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Unit 3 of 4 · B.Com Sem 5

Unit 3: Advanced investment appraisal & valuation

Advanced Financial Management notes · PTU syllabus (BCOP 512-18)

3 min read5 topics10 exam questions
On this page
  1. Unit summary
  2. Capital rationing
  3. Sensitivity analysis and risk-adjusted discount rates
  4. Simulation and scenario analysis
  5. Business valuation: market and asset-based methods
  6. Dividend valuation and discounted free cash flow
  7. Key terms
  8. Quick revision
  9. Important questions

Unit summary

Real investment decisions involve limited funds, uncertainty and valuation of entire businesses. This unit covers single- and multi-period capital rationing with divisible and indivisible projects, sensitivity analysis, risk-adjusted discount rates, simulation and scenario analysis, and business valuation by market capitalisation, asset-based, P/E, dividend valuation and discounted free cash flow methods.

After this unit you can

  • Solve single-period and multi-period capital rationing problems
  • Apply sensitivity analysis, risk-adjusted discount rates, simulation and scenarios
  • Value a business using asset-based, P/E and dividend valuation methods
  • Value a business using discounted free cash flows

PTU syllabus topics

  • Capital rationing — single and multi-period
  • divisible and indivisible projects
  • sensitivity analysis
  • risk-adjusted discount rates
  • simulation and scenario analysis
  • market capitalisation
  • asset-based valuation
  • PE ratio
  • dividend valuation
  • discounted free cash flow
ClassificationValuation methods
Business valuation

  • Market capitalisation

    Share price × shares

  • Asset-based

    Net asset value

  • PE ratio

    Earnings × comparable multiple

  • Dividend valuation

    Present value of dividends

  • Discounted free cash flow

    Present value of future cash flows

1

Topic 1

Capital rationing

  • Single-period rationing — divisible projects: rank by profitability index (NPV ÷ initial outlay) and invest in order, taking a fraction of the marginal project.
  • Indivisible projects: test all feasible combinations within the budget and pick the one with the highest total NPV.
  • Multi-period rationing: funds limited in more than one period — solved by linear programming (maximise NPV subject to budget constraints in each period).

Example

Budget ₹100 lakh. A: outlay 40, NPV 12 (PI 0.30); B: outlay 50, NPV 10 (0.20); C: outlay 30, NPV 9 (0.30); D: outlay 20, NPV 3 (0.15). Divisible: A, C (70) + 30/50 of B (NPV 6) → total NPV 27. Indivisible: best combination A + C + D (90, NPV 24) vs A + B (90, NPV 22) → choose A + C + D.

2

Topic 2

Sensitivity analysis and risk-adjusted discount rates

  • Sensitivity analysis: how much a key variable (sales volume, price, cost, discount rate) can change before NPV becomes zero.
Key formulasSensitivity

  • Sensitivity margin (%)

    NPV ÷ PV of the cash flow affected by the variable × 100

Example

NPV ₹20 lakh; PV of sales revenue ₹200 lakh → sales can fall by 10% before NPV = 0 — a highly sensitive variable.

  • Limitations: changes one variable at a time; no probabilities.
  • Risk-adjusted discount rate (RADR): add a risk premium to the discount rate for riskier projects; or use project-specific beta via CAPM (adjusting for gearing — asset beta and equity beta).
Key formulasBeta adjustments

  • Asset (ungeared) beta

    βa = βe × E ÷ [E + D (1 − t)]

  • Re-geared equity beta

    βe = βa × [E + D (1 − t)] ÷ E

  • Certainty equivalent approach: convert risky cash flows into certain equivalents and discount at the risk-free rate.
3

Topic 3

Simulation and scenario analysis

  • Scenario analysis: compute NPV under best-case, base-case and worst-case scenarios (all variables change together).
  • Monte Carlo simulation: assign probability distributions to variables; generate thousands of random combinations; produce a distribution of NPVs — gives probability of negative NPV.
  • Decision trees: for sequential decisions with probabilities (expand, abandon, delay).
  • Real options: option to expand, abandon, delay or switch — add value to NPV.
ComparisonSensitivity vs scenario vs simulation
Variables changed
Output

Sensitivity analysis

One at a time

Margin of safety for each variable

Scenario analysis

Several together in defined cases

NPV under each scenario

Simulation

All, randomly per distributions

Probability distribution of NPV

4

Topic 4

Business valuation: market and asset-based methods

  • Market capitalisation: share price × number of shares — the value of equity for listed firms; may not reflect control premium.
  • Asset-based valuation: net assets at book value, replacement cost or realisable (break-up) value; useful for asset-rich firms or liquidation, ignores intangibles and earning power.
  • P/E (earnings) method: Value = EPS (or earnings) × suitable P/E ratio of comparable listed firms (adjusted downward for unlisted firms).

Example

Target earnings ₹12 crore; comparable listed P/E 15; discount 25% for being unlisted → P/E 11.25; value ≈ ₹135 crore.

  • Other multiples: EV/EBITDA, price-to-book, price-to-sales.
5

Topic 5

Dividend valuation and discounted free cash flow

Key formulasValuation models

  • Dividend valuation (constant)

    P0 = D ÷ ke

  • Dividend growth model

    P0 = D0 (1 + g) ÷ (ke − g)

  • Growth estimate

    g = b × r (retention × return on equity)

  • Free cash flow to firm

    EBIT (1 − t) + Depreciation − Capital expenditure − Increase in working capital

  • Enterprise value (DCF)

    Σ FCFF ÷ (1 + WACC)^t + Terminal value ÷ (1 + WACC)^n

  • Terminal value (Gordon)

    FCFF(n+1) ÷ (WACC − g)

  • Equity value

    Enterprise value − Net debt

Example

D0 = ₹4, g = 6%, ke = 14%: P0 = 4 × 1.06 ÷ 0.08 = ₹53.

  • DCF is theoretically the most sound; sensitive to WACC, growth and terminal value assumptions.

Key terms

Capital rationing
Limited funds preventing acceptance of all positive-NPV projects
Sensitivity analysis
Testing how much a variable can change before NPV becomes zero
Monte Carlo simulation
Random generation of variable combinations to obtain an NPV distribution
Free cash flow
Cash available to investors after operating costs, taxes and investments
Terminal value
Value of cash flows beyond the explicit forecast period

Quick revision

  • Divisible: rank by PI; indivisible: best NPV combination; multi-period: LP.
  • Sensitivity = NPV ÷ PV of variable.
  • RADR and project beta (ungear/regear).
  • Scenarios, simulation, decision trees, real options.
  • Valuation: market cap, assets, P/E, dividend growth, DCF.

Important exam questions

Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).

Short-answer questions

  1. Q1.What is multi-period capital rationing?
  2. Q2.How is sensitivity margin calculated?
  3. Q3.What is a risk-adjusted discount rate?
  4. Q4.What is Monte Carlo simulation?
  5. Q5.What is asset-based valuation?
  6. Q6.Write the dividend growth model.

Long-answer questions

  1. Q1.Explain capital rationing with divisible and indivisible projects.
  2. Q2.Explain techniques for incorporating risk in investment appraisal.
  3. Q3.Explain business valuation using asset-based and earnings methods.
  4. Q4.Explain dividend valuation and discounted free cash flow valuation.

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