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Finance 3% exam weight

Topic 8

Part of the RBI Grade B study roadmap. Finance topic financ-008 of Finance.

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Topic 8

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

  • Capital Budgeting evaluates long-term investment decisions using cash flows (not accounting profits)
  • NPV is the primary criterion: Accept if NPV > 0; NPV = Σ CFt/(1+r)^t − I₀
  • IRR is the discount rate where NPV = 0; Accept if IRR > cost of capital
  • Payback Period measures how quickly the initial investment is recovered — ignores time value and cash flows beyond payback
  • Profitability Index (PI) = PV of future cash inflows / Initial Investment; Accept if PI > 1
  • ⚡ Always rank mutually exclusive projects by NPV, not IRR — NPV maximises shareholder wealth

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Capital Budgeting — Evaluating Long-Term Investments

Capital budgeting is the process of planning and evaluating long-term investment decisions. These decisions commit large amounts of capital for extended periods, making them among the most consequential choices a firm makes. A wrong investment can destroy shareholder value; a right one can sustain growth for decades.

The Capital Budgeting Process

  1. Identify Investment Opportunities: Generate project proposals
  2. Estimate Cash Flows: Project inflows and outflows over the project’s life
  3. Determine Required Rate of Return (Hurdle Rate): Cost of capital or target return
  4. Evaluate Using NPV, IRR, Payback, PI: Apply decision criteria
  5. Select Projects: Rank and choose based on criteria and budget constraints
  6. Monitor and Review: Post-investment audit against projections

Key Principle: Use Cash Flows, Not Accounting Profits

Capital budgeting is based on incremental cash flows — the actual cash that flows in and out of the project. Key considerations:

  • Ignore sunk costs: Costs already incurred are irrelevant
  • Include opportunity costs: Value of the best alternative foregone
  • Consider working capital changes: Initial inventory buildup, later releases
  • Include terminal cash flows: Salvage value of assets at project end

Methods of Evaluation

1. Net Present Value (NPV)

NPV = −I₀ + Σ[CFt / (1+r)^t]

The most theoretically correct method because:

  • Uses cash flows, not accounting profits
  • Accounts for time value of money
  • Is additive across projects
  • Maximises shareholder wealth

Decision Criteria:

  • NPV > 0: Accept (project creates value)
  • NPV = 0: Indifferent
  • NPV < 0: Reject (project destroys value)

Example — NPV Calculation: A project requires ₹1,00,000 investment. Cash inflows: Year 1: ₹40,000; Year 2: ₹50,000; Year 3: ₹30,000. Cost of capital = 10%.

Year 0: -1,00,000 / 1.00       = -1,00,000
Year 1:  40,000 / 1.10         =   36,364
Year 2:  50,000 / 1.21         =   41,322
Year 3:  30,000 / 1.331        =   22,539
NPV = -1,00,000 + 36,364 + 41,322 + 22,539 = +₹225 ✓ Accept

2. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. Solve for r in: −I₀ + Σ[CFt / (1+IRR)^t] = 0

For the above example, IRR is approximately 15% (NPV = 0 at ~15%). Since IRR (15%) > Cost of Capital (10%) → Accept.

IRR Advantages: Easy to communicate as a percentage; provides a single summary number. IRR Disadvantages: Can produce multiple IRRs for projects with non-conventional cash flows; may mislead when comparing projects of different sizes.

3. Payback Period (PBP)

The time required to recover the initial investment from project cash flows.

Simple (non-discounted) PBP: PBP = Full years before full recovery + (Unrecovered amount / Cash flow in recovery year)

Discounted PBP: Uses discounted cash flows.

For the above example:

  • Year 1: Recover ₹40,000 (cumulative: ₹40,000)
  • Year 2: Recover ₹50,000 (cumulative: ₹90,000)
  • Year 3: Recover ₹30,000 → Project fully recovered during Year 3
  • PBP = 2 + (10,000 / 30,000) = 2.33 years

Limitations: Ignores cash flows beyond payback; ignores time value; no acceptance criterion without a benchmark.

4. Accounting Rate of Return (ARR)

ARR = Average Annual Accounting Profit / Average Investment

Example: Initial investment: ₹1,00,000; Annual profit: ₹20,000 (constant); Salvage: ₹10,000 ARR = 20,000 / [(1,00,000 + 10,000)/2] = 20,000 / 55,000 = 36.4%

Limitation: Based on accounting profits, not cash flows; ignores time value.

5. Profitability Index (PI)

PI = PV of Future Cash Inflows / Initial Investment

PI = (36,364 + 41,322 + 22,539) / 1,00,000 = 1,00,225 / 1,00,000 = 1.002

PI > 1.0 → Accept | PI < 1.0 → Reject

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

NPV Profile and Crossover Rate

When comparing two mutually exclusive projects, plot NPV at various discount rates:

Example — Projects A and B:

  • Project A: I₀ = 1,00,000; CF: 60,000/yr for 3 years
  • Project B: I₀ = 1,00,000; CF: 30,000 (Year 1), 50,000 (Year 2), 80,000 (Year 3)

At r = 0%: NPV(A) = 80,000 | NPV(B) = 60,000 At r = 20%: NPV(A) ≈ 24,000 | NPV(B) ≈ 31,000

The two NPV profiles cross at some crossover rate. Below this rate, choose Project A; above it, choose Project B.

For capital rationing (budget constraint), use the Profitability Index to rank projects — PI maximises NPV within a fixed budget.

Risk in Capital Budgeting

Sensitivity Analysis

Examines how NPV changes when key variables (selling price, volume, cost) change.

  • “What if sales volume falls by 10%?” → Does NPV still remain positive?

Scenario Analysis

Best Case / Base Case / Worst Case cash flows → Three NPVs → Expected NPV and standard deviation.

Risk-Adjusted Discount Rate (RADR)

Apply a higher discount rate to riskier projects:

  • Low-risk project: 10%
  • Medium-risk: 12%
  • High-risk: 15%

Adjusted R = Rf + β × (Km − Rf) — links to CAPM in theory.

Capital Budgeting in RBI Context

RBI’s own investment decisions (e.g., IT infrastructure, branch expansion) follow similar capital budgeting logic. For bank credit analysis, RBI’s supervisory frameworks examine:

  • Whether borrowers’ projects have positive NPVs (viability)
  • IRR vs cost of capital margins
  • Project completion risk (time and cost overruns)

Key Exam Insight: In RBI Phase 2, expect a case study with two mutually exclusive projects. Use NPV as the primary criterion, but discuss IRR and payback as secondary considerations. Always show your calculations — examiners reward step-by-step working.

Practical Application: NPV vs IRR in a Numerical Problem

A company has ₹5,00,000 to invest. Two projects available:

Project X: Cost ₹5,00,000; CFs: 3,00,000 (Yr1), 2,50,000 (Yr2) Project Y: Cost ₹5,00,000; CFs: 1,00,000 (Yr1), 2,00,000 (Yr2), 3,00,000 (Yr3)

At 12% cost of capital:

Project X: NPV = -5,00,000 + 3,00,000/1.12 + 2,50,000/1.2544 = -5,00,000 + 2,67,857 + 1,99,294 = -₹32,849 (Reject!) IRR ≈ 10% (less than 12%) → Reject

Project Y: NPV = -5,00,000 + 1,00,000/1.12 + 2,00,000/1.2544 + 3,00,000/1.4049 = -5,00,000 + 89,286 + 1,59,435 + 2,13,614 = -₹37,665 (Reject!)

Both projects have negative NPVs at 12% — neither should be accepted. This illustrates the fundamental rule: NPV > 0 is the prerequisite for value creation.

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