Business and Security Valuation Models

Introduction

Valuation converts expectations about future economic benefits and risk into an estimate of present value. It supports investment selection, mergers and acquisitions, credit analysis, capital raising, financial reporting and regulatory decisions. Because no model eliminates uncertainty, professional valuation combines internally consistent assumptions, scenario analysis and reconciliation across methods.

Two distinctions are fundamental. First, enterprise value measures the value of operating assets available to all capital providers, whereas equity value belongs to ordinary shareholders after debt-like and senior claims. Second, intrinsic models estimate value from expected cash flows or economic profits, while relative models infer value from comparable market prices.

Learning Objectives

After studying this chapter, students should be able to:

1. Apply FCFF, FCFE, dividend discount, residual income and EVA models.
2. estimate terminal value using perpetual-growth and exit-multiple methods;
3. translate enterprise value into equity value;
4. value ordinary shares, preference shares and debt securities;
5. apply market multiples with appropriate comparability adjustments;
6. evaluate valuation assumptions and model limitations; and
7. reconcile alternative estimates through valuation triangulation.

1. The Valuation Architecture

The appropriate model depends on the claim being valued and the information available.

A correct valuation must match the numerator, discount rate and resulting value. FCFF cannot ordinarily be discounted at the cost of equity, nor can equity cash flow be discounted at WACC.

2. Discount Rates and Present Value

For a cash flow CF_t received at the end of period t, present value is:

Here, r is the required return per period and n is the number of periods. The formula assumes end-of-period cash flows and a discount rate expressed for the same periodicity and risk class.

2.1 Cost of equity

A common estimate is the capital asset pricing model:

where k_e is the cost of equity, r_f is the risk-free rate, β_L is levered equity beta and R_m − r_f is the expected market risk premium. Country, size or other premiums should be added only when theoretically justified and not already reflected elsewhere.

2.2 Weighted average cost of capital

Here, E and D are market values of equity and interest-bearing debt, k_d is the pre-tax cost of debt, and T is the marginal tax rate applicable to deductible interest. Market-value weights and a target sustainable capital structure are generally preferable. The tax adjustment is inappropriate where interest is not deductible or the tax shield cannot reasonably be used.

3. Free Cash Flow Valuation

3.1 Free cash flow to the firm

FCFF represents cash generated by operations for debt and equity investors before financing payments:

EBIT is earnings before interest and tax, D&A is non-cash depreciation and amortisation, and ΔNWC is the increase in operating net working capital. All terms are currency amounts for the same period. Cash, interest-bearing debt and financing-related current accounts are normally excluded from operating working capital.

Enterprise value is:

3.2 Free cash flow to equity

FCFE measures cash available to ordinary shareholders after debt financing effects:

Net borrowing equals debt issued minus debt repaid. Equity value is obtained by discounting FCFE at k_e. FCFE can become volatile when financing policy changes materially, making FCFF more stable for highly leveraged or restructuring businesses.

4. Terminal Value

Terminal value captures cash flows after the explicit forecast period and often constitutes a large percentage of estimated value.

4.1 Perpetual-growth method

The formula applies when cash flow grows perpetually at a constant rate g, with r>g. The terminal cash flow must reflect mature operating margins, reinvestment and competitive conditions. Long-run nominal growth should normally not exceed sustainable growth in the relevant economy indefinitely.

Growth must be supported by reinvestment. For an operating business:

Thus, perpetual growth is not costless. A forecast that raises growth without providing the necessary capital expenditure and working capital investment overstates value.

4.2 Exit-multiple method

For example, terminal EBITDA may be multiplied by a justified EV/EBITDA multiple. This method is market-based rather than a purely intrinsic perpetuity. The multiple must be consistent with the company’s expected terminal growth, risk, profitability and accounting treatment.

Best practice is to calculate both terminal methods and investigate any substantial difference rather than mechanically choosing the higher value.

5. Enterprise-to-Equity Bridge

Enterprise value must be translated into the value attributable to ordinary shareholders.

Debt-like claims may include loans, bonds, lease liabilities and underfunded pensions, depending on how operating earnings and peer multiples were defined. Non-controlling interests are deducted when consolidated operating results include subsidiaries not wholly owned. Double counting must be avoided.

Figure: Adjustments required to convert enterprise value into ordinary equity value.

6. Worked FCFF Valuation

An illustrative company forecasts FCFF of $120 million, $150 million and $180 million for Years 1–3. WACC is 10%, perpetual growth is 3%, interest-bearing debt is $100 million, excess cash is $54 million, and diluted shares are 30 million.

The terminal value at the end of Year 3 is:

The present value of the explicit and terminal cash flows is:

The equity bridge is:

The terminal component is dominant, so WACC, growth, terminal margins and reinvestment assumptions require sensitivity analysis.

7. Dividend Discount Models

The dividend discount model values ordinary equity as the present value of expected dividends:

For constant perpetual growth:

This Gordon growth model requires k_e>g and a stable dividend policy consistent with earnings and reinvestment.

Example. If the most recent dividend is $2.00, expected growth is 5% and the cost of equity is 9%:

A multistage DDM is more appropriate when short-term growth differs from mature growth:

DDM is particularly useful for mature financial institutions whose regulatory capital requirements make FCFF difficult to interpret. It is less informative when dividends are temporarily disconnected from sustainable distributable earnings.

8. Residual Income Valuation

Residual income measures accounting income after charging shareholders for the required return on opening book equity:

where NI_t is net income and BV_t−1 is opening book value of equity. Equity value is:

The model relies on the clean-surplus relationship:

Adjustments may be required where gains, losses or share transactions bypass income.

Example. Opening book equity is $500 million. Net income is $70 million in Year 1 and $77 million in Year 2; dividends are $20 million and $25 million. The cost of equity is 10%.

Book value after Year 1 is $550 million. Residual income equals $20 million in Year 1 and $22 million in Year 2. If residual income grows at 3% perpetually after Year 2:

Residual income is useful where dividends are irregular but accounting book values are meaningful. Its reliability declines when accounting policies seriously distort book equity or earnings.

9. Economic Value Added

Economic value added measures operating profit after charging all capital employed:

NOPAT is net operating profit after tax. If NOPAT is $140 million, opening invested capital is $1,000 million and WACC is 9%:

Subject to consistent accounting adjustments, enterprise value can be expressed as:

Positive EVA indicates that operating returns exceed the capital charge; it does not necessarily mean that market value will rise, because market prices may already anticipate that performance. Common adjustments concern research expenditure, leases, restructuring charges and acquisition accounting.

10. Relative Valuation

Relative valuation estimates value by applying pricing multiples from comparable companies or transactions.

10.1 Common multiples

For an enterprise multiple:

For an equity multiple:

Comparable firms should resemble the subject in growth, risk, margins, capital intensity and accounting policy. Median multiples often reduce outlier influence, but they cannot correct a poorly selected peer group. Forward and historical metrics must not be mixed without adjustment.

Multiples are economically linked to fundamentals. A higher justified P/E generally corresponds to higher expected growth, stronger returns on equity, lower risk and an appropriate payout policy. Relative valuation is therefore not a substitute for fundamental analysis.

11. Valuing Debt and Other Securities

11.1 Fixed-rate bonds

The price of a conventional coupon bond is the present value of coupons and principal:

P is the bond price, C is the coupon per period, F is face value, y is the required yield per period and n is the number of remaining payment periods. Coupon and yield periodicities must match.

Complete numerical example. A four-year bond has a face value of $1,000, pays a 6% annual coupon, and has a required annual yield of 8%. Its annual coupon is $60.

Equivalently:

Because the required yield exceeds the 6% coupon rate, the bond trades below face value. This is the value immediately after a coupon date; between coupon dates, accrued interest must be considered when distinguishing clean and dirty prices.

For default-risky debt, the discount rate incorporates a credit spread, or expected contractual cash flows may be probability-weighted for default and recovery. Analysts must avoid simultaneously reducing expected cash flow for default and applying a full default spread if doing so double-counts credit risk.

11.2 Zero-coupon and floating-rate debt

A default-free zero-coupon bond is valued as:

A floating-rate note tends toward par immediately after a reset when its reference rate and credit spread remain aligned with current market requirements. Caps, floors, credit deterioration and reset lags can cause material deviations.

11.3 Preference and ordinary shares

A perpetual preference share paying a fixed dividend D_p has value:

This formula assumes perpetual, level payments and a required return k_p>0. Ordinary shares have residual claims and are appropriately valued using DDM, FCFE, residual income or justified market multiples.

12. Applied Case: Orion Consumer Products

This is an illustrative case.

Background and problem

Orion’s board requires an equity valuation before considering a strategic investment proposal. Forecast FCFF is $120 million, $150 million and $180 million over three years. WACC is 10%, perpetual growth is 3%, debt is $100 million, excess cash is $54 million and diluted shares are 30 million.

Comparable companies trade at a median forward EV/EBITDA of 8.0×. Orion’s forward EBITDA is $300 million. A separate P/E analysis uses forecast EPS of $6.20 and a justified peer multiple of 12.2×.

Analysis

The corrected FCFF analysis produces enterprise value of $2,358.21 million, equity value of $2,312.21 million and value per share of $77.07.

The EV/EBITDA method gives:

The P/E method gives:

Approach and outcome

The analyst assigns 50% weight to DCF because detailed operating forecasts are available, 30% to EV/EBITDA, and 20% to P/E:

The close range of $75.64–$78.47 provides some reassurance, but it does not prove correctness because the methods may share common assumptions about industry growth. The board receives a central estimate of $77.20 together with sensitivity ranges rather than a false point estimate of certainty.

Learning points

1. Enterprise multiples require an enterprise-to-equity bridge.
2. Terminal value assumptions can dominate DCF results.
3. Triangulation should reflect model relevance and data quality, not equal weighting by default.
4. A narrow valuation range is credible only if assumptions and data sources are independently examined.

13. Sensitivity, Scenarios and Triangulation

DCF value should be tested across plausible WACC and terminal-growth combinations. Scenario analysis should also alter internally connected variables such as sales growth, margins, reinvestment and financing needs. A growth assumption without corresponding reinvestment is economically inconsistent.

Triangulation involves:

1. checking that each model values the same claim and date;
2. normalising earnings and balance-sheet items;
3. explaining differences using growth, risk and accounting assumptions;
4. assigning weights based on relevance and evidence quality; and
5. reporting a range with key sensitivities.

Averaging models mechanically can conceal errors. If DCF materially exceeds comparable-company value, possible explanations include optimistic margins, understated risk, excessive terminal growth or genuinely superior competitive advantages.

14. Limitations, Governance and Contemporary Practice

All valuation models are conditional rather than objectively exact. Forecast error, cyclicality, accounting distortion, illiquidity and changing interest rates may materially affect results. Financial institutions require special care because debt can resemble an operating input and regulatory capital limits distributable cash flow.

Ethical risks include selecting favourable peers, manipulating terminal assumptions, treating recurring costs as exceptional, and presenting precision unsupported by evidence. Good governance requires independent review, transparent data lineage, documented overrides and disclosure of conflicts of interest.

Financial-reporting valuations may also be governed by standards such as IFRS 13 or applicable national rules. A strategic investment value, market-participant fair value and transaction price are not automatically identical.

Spreadsheet systems, valuation platforms and AI can accelerate comparable-company screening, forecast generation and document review. However, automated outputs may embed stale data, survivorship bias or unsupported assumptions. Human professionals remain responsible for model selection, accounting adjustments, validation and final judgement.

Chapter Summary

Business valuation requires consistency among the cash flow, discount rate and claim being valued. FCFF and EVA produce enterprise value, while FCFE, DDM and residual income directly estimate equity value. Terminal value may be estimated through perpetual growth or an exit multiple, but assumptions must be economically sustainable. Enterprise value must be adjusted for excess cash, debt-like claims and other non-operating interests before deriving ordinary equity value.

Debt securities are valued from discounted contractual or probability-adjusted cash flows. Relative valuation uses market evidence but depends on genuine comparability and consistent metrics. Professional conclusions are developed through sensitivity analysis, transparent enterprise-to-equity reconciliation and reasoned triangulation rather than reliance on a single model.

Key Terms

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

Equity value: Residual value attributable to ordinary shareholders.

FCFF: Cash flow available to debt and equity investors before financing payments.

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

WACC: Market-value-weighted required return on debt and equity financing.

Cost of equity: Return required by ordinary shareholders for bearing equity risk.

Terminal value: Value of cash flows beyond the explicit forecast horizon.

Perpetual growth: Constant long-run growth assumed to continue indefinitely.

Dividend discount model: Equity valuation based on the present value of dividends.

Residual income: Net income less the required return on opening book equity.

Clean surplus: Relationship linking book-value changes to income and dividends.

Economic value added: NOPAT less a charge for invested capital.

Invested capital: Operating capital supplied by debt and equity investors.

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

EV/EBITDA: Enterprise value divided by earnings before interest, tax, depreciation and amortisation.

Yield to maturity: Discount rate equating a bond’s promised cash flows with its market price.

Credit spread: Additional yield required for credit risk relative to a benchmark.

Triangulation: Reconciliation of valuation estimates from multiple methods.

Review Questions

Short Answer Questions

1. Distinguish enterprise value from ordinary equity value.
2. Why must FCFF be discounted at WACC rather than the cost of equity?
3. State the condition required for the Gordon growth model.
4. Define residual income and economic value added.
5. Why does a bond trade below face value when its required yield exceeds its coupon rate?

Long Answer Questions

1. Explain the complete process for valuing a company using an FCFF model.
2. Compare FCFE, DDM and residual income valuation, including their appropriate applications.
3. Evaluate the perpetual-growth and exit-multiple approaches to terminal value.
4. Explain how comparable companies should be selected and their financial data normalised.
5. Discuss ethical, governance and regulatory issues affecting professional valuation practice.

Analytical / Application Questions

1. A company forecasts FCFF of $80 million next year, growing perpetually at 4%. If WACC is 9%, calculate enterprise value immediately before the first forecast cash flow and discuss sensitivity to growth.
2. Price a five-year, $1,000 face-value bond paying an annual 7% coupon when the required annual yield is 9%. Explain whether it trades at a premium or discount.
3. A company has estimated values per share of $42 under DCF, $48 under P/E and $44 under residual income. Develop and justify a triangulation approach rather than using a simple average.

Multiple Choice Questions with Answers

Question 1

Which discount rate is generally appropriate for free cash flow to the firm?

A. Cost of equity

B. Weighted average cost of capital

C. Risk-free rate

D. Dividend yield

Correct Answer: B. Weighted average cost of capital

Question 2

FCFF is $180 million in Year 3, terminal value at the end of Year 3 is $2,648.57 million, and WACC is 10%. What is the present value of the combined Year 3 amounts?

A. $1,931.30 million

B. $2,025.15 million

C. $2,125.15 million

D. $2,358.21 million

Correct Answer: C. $2,125.15 million

Question 3

An enterprise has EV of $2,358.21 million, excess cash of $54 million and debt of $100 million. With no other bridge adjustments, what is equity value?

A. $2,204.21 million

B. $2,312.21 million

C. $2,404.21 million

D. $2,512.21 million

Correct Answer: B. $2,312.21 million

Question 4

A share has just paid a $2.00 dividend. If dividends grow perpetually at 5% and the cost of equity is 9%, what is its Gordon-model value?

A. $40.00

B. $50.00

C. $52.50

D. $55.13

Correct Answer: C. $52.50

Question 5

A four-year bond has face value $1,000, a 6% annual coupon and an 8% required annual yield. What is its approximate value immediately after a coupon date?

A. $933.76

B. $1,000.00

C. $1,066.24

D. $1,240.00

Correct Answer: A. $933.76

Question 6

Which relationship is required by the basic residual income model?

A. Assets equal revenue plus expenses

B. Book value equals market value each year

C. Ending book value equals opening book value plus net income minus dividends

D. Dividends equal free cash flow to the firm

Correct Answer: C. Ending book value equals opening book value plus net income minus dividends

Question 7

NOPAT is $140 million, opening invested capital is $1,000 million and WACC is 9%. What is EVA?

A. $50 million

B. $90 million

C. $126 million

D. $140 million

Correct Answer: A. $50 million

Question 8

Why is EV/EBITDA often preferred to P/E when comparing firms with different leverage?

A. EBITDA always equals cash flow

B. EV/EBITDA relates operating performance to value available to all capital providers

C. EV/EBITDA eliminates all accounting differences

D. P/E cannot be calculated for listed companies

Correct Answer: B. EV/EBITDA relates operating performance to value available to all capital providers

Question 9

Which condition is necessary for a constant-growth terminal value TV_n=CF_n+1/(r−g)?

A. g>r

B. g=r

C. r>g

D. r=0

Correct Answer: C. r>g

Question 10

Which statement best describes professional valuation triangulation?

A. Always assign equal weights to every available model

B. Select the model producing the highest value

C. Reconcile estimates using model relevance, data quality and assumption consistency

D. Replace sensitivity analysis with a simple average

Correct Answer: C. Reconcile estimates using model relevance, data quality and assumption consistency