Cost per unit at different volumes, extra orders using spare capacity, yield, rejection rate, first pass yield and rolled throughput yield.
By Manoj Sahukar· October 2026 · 10 min read
How numbers are rounded on these pages. Calculations are done at full precision and rounded only at the end, half up. Rupee amounts are rounded to the nearest rupee unless shown with paise, in which case to the nearest paisa. Percentages are shown to two decimal places; payback periods in years, and ratios such as degree of operating leverage, to two decimal places. Quantities you must start, buy or sell to reach a target are rounded up to the next whole unit or kg. Depreciation uses textbook straight line and written down value methods, not the rates or lives set by tax or company law. All examples and quiz questions are Hypothetical: they show the method, not real prices or rates.
Capacity utilisation and cost per unit at different volumes
Capacity utilisation is how much of what the plant could make it actually makes. Because fixed costs are spread over the units made, cost per unit falls as utilisation rises, and rises when the plant runs half-empty.
When there is spare capacity and fixed costs will not change, an extra order is worth taking if its price is above variable cost: every unit adds contribution. Judging it against full cost per unit gives the wrong answer. Check that the order does not need overtime, a new shift or extra tooling (step costs), and that it will not undercut your normal prices.
The standard formulas
Capacity utilisation % = Actual outputCapacity output × 100
Cost per unit at a volume = Variable cost per unit + Fixed costsUnits made
Extra orderExtra order profit (spare capacity, no change in fixed costs) = Units × (Price − Variable cost per unit)
Target cost per unitUnits needed for a target cost per unit = Fixed costsTarget cost − Variable cost per unit
Terms used
Capacity
The output a plant can make in a period under normal working (shifts, maintenance) assumptions.
Capacity utilisation
Actual output as a percentage of capacity.
Spare (idle) capacity
Capacity not being used.
Step cost
A fixed cost that jumps once output passes a level, such as a new shift.
Worked examples
HypotheticalBasicHow full is the plant?
A moulding plant can make 50,000 parts a month and made 35,000.
HypotheticalAdvancedAn extra order below full cost
At 35,000 parts, an OEM offers an extra order of 10,000 parts at ₹80, below the ₹100 full cost. Fixed costs stay ₹14,00,000.
Extra contribution = 10,000 × (₹80 − ₹60) = ₹2,00,000 more profit a month
Average cost per part at 45,000 parts = ₹60 + ₹14,00,000 ÷ 45,000 = ₹91.11
Worth taking, provided it fits in spare capacity and does not set the price for regular orders.
Scrap, yield, rejection and first pass yield
Not everything that goes into a process comes out as good product. Yield is the good output as a share of input. Rejection rate is the share of inspected units that fail. Scrap is material or units that cannot be used (some may be sold as scrap).
First pass yield (FPY) counts only the units that pass the first time, without rework. Rework hides problems: a line can have 98% final yield but only 94% FPY. When a product passes through several stages, multiply the stage FPYs to get rolled throughput yield (RTY): the chance a unit gets through every stage right first time.
Yield losses raise cost per good unit, because you pay for all the input but can sell only the good output.
The standard formulas
Yield % = Good outputInput × 100Rejection rate % = Units rejectedUnits inspected × 100
First pass yield % = Units passing first time (no rework)Units entering the process × 100
Rolled throughput yield = FPY1 × FPY2 × … × FPYn
Cost and planningInput needed = Good output requiredYieldCost per good unit = Total cost − Scrap sale valueGood units
Terms used
Yield
Good output as a percentage of input (units or kg).
Scrap
Material or units that cannot be used as product.
Rejection rate
Share of inspected units that fail inspection.
Rework
Fixing a defective unit so it passes.
First pass yield (FPY)
Share of units that pass a process the first time without rework or scrap.
Rolled throughput yield (RTY)
The product of the FPYs of all stages.
Worked examples
HypotheticalBasicFPY versus final yield
10,000 castings were made. 9,400 passed first time, 400 were reworked and then passed, and 200 were scrapped.
HypotheticalIntermediateMaterial yield and cost per good kg
1,000 kg of steel at ₹70 a kg gives 850 kg of good parts; the rest is sold as scrap at ₹20 a kg.
Yield = 850 ÷ 1,000 × 100 = 85.00%
Steel needed for 2,000 kg of good parts = 2,000 ÷ 85% = 2,352.94, so buy 2,353 kg
Net material cost per good kg = (₹70,000 − 150 × ₹20) ÷ 850 = ₹78.82, against ₹70 on the invoice
HypotheticalAdvancedRolled throughput yield over three stages
Machining, plating and assembly have first pass yields of 98%, 95% and 97%.
RTY = 0.98 × 0.95 × 0.97 = 0.90307 = 90.31%
Of 10,000 units started, about 9,031 go through all three stages right first time; the rest need rework or are scrapped.
The plating stage loses most; that is where improvement pays first.
Quiz: capacity utilisation and yield
Pick an answer to see at once whether it is right, with a short explanation. Each question takes one try; your score appears at the end. No answers are sent anywhere. (Without JavaScript, open “Show answer” under each question.)