Engineering economics and costing

Mechanical Engineering (B.E./B.Tech) · Industrial engineering · free study notes for exams, placements and interviews

In short

Engineering economics compares alternative technical choices in money terms over time — buy or lease, repair or replace, manual or automated — using interest, present worth, annual cost and rate of return. Costing is its companion: it works out what a product actually costs to make (material, labour, overhead) so a selling price, a quotation or a break-even volume can be defended. Both are examined in GATE ME (Industrial Engineering), in university Industrial Engineering and Engineering Economics papers, and in professional-body syllabi; they are also what cost accountants, production and project engineers at L&T, Tata Motors, BHEL, Maruti, ONGC, NTPC and every MSME tool-room actually use. Placement aptitude and technical rounds lean on break-even, payback, depreciation and simple interest-rate arithmetic. Indian practice adds GST, Companies Act depreciation and Income-tax Act block depreciation on top of the classical methods.

Explained

Cost concepts and classification

Cost is the resource sacrificed, measured in rupees, to make a product or render a service; price is what the customer pays; value is the worth to the customer.
By element: (i) material — direct (becomes part of the product: steel bar for a shaft) and indirect (consumables: coolant, cotton waste); (ii) labour — direct (machinist on the job) and indirect (storekeeper, supervisor); (iii) expenses — direct (job-specific jig hire, pattern cost) and indirect (factory rent, power, depreciation).
By traceability: direct cost is chargeable to a single job or product; indirect cost (overhead) is shared and must be apportioned.
By behaviour with volume: fixed cost stays constant in total over the relevant range (rent, salaries, insurance, machine depreciation on time basis); variable cost changes in proportion to output (material, piece-rate wages, power on machining); semi-variable / mixed has both parts (electricity with a fixed demand charge, maintenance).
By function: factory (works) overhead, administration overhead, selling and distribution overhead.
Decision-relevant costs: marginal cost (cost of one more unit ≈ variable cost per unit), incremental/differential cost (difference between two alternatives), opportunity cost (benefit forgone from the next-best use of a resource), sunk cost (already incurred, never relevant to a future decision), imputed/notional cost (no cash flow, e.g. interest on owner's capital), out-of-pocket cost (actual cash outgo), replacement cost, standard cost (pre-determined target used for variance analysis).
Economy of scale: unit fixed cost falls as volume rises; beyond capacity, overtime and congestion push unit cost up again.

Ladder of costs and estimation

The standard build-up, each step adding one layer:
1. Prime cost = direct material + direct labour + direct expenses.
2. Factory (works) cost = prime cost + factory overhead (± work-in-progress adjustment).
3. Cost of production = factory cost + administration overhead.
4. Cost of goods sold = cost of production + opening finished stock − closing finished stock.
5. Cost of sales (total cost) = cost of goods sold + selling and distribution overhead.
6. Selling price = total cost + profit. (GST is charged on the selling price and is not a cost to a registered manufacturer, who takes input tax credit.)
Estimating is predicting the cost before manufacture — needed for quotations, tenders and make-or-buy. Costing is recording it after. The two must be reconciled.
Estimation procedure: study the drawing and specification → list operations and sequence → compute material volume and mass, add scrap allowance → price material at current market rate → estimate machine/operation times (setting + handling + machining + idle + fatigue allowance) → apply labour rates → add overhead → add profit and discount.
Material cost = net mass × rate + scrap allowance − scrap credit; mass = volume × density (mild steel ≈ 7,850 kg/m³, cast iron ≈ 7,200, aluminium ≈ 2,700).
Methods of costing: job costing (tool room, fabrication to order), batch costing (pharma, fasteners), process costing (cement, fertiliser, refining — with normal/abnormal loss), contract costing (construction, with work certified), operation/unit costing, activity-based costing (ABC) — overhead traced through cost drivers (number of setups, inspections) instead of one blanket rate; much fairer where products differ in complexity.
Techniques: absorption (full) costing charges all fixed overhead to the product; marginal (variable) costing charges only variable cost and treats fixed cost as a period cost — the basis of contribution analysis.

Overhead allocation, apportionment and absorption

Allocation: whole item charged to one cost centre (foreman's salary of shop A to shop A). Apportionment: shared item split on a fair basis (factory rent on floor area, power on kW-hours, canteen on headcount, depreciation on asset value).
Secondary distribution: service-centre cost (maintenance, stores, tool room) reapportioned onto production centres — direct, step-ladder or reciprocal (simultaneous-equation) method.
Absorption rates — charging centre overhead onto the job:
- Percentage of direct material = overhead/direct material × 100 (crude; ignores time).
- Percentage of direct labour cost = overhead/direct wages × 100 (common, simple).
- Percentage of prime cost.
- Labour-hour rate = overhead/direct labour hours (₹/hour) — fair in labour-intensive shops.
- Machine-hour rate = overhead of the machine/machine hours worked (₹/hour) — the correct rate for machine-intensive work (CNC); include depreciation, power, space, supervision, maintenance.
Under-absorption / over-absorption: actual overhead minus absorbed overhead; small amounts are charged to the costing P&L, large amounts carried by a supplementary rate.
Limitation: blanket rates distort product cost badly when a plant mixes manual and automated routes — the standard argument for ABC.

Interest and the time value of money

A rupee today is worth more than a rupee next year because it can earn interest; cash flows at different dates must be moved to one date before comparison.
Simple interest: interest only on the principal. Compound interest: interest on interest — the basis of all engineering-economy factors.
Nominal versus effective rate: a nominal 12% per annum compounded monthly has an effective annual rate of (1 + 0.12/12)¹² − 1 = 12.68%. Always convert to the rate per compounding period before using a factor.
Cash-flow diagram: horizontal time line, upward arrows for receipts, downward for payments; end-of-period convention. "Present" is the start of period 1; an annuity's first payment is at the end of period 1.
The six standard factors (i = rate per period, n = number of periods):
- Single payment compound amount (F/P), present worth (P/F).
- Uniform series compound amount (F/A), sinking fund (A/F).
- Capital recovery (A/P) — converts a first cost into an equal annual cost, present worth of annuity (P/A).
Gradient series: arithmetic gradient G (payments rising by a fixed amount) and geometric series (rising by a fixed percentage, e.g. escalating energy cost).
Perpetuity / capitalised cost: P = A/i — used for roads, bridges, dams and endowments where life is treated as infinite.
Inflation: a cash flow in current (inflated) rupees must be discounted at the market rate; one in constant rupees at the real rate, where (1 + market) = (1 + real)(1 + inflation).

Comparing alternatives and investment appraisal

Present worth (PW/NPV) method: discount all cash flows to time zero at the minimum attractive rate of return (MARR); choose the highest PW (or lowest PW of cost). Alternatives with unequal lives must be compared over the least common multiple of lives or by annual worth.
Annual worth / equivalent uniform annual cost (EUAC): convert everything to an equal annual amount; handles unequal lives directly — the method of choice in exams for repair-or-replace.
Future worth method: compare at the end of the horizon; used when a terminal fund matters.
Rate of return (IRR): the i at which PW = 0; accept if IRR > MARR. Found by trial and interpolation. Pitfalls: multiple roots when signs change more than once, and wrong ranking between projects of different size — settle ranking by incremental IRR on the extra investment.
Benefit–cost ratio (B/C): PW of benefits / PW of costs; accept if ≥ 1. Standard for public projects (irrigation, highways, metro) where disbenefits and user savings are counted.
Payback period: first cost / annual net saving (or cumulative-cash-flow year). Simple and widely used in Indian MSMEs, but ignores the time value of money and everything after payback; discounted payback fixes the first defect only.
Return on investment (ROI) = average annual profit / average investment × 100 — accounting measure, ignores timing.
Depreciation methods:
- Straight line (SLM): D = (P − S)/n — equal charge each year.
- Declining balance / written-down value (WDV): D_t = r × book value at start; r = 1 − (S/P)^1/n for the Matheson formula; double-declining uses r = 2/n.
- Sum-of-years-digits (SOYD): D_t = (P − S) × remaining life / Σ years.
- Sinking fund: a fixed annual deposit earning interest accumulates to (P − S).
- Production/service output (units-of-use) method: charge per unit produced or hour run.
- Indian practice: the Companies Act 2013, Schedule II prescribes *useful lives* (plant and machinery commonly 15 years, general factory buildings 30 years, computers 3 years) and lets the company choose SLM or WDV; the Income-tax Act instead uses block-of-assets WDV rates (general plant and machinery 15%, with additional depreciation for new manufacturing plant subject to conditions). Rates and conditions change with Finance Acts — verify the current year's rate before using it in real work.
Replacement analysis: compare the EUAC of the defender (existing asset, valued at its current market value, not its book value — the original cost is sunk) against the EUAC of the challenger at its economic life. Economic life is the life at which EUAC is minimum, where falling capital recovery meets rising operating and maintenance cost.
Obsolescence (better technology, changed product) and deterioration (wear) are the two reasons for replacement; sudden-failure replacement policy (group versus individual) is handled in operations research.

Break-even, make-or-buy and value engineering

Contribution per unit = selling price − variable cost per unit; it first covers fixed cost, then becomes profit.
Break-even quantity (BEQ) = fixed cost / contribution per unit; at BEQ, profit is zero.
Margin of safety = actual sales − break-even sales; expressed as a percentage it measures risk cushion.
P/V ratio (contribution margin ratio) = contribution / sales; break-even sales in rupees = fixed cost / (P/V ratio).
Angle of incidence: the angle between the sales line and the total-cost line beyond break-even — wider means profit grows faster.
Operating leverage = contribution / profit; a high-fixed-cost, automated plant has high leverage — profits swing sharply with volume.
Limitations of break-even charts: linearity of price and variable cost assumed, single product or fixed sales mix, fixed cost constant, production = sales.
Make-or-buy: compare the relevant cost of making (variable cost + any avoidable fixed cost + opportunity cost of capacity) against the bought-out price including freight and inspection; the indifference volume is where the two total costs are equal. Make above it if make has higher fixed and lower variable cost. Quality, confidentiality, capacity and supplier reliability are judged alongside the numbers.
Value analysis / value engineering: improve value = function / cost by removing cost that adds no function — function analysis, FAST diagrams, brainstorming alternatives, then verification. Applied widely in Indian auto component cost-down programmes.
Cost reduction versus cost control: control holds cost to a pre-set standard (budgets, variance analysis); reduction permanently lowers the standard itself.
Depreciation, interest and taxes in product cost: machine-hour rate carries depreciation and interest on capital, so quoting on a machine-hour rate automatically recovers the investment.

Key points

Prime cost - direct material + direct labour + direct expenses; the only fully traceable layer.
Overhead - all indirect cost; allocated, apportioned and finally absorbed onto jobs.
Machine-hour rate - overhead per hour of machine running; the correct absorption base for capital-intensive shops.
Fixed versus variable - fixed is constant in total and falls per unit with volume; variable is constant per unit.
Contribution - selling price minus variable cost; the engine of break-even and marginal costing.
Break-even quantity - fixed cost ÷ contribution per unit; profit is zero there.
Margin of safety - how far sales exceed break-even; the cushion against a demand fall.
Sunk cost - past and irrecoverable; must be excluded from every forward-looking decision.
Opportunity cost - the value of the best alternative forgone; relevant even without a cash flow.
Time value of money - cash flows at different dates are compared only after moving them to one date at rate i.
Capital recovery factor - converts first cost into an equal annual cost; the basis of EUAC.
Present worth method - discount everything to t = 0; needs equal study periods (use LCM of lives).
Annual worth / EUAC - handles unequal lives without LCM; the standard for replacement decisions.
IRR - rate where PW = 0; accept if above MARR, but rank competing projects by incremental IRR.
Payback - first cost ÷ annual saving; ignores time value and post-payback life.
Depreciation - SLM is equal, WDV is front-loaded, SOYD is front-loaded and linear in charge, sinking fund builds a replacement corpus.
Economic life - life where EUAC is minimum; defender is valued at market value, not book value.
Indian codes - Companies Act 2013 Schedule II gives useful lives (SLM or WDV); the Income-tax Act uses block WDV rates (general plant 15%); GST input credit keeps tax out of a registered manufacturer's product cost.

Formulas and examples

Prime cost = direct material + direct labour + direct expenses (₹)
Factory cost = prime cost + factory overhead; Cost of production = factory cost + admin overhead
Total cost = cost of production ± stock change + selling and distribution overhead; Selling price = total cost + profit
Machine-hour rate = total overhead of the machine (₹) / machine hours worked (h)
Material cost = volume (m³) × density (kg/m³) × rate (₹/kg) + scrap allowance − scrap credit
Contribution per unit c = s − v (₹/unit); BEQ = F / (s − v) (units); BE sales = F / (P/V ratio) (₹)
P/V ratio = (s − v)/s; Profit = Q(s − v) − F; Margin of safety = (actual Q − BEQ)/actual Q × 100 (%)
Simple interest F = P(1 + i·n); Compound amount F = P(1 + i)ⁿ; Present worth P = F / (1 + i)ⁿ
Effective annual rate = (1 + r/m)^m − 1 (r = nominal rate/year, m = compoundings/year)
F/A: F = A[((1 + i)ⁿ − 1)/i]; A/F (sinking fund): A = F[i/((1 + i)ⁿ − 1)]
P/A: P = A[((1 + i)ⁿ − 1)/(i(1 + i)ⁿ)]; A/P (capital recovery): A = P[i(1 + i)ⁿ/((1 + i)ⁿ − 1)]
Capitalised cost (perpetuity) P = A / i; EUAC = (P − S)(A/P, i, n) + S·i + annual O&M
Straight line D = (P − S)/n; WDV D_t = r·B_{t−1}, r = 1 − (S/P)^1/n; SOYD D_t = (P − S)·(n − t + 1)/[n(n + 1)/2]
Payback = first cost / annual net cash inflow (years); B/C = PW(benefits)/PW(costs)
i = rate per period (decimal), n = periods, P = present value (₹), F = future value (₹), A = equal annual amount (₹/yr), S = salvage value (₹), Q = quantity (units), F in break-even formulas = fixed cost (₹/period)

Example 1 — full cost sheet and selling price. A pump maker's month: direct material ₹4,80,000; direct wages ₹2,20,000; direct expenses (pattern hire) ₹20,000; factory overhead 60% of direct wages; administration overhead ₹75,000; selling and distribution ₹1,05,000; 2,000 pumps made and sold; profit at 20% of total cost.

Prime cost = 4,80,000 + 2,20,000 + 20,000 = ₹7,20,000
Factory overhead = 0.60 × 2,20,000 = ₹1,32,000 → factory cost = ₹8,52,000
Cost of production = 8,52,000 + 75,000 = ₹9,27,000
Total cost = 9,27,000 + 1,05,000 = ₹10,32,000 → cost per pump = 10,32,000/2,000 = ₹516
Profit = 0.20 × 10,32,000 = ₹2,06,400 → sales = ₹12,38,400 → selling price ₹619.20 per pump (GST extra on the invoice).

Example 2 — machine-hour rate. A CNC turning centre costs ₹40,00,000, salvage ₹4,00,000 after 10 years, runs 2,000 productive hours a year. Annual costs: power 15 kW × 0.7 load × 2,000 h × ₹8/kWh; maintenance ₹1,20,000; operator ₹3,60,000; floor space and supervision ₹90,000. Interest on average investment at 10%.

Depreciation (SLM) = (40,00,000 − 4,00,000)/10 = ₹3,60,000/yr
Interest on average investment = 0.10 × (40,00,000 + 4,00,000)/2 = ₹2,20,000/yr
Power = 15 × 0.7 × 2,000 × 8 = ₹1,68,000/yr
Total = 3,60,000 + 2,20,000 + 1,68,000 + 1,20,000 + 3,60,000 + 90,000 = ₹13,18,000/yr
Machine-hour rate = 13,18,000 / 2,000 = ₹659/hour. A job needing 1.5 h absorbs ₹988.50 of machine overhead.

Example 3 — break-even, margin of safety and a price cut. Fixed cost ₹18,00,000 a year; selling price ₹900/unit; variable cost ₹540/unit; present sales 7,500 units.

Contribution = 900 − 540 = ₹360/unit; P/V ratio = 360/900 = 40%
BEQ = 18,00,000/360 = 5,000 units; BE sales = 5,000 × 900 = ₹45,00,000 (check: 18,00,000/0.40 = ₹45,00,000)
Profit at 7,500 = 7,500 × 360 − 18,00,000 = ₹9,00,000; margin of safety = (7,500 − 5,000)/7,500 = 33.3%
Price cut to ₹810: contribution = ₹270 → new BEQ = 18,00,000/270 = 6,667 units; to hold ₹9,00,000 profit, Q = (18,00,000 + 9,00,000)/270 = 10,000 units — a 10% price cut needs a 33% volume rise.

Example 4 — present worth, EUAC and payback for two machines. MARR 12%. Machine A: first cost ₹8,00,000, O&M ₹1,20,000/yr, salvage ₹80,000, life 6 years. Machine B: first cost ₹12,00,000, O&M ₹60,000/yr, salvage ₹1,50,000, life 6 years.

Factors at 12%, 6 years: (1.12)⁶ = 1.9738; (P/A) = (1.9738 − 1)/(0.12 × 1.9738) = 4.1114; (P/F) = 1/1.9738 = 0.5066; (A/P) = 1/4.1114 = 0.24323
PW(cost) A = 8,00,000 + 1,20,000(4.1114) − 80,000(0.5066) = 8,00,000 + 4,93,368 − 40,528 = ₹12,52,840
PW(cost) B = 12,00,000 + 60,000(4.1114) − 1,50,000(0.5066) = 12,00,000 + 2,46,684 − 75,990 = ₹13,70,694
EUAC A = 12,52,840 × 0.24323 = ₹3,04,728/yr; EUAC B = 13,70,694 × 0.24323 = ₹3,33,391/yr → choose A (lower cost by about ₹28,700/yr)
Incremental view: B costs ₹4,00,000 more to save ₹60,000/yr → simple payback = 4,00,000/60,000 = 6.67 years, longer than the 6-year life, so the extra investment cannot pay back — consistent with the PW answer. (Payback alone would have shown this; it would not have quantified the ₹28,700 annual penalty.)

Example 5 — depreciation methods compared and a make-or-buy. Asset P = ₹10,00,000, S = ₹1,00,000, n = 5 years.

SLM: D = (10,00,000 − 1,00,000)/5 = ₹1,80,000 every year.
WDV (Matheson): r = 1 − (1,00,000/10,00,000)^1/5 = 1 − 10^−0.2 = 1 − 0.6310 = 36.90%.
SOYD: Σ years = 15; year 1 = 9,00,000 × 5/15 = ₹3,00,000; year 5 = 9,00,000 × 1/15 = ₹60,000.
Sinking fund at 10%: A = 9,00,000 × [0.10/((1.1)⁵ − 1)] = 9,00,000 × 0.10/0.61051 = ₹1,47,420/yr.

Year	SLM D (₹)	WDV D at 36.90% (₹)	WDV book value end (₹)	SOYD D (₹)
1	1,80,000	3,69,000	6,31,000	3,00,000
2	1,80,000	2,32,839	3,98,161	2,40,000
3	1,80,000	1,46,921	2,51,240	1,80,000
4	1,80,000	92,708	1,58,532	1,20,000
5	1,80,000	58,498	1,00,034	60,000

Make-or-buy: a bracket can be bought at ₹240/unit or made with a ₹6,00,000 die (one-off) plus variable cost ₹165/unit. Indifference volume = 6,00,000/(240 − 165) = 8,000 units/yr. Below 8,000 buy; above it make. At 20,000 units/yr, making saves 20,000 × 75 − 6,00,000 = ₹9,00,000.

Method	What it answers	Time value	Main limitation
Payback	How soon is money back?	No (unless discounted)	Ignores life after payback
ROI	Average accounting return	No	Uses profit, not cash flow
PW / NPV	Rupee gain at MARR	Yes	Needs equal lives (LCM)
EUAC / AW	Annual cost of owning	Yes	Assumes repetition of the cycle
IRR	Earning rate of the project	Yes	Multiple roots; poor at ranking
B/C ratio	Public-project worth	Yes	Benefit/disbenefit classification is debatable

Where it is used

Capital budgeting and project engineering: NTPC, NHPC, ONGC, Indian Railways and metro corporations appraise schemes by NPV, IRR and B/C ratio in the Detailed Project Report; PPP concessions are decided on discounted cash flow.
Automotive and component costing: Maruti Suzuki, Tata Motors, Bosch and their tier-1 suppliers run should-cost models, value-engineering cost-down workshops and annual price negotiations built on material-plus-conversion cost sheets.
Tool rooms, job shops and MSMEs: quotations on machine-hour rates; MSME investment decisions (CNC purchase, solar rooftop) typically judged on payback, supported by schemes such as CLCSS/credit-linked subsidies — scheme terms change, so check the current guidelines.
Maintenance and plant engineering: repair-versus-replace and economic-life studies for compressors, DG sets, pumps and vehicle fleets using EUAC.
Job roles: cost engineer, estimation engineer, proposals/tendering engineer, production planning engineer, techno-commercial and purchase engineer, management trainee in operations; L1 bid evaluation and reverse auctions in PSU procurement rest on these numbers.
Energy and sustainability projects: rooftop solar, VFD retrofits, LED relamping and waste-heat recovery sold to Indian plants on simple payback (usually 1–4 years) and life-cycle cost.

Interview questions

Q: What is the difference between cost estimation and costing? A: Estimation predicts cost before manufacture from drawings and process plans for quoting; costing records the actual cost after manufacture from vouchers and time sheets, and the two are reconciled to improve future estimates.
Q: Why is a sunk cost irrelevant in a replacement decision? A: It has already been incurred and no future choice can change it; the defender is valued at its current market value, which is the amount actually sacrificed by keeping it.
Q: Define contribution and explain why break-even uses it. A: Contribution is selling price minus variable cost per unit; it is the amount each unit gives towards fixed cost, so fixed cost divided by contribution is the volume at which fixed cost is exactly covered and profit is zero.
Q: A machine shop quotes on a percentage of direct wages. What goes wrong when it buys a CNC? A: The CNC needs few labour hours but carries heavy depreciation and power, so a labour-based rate under-absorbs its overhead and the quote is too low; a machine-hour rate or ABC is needed.
Q: Which is better, present worth or annual worth? A: They always give the same ranking at the same MARR; annual worth is preferred when lives are unequal or when an annual figure is wanted, present worth when a total rupee gain is wanted.
Q: Why can IRR mislead when ranking two projects? A: A small project can show a high IRR but add little value; the correct test is the incremental IRR on the extra investment, or simply the higher NPV at the MARR.
Q: SLM or WDV — which does a company use in India? A: For the books, the Companies Act 2013 Schedule II allows either, based on prescribed useful lives; for income tax, the block-of-assets WDV method with notified rates is used, so most firms maintain both.
Q: What is economic life and how is it found? A: The ownership period at which equivalent uniform annual cost is minimum; capital recovery falls with years while operating and maintenance cost rises, and the EUAC total bottoms out at that year.
Q: 12% per annum compounded quarterly — what is the effective rate? A: (1 + 0.03)⁴ − 1 = 12.55% per annum, higher than the nominal rate because interest earns interest within the year.
Q: When would you prefer to buy rather than make, even if making is cheaper per unit? A: When capacity is needed for higher-contribution work, the volume is below the indifference quantity, the technology or quality is outside your competence, or demand is uncertain and you want to avoid fixed cost.
Q: Is GST part of product cost? A: For a registered manufacturer, no — input GST is set off as input tax credit; only non-creditable taxes and duties become part of cost.
Q: What is the main weakness of a break-even chart? A: It assumes linear revenue and variable cost, a constant fixed cost and a fixed sales mix, none of which holds over a wide range of output.

Common mistakes

Treating depreciation as a cash flow in a present-worth analysis — it is not; only its tax effect matters in after-tax studies.
Comparing alternatives of unequal lives by present worth without using the LCM of lives or switching to annual worth.
Using the nominal rate directly when compounding is monthly or quarterly, instead of the rate per period or the effective annual rate.
Mixing up the sinking-fund factor (A/F) and the capital-recovery factor (A/P), or reading factor tables at the wrong n.
Including book value or original cost of the existing machine in a replacement study instead of its market value.
Calling fixed cost "fixed per unit" — total fixed cost is constant, so fixed cost per unit falls as volume rises.
Absorbing overhead on direct wages in a highly automated shop, and forgetting that under- or over-absorption must be adjusted.
Adding profit as a percentage of selling price when the question says percentage of cost (or the reverse) — the two give different prices.