Chemegate
Home/Topics/Applied/Plant Design & Economics
Topic Guide

Plant Design
& Economics Guide

Cost estimation, depreciation, payback period, NPV, and rate of return for the GATE Chemical Engineering paper.

Practice

Solved PYQs →

Overview

Plant Design & Economics is where chemical engineering meets the balance sheet, the section that asks whether a technically sound process is also a financially sound investment. In the GATE CH syllabus it's a smaller but very predictable section: a handful of standard formulas (cost estimation, depreciation, payback period, net present value) that repeat across years with different numbers, making it one of the highest marks-per-minute-of-study subtopics on the whole paper.

The syllabus covers two related but distinct skills. The first is estimating capital and operating costs before a plant exists, using capacity-based cost scaling (the six-tenths-factor rule), cost indices to adjust historical cost data for inflation, and total capital investment breakdowns (fixed capital + working capital). The second is evaluating whether that investment is worthwhile over time, using depreciation methods (straight-line, declining-balance) to spread capital cost against taxable income, and profitability measures (payback period, net present value, rate of return) that account for the time value of money.

Every numerical in this section reduces to careful bookkeeping with a formula and a calculator, there's no conceptual subtlety on the level of, say, non-ideal VLE. That makes it one of the best sections to lock in as reliable marks: memorize the half-dozen formulas below, practice reading which one a given word problem is asking for, and this section becomes fast, accurate points on exam day.

Real GATE CH PYQ Frequency (2024–2026)

2024202520263-Yr Avg
2222

Computed directly from 6 real questions tagged to this topic across our GATE CH 2024–2026 archive, averaging 2 questions/year. Browse the underlying 6 questions for this topic in the PYQ archive, or see the full topic weightage comparison across all topics.

GATE Weightage

Plant Design & Economics typically contributes 2–4 questions (about 3–6 marks) to the GATE CH paper, concentrated in cost estimation, depreciation, and profitability (payback/NPV) numericals.

Sub-areaApprox. Marks
Cost estimation (capacity scaling, cost indices)~1–2
Depreciation methods~1
Profitability (payback, NPV, rate of return)~1–2

Sub-area split is a directional estimate (our archive doesn't tag marks at this granularity), for the real, computed topic-level total, see "Real GATE CH PYQ Frequency" above.

Key Subtopics

1

Capital cost estimation

The six-tenths-factor rule for scaling equipment cost with capacity, and cost indices (e.g., CEPCI) for adjusting historical cost data to a current year.

2

Total capital investment

Fixed capital investment (equipment, installation, piping, instrumentation) plus working capital (inventory, accounts receivable, cash on hand) needed to start and run the plant.

3

Operating costs

Fixed costs (independent of production rate, labor, insurance, property tax) versus variable costs (raw materials, utilities, scaling with output).

4

Depreciation

Straight-line depreciation (equal annual charges) and declining-balance depreciation (larger charges early, useful for accelerated tax benefit) as methods for allocating capital cost over an asset's useful life.

5

Time value of money

Present worth and future worth factors that discount future cash flows to a common basis, the foundation for every profitability measure below.

6

Payback period

The simplest profitability measure, time required for cumulative cash flow to recover the initial investment, ignoring the time value of money.

7

Net present value (NPV) & rate of return

NPV discounts all future cash flows to present value at a chosen interest rate; the internal rate of return is the discount rate at which NPV = 0.

8

Equipment replacement & break-even analysis

Comparing an aging asset's rising maintenance cost against a replacement's capital cost, and break-even capacity where total revenue equals total cost.

Essential Formulas

Full formula reference →

C2C1=(S2S1)0.6\dfrac{C_2}{C_1} = \left(\dfrac{S_2}{S_1}\right)^{0.6}

Six-tenths-factor rule for scaling equipment cost C with capacity S

C2=C1×I2I1C_2 = C_1 \times \dfrac{I_2}{I_1}

Cost index scaling, adjusts a historical cost C1 (index I1) to present-day cost C2 (index I2)

D=C−SvnD = \dfrac{C - S_v}{n}

Straight-line depreciation, original cost C, salvage value Sv, useful life n years

Dt=C(1−f)t−1fD_t = C(1-f)^{t-1}f

Declining-balance depreciation in year t, with fixed depreciation rate f

PW=FW(1+i)nPW = \dfrac{FW}{(1+i)^n}

Present worth of a future cash flow FW, n years away, at interest rate i

Payback period=Fixed capital investmentAnnual cash flow (avg.)\text{Payback period} = \dfrac{\text{Fixed capital investment}}{\text{Annual cash flow (avg.)}}

Simple payback period, ignores the time value of money

NPV=∑t=0nCFt(1+i)tNPV = \sum_{t=0}^{n} \dfrac{CF_t}{(1+i)^t}

Net present value, sum of all discounted cash flows, including the initial (negative) investment at t = 0

NPV(IRR)=0NPV(IRR) = 0

Internal rate of return (IRR), the discount rate that makes NPV exactly zero

Break-even capacity: R(Q)=CF+CV(Q)\text{Break-even capacity: } R(Q) = C_F + C_V(Q)

Break-even point where total revenue R equals total cost (fixed CF plus variable CV) at production rate Q

Visual Reference

An industrial factory exterior with a smoking chimney
The capital investment every cost-estimation formula in this guide is ultimately sizing — a real plant, not an abstract number on a balance sheet. Unknown author, CC0, via Wikimedia Commons.

Derivations & Physical Insight

Why the Six-Tenths-Factor Rule Uses an Exponent Less Than 1

Equipment cost doesn't scale linearly with capacity because a lot of the cost is tied to surface area (shells, heads, jackets) or component count (nozzles, supports), which grow more slowly than volume or throughput capacity as a piece of equipment gets bigger. A vessel's volume scales with the cube of a characteristic length, but its shell surface area, which drives most of the material and fabrication cost, only scales with the square, so cost per unit capacity actually falls as scale increases. This is the physical basis for economies of scale in process equipment.

The exponent 0.6 is an empirical average across many equipment types (individual pieces of equipment range roughly from 0.3 to 0.9 depending on how area-dominated versus volume-dominated their cost driver is), which is why it's called a "rule of thumb" rather than derived from a single physical law, but the underlying reason it's below 1 (rather than above) is always this same area-versus-volume scaling argument.

Why NPV Is the Correct Way to Compare Investments (and Payback Period Is Not)

Payback period only asks "when do I get my money back," treating every dollar of cash flow the same regardless of when it arrives, it implicitly assumes a dollar received in year 1 is worth exactly the same as a dollar received in year 10. That assumption is wrong in any real economy, because money available today can be invested to earn a return, making it strictly more valuable than the same amount received later.

NPV fixes this by discounting every future cash flow back to a present-value equivalent using the time value of money (a chosen interest/discount rate i, representing the return available on alternative investments), then summing across all years including the initial negative investment at t = 0. A positive NPV means the project earns more than the discount rate's opportunity cost after accounting for exactly when cash arrives, which is why NPV (and the related internal rate of return) is the standard profitability criterion in real capital budgeting, while payback period is used only as a quick, rough screening tool for risk (how fast is capital exposed) rather than true profitability.

Worked Practice Problems

Original practice problems in the GATE CH style, not copied from any question bank. Work them before reading the solution.

1-mark · NAT

Equipment Cost Scaling with the Six-Tenths-Factor Rule

Problem: A reactor of capacity 500 L cost ₹8,00,000. Estimate the cost of a similar reactor with capacity 1500 L using the six-tenths-factor rule.

Given: C1 = ₹8,00,000, S1 = 500 L, S2 = 1500 L, exponent = 0.6.

C2C1=(S2S1)0.6=(1500500)0.6=30.6\dfrac{C_2}{C_1} = \left(\dfrac{S_2}{S_1}\right)^{0.6} = \left(\dfrac{1500}{500}\right)^{0.6} = 3^{0.6}
C2=8,00,000×30.6=8,00,000×1.933C_2 = 8{,}00{,}000 \times 3^{0.6} = 8{,}00{,}000 \times 1.933

Answer: C2 ≈ ₹15,46,000 (about ₹15.5 lakh).

2-mark · NAT

NPV of a Proposed Project Over 3 Years

Problem: A project requires an initial investment of ₹10,00,000 and generates cash flows of ₹4,00,000, ₹4,50,000, and ₹5,00,000 at the end of years 1, 2, and 3. At a discount rate of 10%, find the NPV and state whether the project should be accepted.

Given: Investment at t=0: −₹10,00,000. CF1 = ₹4,00,000, CF2 = ₹4,50,000, CF3 = ₹5,00,000, i = 10%.

PW1=4,00,0001.101=3,63,636PW_1 = \dfrac{4{,}00{,}000}{1.10^1} = 3{,}63{,}636
PW2=4,50,0001.102=3,71,901PW_2 = \dfrac{4{,}50{,}000}{1.10^2} = 3{,}71{,}901
PW3=5,00,0001.103=3,75,657PW_3 = \dfrac{5{,}00{,}000}{1.10^3} = 3{,}75{,}657
NPV=−10,00,000+3,63,636+3,71,901+3,75,657NPV = -10{,}00{,}000 + 3{,}63{,}636 + 3{,}71{,}901 + 3{,}75{,}657

Answer: NPV ≈ ₹11,194 (positive), the project should be accepted at a 10% discount rate, though the margin is thin.

Topic-wise PYQ Frequency

Medium

Depreciation

GATE 2024 Q35 tested depreciation directly, a reliable, formula-driven numerical.

Medium

Capital cost & equipment selection

GATE 2024 Q49 (equipment selection) and GATE 2025 Q26 (capital cost) both drew on cost-estimation concepts.

Medium

Time value of money & profitability

GATE 2026 Q29 (time value of money) and Q46 (payback period) confirm this is tested every year in some form.

Low

Equipment replacement analysis

GATE 2025 Q63 tested equipment replacement, a less frequent but still recurring application.

Recommended Study Order

  1. 1

    1. Cost estimation (six-tenths-factor rule, cost indices)

    Quick to learn and directly tested, a two-formula subtopic with high marks-per-minute-of-study.

  2. 2

    2. Depreciation methods

    A short, formula-driven subtopic, memorize both straight-line and declining-balance forms.

  3. 3

    3. Time value of money

    The prerequisite concept for every profitability measure that follows.

  4. 4

    4. Payback period & NPV

    The highest-yield profitability subtopic, practice both so you recognize which the question is asking for.

  5. 5

    5. Break-even & equipment replacement analysis

    Lowest frequency, a quick formula review is usually enough given the limited time this section deserves relative to CRE or Thermodynamics.

Common Pitfalls

✗ Using a linear cost scaling instead of the six-tenths-factor (power-law) rule.

✓ Equipment cost scales with capacity raised to roughly 0.6, not 1, a doubled capacity does not mean doubled cost.

✗ Confusing payback period (ignores time value of money) with NPV/discounted payback (accounts for it).

✓ If a problem gives a discount/interest rate, it expects NPV or discounted cash flow analysis, plain payback period never uses a discount rate.

✗ Mixing up salvage value treatment between straight-line and declining-balance depreciation.

✓ Straight-line depreciation explicitly subtracts salvage value from cost before dividing by useful life; declining-balance depreciation applies a fixed rate to the undepreciated balance each year and doesn't subtract salvage value directly in the formula.

✗ Forgetting to discount the initial investment or treating it as occurring at t = 1 instead of t = 0.

✓ The initial investment is a cash flow at t = 0 (already in present-value terms, no discounting needed), only cash flows from t = 1 onward get discounted.

Put It Into Practice

Work the cost-scaling and NPV problems above by writing out each cash flow explicitly, then apply the same formulas to the plant economics questions in the full GATE previous-year test set.

Take a Practice Test →Browse Solved PYQs →

Keep Exploring

Related

Chemical Technology

Chlor-alkali, fertilizers, cement, petroleum refining, petrochemicals, and polymers for GATE CH.

Open →

Engineering Mathematics

Linear algebra, calculus, differential equations, probability, and numerical methods for GATE CH.

Open →

GATE CH Formula Sheet

Every core GATE Chemical Engineering formula in one place, grouped by topic with variable definitions.

Open →

GATE Practice Tests by Year

Full-length, timed GATE CH practice tests (2024–2026) with instant, step-by-step-explained results.

Open →