Does the plant pay?

A design that works but loses money won't be built. Engineers estimate costs early and refine them as the design firms up; an early estimate can easily be 30% off, a final one 10%.

Equipment and plants get cheaper per tonne as they get bigger. The six-tenths rule estimates the cost of a different size from a known one: cost₂ = cost₁ × (capacity₂ ÷ capacity₁)^0.6. A plant that cost $10 million for 100,000 tonnes a year would cost about 10 × 2^0.6 = $15.2 million at 200,000: double the size for about 50% more money. Cost indexes adjust old prices to today's.

Operating costs come every year: raw materials (often the biggest share), utilities like steam, power and cooling water, labour, maintenance, catalyst, and overheads. Revenue minus operating costs is the yearly cash flow the plant brings in.

Payback time is the simplest test: capital cost ÷ yearly cash flow. A $5 million project earning $1.25 million a year pays back in 4 years. It's easy to understand but ignores what happens after payback and the fact that money later is worth less than money now.

Net present value (NPV) fixes that. Each future year's cash is divided by (1 + i)ⁿ, where i is the interest rate the company requires and n the year, then added up and the investment taken off. Spend $1000 now for $400 a year for 3 years at 10%: 400/1.1 + 400/1.21 + 400/1.331 = 363.6 + 330.6 + 300.5 = $994.7, so NPV = −$5.3. It pays back in 2.5 years yet just fails to earn 10%. A positive NPV means the project beats the required return.