GTU 3170615 Engineering Economics, Estimation and Costing Summer 2026 Solved Paper & Solutions

Estimating is the process of calculating the quantities of items of work and their probable cost before construction starts.

Purposes of estimating:

1. To know the probable cost of the project, so the owner can decide whether to build it.
2. To get administrative approval and technical sanction, and to arrange funds.
3. To find the quantities of materials and labour needed, and to plan their procurement.
4. To invite tenders and to check the contractors' rates.
5. To control the expenditure during construction and to prepare bills.
6. To value a property, or work out rent or taxes.

1) Work charged establishment

The staff employed for a particular work (not on the permanent establishment), such as work-sarkars, chowkidars, mistries and work supervisors, who supervise the work, take measurements, keep records and guard materials at site. Their salary is charged to the work itself. A provision of about 1.5 to 2% of the estimated cost is made for it in the estimate. They are paid from the work's budget and are discharged when the work is over.

2) Prime cost

Prime cost (P.C.) is the actual cost of an article or material at the shop or factory, which is not decided in detail at the time of the estimate, such as sanitary fittings, door and window fittings, electrical fittings and special flooring. A lump sum provision is made in the estimate for such items. The prime cost does not include the cost of carriage, fixing and the contractor's profit, which are added separately when the item is used. Example: "P.C. of Rs. 1,500 per wash basin", where the contractor buys the basin at actual cost and is paid separately for fixing.

Reading of Figure-1:

• Centre-line dimensions: 9.00 m × 7.30 m (3.50 + 3.80). Rooms: bed room 4.20 × 3.20, kitchen 2.10 × 3.20, drawing room and dining room 4.20 × 3.50 each. So the main walls are 0.30 m thick (4.20 + 0.30 = 4.50).
• Section AB: P.C.C. 0.80 m wide × 0.20 m deep; brick footings in three courses of 0.60, 0.50 and 0.40 m width, each 0.30 m high; wall 0.30 m thick above ground level.

Assumptions:

1. Walls with foundations: the outer walls, the central horizontal wall, the central vertical wall and the wall between the toilet and kitchen. The thin toilet partitions are taken as half-brick partitions with no separate foundation.
2. The top of the footings is at ground level, so the depth of excavation $= 0.20 + 3 \times 0.30 = 1.10$ m.
3. As stated in the question, brick masonry in the plinth is taken 0.15 m high and 0.30 m wide.

Total centre-line length (centre line method):

Junctions: the inner walls meet other walls at 8 T-junctions (horizontal wall 2, vertical wall 2 at the ends + 2 at the crossing, toilet-kitchen wall 2). For each item, deduct $8 \times \frac{\text{width}}{2}$.

1) Earthwork in excavation for foundation (width 0.80 m, depth 1.10 m)

2) P.C.C. (1:4:8) in foundation (0.80 m × 0.20 m)

3) Brick masonry in C.M. (1:6) up to plinth level

Cash flow is the movement of money into and out of a project or business over time. Money received (revenue, salvage value) is a cash inflow; money paid (investment, operating cost) is a cash outflow. Net cash flow = inflow − outflow.

Cash flow diagram: a horizontal time line divided into periods (years). Upward arrows show inflows and downward arrows show outflows, drawn at the time they occur.

It helps compare alternatives using interest formulas.

Types of estimates:

1. Preliminary (approximate or rough cost) estimate
2. Plinth area estimate
3. Cube rate (cubical content) estimate
4. Approximate quantity method estimate
5. Detailed estimate
6. Revised estimate
7. Supplementary estimate
8. Annual repair (maintenance) estimate

Detailed estimate (explained):

A detailed estimate is the most accurate estimate. It is prepared by calculating the quantities of each item of work (earthwork, concrete, brickwork, plaster, flooring and so on) from the detailed drawings and specifications, and multiplying each quantity by its rate from the schedule of rates or rate analysis.

Steps:

1. Details of measurement: length, breadth and height of each item are taken from the drawings and quantities are worked out.
2. Abstract of estimate: quantities are multiplied by rates to get the cost of each item, and the costs are added.
3. Extra provisions are added: about 3% contingencies, 1.5 to 2% work charged establishment, and provisions for water supply, electrification and sanitation.

Documents with it: report, drawings, specifications and rate analysis. It is needed for technical sanction and for calling tenders.

Break-even point

The break-even point (BEP) is the level of output (or sales) at which total revenue equals total cost, so there is no profit and no loss. Below it, the firm makes a loss; above it, a profit.

Formula: with fixed cost $F$, selling price per unit $P$ and variable cost per unit $V$:

$P - V$ is called the contribution per unit.

Example: $F = \text{Rs. } 2{,}00{,}000$, $P = \text{Rs. } 50$, $V = \text{Rs. } 30$. BEP $= \dfrac{2{,}00{,}000}{20} = 10{,}000$ units.

Break-even chart

• Fixed cost line: horizontal at height F.
• Total cost line: starts at F and rises with slope V.
• Total revenue line: starts at the origin and rises with slope P.
• They cross at the BEP ($Q^*$). The area to the left is loss and to the right is profit. The distance between actual sales and break-even sales is the margin of safety.

Assumptions of break-even analysis

1. All costs can be divided into fixed and variable costs.
2. Fixed costs remain constant at all levels of output.
3. Variable cost per unit is constant, so total variable cost changes in proportion to output.
4. The selling price per unit is constant, whatever the quantity sold.
5. Production equals sales; there is no change in stock.
6. Only one product is made, or the sales mix is constant.
7. Efficiency, technology and prices of inputs do not change during the period.

These make the cost and revenue lines straight, which is a simplification of real conditions.

Specification is a detailed written description of the materials, workmanship, method of construction, quality and tests for each item of work, given along with the drawings.

Objectives:

1. To state clearly the quality of materials and workmanship required.
2. To help the contractor quote correct rates in the tender.
3. To guide the execution and supervision of work at site.
4. To serve as a legal document in case of disputes.
5. To help in rate analysis and checking the work.

Essential principles of good specification writing:

1. Clear and simple language: short, exact sentences that cannot be misunderstood; no vague words like "good quality" or "as required".
2. Complete: covers materials, mix, workmanship, method, tests, measurement and payment for every item.
3. Concise: no repetition; refer to standard specifications (BIS codes, PWD specifications) instead of repeating them.
4. Logical order: the same order as the work is done (materials, preparation, execution, curing, finishing, measurement).
5. Fair to both parties: reasonable requirements that can be achieved and checked; no impossible demands.
6. Consistent with drawings and other contract documents; no conflicts.
7. Specify quality by measurable standards (strength, grade, size, tolerances, test methods).
8. Use standard abbreviations and units only.
9. Clause numbering, so that items can be referred to easily.

Tender

A tender is a written offer submitted by a contractor, in response to an invitation (tender notice), to carry out a specified work or supply for a stated price and within a stated time, according to the drawings, specifications and conditions of contract. When the owner accepts it, it becomes a contract.

Classification of tenders

A. Based on the method of inviting

1. Open tender (public tender): invited by public advertisement in newspapers and on the e-tender portal; any eligible contractor can apply. Used for most government works; gives competition and transparency.
2. Limited tender (selective tender): invited only from a limited number of approved contractors, by direct letters. Used for small or urgent works and specialised work.
3. Single tender: invited from only one contractor, for proprietary items, urgent work or when only one firm can do it.
4. Negotiated tender: the rate is fixed by negotiation with one or a few selected contractors, used when competition is not possible.
5. Global tender: invited from contractors of all countries, for very large or specialised projects.

B. Based on the method of submission

1. Single bid (one cover) system: technical and financial details in one envelope.
2. Two bid (two cover) system: a technical bid (qualification, experience, equipment) and a financial (price) bid in separate covers; price bids are opened only for technically qualified bidders.
3. E-tendering: tenders are invited, submitted and opened online, as on the Government of Gujarat and central portals; transparent and quick.

C. Based on the type of contract

1. Item rate tender: rates quoted for each item of work.
2. Percentage rate tender: a percentage above or below the departmental estimated rates is quoted.
3. Lump sum tender: one total amount quoted for the whole work.
4. Cost plus tender: actual cost plus a fixed fee or percentage.
5. Turnkey (design and build) tender: the contractor designs and constructs the whole project.

D. Based on stages

1. Pre-qualification tender: first select qualified contractors, then invite prices from them.
2. Rate contract tender: rates for supply over a period.

Documents of a tender

Tender notice, form of tender, drawings, specifications, schedule of quantities (Bill of Quantities), conditions of contract, earnest money and security deposit details.

A schedule of rates (SOR) is a list of rates for different items of work (with their units and specifications), prepared and published by a government department, such as the PWD or R&B department, usually every year, for a particular region.

Uses:

1. For preparing estimates of works.
2. As the base for percentage rate tenders.
3. For checking contractors' rates and for payment of extra items.

Rates include materials, labour, tools, overheads and contractor's profit, and are based on rate analysis and market rates.

Given: cement concrete 1:4:8, wet volume 10 m³.

Density of cement = 1440 kg/m³: $1.169 \times 1440 = 1684$ kg $= \dfrac{1684}{50} \approx 33.7$, say 34 bags.

A contract is an agreement enforceable by law (Section 2(h), Indian Contract Act, 1872). In construction, it is the agreement between the owner and the contractor to carry out the work for a payment. Under Section 10 of the Act, an agreement is a valid contract only if it meets the following requirements.

Essential requirements of a valid contract

1. Offer and acceptance: there must be a lawful offer by one party (the contractor's tender) and its absolute and unconditional acceptance by the other (the owner's acceptance letter). A conditional acceptance is only a counter-offer.

2. Free consent: both parties must agree freely, without coercion, undue influence, fraud, misrepresentation or mistake. Consent obtained by threat or cheating makes the contract voidable.

3. Competent parties: both parties must be legally capable: of age of majority (18 years), of sound mind, and not disqualified by law (for example, an insolvent). A contract with a minor is void.

4. Lawful consideration: each party must get something in return (consideration): the contractor gets payment, and the owner gets the completed work. The consideration must be lawful.

5. Lawful object: the purpose of the contract must be legal, not fraudulent, not harmful to anyone, and not against public policy. A contract to build an illegal structure is void.

6. Intention to create legal relations: both parties must intend the agreement to be legally binding, as in business agreements (not social or domestic promises).

7. Certainty of meaning: the terms must be clear and definite: scope of work, price, time, specifications. Vague agreements cannot be enforced.

8. Possibility of performance: the work must be possible to perform. An agreement to do an impossible act is void.

9. Not expressly declared void: the agreement must not be one that the law declares void, such as an agreement in restraint of trade or legal proceedings.

10. Legal formalities: where required, the contract should be in writing, signed, stamped and registered. Government works contracts are always written and signed on behalf of the Governor.

Contract documents in construction

Tender notice, tender form, drawings, specifications, bill of quantities, general and special conditions of contract, letter of acceptance and the signed agreement.

Example: a house that cost Rs. 30 lakh to build 15 years ago may today be valued at Rs. 60 lakh because of its location, even after depreciation.

Outgoings are the expenses that an owner has to spend regularly to maintain a property and earn rent from it. They are deducted from the gross income (gross rent) to find the net income, which is used in valuation.

Types of outgoings

1. Taxes

• Municipal (property) taxes levied by the local body on the annual rental value: general tax, water tax, conservancy tax, education cess. Usually paid by the owner.
• Income tax on rental income is generally not treated as an outgoing in valuation.

2. Repairs and maintenance

• Annual and periodic repairs, painting and whitewashing to keep the building in good condition.
• Usually taken as 10 to 15% of gross rent for buildings (or a percentage of cost).

3. Management and collection charges

• Expenses of managing the property: rent collection, caretaker or manager's salary, advertisement for tenants, legal expenses.
• Usually 5 to 10% of gross rent for large properties.

4. Insurance premium

• Premium paid to insure the building against fire, earthquake and other risks.

5. Sinking fund

• A fund set aside every year so that, by the end of the building's life, enough money is collected to rebuild it.
• Annual instalment $= C \times \dfrac{i}{(1 + i)^n - 1}$, where $C$ is the replacement cost, $n$ the life and $i$ the interest rate.

6. Loss of rent (vacancy allowance)

• Allowance for periods when the property is vacant or tenants do not pay. Usually about one month's rent per year, depending on demand.

7. Ground rent

• Rent paid to the landowner if the building stands on leasehold land.

8. Service charges

• Cost of services provided by the owner: lift operation, common lighting, water supply, security, sweeping, and similar.

9. Other charges

• Society charges, maintenance of gardens and parking.

Example

Gross annual rent Rs. 3,00,000; outgoings: taxes Rs. 30,000, repairs Rs. 36,000, management Rs. 15,000, insurance Rs. 5,000, sinking fund Rs. 14,000. Total outgoings = Rs. 1,00,000. Net income = Rs. 2,00,000, which is capitalised to find the value.