Chapter 4: Valuation Methodologies (Part 8 of 8) — Master Review, Formula Reference, Solved Worksheets & Exam MCQs
1. Master Formula Reference Sheet for Chapter 4
All mathematical formulas across Chapter 4 of the NCFM Fundamental Analysis Module Workbook are compiled below in simple single-line text format for quick study and direct application.
1.1 Capital Cost & Risk Formulas
- Capital Asset Pricing Model (CAPM) Cost of Equity:
- Inline Formula: Cost of Equity (Ke) = Risk-Free Rate + Beta * (Market Required Rate of Return - Risk-Free Rate)
- Inline Formula: Ke = Rf + Beta * (Rm - Rf)
- Equity Risk Premium:
- Inline Formula: Equity Risk Premium = Market Required Rate of Return - Risk-Free Rate
1.2 Dividend Discount Model (DDM) Formulas
- General Infinite Dividend Discount Model:
- Inline Formula: Value per share of stock = Sum of [ Expected Dividend in Period t / (1 + Cost of Equity)^t ]
- Gordon Growth Model (GGM) — Single-Stage Constant Growth:
- Inline Formula: Value per share of stock = DPS1 / (Ke - g)
- Where: DPS1 = Expected dividend next year; Ke = Cost of equity; g = Perpetual growth rate.
- Perpetual Retention-Driven Growth Rate:
- Inline Formula: Expected Growth Rate (g) = Return on Equity * Retention Ratio
- Inline Formula: g = ROE * (1 - Dividend Payout Ratio)
- Two-Stage DDM Terminal Value (Pn):
- Inline Formula: Pn = DPS_n+1 / (Ke_st - gn)
- Inline Formula: Stock Price (P0) = Sum of [ DPSt / (1 + Ke_hg)^t ] + [ Pn / (1 + Ke_hg)^n ]
- Stable Period Dividend Payout Ratio:
- Inline Formula: Stable Payout Ratio = Stable Growth Rate / Stable Period ROE
1.3 Cash Flow Valuation (FCFF & FCFE) Formulas
- FCFF from Net Income (NI):
- Inline Formula: FCFF = NI + NCC + Interest * (1 - T) - FC - WC
- FCFF from Earnings Before Interest and Taxes (EBIT):
- Inline Formula: FCFF = EBIT * (1 - T) + NCC - FC - WC
- FCFF from Cash Flow from Operations (CFO):
- Inline Formula: FCFF = CFO - FC + Interest * (1 - T)
- FCFE from FCFF:
- Inline Formula: FCFE = FCFF - Interest * (1 - T) + Net Borrowing
- FCFE from Net Income (NI):
- Inline Formula: FCFE = NI + NCC - FC - WC + Net Borrowing
- FCFE from Cash Flow from Operations (CFO):
- Inline Formula: FCFE = CFO - FC + Net Borrowing
- FCFE under Constant Debt Ratio (DR):
- Inline Formula: FCFE = NI - (1 - DR) * (Capital Spending - Depreciation) - (1 - DR) * Change in WC
- Constant Growth FCFE Terminal Value:
- Inline Formula: Terminal Value = FCFE_t+1 / (Ke - g)
- Intrinsic Value per Share via FCFE:
- Inline Formula: Value per Share = Total Present Value of Equity / Outstanding Common Shares
1.4 Relative Valuation Multiples
- Price to Earnings (P/E) Ratio:
- Inline Formula: P/E Ratio = Market Price per Share / Earnings Per Share
- Earnings Yield:
- Inline Formula: Earnings Yield = Earnings Per Share / Market Price per Share = 1 / P/E Ratio
- Target Price via Forward P/E:
- Inline Formula: Target Price = Forward P/E Multiple * Estimated Future EPS
- Price to Book Value (P/B) Ratio:
- Inline Formula: P/B Ratio = Current Stock Price / Book Value per Share
- Inline Formula: Book Value per Share = (Total Assets - Intangible Assets - Total Liabilities) / Shares Outstanding
- Enterprise Value (EV):
- Inline Formula: Enterprise Value = Market Value of Equity + Market Value of Debt - Cash and Cash Equivalents
- EV / EBITDA Ratio:
- Inline Formula: EV to EBITDA Ratio = Enterprise Value / EBITDA
- Price to Sales (P/S) Ratio:
- Inline Formula: P/S Ratio = Market Capitalization / Total Annual Revenue
- Inline Formula: P/S Ratio = Current Stock Price / Sales per Share
1.5 Banking Sector Financial & Operational Ratios
- Net Interest Income (NII):
- Inline Formula: Net Interest Income = Interest Earned - Interest Expended
- Net Interest Margin (NIM):
- Inline Formula: NIM = Net Interest Income / Average Earning Assets
- Banking Operating Profit Margin (OPM):
- Inline Formula: OPM = (Net Interest Income - Operating Expenses) / Total Interest Income
- Cost to Income Ratio:
- Inline Formula: Cost to Income Ratio = Operating Expenses / (Net Interest Income + Non-Interest Income)
- Credit to Deposit (CD) Ratio:
- Inline Formula: CD Ratio = Total Loans Given / Total Customer Deposits
- Capital Adequacy Ratio (CAR):
- Inline Formula: CAR = (Tier I Capital + Tier II Capital) / Risk Weighted Assets
- Net NPA Ratio:
- Inline Formula: Net NPA Ratio = Net Non-Performing Assets / Total Loans Given
- Inline Formula: Net Non-Performing Assets = Gross NPAs - Cumulative Provisions
- Provision Coverage Ratio (PCR):
- Inline Formula: Provision Coverage Ratio = Cumulative Provisions / Gross NPAs
- Adjusted Book Value per Share (Banking):
- Inline Formula: Adjusted Book Value = Stated Net Worth - Net Non-Performing Assets
2. Comprehensive Multi-Model Valuation Comparison Matrix
| Valuation Model | Primary Cash Flow / Input Metric | Key Discount Rate | Best Suited Business Context | Major Limitation / Risk | Source Reference |
|---|---|---|---|---|---|
| Gordon Growth Model (GGM) | Expected Dividends (DPS1) | Cost of Equity (Ke) | Mature, stable firms with predictable dividend payout policies | Hyper-sensitive to growth input; fails if g >= Ke | Section 4.3 |
| Two-Stage DDM | Dividends across explicit & terminal phases | Cost of Equity (Ke_hg, Ke_st) | Companies with temporary patent protection or high entry barriers | Assumes abrupt growth cliff at year n | Section 4.3 |
| FCFF Model | Cash available to all capital providers | WACC | Highly leveraged firms or capital structure restructurings | Requires estimating WACC and market value of debt | Section 4.4 |
| FCFE Model | Residual cash flow after debt service | Cost of Equity (Ke) | Non-dividend paying firms or firms retaining excess cash | Negative cash flows during heavy capex render model complex | Section 4.4 |
| Sum Of The Parts (SOTP) | SBU-level cash flows or peer multiples | Division-specific discount rates | Multi-industry conglomerates with distinct operating divisions | High data requirements for divisional segment accounting | Section 4.5 |
| Price / Earnings (P/E) | Net Income / Profit after Tax (EPS) | Market peer multiple benchmark | Established, profitable companies with stable earnings | Fails when Net Income is negative | Section 4.6 |
| Price / Book Value (P/B) | Balance sheet Net Worth (BVPS) | Asset net worth comparison | Banks, financial institutions, asset-heavy firms | Affected by accounting policies and historical asset cost biases | Section 4.7 |
| EV / EBITDA | Capital-structure-neutral operating profit | Enterprise value peer multiple | Debt-heavy firms, capital-intensive manufacturing | Ignores ongoing capital spending needed to replace worn assets | Section 4.8 |
| Price / Sales (P/S) | Top-line gross revenue per share | Industry sales multiple | Early-stage growth firms, loss-making startups | Ignores operating margin differences and cost structure efficiency | Section 4.9 |
3. Integrated Numerical Problem-Solving Worksheets
Worksheet 1: Gordon Growth Model Sensitivity & Calculation
Problem: ABC Ltd. paid a dividend per share of Rs. 2.27 in the current year. The expected dividend next year (DPS1) is Rs. 2.50. The stock's Beta is 1.15, the risk-free 10-year government bond rate is 7.8%, and the market required return is 14.0%.
- Calculate the Cost of Equity (Ke) using CAPM.
- Calculate the intrinsic stock value assuming a perpetual dividend growth rate (g) of 5.0%.
- Calculate the new intrinsic value if the growth rate assumption increases to 10.0%.
Step-by-Step Solution:
- Step 1 — CAPM Cost of Equity:
- Inline Formula: Ke = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
- Inline Formula: Ke = 7.8% + 1.15 * (14.0% - 7.8%) = 7.8% + 1.15 * 6.2% = 7.8% + 7.13% = 14.93% (rounded to 15.0%)
- Step 2 — Value at 5% Perpetual Growth:
- Inline Formula: Value = DPS1 / (Ke - g)
- Inline Formula: Value = 2.50 / (0.15 - 0.05) = 2.50 / 0.10 = Rs. 25.00 per share
- Step 3 — Value at 10% Perpetual Growth:
- Inline Formula: Value = 2.50 / (0.15 - 0.10) = 2.50 / 0.05 = Rs. 50.00 per share
- Takeaway: Doubling the perpetual growth rate from 5% to 10% doubles the estimated stock value from Rs. 25 to Rs. 50, demonstrating extreme GGM input sensitivity.
Worksheet 2: Practical Multi-Stage FCFE Valuation (XYZ Technologies Ltd.)
Problem: Value XYZ Technologies Ltd. using the 7-year multi-stage FCFE model from the NCFM curriculum:
- Base FCFE (FCFE0): Rs. 4,540 Crores
- High-growth phase (Years 1–7): Growth rate g = 20.0% per annum
- Cost of Equity (Ke): 12.8% per annum
- Constant growth phase (Year 8 onward): Stable growth rate gn = 4.0% forever
- Shares Outstanding: 57 Crores
Step-by-Step Solution:
- Step 1 — Forecast Explicit FCFE Streams (Years 1–7) & Discount to Present Value:
- Inline Formula: FCFEt = FCFE_t-1 * (1 + 0.20)
- Inline Formula: PV Factor = 1 / (1 + 0.128)^t
- Year 1 FCFE = 5,459 Cr ---> Discount Factor = 0.8865 ---> PV = Rs. 4,842 Cr
- Year 2 FCFE = 6,565 Cr ---> Discount Factor = 0.7859 ---> PV = Rs. 5,163 Cr
- Year 3 FCFE = 7,894 Cr ---> Discount Factor = 0.6967 ---> PV = Rs. 5,506 Cr
- Year 4 FCFE = 9,493 Cr ---> Discount Factor = 0.6177 ---> PV = Rs. 5,872 Cr
- Year 5 FCFE = 11,415 Cr ---> Discount Factor = 0.5476 ---> PV = Rs. 6,262 Cr
- Year 6 FCFE = 13,727 Cr ---> Discount Factor = 0.4854 ---> PV = Rs. 6,678 Cr
- Year 7 FCFE = 16,506 Cr ---> Discount Factor = 0.4304 ---> PV = Rs. 7,121 Cr
- Inline Formula: Sum of Explicit PV (Years 1–7) = 4,842 + 5,163 + 5,506 + 5,872 + 6,262 + 6,678 + 7,121 = Rs. 41,444 Crores
- Step 2 — Calculate Constant Growth FCFE & Terminal Value:
- Year 8 FCFE = FCFE7 * (1 + gn) = 16,506 * (1 + 0.04) = Rs. 17,166.24 Crores (rounded to 17,167 Cr)
- Inline Formula: Terminal Value at Year 7 (P7) = FCFE8 / (Ke - gn) = 17,167 / (0.128 - 0.04) = 17,167 / 0.088 = Rs. 195,079.55 Crores
- Inline Formula: PV of Terminal Value = Terminal Value * Year 7 Discount Factor = 195,079.55 * 0.4304 = Rs. 84,546 Crores
- Step 3 — Total Intrinsic Equity Value & Value Per Share:
- Inline Formula: Total PV of Equity = PV of Explicit Cash Flows + PV of Terminal Value = 41,444 + 84,546 = Rs. 1,25,990 Crores
- Inline Formula: Intrinsic Value per Share = Total PV of Equity / Outstanding Shares = 125,990 / 57 = Rs. 2,195 per share
Worksheet 3: Banking Adjusted Book Value & Net Interest Margin (NIM)
Problem: Alpha Bank reported the following financials:
- Total Interest Earned: Rs. 12,000 Crores
- Total Interest Expended: Rs. 7,500 Crores
- Average Interest-Earning Assets: Rs. 125,000 Crores
- Reported Equity Net Worth: Rs. 15,000 Crores
- Gross Non-Performing Assets (Gross NPAs): Rs. 3,000 Crores
- Cumulative Bad Debt Provisions: Rs. 1,800 Crores
- Total Outstanding Shares: 100 Crores
- Calculate Net Interest Income (NII) and Net Interest Margin (NIM).
- Calculate Net NPAs and Provision Coverage Ratio (PCR).
- Calculate Adjusted Book Value per share.
Step-by-Step Solution:
- Step 1 — NII & NIM Calculation:
- Inline Formula: Net Interest Income (NII) = Interest Earned - Interest Expended = 12,000 - 7,500 = Rs. 4,500 Crores
- Inline Formula: Net Interest Margin (NIM) = NII / Average Earning Assets = 4,500 / 125,000 = 3.60%
- Step 2 — Net NPAs & PCR Calculation:
- Inline Formula: Net NPAs = Gross NPAs - Cumulative Provisions = 3,000 - 1,800 = Rs. 1,200 Crores
- Inline Formula: Provision Coverage Ratio (PCR) = Cumulative Provisions / Gross NPAs = 1,800 / 3,000 = 60.0%
- Step 3 — Adjusted Book Value per Share:
- Inline Formula: Adjusted Net Worth = Stated Equity Net Worth - Net NPAs = 15,000 - 1,200 = Rs. 13,800 Crores
- Inline Formula: Adjusted Book Value per Share = Adjusted Net Worth / Total Shares = 13,800 / 100 = Rs. 138.00 per share
4. Exam-Style Multiple Choice Questions (MCQs)
Question 1
Which of the following economic indicators moves in the opposite direction of the overall economy and is categorized as lagging? A) Gross Domestic Product (GDP)
B) Stock Market Returns
C) Unemployment Rate
D) Business Inventories
Answer: C
Explanation: Unemployment is a countercyclical indicator (moves opposite to the economy) and lagging indicator (turns 2 to 3 quarters after the economy changes direction).
Question 2
In the Capital Asset Pricing Model (CAPM), if the Risk-Free Rate is 7.8%, Stock Beta is 0.8, and the Market Required Return is 14.0%, what is the expected Cost of Equity? A) 11.2%
B) 12.8%
C) 14.0%
D) 15.6%
Answer: B
Explanation: Cost of Equity = 7.8% + 0.8 * (14.0% - 7.8%) = 7.8% + 0.8 * 6.2% = 12.8%.
Question 3
Under the Gordon Growth Model (GGM), what happens to the calculated stock value as the perpetual dividend growth rate (g) approaches the cost of equity (Ke)? A) Stock value approaches zero
B) Stock value approaches infinity
C) Stock value becomes negative
D) Stock value becomes equal to current EPS
Answer: B
Explanation: As g approaches Ke, the denominator (Ke - g) approaches zero, causing calculated share value to approach infinity.
Question 4
When calculating Free Cash Flow to Firm (FCFF) starting from Net Income (NI), why is interest expense added back after tax adjustment + Interest * (1 - T)? A) Because interest is a non-cash expense like depreciation
B) Because FCFF represents cash available to all capital suppliers prior to debt servicing payments
C) Because interest payments increase working capital
D) Because Net Income excludes operating expenses
Answer: B
Explanation: FCFF belongs to both debt and equity holders; interest was previously subtracted in deriving Net Income, so after-tax interest must be added back.
Question 5
Which valuation multiple is most appropriate for valuing early-stage technology startups that generate top-line growth but have negative operating earnings? A) Price to Earnings (P/E)
B) EV / EBITDA
C) Price to Sales (P/S)
D) Dividend Yield
Answer: C
Explanation: When earnings and EBITDA are negative, P/E and EV/EBITDA ratios are non-viable, making top-line Price to Sales (P/S) the standard metric.
Question 6
Why do analysts prefer Price-to-Book Value (P/B) over Price-to-Earnings (P/E) when valuing commercial banking stocks? A) Banks do not report income statements
B) Bank growth is constrained by capital net worth (capital adequacy), making balance sheet net worth the anchor for long-term earnings
C) Banks are exempt from tax regulations
D) P/E ratios are illegal under the Banking Regulation Act
Answer: B
Explanation: Bank lending and asset growth depend directly on available capital (net worth) under RBI capital adequacy rules, making P/B the primary valuation multiple.
Question 7
To determine a bank's true underlying book value available for future growth, what adjustment must analysts make to stated equity net worth? A) Add Gross NPAs
B) Subtract Net NPAs
C) Add total customer deposits
D) Subtract Statutory Liquidity Ratio (SLR) investments
Answer: B
Explanation: Net Non-Performing Assets represent unprovided bad loans that erode capital, so they must be deducted from net worth to calculate true adjusted book value.
Question 8
What is the primary operational motive behind horizontal and vertical corporate acquisitions? A) To increase short-term tax liabilities
B) To achieve corporate synergies, cost reductions, and supply security
C) To convert equity into unsecured loans
D) To avoid filing a Draft Red Herring Prospectus (DRHP)
Answer: B
Explanation: Corporate acquisitions aim to create operational or strategic synergies, such as vertical integration or securing raw material supply channels.
5. Exam-Relevant Key Takeaways & Important Terms Summary
Key Takeaways for Chapter 4
- Curriculum Weightage: Chapter 4 (Valuation Methodologies) carries 35% weight in the NCFM Fundamental Analysis examination.
- Methodology Triad: Equity valuation combines Top-Down EIC Macro Analysis, Absolute DCF Models (DDM, FCFF, FCFE), and Relative Price Multiples (P/E, P/B, EV/EBITDA, P/S).
- Macro Predictive Utility: Leading economic indicators (stock share indices, Baltic Dry Index, housing starts, inventory shifts) provide predictive signals for equity valuation.
- Sector Tailoring: Use DDM for stable dividend payers, FCFF/FCFE for corporate going-concerns, SOTP for conglomerates, P/S for loss-making startups, and P/B for banking entities.
Important Terms
- EIC Framework: Sequential valuation starting with Economy, progressing to Industry, and concluding with Company analysis.
- Gordon Growth Model (GGM): Single-stage DDM assuming constant perpetual dividend growth.
- FCFF vs. FCFE: FCFF measures cash for all capital providers discounted at WACC; FCFE measures residual cash for equity holders discounted at Ke.
- Sum Of The Parts (SOTP): Conglomerate valuation aggregating standalone SBU values.
- Net Interest Margin (NIM): Net interest income expressed as a percentage of average interest-earning assets.
- Provision Coverage Ratio (PCR): Proportion of bad loan provisions set aside relative to gross NPAs.
- Control Premium: Excess price paid above market value to secure controlling equity ownership in a takeover target.