation 3: Breakeven volume
Formula: fixed costs / contribution margin per unit
$900,000 / $14 = 64,286 units per month
Compare this to actual output: 61,000 units. This plant is running below breakeven. That single comparison, output vs. breakeven, is the fastest way to know whether a "record production month" headline is actually good news or just less bad news.
Calculation 4: days of inventory (DIO)
Formula: (average inventory / COGS) x 365... but adjusted for monthly figures: (average inventory / monthly COGS) x 30
$3.2M / $6.5M x 30 = 14.8 days
Context: automotive parts suppliers often target 15 to 30 days of inventory given just-in-time (JIT) delivery expectations from OEMs (Original Equipment Manufacturers, the car makers themselves). Consumer goods manufacturers may run 45 to 60 days. Higher DIO ties up cash and raises obsolescence risk; lower DIO raises stockout risk if a supplier hiccups. Neither extreme is automatically "better," but a sudden jump in DIO quarter over quarter is a common early warning sign of slowing sales or a supply chain problem building up.
Quick reference: market scale for context (estimates, 2025 to 2026)
US manufacturing sector value added: roughly $2.8 to $2.9 trillion annually, about 10 to 11% of US GDP (estimate, US Bureau of Economic Analysis, bea.gov)
Eurozone manufacturing: roughly 15 to 16% of EU GDP, with Germany alone accounting for close to a quarter of EU manufacturing output (estimate, Eurostat, ec.europa.eu/eurostat)
Global Purchasing Managers' Index (PMI), a monthly survey-based indicator where above 50 signals expansion, below 50 signals contraction, is the single most-watched leading indicator in manufacturing boardrooms (S&P Global / ISM, published monthly)
These numbers matter less as trivia and more as calibration: when someone quotes a "10% growth" figure for a niche segment, you should have a rough sense of whether that's plausible against overall sector growth, which in mature US/EU manufacturing typically runs low single digits annually (estimate).
Knowledge check
1. A plant manager reports capacity utilization of 61% and calls it 'up nicely.' Why should this framing prompt a follow-up question?
2. What is the key distinction between capacity utilization and OEE (Overall Equipment Effectiveness)?
3. A company reports 'healthy margins' but doesn't specify which margin. Why does checking contribution margin specifically matter for a quick sanity check?
MULTIPLE CHOICE
4. Select ALL correct answers about why quick factory-math checks (utilization, contribution margin, breakeven, inventory days) are valuable in professional settings.
Select all the correct answers.
MULTIPLE CHOICE
5. Select ALL correct answers about Days of Inventory Outstanding (DIO) and its role in factory math.
Select all the correct answers.
The due-diligence habit: run the four checks together
When you see a plant's numbers in a pitch deck, earnings call, or supplier review, run this sequence:
1. Utilization vs. breakeven-implied utilization. Convert breakeven volume back into a utilization percentage (64,286 / 100,000 = 64.3%). If actual utilization (61%) is below breakeven utilization, the plant is losing money at the operating level, regardless of what net income shows after other adjustments.
2. Contribution margin trend, not just level. A stable 35% margin sounds fine until you learn it was 42% last year. Always ask for the prior period.
3. DIO direction. Rising DIO plus flat or falling utilization together often mean demand is softening faster than production has adjusted; that combination is a classic recession-lag signal in manufacturing.
4. Sanity-check the BOM. If variable cost per unit seems to have barely moved despite known input price swings (steel, resin, semiconductors), ask why. Either hedging is working, or the numbers are stale.
None of this requires a spreadsheet. It requires knowing which four numbers to ask for and doing the division in your head or on a napkin.
🎬 [VIDEO: "Capacity Utilization Explained" - youtube.com - search for recent explainer videos from manufacturing-operations channels covering capacity utilization and OEE with worked plant examples]
Key Takeaways
Four calculations cover 90% of factory-floor conversations: capacity utilization (output/capacity), contribution margin per unit (price minus variable cost), breakeven volume (fixed costs/contribution margin), and days of inventory ((inventory/COGS) x days).
Convert breakeven volume into a utilization percentage and compare it directly to actual utilization; this single comparison reveals whether a plant is structurally profitable at current volumes.
Contribution margin in isolation is meaningless; always compare it to the prior period to see the trend, not just the snapshot.
US manufacturing is roughly 10 to 11% of GDP, EU manufacturing roughly 15 to 16% of GDP (both estimates); use these as rough sanity checks against sector growth claims, not precise benchmarks.
These calculations take under five minutes and require no tools beyond the four numbers themselves, which is exactly why insiders run them live, in the room, before the next slide loads.