Concept

Capital recovery factor (CRF)

Overview

The capital recovery factor (CRF) is the multiplier that converts a one-time capital sum into the constant annual payment that would repay it, with interest, over the asset’s life — turning a stock of capital into an equivalent yearly flow. It’s the standard way to put up-front capex on the same annual footing as opex, so the two can be added into a levelized cost.

Body

What it does. Capital is spent once; operating cost recurs yearly. To combine them, express the capital as the yearly charge that, over the plant’s life and at a required return, is financially equivalent to the lump sum:

annual capital charge = CRF × total capex

           i (1 + i)ᴺ
CRF =  ─────────────────
         (1 + i)ᴺ − 1

i is the discount rate — the cost of capital; N is the asset life in years. Both are modeling choices, not given constants. As N grows large, CRF → i; for finite N it sits above it (the extra repays principal over a finite horizon). Annualize total capex — the loaded figure — not ISBL or equipment cost alone.

Why it’s the maturity-anchor tool. The CRF collapses the whole time-value calculation into one multiplier. For capital spent once and then run at roughly steady state, it gives the same answer as a full year-by-year discounted cash flow — without building one. The heavier DCF is reserved for when timing isn’t flat.

Typical magnitude. With i ~8–12% and N ~20–25 years, CRF lands roughly in the 0.10–0.13 range — an annual charge of about a tenth to an eighth of total capex. Spread over the plant’s output (set by the capacity factor), it becomes the capital share of levelized cost.

Limits & typical error

• It assumes one up-front outlay and uniform operation — exact only for capital spent once and a flat profile after. Staged capital, mid-life replacements, or a production ramp violate that; applying CRF to full capex from year one overstates the early charge, where a DCF is right.
• The result is highly sensitive to two assumed inputs — moving i from 8% to 12% raises CRF by ~a third; shortening N raises it further. Both are assumptions easy to set without justification, and the capital share swings on them.
• Real-vs-nominal mismatch is a classic error — a nominal i needs nominal (escalating) cash flows, a real rate real ones; mixing biases the annualized figure.
• It’s an equivalent levelization, not a financing schedule — a smooth annual equivalent, not the actual debt-service or equity cash flows; it abstracts gearing and the repayment profile.
• It ignores salvage, tax, and depreciation — residual value and the depreciation tax shield sit outside CRF; where they matter, a DCF carries them.

Mini-example

Annualizing the green ammonia plant’s capital. Total capex ≈ $1.0bn (the total-capex roll-up), i = 10%, N = 20 years — both round assumptions, not sourced terms:

CRF = 0.10·(1.10)²⁰ / ((1.10)²⁰ − 1) ≈ 0.117
annual capital charge ≈ 0.117 × $1.0bn ≈ $117M / yr

Over ~330,000 t/yr of output (1,000 t/day × 365 × 0.90 capacity factor), that’s a capital share of roughly $355/t — the number that goes into levelized cost alongside opex.

Edge case: change i to 12% and CRF rises to ~0.134 — annual charge ~$134M, capital share ~$405/t — a ~14% swing in capital cost per tonne from a single assumed input, nothing physical changed.

See also

• Total capex (battery-limits → total plant)
• Capex
• Cost of capital
• Discounted cash flow (DCF)
• Levelized cost (e.g., $/t NH₃)
• Capacity factor