Concept

Fixed vs. variable cost

Overview

Fixed and variable costs are the two classes a cost falls into by how it responds to output: a variable cost rises and falls with how much the plant makes; a fixed cost stays roughly constant regardless. The split determines how a process’s per-unit cost responds to utilization — and so which costs a low-output year hurts and which it doesn’t.

Body

The distinction. Variable costs are proportional to production — feedstock and energy per unit, consumables, per-unit waste handling. Fixed costs are incurred to have the capacity at all, independent of output over the normal range — operating labor, maintenance, overheads, and, critically, the annualized capital charge (capex via the CRF).

Why it drives per-unit cost. Total annual cost is fixed + variable_per_unit × output, so:

cost per unit = fixed / output  +  variable_per_unit

The fixed term is spread over output, so per-unit fixed cost falls as 1/output — for a given nameplate, as 1/capacity factor. The variable term is roughly constant per unit. Utilization moves the fixed share and leaves the variable share alone.

Annualized capital is the big fixed cost. Because CRF × total capex is a fixed annual charge, a capital-intensive process is fixed-cost-heavy — per-unit cost sensitive to utilization, hyperbolic at low capacity factor. A feedstock-dominated process is variable-cost-heavy — per-unit cost flat with utilization, tracking input prices. The fixed/variable mix is the cost structure.

Fixed only over a range. A fixed cost is fixed within a capacity range and time horizon, not absolutely. Adding a train or crew steps it up (see numbering up / down); over a long enough horizon, every cost becomes variable.

Limits & typical error

• The clean dichotomy is an idealization — maintenance is partly fixed, partly throughput-driven; labor comes in discrete crews that step up. Forcing every cost into a pure bin misstates how total cost responds between the extremes.
• “Fixed” depends on the range and horizon assumed — a cost fixed at design throughput isn’t fixed across an expansion, and none is over the long run; applying the label outside its range breaks it.
• Misclassifying the capital charge breaks the utilization response — annualized capex is fixed; treating it as variable removes the 1/CF behavior that dominates a capital-intensive plant’s sensitivity to a low-output year.
• Confusing economy of scale with variable-cost behavior — per-unit cost falling with plant size is a capital (fixed-cost-spreading and six-tenths) effect; per-unit variable cost is roughly flat with scale. Conflating them expects the wrong mechanism.

Mini-example

Green ammonia’s per-tonne cost shows the two classes responding differently to utilization. At capacity factor ~0.90 (continuous baseline), the cost splits into a fixed part — annualized capital ~$355/t (from CRF) + fixed opex ~$50/t — and a variable part, mainly electricity ~$400/t. Run the same plant at ~0.45 and the fixed ~$405/t roughly doubles per tonne to ~$810/t (spread over half the output), while the variable ~$400/t is essentially unchanged.

Edge case: gray ammonia, less capital-intensive and more feedstock-driven, carries a larger variable share, so its per-tonne cost is flatter across utilization and tracks the gas price more than uptime — the opposite cost-structure response to the same change in capacity factor.

See also

• Opex
• Capacity factor
• Capital recovery factor (CRF)
• Levelized cost (e.g., $/t NH₃)
• Feedstock & energy cost
• Numbering up / down