Guide · Layer 3

Capital Costs

Written for: seed / Series A scientist-founder

Before building capital from the equipment up, get a top-down baseline: what does a capital project of this size cost? Pull three to five references for a comparable plant. That high-level anchor catches an equipment build-up that’s drifted an order of magnitude off before you’ve sunk a day into it.

Size and cost the equipment

Build capex from the equipment up — not every pump and valve, just the few items that actually carry the cost:

• Size the 2–3 heavy hitters per unit operation to their duty from the upstream flow, and peanut-butter the small stuff at ~20%
• Scale from a known cost with the six-tenths rule — C₂ = C₁·(S₂/S₁)ⁿ. Half-size costs a bit more than half; double costs a bit less than double. Read the per-class exponent and move on
• Switch to numbering up when the size step gets big — past ~2–3× you’re not building one giant unit, you’re building several (modular units in parallel). Keep scaling there and you claim an economy of scale modular units don’t deliver
• Be picky with your sources — good data is scattered around the internet, best ones first:
  • an existing TEA for your process (an old NREL/Aspen table)
  • a public equipment-cost database
  • a similar-but-different industry
  • an auction price

🧭 Coach’s Read

Almost all the capital signal is in those few big items, so that’s where the hours go. Don’t tune the six-tenths exponent — across the normal range it barely moves the answer; put that hour into a better reference cost instead. And don’t chase any single number for more than a day or two: once three roughly-agreeing sources point the same direction, you’ve got your bracket.

Build up to the true capex number

Purchased equipment is only a fraction of the total. The number that actually gets financed and annualized is total capital investment — several times the equipment cost. The build-up, rung by rung:

• Purchased equipment + delivery & installation → installed ISBL (the process units inside the fence)
• + OSBL — utilities, storage, and the other off-sites the system boundary puts in
• + indirects (engineering, fees) + contingency — the expected cost of what you haven’t figured out yet, sized to the accuracy class
• + working capital → total capital investment

A fast gut check: the Lang factor — total capital ÷ purchased equipment — usually lands around 4–6×. Down at 2–3×, you’re probably undercounting something. This total is the overnight cost: what you’d pay to build the whole plant today, financing aside.

🧭 Coach’s Read

When someone asks “what’s the capex?”, quote this number — the inner figures can be half the real plant cost, so quoting equipment or ISBL halves your cost per tonne by accident. Don’t drop contingency to look tighter; that reports your best case as if it were the expected one. And watch what each factor already contains — a Lang factor bundles installation, OSBL, and indirects, so applying it and then adding OSBL double-counts.

Annualize it

We now have a yearly cost to run the plant and one very large number to build it, with no obvious way to add them. Annualizing turns that one-time capex into a per-year charge you can add to opex and divide by output. The tool is the capital recovery factor: annual capital charge = CRF × total capex.

• CRF is just the annuity formula — it spreads the capital over the plant’s life and charges for the money tied up in it
• Straight-line depreciation gets this wrong — it charges nothing for capital. A $200M plant over 20 years looks like $10M/yr that way; with a real cost of capital it’s closer to ~$23M/yr, and that ~2× gap is often what decides whether the economics pencil out
• It rides on two assumptions — a discount rate (cost of debt is roughly 8–12%) and a life N. Pick a reasonable rate and show the sensitivity rather than agonizing

🧭 Coach’s Read

Use CRF, not a full DCF, at this stage — a DCF bolts on a price path, a ramp, and a tax schedule, none of which make an uncertain capex more accurate; it mostly buys false precision. The one thing CRF is sensitive to is the discount rate — 8% to 12% moves the annual charge about a third with nothing physical changing — so state your rate, and sensitize it in Layer 4.