Projects and Implementation: Partnerships, Viability, Monitoring, Asset Management and Institutions
2. Risk allocation, annuity payments and viability gap funding
The first rule of PPP design is to allocate each risk to the party best able to control it or bear it at least cost. A risk placed on the party that cannot manage it is priced into the bid, or comes back to the authority in a renegotiation.
| Risk | Best placed | Why |
|---|---|---|
| Design and construction: cost and time overrun | Private party | It controls the design, contractor and schedule |
| Operation and maintenance performance | Private party | It controls the day-to-day running |
| Demand and traffic | Private party under a user tariff; authority under an annuity | Whoever collects the revenue holds the volume risk |
| Land acquisition, clearances, utility shifting | Authority | Only the State can use sovereign powers |
| Change in law, policy and tariff approval | Authority | The private party cannot influence them |
| Force majeure | Shared, with insurance | Neither controls it; insurable parts go to the market |
Annuity and hybrid annuity. In an annuity concession the private party builds and finances the whole project and the authority pays equal instalments over the term, so the traffic or revenue risk stays with the authority. In the hybrid form the authority pays a stated share of the cost in construction-linked instalments and the rest through annuities. An equal annuity is the capital recovery payment A = P × i(1 + i)ⁿ ÷ [(1 + i)ⁿ − 1]. For a ₹100 crore project, ten years and 10%: A = 100 × 0.16275 = ₹16.27 crore a year. If the authority pays 30% in construction, the financed 70 gives 70 × 0.16275 = ₹11.39 crore a year (ignoring construction-period interest and O&M).
Viability gap funding (VGF) is a capital grant, normally capped at a fraction of project cost and paid during construction, to a project that is economically justified but not financially viable: its social benefits are high but its tariff, kept affordable, cannot repay the capital. Lenders then see a bankable project and the user keeps an affordable price. It is not a subsidy for a project that fails the economic test, and it is competitively set: the bid variable is often the smallest grant sought.
3. Financial viability: NPV, IRR, benefit-cost ratio, payback and DSCR
Financial analysis asks whether the project earns enough cash, at market prices and to its owner or lender, to be worth doing and to repay its debt. It uses the project’s cash flows, discounted at the required rate of return or cost of capital. The decision measures answer different questions, and the exam usually asks which one fits.
| Measure | Definition | Accept when | Weakness |
|---|---|---|---|
| Net present value (NPV) | Sum of discounted cash flows less the initial outlay | NPV > 0 | Depends on the discount rate; an absolute amount, so favours large projects |
| Internal rate of return (IRR) | The rate at which NPV is zero | IRR > required rate | Can be multiple or none when cash flows change sign more than once; can misrank mutually exclusive projects |
| Benefit-cost ratio (BCR) | Present value of benefits ÷ present value of costs | BCR > 1 | Changes with how O&M is classified (netted off benefits or counted as cost); state the convention |
| Payback period | Years until cumulative inflows recover the outlay | Shorter than the limit set | Ignores time value and all flows after payback |
| Discounted payback | Years until cumulative discounted inflows recover the outlay | Within the limit set | Includes time value, but still ignores flows after payback |
| Project DSCR | Cash flow available for debt service ÷ (interest + principal) | Comfortably above 1 every year | Shows whether debt can be paid, not whether the project is worthwhile |
- NPV. Outlay 1,000 at year 0; inflow 400 a year for years 1 to 4; r = 10%. The annuity factor is 3.1699, so PV of inflows = 400 × 3.1699 = 1,267.95 and NPV = 267.95. BCR on this basis = 1,267.95 ÷ 1,000 = 1.27.
- IRR. Cash flows −2,000, +1,100, +1,210 at years 0, 1, 2 have NPV zero at 10% (1,000 + 1,000 = 2,000), so IRR = 10%. When the rate cannot be found by inspection it is interpolated: if NPV is +120 at 10% and −80 at 15%, IRR ≈ 10 + 5 × 120 ÷ 200 = 13% by linear interpolation.
- Payback. Outlay 1,200; inflows 300, 400, 500, 600. Cumulative: 300, 700, 1,200, so payback is exactly 3 years. Discounted at 10%, the cumulative values are 272.73, 603.31, 978.96, 1,388.77, so discounted payback = 3 + (1,200 − 978.96) ÷ 409.81 = 3.54 years (flows taken as even within the year).
- DSCR. Cash flow available for debt service 360; interest 120; principal 150. DSCR = 360 ÷ (120 + 150) = 1.33.
4. Social cost-benefit analysis: shadow prices, discount rate and sensitivity
Economic (social) cost-benefit analysis asks whether the project makes society better off, compared with the situation without it. It values what society gains (time saved, lower vehicle operating cost, fewer accidents, health, avoided damage) and gives up, whoever receives it. A project can fail the financial test and pass the economic one, which is the case for a grant such as VGF, or the reverse.
| Item | Financial analysis | Economic analysis |
|---|---|---|
| Taxes and subsidies | Counted as cost or income | Transfers within society; excluded |
| Interest and loan repayment | Counted in the debt and equity cash flow | Excluded from project NPV; the cost of capital sits in the discount rate |
| Labour | Market wage | Shadow wage, below the market wage where labour is in surplus |
| Land | Price paid | Opportunity cost: value in its best alternative use |
| Foreign exchange | Official rate | Shadow rate that reflects its scarcity value |
| Externalities | Usually ignored | Valued where possible: congestion, pollution, safety |
| Discount rate | Cost of capital or hurdle rate | Social discount rate |
A shadow price is the true opportunity cost or benefit of a resource when market prices are distorted by taxes, controls, monopoly or unemployment. The social discount rate is the rate at which society trades present for future consumption. It is usually argued to lie below commercial borrowing rates because society takes a longer view, and it matters most for long-lived projects whose benefits come late: a higher rate cuts their NPV the most. Cash flows and the rate must be on the same footing, real flows with a real rate and nominal flows with a nominal rate. Sunk costs are ignored, and only incremental flows, with the project minus without it, count.
Sensitivity analysis shows how robust the answer is. Vary one input at a time (cost, demand, tariff, delay, discount rate) and recompute NPV or IRR; the switching value is the value of an input at which NPV reaches zero. Scenario analysis moves several inputs together (optimistic, base, pessimistic), and probabilistic (Monte Carlo) analysis attaches distributions. Take the NPV example above (outlay 1,000; inflow 400 a year for four years; 10%). If inflows fall 10% to 360, PV = 360 × 3.1699 = 1,141.15 and NPV = 141.15. The switching value of the annual inflow is 1,000 ÷ 3.1699 = 315.47, a fall of about 21% from 400.
5. Project implementation, monitoring and evaluation
A project passes through a cycle: identification, preparation (feasibility study and detailed project report), appraisal (technical, financial, economic, social, environmental and institutional), approval and financing, procurement, implementation, completion and handover, operation and maintenance, and evaluation, whose lessons feed the next project. Most failures are decided early: an unappraised scope, unresolved land, an unfunded O&M plan. Milestones are measurable events (land handed over, financial closure, design approved, commissioning) that mark progress, trigger stage payments in a contract and give the monitoring system something to test.
The logical framework (logframe) is a four-by-four matrix that states a project’s logic and how it will be checked. Read it from the bottom up: if the activities are done and the assumptions hold, the outputs follow; if the outputs are delivered and the assumptions hold, the purpose is achieved; and the purpose contributes to the goal.
| Level | Narrative summary | Indicator and means of verification | Assumption |
|---|---|---|---|
| Goal (impact) | Better public health in the city | Fall in water-borne disease, from health-department records | Sanitation and hygiene services keep pace |
| Purpose (outcome) | Households get safe water every day | Share of households served and hours of supply, from the billing database and survey | Raw-water source stays dependable |
| Outputs | Treatment plant, distribution network, connections, meters | Works completed to specification, from the engineer’s completion certificates | Funds and clearances arrive on time |
| Activities | Design, procure, lay pipe, commission, train operators | Inputs and progress against schedule, from the progress reports | Contractors perform; land is available |
Earned value management compares three numbers at a date: planned value (PV, budgeted cost of work scheduled), earned value (EV, budgeted cost of work actually performed) and actual cost (AC). Cost variance CV = EV − AC and schedule variance SV = EV − PV (negative is bad); cost performance index CPI = EV ÷ AC and schedule performance index SPI = EV ÷ PV (below 1 is bad). If cost performance continues, estimate at completion EAC = BAC ÷ CPI. Worked example. Budget at completion 1,000; PV 400; EV 350; AC 500. CV = −150; SV = −50; CPI = 0.70; SPI = 0.875; EAC = 1,000 ÷ 0.70 = 1,428.57.
A management information system (MIS) carries physical and financial progress from site to the project unit and the decision-makers: periodic reports, geo-tagged photographs, dashboards that flag delay, and third-party quality audit. Monitoring is continuous tracking of inputs, activities and outputs against plan so that corrections are made in time. Evaluation is a periodic judgement of whether the project was worth doing, against criteria such as relevance, effectiveness, efficiency, impact and sustainability, done before (ex ante), midway, at the end, or years later as an impact evaluation that compares with a counterfactual of what would have happened without the project.
6. Asset management and life-cycle cost
Asset management is the systematic, whole-life management of physical assets (roads, pipes, drains, buildings, vehicles) to deliver an agreed level of service at the lowest long-run cost and acceptable risk. Its steps run in a loop: build an asset register (what exists, where, its age, condition and value, often in GIS); fix the level of service; assess condition and criticality (how likely to fail and how bad is the failure); choose maintain, rehabilitate, renew or dispose; fund it through an asset-management plan; and review. Capital works are the small part of what an asset costs; most of the cost falls after commissioning.
Life-cycle cost (LCC) is the present value of everything the asset costs over its life: capital, operation, maintenance, renewal and disposal, less salvage value. Comparing options on first cost alone is the standard mistake. Worked example. Two pipelines last 20 years at 8%; the annuity factor is 9.8181. Pipe A costs 400 and 30 a year to run; pipe B costs 600 and 5 a year. LCC of A = 400 + 30 × 9.8181 = 694.54; LCC of B = 600 + 5 × 9.8181 = 649.09. B is cheaper over its life although it costs 50% more to build.
When options have unequal lives, compare equivalent annual cost (EAC) = capital × capital recovery factor + annual O&M. Machine X costs 100, lasts 5 years and costs 10 a year to run; machine Y costs 150, lasts 8 years and costs 5 a year; the rate is 10%. With recovery factors 0.26380 (5 years) and 0.18744 (8 years): EAC of X = 100 × 0.26380 + 10 = 36.38; EAC of Y = 150 × 0.18744 + 5 = 33.12. Y is cheaper per year despite the dearer purchase.
7. Depreciation methods and the replacement cycle
Depreciation spreads the cost of an asset over its useful life as the asset is consumed. It is an accounting charge, not a cash outflow; set aside as a renewal reserve, it is also the ULB’s way of saving for replacement. Book value is cost less accumulated depreciation.
| Method | Annual charge | Pattern | Worked figure |
|---|---|---|---|
| Straight line | (Cost − salvage) ÷ life | Equal every year | Cost 500, salvage 50, life 9 years: 50 a year |
| Declining balance (written-down value) | Fixed rate × opening book value | High early, falling; book value never reaches zero | Cost 1,00,000 at 20%: book value after 2 years 1,00,000 × 0.8² = 64,000 |
| Double declining balance | (2 ÷ life) × opening book value | Fastest write-off in the early years | Life 5 years, rate 40%: book value after 3 years 1,00,000 × 0.6³ = 21,600 |
| Sum of years’ digits | (Remaining life ÷ sum of digits) × (cost − salvage) | Falling, but reaching salvage exactly | Life 5 years: sum 15, so the first-year share is 5 ÷ 15 |
| Units of production | (Cost − salvage) ÷ total expected output × output this year | Follows use | Suits vehicles and plant that wear with use |
| Sinking fund | Equal deposit that grows with interest to the replacement cost | Small early charges, interest does the rest | Used to provide for replacement of long-lived assets |
The replacement cycle. An asset has a physical life (until it cannot work), a technological or functional life (until it is obsolete or no longer meets demand) and an economic life (the age at which keeping it costs more than replacing it). Rising maintenance and falling reliability push cost up with age while the capital charge spreads thinner; economic life is the age at which the average annual cost is least. Keep the asset while the next year’s cost is below the current average, and replace it when the next year’s cost exceeds that average.
| Year n | O&M in year n | Average annual cost = (100 + total O&M) ÷ n |
|---|---|---|
| 4 | 22 | 41.00 |
| 5 | 26 | 38.00 |
| 6 | 30 | 36.67 |
| 7 | 34 | 36.29 |
| 8 | 38 | 36.50 |
8. Operation and maintenance
Operation is running the asset to deliver the service (operating pumps, valves and treatment plants, collecting waste). Maintenance is the work that keeps the asset able to deliver. A built asset gives its service only as long as it is operated and maintained; the typical failure of urban schemes is that capital grants build the asset and the ULB cannot afford to run it. A detailed project report should therefore carry an O&M plan: tasks, staff, spares, cost and the source of funds (tariff, earmarked budget).
| Kind | What it is | Example |
|---|---|---|
| Routine | Frequent small tasks that keep the asset working | Clearing drain gratings, greasing valves |
| Preventive (planned) | Scheduled by time or use before failure | Servicing a pump every set number of running hours |
| Predictive (condition-based) | Act when a monitored indicator crosses a threshold | Vibration monitoring, CCTV survey of sewers |
| Periodic (major) | Large works at intervals of years | Resurfacing a road |
| Corrective (breakdown) | Repair after failure | Replacing a burst main |
The choice is a trade-off. More preventive work raises maintenance cost but cuts failure cost (loss of service, emergency repair, damage); too little does the reverse. Total cost is the sum of the two and is least at an intermediate level of maintenance, not at zero and not at the maximum. Cost-effective practice mixes the kinds: preventive and predictive work on critical assets, corrective work on assets whose failure is cheap and harmless.
O&M is paid for from the revenue account, so it connects to the earlier chapter: tariffs that do not cover O&M, collection that leaks and non-revenue water all starve it, and the first line cut in a tight budget is maintenance. Contractual remedies are performance-based O&M contracts (payment tied to service levels such as hours of supply or leakage rate, not to inputs) and a computerised maintenance-management system that logs work orders and costs by asset.
9. Institutional structures, accountability and capacity building
How a project is organised decides whether it is delivered. A city’s services are often split among the ULB, a State water board, a development authority and a transport agency, so that each controls a part and none answers for the whole. Institutional design therefore asks: who plans, who builds, who finances, who operates, and who is accountable for the result?
| Form | What it is | Strength | Weakness |
|---|---|---|---|
| ULB department | The service is run within the municipal administration | Direct democratic control | Civil-service rules, weak ring-fencing of money, thin technical staff |
| Corporatised utility | A ULB-owned body with its own accounts and board | Commercial discipline, ring-fenced accounts | Needs a tariff-setting rule or it drifts into subsidy |
| Special purpose vehicle (SPV) | A separate company formed for one project or programme | Ring-fenced cash flows, limited-recourse finance, focus | May bypass the elected council; dies when the project ends |
| Project management unit (PMU) | A dedicated multi-disciplinary team that plans, coordinates and monitors | Specialist skills and one point of responsibility | Consultant-heavy units leave no lasting skill behind |
| State parastatal | A State-level board or authority for a sector | Scale and technical depth | Weak answerability to the city; fragmented services |
An SPV is a legally separate entity whose only business is the project. In a PPP the concessionaire is an SPV owned by its sponsors, so lenders lend against the project’s cash flows and security rather than against the sponsors’ whole balance sheets (project finance, with limited recourse to the sponsors). A city may also form its own SPV with the State, as a company, to carry a programme of projects. A PMU supports the implementing agency and is normally overseen by a steering committee; project-management consultants and an independent engineer or authority’s engineer verify quality and progress.
Accountability needs four things: clear assignment (one named agency answers for each outcome); measurable commitments (service-level agreements, performance contracts, milestones); disclosure (published budgets, accounts, citizen charters, progress reports); and independent checking (internal and statutory audit, third-party quality audit, social audit, grievance redressal). A body accountable to no one for results will optimise for something else.
Capacity building works at three levels: individuals (skills, through training), the organisation (structure, posts, systems such as accounts and MIS, incentives, a specialist cadre of engineers, planners and finance staff) and the enabling environment (rules, devolution of functions and funds, a predictable State framework). Steps are a training-needs assessment, training, systems, retention and then review.
Key takeaways
- A PPP gives a private party design, finance, construction, operation and risk for performance-based payment without selling the asset; the contract spectrum runs service, management, lease or affermage, concession (BOT, BOOT, DBFOT) and BOO, with annuity and hybrid annuity leaving demand risk with the authority. Allocate each risk to the party best able to manage it; VGF is a capital grant for a project that is economically justified but not financially viable.
- Accept a project on NPV > 0, IRR above the required rate, BCR > 1; payback ignores time value and later flows, discounted payback ignores later flows; DSCR tests debt service, not worth. Choose among exclusive projects by NPV or equivalent annual cost, not IRR.
- Social analysis uses shadow prices and the social discount rate, excludes transfers (taxes, subsidies) and financing, and counts externalities; sensitivity analysis finds the switching value at which NPV is zero.
- Monitoring tracks the plan (logframe, milestones, MIS, earned value: CPI = EV ÷ AC, SPI = EV ÷ PV, EAC = BAC ÷ CPI); evaluation judges relevance, effectiveness, efficiency, impact and sustainability.
- Compare assets on life-cycle cost and, for unequal lives, equivalent annual cost; depreciation (straight line, declining balance, sum of years’ digits, units of production, sinking fund) spreads cost, while economic life is the age of least average annual cost.
- O&M needs a plan and a funding source at DPR stage; total maintenance cost is least at an intermediate level. SPVs ring-fence project cash flows, PMUs concentrate skill and responsibility, accountability needs assignment, targets, disclosure and independent audit, and capacity building spans people, organisation and enabling environment.
Practice questions (20)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
In which contract does the private operator run and maintain existing assets, keep the revenue from users and pay a fee to the authority, while the authority continues to fund new investment?
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Answer: A — lease (affermage)
In a lease the operator takes commercial risk by keeping the user revenue, while capital investment stays with the authority. A management contract pays the operator a fee with no revenue risk, a service contract covers one defined task, and a build-own-operate concession has the private party financing and owning the asset.Under a pure annuity PPP road concession, the risk that actual traffic and toll collection fall short of forecast is borne mainly by
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Answer: C — the authority, which collects the toll and pays the fixed annuity whatever the traffic
In an annuity concession the authority pays equal instalments and itself collects the toll, so volume risk stays with the authority. The tempting view that the concessionaire carries it describes a toll BOT, where the concessionaire’s repayment is the toll.A water-treatment PPP has an economic return well above the social discount rate, but the tariff the city can keep affordable gives a financial return below what lenders require. Which response fits best?
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Answer: B — A capital grant sized to close the gap, with bidders competing on the smallest grant they need
This is the case viability gap funding exists for: economically justified, financially short. A grant sized to the gap, competitively bid, makes the project bankable at an affordable tariff. Financial failure does not imply economic failure, and ownership structure does not create revenue the tariff cannot supply.Lenders to a PPP concession usually require that the concessionaire be a separate special purpose vehicle, mainly because it
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Answer: D — keeps the project’s cash flows and security apart from the sponsors’ other businesses, supporting limited-recourse finance
A separate SPV owns only the project, so lenders lend against its cash flows and security and have limited claim on the sponsors’ other assets. It does not discharge the sponsors’ contractual duties, replace the authority’s monitoring, or guarantee any return.Which of the following risks are best allocated to the public authority in a PPP?
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Answer: A — Delay in handing over the acquired land; C — An adverse change in law that raises the project’s costs
Land handover and change in law lie within the State’s sovereign control and the concessionaire cannot manage them. Construction planning and day-to-day O&M performance are controlled by the private party, which can manage them at least cost.A ₹100 crore project is built by a concessionaire under a hybrid annuity arrangement. The authority pays 30% of the cost in construction-linked instalments; the concessionaire finances the remaining 70% and is repaid through ten equal annual annuities at 10% a year. Taking the capital recovery factor for 10 years at 10% as 0.16275 and ignoring construction-period interest and O&M, the annual annuity, in ₹ crore to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 11.39
The financed amount is 70% of 100 = ₹70 crore. Annuity = 70 × 0.16275 = 11.3925, so ₹11.39 crore a year. Applying the factor to the whole ₹100 crore would give 16.275, which ignores the authority’s 30% share.Two mutually exclusive projects are compared at a required rate of 10%, with no shortage of funds. Project X has IRR 24% and NPV 40; project Y has IRR 16% and NPV 90. Which should be chosen, and why?
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Answer: B — Y, because NPV at the required rate measures the gain in value, while IRR can misrank exclusive projects
With funds not constrained and the projects exclusive, the rule is the larger NPV at the proper discount rate, so Y adds 90 against 40. A higher IRR is not a larger gain: X earns a high rate on a smaller or shorter investment. Nothing links a higher IRR to a shorter payback, and closeness to the required rate is not safety.In an economic (social) cost-benefit analysis, which of the following is excluded because it is only a transfer within society?
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Answer: A — A subsidy paid by the government to the operator
A subsidy moves money from the exchequer to the operator and leaves society’s total resources unchanged, so it is dropped in the economic analysis though it appears in the financial one. Time saved and accidents avoided are real benefits, and land at opportunity cost is a real cost.In a region with widespread unemployment, the shadow wage of unskilled labour used in economic analysis is usually
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Answer: C — below the market wage, because the opportunity cost of employing otherwise idle labour is low
A shadow price is the opportunity cost. If labour would otherwise be idle, what society gives up by employing it is small, so the shadow wage falls below the market wage. It is not zero in every case, since some workers would otherwise earn something, and it equals the market wage only where labour markets clear.Which of the following statements about sensitivity analysis are correct?
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Answer: A — One input at a time is varied while the others are held at their base values; B — The switching value of an input is the value at which the NPV becomes zero; D — Scenario analysis moves several inputs together, as in optimistic and pessimistic cases
Sensitivity analysis varies one input from a base case and finds the switching value where NPV reaches zero; scenario analysis moves inputs together. It needs a base-case NPV to start from, so the statement that it removes that need is wrong.A project costs ₹1,000 lakh now and returns ₹600 lakh at the end of year 1 and ₹720 lakh at the end of year 2. Its internal rate of return, in per cent, is ____.
Numerical answer — type the value.
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Answer: 20
Test 20%: 600 ÷ 1.20 = 500 and 720 ÷ 1.44 = 500, which sum to 1,000, equal to the outlay, so NPV = 0 and IRR = 20%. Check with the equation: 1,000(1 + r)² = 600(1 + r) + 720 gives r = 0.20. At 10% the NPV would still be positive, so the rate must be higher.A project costs ₹900 and returns ₹300, ₹400 and ₹500 at the end of years 1, 2 and 3. At a discount rate of 10%, taking flows as even within each year, its discounted payback period, in years to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 2.79
Discounted inflows: 300 ÷ 1.1 = 272.73; 400 ÷ 1.21 = 330.58; 500 ÷ 1.331 = 375.66. Cumulative after year 2 = 603.31, so 900 − 603.31 = 296.69 is still to recover in year 3. Fraction = 296.69 ÷ 375.66 = 0.79. Discounted payback = 2.79 years. The simple payback would be 2 + 200 ÷ 500 = 2.40 years.In a logical framework, the level that states the immediate change expected for the target group, as distinct from the goods and services delivered, is the
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Answer: B — purpose (the immediate outcome for the beneficiaries)
The purpose or outcome is the change in the beneficiaries’ situation, such as households getting safe water. Outputs are the deliverables (plant, pipes), activities are the tasks that produce them, and the goal is the higher, longer-term development impact the purpose contributes to.At a review date a project shows a cost performance index of 0.80 and a schedule performance index of 1.10. This indicates that
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Answer: D — the work done has cost more than its budgeted value, although progress is ahead of the plan
CPI = EV ÷ AC below 1 means each rupee spent earned less than a rupee of budgeted work, so costs are over. SPI = EV ÷ PV above 1 means more work has been done than was planned, so progress is ahead. The two indices are read separately.A machine costs 100 and has zero salvage value. Its operating and maintenance cost is 10 in year 1 and rises by 4 each year. Ignoring discounting, its economic life, in years, is
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Answer: C — 7 years
Average annual cost = (100 + total O&M) ÷ n gives 36.67 at 6 years, 36.29 at 7 and 36.50 at 8, so it is least at 7 years. Equivalently, year 7 costs 34, below the 6-year average, while year 8 costs 38, above the 7-year average. Physical life, the time to breakdown, has no bearing on this.A machine costing ₹1,00,000 with a five-year life is depreciated by the double declining balance method. Its book value after two years, in rupees, is
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Answer: A — 36,000
The double declining rate is 2 ÷ 5 = 40% of the opening book value: year 1 charge 40,000 leaves 60,000; year 2 charge 24,000 leaves 36,000, which equals 1,00,000 × 0.6². The figure 64,000 is the book value at 20% a year, 60,000 is the value after one year, and 40,000 is the first-year charge.Which of the following statements about maintenance are correct?
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Answer: A — Preventive maintenance is scheduled by time or use before a failure occurs; C — A detailed project report should show the O&M plan and its source of funds; D — Predictive maintenance acts when a monitored condition indicator crosses a threshold
Preventive work is scheduled ahead of failure, predictive work follows a condition indicator, and a DPR should carry the O&M plan and funding so the asset can be kept in service. Total cost is least at an intermediate level of maintenance, so doing none is wrong.Which of the following strengthen accountability for a municipal project?
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Answer: A — Naming one agency as answerable for each outcome; C — Publishing budgets, accounts and progress reports with service-level targets
Accountability needs clear assignment of responsibility and disclosure against targets, so naming one answerable agency and publishing accounts and progress strengthen it. Fragmenting ownership and withholding performance data weaken it.A machine costs ₹120 lakh, lasts 6 years and costs ₹8 lakh a year to operate and maintain. At a discount rate of 12% the capital recovery factor for 6 years is 0.24323. Its equivalent annual cost, in ₹ lakh to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 37.19
Annualised capital = 120 × 0.24323 = 29.19. EAC = 29.19 + 8 = 37.19 lakh a year. Adding 8 to a plain 120 ÷ 6 = 20 would give 28, which ignores the interest on the capital.A project has a budget at completion of ₹1,800 lakh. At a review its earned value is ₹600 lakh and its actual cost is ₹800 lakh. If the current cost efficiency continues for the rest of the work, the estimate at completion, in ₹ lakh, is ____.
Numerical answer — type the value.
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Answer: 2400
CPI = EV ÷ AC = 600 ÷ 800 = 0.75. EAC = BAC ÷ CPI = 1,800 ÷ 0.75 = 2,400. The tempting figure 1,800 + (800 − 600) = 2,000 assumes the overrun so far will not recur, which contradicts the stated continuing efficiency.