Investment & Portfolio Management

Chapter 4
Equity Analysis and Valuation

Bachelors Program in Banking Finance and Insurance
Investment & Portfolio Management   •   Bachelor

Equity Analysis and Valuation

Introduction

Equity valuation estimates the value of a residual ownership claim on a business. Unlike debt holders, ordinary shareholders receive cash only after operating costs, taxes and contractual financing claims have been satisfied. Equity value therefore depends on expected cash flows, growth, risk, competitive advantage, capital structure and corporate governance.

Valuation is not the search for one indisputably correct number. It is a disciplined process for translating assumptions into an estimated value or valuation range. Analysts should use internally consistent assumptions, compare more than one method and disclose uncertainty.

Learning Objectives

After studying this chapter, students should be able to:

  • distinguish enterprise value from equity value;
  • estimate required return and sustainable growth;
  • apply dividend discount, free cash flow and residual income models;
  • conduct relative valuation using appropriate multiples;
  • evaluate competitive advantage and growth persistence;
  • analyse dividends, repurchases, splits and rights issues;
  • perform sensitivity, scenario and reverse-valuation analysis; and
  • communicate valuation conclusions responsibly.

1. The Equity Valuation Framework

A sound valuation begins with the business rather than the formula. The analyst should:

  1. understand the company, industry and accounting policies;
  2. assess historical performance and normalize unusual items;
  3. forecast operating results and financing needs;
  4. estimate the required return;
  5. select models consistent with the company’s characteristics;
  6. calculate and cross-check value;
  7. test uncertainty and compare estimated value with market price.
Equity valuation process Business andaccounting analysis Forecast cashflows and growth Estimate risk andrequired return Apply andcross-check models Value range anddecision Sensitivity and scenario analysis feed back into every stage.
Equity valuation process from business analysis to investment decision
Figure: Equity valuation process from business analysis to investment decision

Figure: An integrated equity valuation process.

Enterprise value and equity value

Enterprise value is the value of operations available to all capital providers. Equity value is the residual attributable to ordinary shareholders. A commonly used bridge is:

Equity\ value = Enterprise\ value + Nonoperating\ cash - Debt - Preferred\ equity - Other\ senior\ claims

Adjustments should reflect the facts of the company. For example, unfunded pension deficits, minority interests and investments in associates may require separate treatment. Per-share value is equity value divided by diluted shares outstanding, not necessarily basic shares.

2. Forecasting Growth and Competitive Advantage

2.1 Sources of growth

Revenue can grow through higher volume, pricing, new products, acquisitions or expansion into new markets. Earnings growth also depends on margins, asset efficiency, leverage, taxes and share count. Growth creates value only when returns on incremental investment exceed the capital required to finance it.

For a stable firm retaining a fraction b of earnings, the sustainable growth relation is:

g = b × ROE

Here, g is the long-run growth rate, b is the retention ratio and ROE is return on equity. If the dividend payout ratio is p, then b=1-p. This relationship assumes stable profitability, payout and financial leverage. It is conventionally called sustainable growth, not internal growth.

The internal growth rate, which assumes growth is financed without external debt or equity, is instead:

Internal\ growth\ rate = \frac{ROA × b}{1-ROA × b}

This formula uses return on assets, ROA, and requires consistent definitions of income and assets.

Example. If ROE is 15% and 40% of earnings is retained, sustainable growth is 0.40×15%=6%. Growth is not automatically valuable: if the required return on equity exceeds the return earned on new equity investment, retaining more earnings can reduce value.

2.2 Competitive advantage period

High returns attract competition. A company may temporarily sustain excess returns through patents, network effects, regulation, switching costs, brands, cost leadership or scarce resources. The period during which return on invested capital exceeds the cost of capital is the competitive advantage period.

Forecasts should normally allow exceptional margins and returns to fade toward economically defensible levels. Perpetual growth should not exceed long-run nominal economic growth indefinitely unless a special and clearly justified setting applies.

3. Required Return on Equity

The required return compensates investors for the time value of money and non-diversifiable risk. Under the Capital Asset Pricing Model (CAPM):

re = rf + βe(Rm-rf)

where re is the required return on equity, rf is the risk-free rate, βe is equity beta and Rm-rf is the expected market risk premium. All rates must use a consistent nominal or real basis and the same currency.

If the risk-free rate is 4%, beta is 1.2 and the market risk premium is 5.5%, then:

re = 4% + 1.2(5.5%) = 10.6%

CAPM estimates are sensitive to the beta period, market benchmark and risk-premium estimate. Analysts sometimes supplement CAPM with country, size or other risk adjustments, but should avoid adding overlapping premiums that double-count risk.

4. Dividend Discount Models

The dividend discount model (DDM) values equity as the present value of expected dividends:

V0 = \sumt=1∞\frac{Dt}{(1+re)t}

Here, V0 is current value per share, Dt is the dividend per share at time t, and re is the required return. Dividends and value are in currency units (CU) per share, while rates are percentages or decimals per period.

The DDM is most useful when dividends reflect sustainable distributable capacity, payout policy is reasonably stable and the firm is a going concern.

4.1 Gordon growth model

If dividends grow forever at a constant rate g, then Dt=D1(1+g)t-1. Substitution into the general DDM gives a geometric series:

V0 = \frac{D1}{re-g}

This special-case formula requires re>g, constant growth and a dividend next period, D1. If the most recent dividend is D0, then D1=D0(1+g).

Example. A share is expected to pay CU1.80 next year. With re=10% and g=4%:

V0 = \frac{1.80}{0.10-0.04}=CU30.00

4.2 Multistage DDM

A multistage model accommodates changing growth or explicitly forecast dividends:

V0 = \sumt=1N\frac{Dt}{(1+re)t}+\frac{VN}{(1+re)N}

If stable growth begins after year N, the continuing value at that date is usually:

VN = \frac{DN+1}{re-g}

The first stable-period dividend is DN+1, not DN.

Meridian dividend calculation. Suppose Meridian is expected to pay dividends of CU1.20, CU1.50 and CU1.80 in years 1–3. Its independently estimated continuing value at the end of year 3 is CU26.22, and re=10%. Then:

V0=\frac{1.20}{1.10}+\frac{1.50}{1.102}+\frac{1.80+26.22}{1.103}
V0=1.0909+1.2397+21.0518=CU23.3824≈CU23.38

The year-3 dividend and end-of-year-3 continuing value are discounted together because both occur at that date.

5. Free Cash Flow Valuation

Dividends may differ from economic capacity because management can retain cash or alter payout policy. Free cash flow models value cash available after operating and reinvestment requirements.

5.1 Free cash flow to the firm

FCFF = EBIT(1-T)+Depreciation-Capital\ expenditure-ΔWorking\ capital

FCFF is free cash flow to the firm, EBIT is earnings before interest and tax, T is the operating tax rate, and ΔWorking\ capital is the increase in operating working capital. An increase is a cash outflow. FCFF excludes interest because it is available to debt and equity investors.

FCFF is discounted at the weighted average cost of capital:

WACC=were+wdrd(1-T)

The weights we and wd are normally market-value proportions; rd is the pre-tax cost of debt. This standard form assumes interest tax deductibility and a reasonably stable target capital structure.

For constant growth:

Enterprise\ value = \frac{FCFF1}{WACC-g},\quad WACC>g

Example. If next year’s FCFF is CU15 million, WACC is 9% and perpetual growth is 4%:

Enterprise\ value=\frac{15}{0.09-0.04}=CU300\ million

If debt is CU80 million, surplus cash is CU12 million and there are no other adjustments, equity value is 300+12-80=CU232 million. With 10 million diluted shares, estimated value is CU23.20 per share.

5.2 Free cash flow to equity

A practical formulation is:

FCFE=Net\ income+Depreciation-Capital\ expenditure-ΔWorking\ capital+Net\ borrowing

Net borrowing equals debt issued minus debt repaid. FCFE is discounted at the required return on equity because it belongs only to ordinary shareholders:

Equity\ value=\sumt=1∞\frac{FCFEt}{(1+re)t}

Under stable growth, V0=FCFE1/(re-g), provided re>g and leverage is consistent with the forecast. FCFF is often preferable when leverage is changing substantially.

6. Residual Income Valuation

Residual income measures accounting profit after charging equity capital:

RIt=NIt-reBt-1

Here, RIt is residual income in period t, NIt is net income available to ordinary shareholders and Bt-1 is beginning book value of equity. Equivalently:

RIt=(ROEt-re)Bt-1

Equity value is:

V0=B0+\sumt=1∞\frac{RIt}{(1+re)t}

The model follows from the DDM when clean-surplus accounting holds:

Bt=Bt-1+NIt-Dt

Clean surplus requires changes in book equity, other than owner transactions, to pass through comprehensive income. Analysts must adjust significant accounting distortions, such as inconsistent research capitalization or major items recorded directly in equity.

Example. Beginning book value is CU20 per share, forecast ROE is 14%, and re=10%. Next year’s residual income is:

RI1=(0.14-0.10)(20)=CU0.80

If CU0.80 is expected to continue perpetually without growth, its present value is 0.80/0.10=CU8.00. Estimated equity value is therefore CU28.00 per share. Residual income is particularly useful for firms with negative near-term cash flow but meaningful book value.

7. Relative Valuation

Relative valuation estimates value from prices paid for comparable companies. Common multiples include:

MultipleNumeratorDenominatorMain driver
P/EEquity priceEarnings per shareGrowth, risk, payout, earnings quality
P/BEquity priceBook value per shareROE relative to required return
EV/EBITDAEnterprise valueEBITDAOperating growth and capital intensity
EV/SalesEnterprise valueRevenueMargins and growth
Dividend yieldDividend per shareShare pricePayout and required return

The numerator and denominator must correspond to the same capital claim. P/E uses equity measures; EV/EBITDA uses enterprise measures. Forward and trailing data should not be mixed without disclosure.

For a stable-growth company, the Gordon model implies a justified forward P/E:

\frac{P0}{E1}=\frac{p}{re-g}

where p=D1/E1 is the payout ratio. If payout is 40%, required return is 10% and growth is 4%, justified forward P/E is 0.40/(0.10-0.04)=6.67. A higher peer multiple is not automatically evidence of undervaluation; peers may have faster growth, lower risk or superior earnings quality.

A good comparable-company analysis screens for industry, geography, business mix, size, leverage, profitability, accounting methods and expected growth. Median multiples are often more robust than means when extreme observations exist.

8. Corporate Actions and Per-Share Value

Dividends and repurchases

A dividend transfers cash from the company to shareholders and normally reduces the ex-dividend share price by approximately the dividend, other things equal. A repurchase reduces cash and shares outstanding. It creates value for continuing shareholders only if shares are repurchased below intrinsic value, or if other benefits exceed execution, tax and agency costs. Repurchasing overvalued shares transfers wealth toward selling shareholders.

Share splits and bonus issues

A share split increases the number of shares and proportionately reduces price per share without changing total company value. A two-for-one split should approximately halve value per share, absent signalling or market-friction effects.

Rights issues

A rights issue allows existing shareholders to buy new shares, usually at a subscription price below the cum-rights market price. If n old shares are required to buy one new share, the theoretical ex-rights price (TERP) is:

TERP=\frac{nP0+S}{n+1}

where P0 is the cum-rights price and S is the subscription price. This formula assumes full subscription, no transaction costs and no new information affecting business value.

Example. A company offers one new share at CU40 for every four old shares. The cum-rights price is CU50:

TERP=\frac{4(50)+40}{5}=CU48

The theoretical value of the right attached to each old share is:

P0-TERP=50-48=CU2

Four rights are needed to buy one new share, so the package of four rights is worth 4×2=CU8, also equal to TERP-S=48-40=CU8. An investor holding four old shares initially owns CU200. After exercising, the investor owns five shares worth theoretically 5×48=CU240 after paying CU40. Ignoring costs and information effects, the issue is wealth-neutral when rights are exercised or sold; allowing valuable rights to expire causes loss.

9. Sensitivity and Valuation Uncertainty

Terminal value often represents a large proportion of estimated value. Small changes in required return or perpetual growth can therefore cause large changes.

For a Gordon model with D1=CU1.80:

Required returnGrowthValue
10%4%CU30.00
11%4%CU25.71
10%5%CU36.00
12%3%CU20.00

These scenarios demonstrate genuine sensitivity because the spread re-g changes. Analysts should not vary assumptions independently when they are economically connected; higher inflation may raise both nominal growth and discount rates.

Useful uncertainty techniques include:

  • sensitivity analysis: change one or two inputs;
  • scenario analysis: combine coherent downside, base and upside assumptions;
  • Monte Carlo simulation: assign probability distributions to uncertain inputs;
  • reverse valuation: infer the growth or margin required to justify market price;
  • valuation range: report defensible bounds rather than false precision.

A margin of safety is the difference between estimated intrinsic value and market price. It protects against model error but does not eliminate risk.

10. Illustrative Integrated Case: Meridian Consumer Finance

Background and problem

Meridian Consumer Finance is a fictional listed company operating a mature lending and payments franchise. Its current share price is CU29. Management forecasts rising dividends, but analysts are concerned about digital competition, credit losses and whether terminal growth can be sustained. An analyst must estimate intrinsic value using several methods.

Approach and analysis

1. Dividend valuation. Forecast dividends are CU1.20, CU1.50 and CU1.80 in years 1–3. The end-of-year-3 continuing value is CU26.22 and the required return is 10%. As calculated earlier, DDM value is CU23.38 per share.

2. FCFE valuation. Normalized next-year FCFE is CU2.10 per share. If long-run growth is 2.5% and required return is 11%:

V0=\frac{2.10}{0.11-0.025}=CU24.71

This result assumes stable leverage and that CU2.10 is a sustainable next-period cash flow.

3. Residual income valuation. Current book value is CU18 per share, next year’s residual income is CU0.72, residual income is expected to grow at 3%, and required return is 10%:

V0=18+\frac{0.72}{0.10-0.03}=CU28.29

The relatively high result reflects an assumption that excess returns persist indefinitely. If competition causes residual income to fade more quickly, value will be lower.

4. Relative valuation. Normalized forward EPS is CU2.00. Comparable firms trade at a median forward P/E of 13, implying CU26.00. Meridian’s weaker asset quality may justify a discount; a 12 times multiple would imply CU24.00.

MethodIndicated value per sharePrincipal dependence
Multistage DDMCU23.38Dividend policy and continuing value
Stable FCFECU24.71Sustainable cash flow and leverage
Residual incomeCU28.29Persistence of excess ROE
Relative valuationCU24.00–CU26.00Peer comparability and earnings quality

Outcome

The evidence supports a broad valuation range of approximately CU23–CU28, with the upper end dependent on persistent residual income. At a market price of CU29, the shares offer no margin of safety under the stated assumptions. A prudent analyst would not average the estimates mechanically; the DDM and FCFE estimates may deserve greater weight if cash distributions are forecast reliably.

Learning points

  • Different models illuminate different economic assumptions.
  • The corrected Meridian DDM value is CU23.38, not a lower rounded figure.
  • A valuation range is more defensible than a single-point estimate.
  • Competitive fade and credit risk should be reflected in cash flows, growth or discount rates without double counting.

11. Governance, Ethics and Regulation

Valuation can be biased by investment-banking relationships, compensation incentives or pressure to support a desired transaction price. Ethical analysts should distinguish facts from assumptions, disclose conflicts, use current information consistently and preserve model audit trails.

Accounting estimates require scrutiny. Aggressive revenue recognition, understated credit provisions, capitalized expenses and related-party transactions can inflate earnings and book value. Analysts must avoid selectively adjusting only the evidence that supports their preferred conclusion.

Material non-public information must not be used for trading. Research communications should comply with securities regulation, fair-disclosure rules and professional standards applicable in the relevant jurisdiction.

12. Technology and Contemporary Practice

Data platforms and AI can accelerate peer screening, document extraction, scenario generation and anomaly detection. They do not remove the need for economic judgment. Historical data may contain survivorship bias, accounting inconsistencies or structural breaks, while AI-generated forecasts may be opaque or unsupported.

Best practice is to verify source data, reconcile forecasts with financial statements, document model versions, test formulas, protect confidential data and require human review of material conclusions. Contemporary analysis increasingly incorporates intangible assets, climate-transition exposure, cyber risk and alternative data, but these factors should affect valuation only through defensible changes to cash flow, growth, risk or asset values.

Chapter Summary

Equity valuation converts expectations about cash flow, growth and risk into an estimate of shareholder value. Dividend discount models are appropriate when distributions represent economic capacity; FCFF and FCFE models focus on cash generated after reinvestment; residual income models combine book value with expected excess returns; and relative valuation benchmarks a company against comparable market prices.

Growth should be linked to retention and profitability, while extraordinary returns should normally fade as competition responds. Corporate actions alter per-share claims and must be analysed carefully; for rights issues, TERP and the value of rights protect investors from mistaking a lower ex-rights price for a loss in economic wealth. Because estimates are highly sensitive to terminal assumptions, professional valuation requires scenarios, cross-checks, transparent judgment and ethical communication.

Key Terms

Enterprise value: Value of operating assets attributable to all capital providers.

Equity value: Residual value attributable to ordinary shareholders.

Intrinsic value: Value implied by a reasoned assessment of expected benefits and risk.

Required return: Minimum expected return investors demand for bearing risk.

Sustainable growth: Growth supported by retained earnings and a stable return on equity and leverage policy.

Dividend discount model: Valuation based on the present value of expected dividends.

Gordon growth model: Constant-growth special case of the dividend discount model.

Continuing value: Value at a forecast horizon of cash flows expected thereafter.

FCFF: Cash flow available to debt and equity capital providers.

FCFE: Cash flow available to ordinary shareholders after financing effects.

WACC: Weighted average required return of debt and equity providers.

Residual income: Net income less a charge for beginning equity capital.

Clean-surplus accounting: Relation linking book value changes to income and owner distributions.

Relative valuation: Valuation based on market multiples of comparable firms.

Competitive advantage period: Period during which returns exceed the cost of capital.

TERP: Theoretical ex-rights price following a rights issue.

Margin of safety: Excess of estimated intrinsic value over market price.

Reverse valuation: Analysis of assumptions implied by the current market price.

Review Questions

Short Answer Questions

  1. Distinguish enterprise value from equity value.
  2. State the applicability conditions for the Gordon growth model.
  3. Why is FCFF discounted at WACC rather than the required return on equity?
  4. Define residual income and clean-surplus accounting.
  5. What is the theoretical ex-rights price?

Long Answer Questions

  1. Explain the complete equity valuation process, from business analysis to investment conclusion.
  2. Compare dividend discount, FCFE and residual income valuation, including their strengths and limitations.
  3. Discuss how competitive advantage, reinvestment and profitability jointly determine value-creating growth.
  4. Evaluate the use of P/E, P/B and EV/EBITDA in comparable-company analysis.
  5. Discuss governance, ethical and technological issues affecting professional equity valuation.

Analytical / Application Questions

  1. A company will pay dividends of CU1.00, CU1.30 and CU1.60 over the next three years. Its end-of-year-3 continuing value is CU24.00 and the required return is 9%. Calculate current value per share.
  2. A firm has next-year FCFF of CU20 million, WACC of 8%, perpetual growth of 3%, debt of CU90 million, surplus cash of CU10 million and 16 million diluted shares. Estimate value per share.
  3. For a share with next-year dividend of CU1.80, compare values under (a) re=10%,g=4% and (b) re=11%,g=3%. Explain why the values differ.

Multiple Choice Questions with Answers

Question 1

Which valuation measure represents the value attributable to both debt and equity capital providers?

A. Market capitalization

B. Enterprise value

C. Book value of equity

D. Dividend value

Correct Answer: B. Enterprise value

Question 2

A company retains 40% of earnings and earns a stable ROE of 15%. Under the sustainable growth relation, its growth rate is:

A. 4%

B. 6%

C. 9%

D. 15%

Correct Answer: B. 6%

Question 3

A share will pay CU2.00 next year. If the required return is 11% and perpetual growth is 3%, its Gordon-model value is:

A. CU18.18

B. CU22.00

C. CU25.00

D. CU28.57

Correct Answer: C. CU25.00

Question 4

Meridian pays CU1.20, CU1.50 and CU1.80 in years 1–3, has a CU26.22 end-of-year-3 continuing value and a 10% required return. Its value is approximately:

A. CU21.05

B. CU23.38

C. CU26.22

D. CU28.02

Correct Answer: B. CU23.38

Question 5

Which item is added when calculating FCFE from net income?

A. An increase in operating working capital

B. Capital expenditure

C. Net borrowing

D. Dividends paid

Correct Answer: C. Net borrowing

Question 6

Beginning book value is CU30, forecast ROE is 13% and required return is 9%. Next year’s residual income is:

A. CU1.20

B. CU2.70

C. CU3.90

D. CU6.60

Correct Answer: A. CU1.20

Question 7

Which multiple maintains a consistent capital-provider basis?

A. Enterprise value divided by EBITDA

B. Enterprise value divided by earnings per share

C. Share price divided by total company revenue

D. Equity market value divided by interest expense

Correct Answer: A. Enterprise value divided by EBITDA

Question 8

A one-for-four rights issue has a CU40 subscription price and a CU50 cum-rights price. The TERP is:

A. CU42

B. CU46

C. CU48

D. CU50

Correct Answer: C. CU48

Question 9

For D1=CU1.80, which assumption set gives a Gordon-model value of CU36?

A. re=9%, g=3%

B. re=10%, g=4%

C. re=10%, g=5%

D. re=11%, g=4%

Correct Answer: C. re=10%, g=5%

Question 10

Which practice best addresses valuation uncertainty?

A. Reporting only the most optimistic estimate

B. Using the same multiple for every company

C. Ignoring terminal value because it is uncertain

D. Testing coherent scenarios and reporting a defensible range

Correct Answer: D. Testing coherent scenarios and reporting a defensible range
Investment & Portfolio Management
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