47  Capital Budgeting and Investment Evaluation

47.1 What is Capital Budgeting?

Capital Budgeting is the process of planning, evaluating and selecting long-term investments whose returns are expected over a period exceeding one year. Also called Investment Decision or Capital Expenditure Decision, it is at the heart of the firm’s investment function. Joel Dean’s Capital Budgeting (1951) is the foundational text.

TipWorking definitions
Author Definition
Charles T. Horngren “Capital budgeting is long-term planning for making and financing proposed capital outlays.”
G.C. Philippatos “Capital budgeting is concerned with the allocation of funds among investment alternatives.”
Joel Dean “It is the process of evaluating and selecting long-term capital investment proposals.”
Lynch “Capital budgeting consists of planning, development of available capital for the purpose of maximising long-term profitability.”
I.M. Pandey “Capital budgeting decisions are decisions on which financial resources are committed for relatively long periods in expectation of yields over future periods.”

47.2 Importance of Capital Budgeting

TipWhy capital budgeting matters
  • Long-term commitment — funds locked for years.
  • Substantial outlays — typically large amounts.
  • Irreversibility — exit is costly.
  • Risk and uncertainty — long horizon = more uncertainty.
  • Profitability and growth of the firm.
  • Strategic direction — capacity, technology, markets.
  • Effect on competitive position.
  • Difficulty of decision — multiple variables.

47.3 Types of Capital Investments

TipCategories of capital projects
Type Examples
Replacement Old machinery → new
Expansion Capacity addition, new factory
Modernisation Automation, new technology
Diversification New product line / market
Research & Development New product development
Mandatory / Regulatory Pollution control, safety
Welfare Canteen, recreation
Strategic Acquisitions, JVs

47.4 The Capital Budgeting Process

flowchart LR
  ID[1. Identify<br/>Proposals] --> SC[2. Screen]
  SC --> EV[3. Evaluate<br/>NPV/IRR/etc.]
  EV --> RNK[4. Rank &<br/>Select]
  RNK --> IM[5. Implement]
  IM --> MON[6. Monitor &<br/>Post-Audit]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

TipSix-step process
  1. Identify investment opportunities.
  2. Screen and shortlist.
  3. Evaluate using techniques (NPV, IRR, etc.).
  4. Rank and select projects within capital constraints.
  5. Implement and execute.
  6. Monitor and post-audit — compare actuals to estimates.

47.5 Cash Flow Estimation

Capital budgeting uses incremental, after-tax cash flows, not accounting profits:

TipPrinciples of cash-flow estimation
  • Incremental cash flows only — what changes due to the project.
  • After-tax basis.
  • Ignore sunk costs — past, irrecoverable.
  • Include opportunity costs.
  • Include working-capital changes.
  • Side effects — cannibalisation, externalities, synergies.
  • Allocated overheads — only incremental portion.
  • Inflation consistency — nominal cash flows with nominal rate, or real with real.
  • Salvage value at terminal year.
  • Depreciation tax shield — non-cash but reduces tax.

47.5.1 Initial, Operating and Terminal Cash Flows

TipThree phases of project cash flow
Phase Includes
Initial Investment (CF₀) Cost of asset + installation + working-capital outlay − tax savings on disposal of old
Operating Cash Flows (CFt) (EBIT − Tax) + Depreciation = EBIT(1−t) + Dep · Tax Shield
Terminal Cash Flow Salvage value (after tax) + Recovery of working capital

47.6 Evaluation Techniques

Capital-budgeting techniques fall into two families:

flowchart TB
  CB[Capital Budgeting<br/>Techniques]
  CB --> TRD[Traditional /<br/>Non-DCF]
  CB --> DCF[Discounted<br/>Cash Flow]
  TRD --> PB[Payback Period]
  TRD --> ARR[ARR / ROI]
  DCF --> NPV[NPV]
  DCF --> IRR[IRR]
  DCF --> PI[Profitability Index]
  DCF --> MIRR[Modified IRR]
  DCF --> DPB[Discounted Payback]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

47.7 Traditional / Non-DCF Techniques

47.7.1 1. Payback Period (PB)

TipPayback Period

Time taken for cumulative cash inflows to recover the initial outlay.

  • Uniform CFs: PB = Initial Investment / Annual CF.
  • Uneven CFs: PB = Year before recovery + (Unrecovered amount / CF in recovery year).
  • Decision rule: Accept if PB < cut-off; for mutually exclusive, choose shortest PB.
TipPayback — pros and cons
  • Pros: Simple · Quick liquidity check · Useful in capital-constrained environments.
  • Cons: Ignores time value of money · Ignores cash flows beyond payback · No measure of profitability.

47.7.2 2. Average Rate of Return (ARR) / Accounting Rate of Return

TipARR formula

\[\text{ARR} = \frac{\text{Average Annual Profit (after tax)}}{\text{Average Investment}} \times 100\]

Where Average Investment = (Initial + Scrap) / 2 + Working Capital.

Decision rule: Accept if ARR > required rate.

TipARR — pros and cons
  • Pros: Simple · Uses accounting profits.
  • Cons: Ignores time value of money · Uses accounting profit, not cash flow · Multiple definitions of “average investment”.

47.8 Discounted Cash Flow (DCF) Techniques

47.8.1 1. Net Present Value (NPV)

\[\text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1+k)^t} - CF_0\]

NPV is the most theoretically sound technique. Accept if NPV > 0; for mutually exclusive, choose the project with highest NPV.

TipNPV — pros and cons
  • Pros: Recognises TVM · Considers all cash flows · Additive (sum of NPVs of components = NPV of project) · Direct measure of value addition · Consistent with wealth maximisation.
  • Cons: Sensitive to discount rate · Difficult to estimate cost of capital · Cannot rank projects of very different size on its own.

47.8.2 2. Internal Rate of Return (IRR)

IRR = the discount rate at which NPV = 0.

\[\sum_{t=1}^{n} \frac{CF_t}{(1+\text{IRR})^t} = CF_0\]

Accept if IRR > Cost of Capital.

TipIRR — pros and cons
  • Pros: Considers TVM · Intuitive (a %) · No need to pre-specify discount rate · Widely used.
  • Cons: Multiple IRRs with non-conventional cash flows · Conflict with NPV in mutually exclusive projects · Implicit reinvestment at IRR (often unrealistic) · Cannot handle scale differences.

47.8.3 3. Profitability Index (PI) / Benefit-Cost Ratio

TipPI formula and rule

\[\text{PI} = \frac{\text{PV of Future Cash Flows}}{\text{Initial Investment}}\]

Accept if PI > 1; for mutually exclusive choose highest PI.

NoteWhy PI matters under capital rationing

When capital is constrained, PI ranks projects by value created per rupee of investment — more useful than absolute NPV.

47.8.4 4. Modified Internal Rate of Return (MIRR)

MIRR corrects IRR’s reinvestment-rate assumption by reinvesting positive CFs at the cost of capital (not IRR):

\[\text{MIRR} = \left(\frac{\text{Terminal Value of Inflows}}{\text{PV of Outflows}}\right)^{1/n} - 1\]

47.8.5 5. Discounted Payback Period

Adjusts the simple payback by discounting cash flows. Still ignores cash flows beyond the discounted-payback period.

47.9 NPV vs IRR — Conflict and Resolution

TipWhen NPV and IRR conflict
Cause Why it leads to conflict
Scale differences Larger project has higher NPV; smaller may have higher IRR
Timing differences Different cash-flow patterns
Project life differences Reinvestment over different horizons
Multiple IRRs Non-conventional cash flows (sign changes)
NoteCrossover (Fisher) Rate

The Fisher / Crossover Rate is the discount rate at which NPVs of two projects are equal. Below it, the project with higher late cash flows is preferable; above it, the project with higher early cash flows.

Decision rule for conflict — choose NPV. NPV is consistent with shareholder-wealth maximisation; IRR can mislead.

47.10 Capital Rationing

Capital Rationing = the situation where the firm has more profitable projects than available capital. Decision rule: maximise total NPV subject to the capital constraint.

TipCapital rationing — solution techniques
  • Rank by PI when projects are independent and divisible.
  • Combinatorial selection for indivisible projects — pick the bundle with highest NPV within budget.
  • Linear / Integer Programming — for complex multi-period constraints.
  • Hard rationing — externally imposed; Soft rationing — internally imposed.

47.11 Risk Analysis in Capital Budgeting

TipRisk-handling techniques
Technique Idea
Risk-Adjusted Discount Rate Higher k for riskier projects
Certainty Equivalent (CE) Method Adjust cash flows downward by risk
Sensitivity Analysis One-variable-at-a-time impact
Scenario Analysis Best / Worst / Most-likely scenarios
Monte Carlo Simulation Probability distribution of NPV
Decision Trees Sequential decisions under uncertainty
Standard deviation / Variance Of NPV distribution
Beta-adjusted hurdle rate Use project-specific β in CAPM
Real Options Embedded flexibility

47.11.1 Risk-Adjusted Discount Rate (RADR)

\[\text{RADR} = R_f + \text{Risk Premium for the project}\]

Riskier projects get a higher discount rate.

47.11.2 Certainty-Equivalent Approach

Convert risky CFs into their certainty-equivalent (CE) form by multiplying with α (between 0 and 1), then discount at the risk-free rate:

\[\text{NPV}_{CE} = \sum \frac{\alpha_t \times CF_t}{(1+R_f)^t} - CF_0\]

47.12 Real Options

Real Options apply option-pricing logic to capital budgeting — recognising that managers have flexibility over projects: to defer, expand, contract, abandon, or switch. Stewart Myers (1977) coined the term.

TipCommon real options
  • Option to defer / delay the project.
  • Option to expand / scale up.
  • Option to abandon / exit.
  • Option to contract / scale down.
  • Option to switch inputs/outputs.
  • Compound options — option whose underlying is another option.
  • Growth options — capacity for future growth.
  • Timing options.

47.13 Adjusted Present Value (APV)

Stewart Myers (1974) — APV = NPV (all-equity) + PV of financing side-effects (tax shields, issuance costs). Useful for highly-levered projects (LBOs).

47.14 Inflation in Capital Budgeting

TipInflation — consistency principle
  • Use nominal cash flows with nominal discount rate.
  • Or use real cash flows with real discount rate.
  • Mixing leads to errors — one of the most common errors in capital budgeting.

47.15 Multiple Project Lives — Equivalent Annual Cost

When comparing mutually exclusive projects with different lives, use Equivalent Annual Cost (EAC):

\[\text{EAC} = \frac{\text{NPV of Costs}}{\text{PVIFA}(k, n)}\]

The project with the lower EAC is preferable.

47.17 Practice Questions

Q 01 NPV Easy

An investment proposal should be accepted if its NPV is:

  • APositive
  • BZero
  • CNegative
  • DEqual to IRR
View solution
Correct Option: A
Accept if **NPV > 0** — value-creating.
Q 02 IRR Easy

IRR is the discount rate at which:

  • ANPV = 0
  • BPI = 1
  • CPB = Project life
  • DARR = 0
View solution
Correct Option: A
IRR makes NPV = 0; equivalently PI = 1.
Q 03 Payback Easy

The main limitation of the Payback Period method is that it:

  • AIgnores TVM
  • BIs too complex
  • CConsiders cash flows beyond payback
  • DRequires a hurdle rate
View solution
Correct Option: A
Ignores TVM and cash flows after payback.
Q 04 PI Medium

A project's PI is 1.15. The project should be:

  • ARejected
  • BAccepted
  • CPostponed
  • DIndeterminate
View solution
Correct Option: B
PI > 1 → NPV positive → accept.
Q 05 DCF Easy

Which is NOT a DCF technique?

  • ANPV
  • BIRR
  • CPI
  • DARR
View solution
Correct Option: D
ARR is non-DCF; uses accounting profit, not cash flow.
Q 06 Sunk cost Medium

In capital budgeting, sunk costs should be:

  • AIncluded
  • BIgnored
  • CDoubled
  • DDiscounted
View solution
Correct Option: B
Sunk costs are past, irreversible → ignore.
Q 07 Multiple IRR Hard

Multiple IRRs arise when:

  • ACash flow signs change more than once
  • BProject life > 10 years
  • CCost of capital > 15 %
  • DNPV is positive
View solution
Correct Option: A
Non-conventional cash flows (multiple sign changes) → multiple IRRs possible (Descartes' rule).
Q 08 Conflict Medium

When NPV and IRR conflict for mutually exclusive projects, which should be preferred?

  • AIRR
  • BNPV
  • CPayback
  • DARR
View solution
Correct Option: B
NPV — consistent with wealth maximisation.
Q 09 Reinvestment Hard

NPV assumes intermediate cash flows are reinvested at:

  • AIRR
  • BCost of capital
  • CRisk-free rate
  • DInflation rate
View solution
Correct Option: B
NPV — at cost of capital; IRR — at IRR (often unrealistic).
Q 10 MIRR Hard

MIRR assumes positive cash flows are reinvested at:

  • AIRR
  • BCost of capital
  • CInflation rate
  • DNegative IRR
View solution
Correct Option: B
MIRR corrects IRR's reinvestment-rate assumption by using cost of capital.
Q 11 Crossover Hard

The Fisher / Crossover Rate is the discount rate at which:

  • ANPV = 0
  • BNPVs of two projects are equal
  • CPI = 1
  • DPB = Project life
View solution
Correct Option: B
Crossover rate equates NPVs of two competing projects.
Q 12 Capital rationing Medium

Under capital rationing with independent divisible projects, the best ranking criterion is:

  • ANPV
  • BIRR
  • CProfitability Index (PI)
  • DPayback Period
View solution
Correct Option: C
PI ranks projects by value per rupee of investment.
Q 13 CE Hard

In the Certainty Equivalent method, cash flows are discounted at:

  • ARisk-free rate
  • BRisk-adjusted rate
  • CCost of equity
  • DWACC
View solution
Correct Option: A
CE adjusts CFs for risk → discount at risk-free rate.
Q 14 Operating CF Medium

Operating cash flow for capital budgeting equals:

  • AEBIT × (1 − t)
  • BEBIT(1 − t) + Depreciation
  • CPAT + Interest
  • DPAT + Tax
View solution
Correct Option: B
Add back **depreciation** (non-cash); CF = EBIT(1−t) + Dep.
Q 15 Real options Hard

The "real options" approach to capital budgeting was pioneered by:

  • AStewart Myers
  • BJoel Dean
  • CEugene Fama
  • DHarry Markowitz
View solution
Correct Option: A
Stewart Myers (1977) coined "real options".
Q 16 EAC Hard

EAC (Equivalent Annual Cost) is used to compare projects with:

  • ADifferent lives
  • BSame lives
  • CZero NPV
  • DNegative cash flows only
View solution
Correct Option: A
EAC converts unequal-life NPVs to comparable annual figures.
Q 17 Joel Dean Hard

The foundational text on capital budgeting (1951) was by:

  • AJoel Dean
  • BHorngren
  • CModigliani
  • DBrigham
View solution
Correct Option: A
Joel Dean, *Capital Budgeting* (1951) — Columbia.
Q 18 Sensitivity Medium

Sensitivity analysis examines:

  • AEffect of changing one variable at a time
  • BJoint effect of all variables changing
  • CProbability distribution of NPV
  • DSequential decisions
View solution
Correct Option: A
Sensitivity = one-variable-at-a-time; Scenario = multiple together; Monte Carlo = distribution.
Q 19 APV Hard

Adjusted Present Value (APV) was developed in 1974 by:

  • AStewart Myers
  • BModigliani & Miller
  • CStephen Ross
  • DJoel Dean
View solution
Correct Option: A
Stewart Myers (1974) — APV separates operating and financing effects.
Q 20 Match techniques Hard

Match the technique with its key feature:

(i) Payback (a) NPV = 0
(ii) NPV (b) Time to recover outlay
(iii) IRR (c) PV / CF₀
(iv) PI (d) PV − CF₀
  • A(i)-(b), (ii)-(d), (iii)-(a), (iv)-(c)
  • B(i)-(a), (ii)-(b), (iii)-(c), (iv)-(d)
  • C(i)-(c), (ii)-(d), (iii)-(b), (iv)-(a)
  • D(i)-(d), (ii)-(a), (iii)-(c), (iv)-(b)
View solution
Correct Option: A
PB — time to recover; NPV — PV − CF₀; IRR — NPV = 0; PI — PV / CF₀.

47.17.1 Advanced Format Questions

AR 1Assertion-ReasonHard

A: NPV is theoretically superior to IRR for mutually exclusive projects.
R: IRR can produce multiple rates with non-conventional cash flows.

  • ABoth true; R explains A
  • BBoth true; R does not explain A
  • CA true, R false
  • DA false, R true
View solution
Correct Option: A
S 1Statement-basedMedium

Capital-budgeting methods: (i) Payback. (ii) ARR. (iii) NPV. (iv) IRR.

  • AAll four
  • B(i) and (ii) only
  • C(iii) and (iv) only
  • D(iii) only
View solution
Correct Option: A
N 1NumericalMedium

Initial outlay ₹1 L; uniform CF ₹25,000/yr. Payback (years):

  • A4
  • B3
  • C5
  • D2.5
View solution
Correct Option: A
1,00,000/25,000 = 4 years.
N 2NumericalHard

Project: Initial outflow ₹100; Year 1 inflow ₹110. IRR is:

  • A10 %
  • B5 %
  • C15 %
  • D110 %
View solution
Correct Option: A
−100 + 110/(1+r) = 0 → r = 10%.

47.18 Quick Recall

ImportantQuick recall
  • Capital Budgeting: long-term investment decision. Joel Dean (1951) is the foundational text.
  • 8 importance points: long-term commitment, large outlay, irreversibility, risk, profitability, strategy, competitive position, complexity.
  • Types of projects: Replacement · Expansion · Modernisation · Diversification · R&D · Mandatory · Welfare · Strategic.
  • 6-step process: Identify → Screen → Evaluate → Rank/Select → Implement → Post-audit.
  • Cash-flow rules: incremental · after-tax · ignore sunk · include opportunity · WC changes · side effects · consistency with inflation.
  • 3 phases: Initial (CF₀) · Operating (CFt = EBIT(1−t) + Dep) · Terminal (Salvage + WC).
  • Two families:
    • Non-DCF: Payback · ARR.
    • DCF: NPV · IRR · PI · MIRR · Discounted Payback.
  • Decision rules:
    • NPV > 0 · IRR > Cost of Capital · PI > 1 · PB < cut-off · ARR > required.
  • NPV vs IRR conflict: scale · timing · life · multiple IRRs → prefer NPV.
  • Crossover (Fisher) Rate: NPVs of two projects equal.
  • MIRR: reinvest CFs at cost of capital → corrects IRR’s flaw.
  • Capital Rationing: rank by PI (independent divisible); IP for indivisible; hard vs soft.
  • Risk analysis: RADR · CE method · Sensitivity · Scenario · Monte Carlo · Decision Trees · Real Options.
  • CE method discounts at risk-free rate; RADR discounts at adjusted rate.
  • Real Options — Stewart Myers (1977): defer · expand · abandon · contract · switch · compound · growth · timing.
  • APV — Myers (1974): NPV (all-equity) + PV (financing side effects).
  • Inflation: use nominal-nominal OR real-real consistently.
  • Different lives: use EAC = NPV / PVIFA; lower EAC preferred.
  • Modern trends: real options · Monte Carlo · big-data CFs · ESG-NPV · carbon shadow · stage-gate R&D · platform CapEx · behavioural correction · climate-resilient capex.