Plant Design and Economics
Plant design and economics tests whether you can cost equipment, capitalise a plant and judge whether a project is worth building. Expect cost estimation rules, depreciation, profitability measures and one or two optimisation or safety items.
Core rules
- Six-tenths rule. C₂ = C₁(Capacity₂/Capacity₁)^0.6 for equipment of the same type and material; the exponent is not universal, so use it only as stated.
- Cost indices. Escalate with C₂ = C₁(I₂/I₁), typically using the CEPCI.
- Lang factors. Fixed capital = Lang factor × delivered equipment cost; the factor is larger for solids-handling and fluid-processing plants.
- Depreciation. Straight line: (P − S)/n. Declining balance applies a fixed fraction to the book value and never quite reaches the salvage value; MACRS uses prescribed percentages with a half-year convention.
- Profitability. Payback period ignores the time value of money; NPV discounts at the minimum acceptable rate of return; IRR is the discount rate making NPV zero.
- Break-even. Fixed costs divided by contribution per unit; working capital covers inventories and receivables and is recovered at the end of the project.
Worked example
A unit costs $50,000 at a capacity of 100 t/day. Estimate the cost of a 300 t/day unit. Ratio = 3, so C₂ = 50,000 × 3^0.6 = 50,000 × 1.933 = $96,650. Note the cost rises by only 93% for a threefold capacity increase - that is the economy of scale, and it is exactly why the exponent must be applied to capacity rather than to cost.
Traps
- Applying the six-tenths rule to a whole plant instead of individual equipment.
- Multiplying a Lang factor by the purchased cost of a single item rather than the total delivered equipment cost.
- Escalating with an index ratio applied in the wrong direction.
- Depreciating working capital, or depreciating below the salvage value.
- Reporting IRR when the cash flow changes sign more than once and multiple roots exist.