31  Capital budgeting decisions: Conventional and scientific techniques of capital budgeting analysis

31.1 Concept of Capital Budgeting

Capital budgeting is the process of evaluating, selecting and prioritising long-term investment projects whose returns are expected over more than one year. Examples: building a new plant, launching a new product line, acquiring another company, replacing old machinery, computerising operations. Because the decisions involve large outlays, long horizons, irreversibility and uncertainty, they are arguably the most important decisions a firm’s management makes. Capital-budgeting techniques fall into two families: conventional (Payback, ARR — ignore time value of money) and scientific / discounted (NPV, IRR, PI, Discounted Payback — apply time value).

31.2 Why Capital Budgeting Matters

TipSignificance of Capital Budgeting Decisions
  • Substantial funds — typically large outlays.
  • Long-term — benefits stream over many years.
  • Irreversibility — capital tied up; resale value often low.
  • Determines productive capacity of the firm.
  • Affects competitive position — better technology, better cost.
  • Affects risk profile — operating leverage rises with fixed-asset investment.
  • Affects future cost structure and pricing.

31.3 Classification of Capital Investments

TipTypes of Capital Projects
  • Replacement projects — replace worn-out or obsolete assets.
  • Expansion of existing line — add capacity for existing products.
  • Diversification — new products or markets.
  • Research and Development — usually large risk and uncertain return.
  • Mandatory (regulatory) — pollution-control, safety; not optional.
  • Statutory — required by law (BIS, fire safety).
  • Strategic / Long-range — building competitive advantage.

31.4 Cash-Flow Estimation

Most capital-budgeting methods evaluate cash flows, not accounting profits. Three reasons: cash is objective, time-able, and the only thing that funds future investment or dividends.

TipComputing Project Cash Flows
  • Use after-tax cash flows, not pre-tax.
  • Include incremental cash flows only — change due to the project.
  • Add back depreciation (non-cash) after tax computation.
  • Include opportunity costs of resources diverted from elsewhere.
  • Exclude sunk costs — already incurred, irrelevant.
  • Include side-effects — cannibalisation, synergies.
  • Treat working capital changes as cash outflow when increased; inflow when released.
  • Include terminal / salvage values, net of tax.

31.5 Conventional (Non-Discounted) Techniques

31.5.1 Payback Period

The payback period = number of years to recover the initial investment from project cash inflows.

\[\text{Payback} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} \quad \text{(if cash inflows constant)}\]

For uneven cash flows, accumulate until the outflow is recovered.

TipPayback — Pros and Cons
Pros Cons
Simple and easy to compute Ignores time value of money
Emphasises liquidity and short-term risk Ignores cash flows after the payback period
Useful for risky or rapidly-changing industries Ignores profitability beyond breakeven

31.5.2 Accounting Rate of Return (ARR)

\[\text{ARR} = \frac{\text{Average Annual PAT}}{\text{Average Investment}} \times 100\]

where Average Investment often = (Initial cost + Salvage)/2 or (Initial cost)/2.

TipARR — Pros and Cons
Pros Cons
Uses accounting figures readily available Uses accounting profit, not cash flows
Easy to compute Ignores time value of money
Considers entire project life Multiple formulae give different ARR values

31.6 Scientific (Discounted) Techniques

31.6.1 Net Present Value (NPV)

The NPV is the present value of cash inflows minus the initial investment (and any future outflows), all discounted at the firm’s cost of capital:

\[NPV = -I_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t}\]

TipNPV Decision Rules
  • NPV > 0 → Accept the project.
  • NPV < 0 → Reject.
  • NPV = 0 → Indifferent.
  • For mutually exclusive projects: choose the one with the highest NPV.

31.6.2 Internal Rate of Return (IRR)

The IRR is the discount rate at which NPV = 0:

\[0 = -I_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t}\]

TipIRR Decision Rules
  • IRR > cost of capital → Accept.
  • IRR < cost of capital → Reject.
  • Compute via trial-and-error or interpolation.
  • Limitations: multiple IRRs for non-conventional cash flows; reinvestment assumption at IRR may be unrealistic; can mislead in mutually exclusive projects.

31.6.3 Modified IRR (MIRR)

To address the reinvestment-rate problem, MIRR assumes reinvestment of intermediate cash flows at the cost of capital rather than at the IRR. MIRR is unique and consistent with NPV ranking.

31.6.4 Profitability Index (PI) / Benefit-Cost Ratio

\[PI = \frac{PV \text{ of inflows}}{Initial Investment}\]

TipPI Decision Rules
  • PI > 1 → Accept.
  • PI < 1 → Reject.
  • For capital rationing, rank projects by PI — most NPV per rupee of investment.

31.6.5 Discounted Payback Period

Same as payback but using discounted cash flows. Overcomes the time-value criticism of simple payback but still ignores cash flows after recovery.

31.6.6 Comparison

TipNPV vs IRR — Summary
Aspect NPV IRR
Measure Absolute (₹) Percentage
Reinvestment At cost of capital At IRR
Multiple roots No Yes (non-conventional CF)
Decision in mutually exclusive Reliable Can mislead
Comparability across projects Direct Comparable
Theoretically Superior Less robust
NoteDistractor warning

PYQs often ask: which method is theoretically superior? NPV — because (a) absolute rupee value, (b) consistent with shareholder-wealth maximisation, (c) realistic reinvestment assumption, (d) no multiple-root problem.

flowchart LR
  CB[Capital Budgeting<br/>Techniques] --> NC[Non-Discounted]
  CB --> DC[Discounted]
  NC --> PB[Payback]
  NC --> ARR[ARR]
  DC --> NPV[NPV]
  DC --> IRR[IRR]
  DC --> MIRR[MIRR]
  DC --> PI[PI]
  DC --> DPB[Discounted Payback]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

31.7 Risk in Capital Budgeting

TipTechniques to Handle Risk
  • Risk-adjusted discount rate (RADR) — riskier projects discounted at higher rate.
  • Certainty Equivalent (CE) approach — multiply each risky CF by a CE coefficient (< 1).
  • Sensitivity analysis — change one input at a time; observe NPV.
  • Scenario analysis — multiple coherent scenarios (best, base, worst).
  • Simulation / Monte Carlo — random sampling from input distributions.
  • Decision trees — sequential decision pathways with probabilities.
  • Real options — value the flexibility embedded in projects (expand, abandon, defer).

31.8 Capital Rationing

When the firm cannot finance every NPV-positive project (due to budget constraint), it must ration capital — choose the combination of projects that maximises aggregate NPV within the budget. Methods:

TipCapital Rationing Methods
  • Profitability Index ranking — rank by PI; choose in order.
  • Integer programming — for indivisible projects with multi-period budgets.
  • Project bundles — choose combinations with highest total NPV within budget.

31.9 Practice Questions

Q 01 NPV Easy

Accept a project if:

  • ANPV < 0
  • BNPV > 0
  • CNPV = 0
  • DAlways reject
View solution
Correct Option: B
**NPV > 0** → project adds value → accept.
Q 02 IRR Easy

IRR is the discount rate that makes:

  • ANPV = 0
  • BPI > 1
  • CPayback minimum
  • DARR maximum
View solution
Correct Option: A
IRR — discount rate at which **NPV = 0**.
Q 03 Payback Easy

Initial investment ₹50,000; annual cash inflow ₹10,000. Payback period:

  • A2 years
  • B5 years
  • C10 years
  • D50 years
View solution
Correct Option: B
Payback = 50,000 / 10,000 = **5 years**.
Q 04 PI Medium

PV of inflows ₹1,20,000; Initial investment ₹1,00,000. Profitability Index:

  • A0.83
  • B1.0
  • C1.2
  • D20,000
View solution
Correct Option: C
PI = 1,20,000 / 1,00,000 = **1.2**; accept since > 1.
Q 05 Theory Medium

Which method is theoretically the **best** capital-budgeting technique?

  • APayback
  • BARR
  • CNPV
  • DDiscounted Payback
View solution
Correct Option: C
**NPV** is consistent with wealth maximisation; correctly handles time, risk, reinvestment.
Q 06 Cash flows Medium

For capital-budgeting analysis, the relevant flows are:

  • AAfter-tax incremental cash flows
  • BAccounting profits
  • CSunk costs
  • DAllocated overhead
View solution
Correct Option: A
**After-tax incremental cash flows** — economic measure used in NPV.
Q 07 Sunk Medium

In project evaluation, sunk costs should be:

  • AIncluded
  • BExcluded
  • CAllocated proportionally
  • DCapitalised
View solution
Correct Option: B
Sunk costs are **irrelevant** — already incurred.
Q 08 Limitation Medium

A key limitation of payback is:

  • AIt is too complex
  • BIt ignores the time value of money and cash flows beyond recovery
  • CIt uses cash flows
  • DIt overemphasises long-term risk
View solution
Correct Option: B
Ignores time value of money and post-payback cash flows.
Q 09 Multiple IRR Hard

Multiple IRRs can arise when:

  • ACash flows are conventional
  • BCash flows have more than one sign change (non-conventional)
  • CAll cash flows are positive
  • DDiscount rate is zero
View solution
Correct Option: B
Non-conventional cash flows can produce multiple IRRs (Descartes' rule of signs).
Q 10 Capital rationing Medium

Under capital rationing, projects are typically ranked by:

  • ANPV
  • BProfitability Index
  • CPayback
  • DARR
View solution
Correct Option: B
PI ranks projects by NPV per rupee of investment — best for rationing.
Q 11 ARR Medium

Accounting Rate of Return uses:

  • ACash flow / investment
  • BAverage accounting profit / average investment
  • CIRR / cost of capital
  • DNPV / initial cost
View solution
Correct Option: B
ARR = Avg PAT / Avg Investment × 100.
Q 12 Reinvestment Hard

NPV implicitly assumes intermediate cash flows are reinvested at:

  • AIRR
  • BCost of capital
  • CRisk-free rate
  • DInflation rate
View solution
Correct Option: B
NPV → reinvest at cost of capital; IRR → reinvest at IRR (often unrealistic).
Q 13 MIRR Hard

MIRR addresses which limitation of IRR?

  • ATime value of money
  • BMultiple IRRs and unrealistic reinvestment assumption
  • CSunk costs
  • DInflation
View solution
Correct Option: B
**MIRR** uses cost-of-capital reinvestment and gives a unique value.
Q 14 Risk Medium

Sensitivity analysis is best described as:

  • ATesting many scenarios at once
  • BChanging one input at a time and observing the effect on NPV
  • CMonte Carlo simulation
  • DDecision tree
View solution
Correct Option: B
Sensitivity = one-variable-at-a-time.
Q 15 Discount rate Medium

In NPV computation, the discount rate used is typically:

  • AInflation rate
  • BRisk-free rate
  • CFirm's cost of capital (WACC)
  • DBank deposit rate
View solution
Correct Option: C
**WACC** — for projects of same risk class as firm.
Q 16 Real options Hard

"Real options" in capital budgeting value:

  • AStock options held by managers
  • BFlexibility embedded in projects (defer, expand, abandon, switch)
  • CForeign-exchange options
  • DGovernment concessions
View solution
Correct Option: B
Real options capture *managerial flexibility* not reflected in static NPV.
Q 17 Conventional Easy

Conventional capital-budgeting techniques include:

  • ANPV and IRR
  • BPayback and ARR
  • CPI only
  • DMIRR only
View solution
Correct Option: B
Conventional (non-discounted) = **Payback, ARR**.
Q 18 Working capital Medium

An increase in working capital required by a project is treated as:

  • AA cash inflow at project start
  • BA cash outflow at project start, recovered at project end
  • CAn accounting expense only
  • DIgnored
View solution
Correct Option: B
WC investment → outflow at start; recovery → inflow at end.
Q 19 Indep vs Mut Medium

For *mutually exclusive* projects, when NPV and IRR conflict, you should rely on:

  • AIRR
  • BNPV
  • CPayback
  • DARR
View solution
Correct Option: B
**NPV** is consistent with wealth-maximisation; IRR can mislead on scale.
Q 20 Hurdle Medium

A project's IRR is 14 %; cost of capital is 12 %. The decision is to:

  • AReject
  • BAccept
  • CIndifferent
  • DInsufficient information
View solution
Correct Option: B
IRR > cost of capital → **accept**.

31.10 Quick Recall

ImportantQuick recall
  • Capital budgeting — evaluate long-term investment projects; large, irreversible, long-horizon.
  • Cash-flow rules: after-tax incremental flows; add back depreciation; include opportunity cost; exclude sunk cost; include side-effects; treat WC; include terminal value.
  • Conventional / non-discounted: Payback (= Investment/Annual CF), ARR (= Avg PAT/Avg Investment).
  • Scientific / discounted: NPV (= PV inflows − Investment), IRR (NPV = 0), MIRR, PI (= PV inflows/Investment), Discounted Payback.
  • Decision rules: NPV > 0; IRR > cost of capital; PI > 1.
  • NPV vs IRR: NPV is theoretically superior; IRR can yield multiple roots and unrealistic reinvestment.
  • Risk techniques: RADR, CE, Sensitivity, Scenario, Simulation, Decision trees, Real options.
  • Capital rationing — rank by PI.