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Security Analysis & Business Valuation Atlas

Revision Cards

85 concepts

Intrinsic Value versus Price

V_0 = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t}

Intrinsic value is the present value of expected future cash flows

4 pitfallsquiz

Valuation Foundations

beginner

The Active Investor Thesis

\text{Mispricing} = V_0 - P_0

Active investors seek mispriced securities using public information

4 pitfallsquiz

Valuation Foundations

beginner

Fundamental Analysis: Top-Down and Bottom-Up

Fundamental analysis estimates intrinsic value from business economics

4 pitfallsquiz

Valuation Foundations

intermediate

Reliability and Quality of Public Information

\text{Accruals} = \text{Net Income} - \text{Operating Cash Flow}

A valuation is only as good as the information behind it

4 pitfallsquiz

Valuation Foundations

intermediate

Market Efficiency and Mispricing

P_0 \neq V_0

Efficient markets view: price already reflects available information

4 pitfallsquiz

Valuation Foundations

beginner

The Valuation Process

V_0 = \sum_{t=1}^{n} \frac{FCF_t}{(1 + r)^t} + \frac{TV_n}{(1 + r)^n}

Valuation is a workflow, not a single formula

4 pitfallsquiz

Valuation Foundations

intermediate

Types of Value

V_{\text{going concern}} = \sum_{t=1}^{\infty} \frac{FCF_t}{(1 + r)^t}

Going-concern value assumes the firm keeps operating

4 pitfallsquiz

Required Returns

intermediate

Project Discount Rate versus Firm WACC

r_{project} = WACC \quad \text{only if} \quad \beta_{project} = \beta_{firm}

The right project rate is the opportunity cost of capital for that project’s risk

4 pitfallsquiz

Required Returns

advanced

The Pure-Play Comparable Method

\beta_{U} = \dfrac{\beta_{e}}{1 + (1 - t)\,\frac{D}{E}}

Estimate the project rate from pure-play comparables, not the diversified parent

4 pitfallsquiz

Required Returns

intermediate

Divisional Cost of Capital

WACC_{div} = w_d\,k_d\,(1 - t) + w_e\,k_e^{div}

The divisional method sets one WACC per business unit, not per firm or per project

4 pitfallsquiz

Required Returns

beginner

Hurdle Rates and Investment Policy

\text{Accept if} \quad IRR \geq \text{hurdle rate}

A hurdle rate is the minimum return a project must clear to be funded

4 pitfallsquiz

Required Returns

intermediate

Adjusting the Discount Rate for Project Risk

r_{project} = k_{rf} + \beta_{project}\,(k_m - k_{rf})

Match the discount rate to the project’s systematic risk

4 pitfallsquiz

Required Returns

intermediate

The One-WACC-Fits-All Fallacy

r_{project} = WACC_{firm} \quad \forall\ \text{projects, regardless of } \beta_{project}

The fallacy applies one firm WACC to every project regardless of risk

4 pitfallsquiz

Required Returns

advanced

Cash-Flow and Discount-Rate Consistency

V_{firm} = \sum_{t=1}^{n} \dfrac{FCFF_t}{(1 + WACC)^t}

Match the cash flow to the discount rate of the same claimants

4 pitfallsquiz

Value Creation

intermediate

Value Creation: ROIC versus WACC

\text{Economic profit} = (\mathrm{ROIC} - \mathrm{WACC}) \times \text{Invested capital}

Value is created only when ROIC exceeds WACC

4 pitfallsquiz

Value Creation

advanced

Reinvestment and the Value Drivers

V_0 = \dfrac{\mathrm{NOPAT}_1 \left(1 - \dfrac{g}{\mathrm{ROIC}}\right)}{\mathrm{WACC} - g}

Value is driven by growth, ROIC and WACC together

4 pitfallsquiz

Value Creation

advanced

Competitive Advantage Period and Fade

(\mathrm{ROIC}_t - \mathrm{WACC}) \to 0 \quad \text{as } t \to \text{end of CAP}

The CAP is how long ROIC can stay above WACC

4 pitfallsquiz

Value Creation

intermediate

EPS Accretion and Dilution

\text{Accretive} \iff \mathrm{ROE}_{\text{project}} > \dfrac{E}{P}

Accretive raises EPS, dilutive lowers it

4 pitfallsquiz

Value Creation

intermediate

Incentive Compensation and EVA

\mathrm{EVA} = \mathrm{NOPAT} - \mathrm{WACC} \times \text{Invested capital}

Incentive pay aligns managers with owners, but the metric drives behaviour

4 pitfallsquiz

Value Creation

intermediate

Managerial Myopia and Short-Termism

\text{Myopia} \implies \text{maximise } \mathrm{EPS}_1 \text{ rather than } \mathrm{NPV}

Myopia favours near-term earnings over long-run value

4 pitfallsquiz

Value Creation

intermediate

Agency Conflicts

\text{Agency costs} = \text{Monitoring} + \text{Bonding} + \text{Residual loss}

Agency conflict: managers control the firm but do not fully bear owners’ outcomes

4 pitfallsquiz

Value Creation

intermediate

Project Selection and Capital Rationing

\mathrm{PI} = \dfrac{\text{PV of future cash flows}}{\text{Initial investment}}

With unlimited funds, accept every positive-NPV project

4 pitfallsquiz

Project Risk

beginner

Sensitivity Analysis

\text{Sensitivity}_i = \frac{\Delta \mathrm{NPV}}{\Delta x_i} \quad \text{with all } x_{j \ne i} \text{ fixed}

Flex one input at a time, holding all others at their expected values

4 pitfallsquiz

Project Risk

beginner

Scenario Analysis

\mathrm{NPV}_s = \sum_{t=0}^{n} \frac{\mathrm{FCF}_{t,s}}{(1 + r)^{t}}

Builds a few coherent stories, typically base, optimistic and pessimistic

4 pitfallsquiz

Project Risk

intermediate

Break-Even Sensitivity Analysis

\mathrm{NPV}(x_i^{*}) = 0

Finds the critical value of a driver that pushes NPV to zero

4 pitfallsquiz

Project Risk

advanced

Monte Carlo Simulation

\mathrm{NPV}^{(k)} = \sum_{t=0}^{n} \frac{\mathrm{FCF}_{t}\big(x_1^{(k)}, \dots, x_m^{(k)}\big)}{(1 + r)^{t}}

Assigns a probability distribution to each uncertain input

4 pitfallsquiz

Project Risk

intermediate

Decision Trees and Project Flexibility

E[\mathrm{NPV}] = \sum_{j} p_j \, \mathrm{NPV}_j

Map flexibility to expand, delay or abandon as information arrives

4 pitfallsquiz

Project Risk

beginner

Risk versus Uncertainty

E[X] = \sum_{j} p_j \, x_j

Risk means outcomes unknown but probabilities known, like a fair die

4 pitfallsquiz

Project Risk

intermediate

Macro and Geopolitical Risk in Projects

r = r_f + \beta \,(r_m - r_f) + \text{country risk premium}

Macro risk spans interest rates, inflation, exchange rates and the cycle

4 pitfallsquiz

Advanced & Applied

advanced

Valuation in a Private Equity Setting

\text{Equity}_{\text{exit}} = \text{EBITDA}_{\text{exit}} \times \text{EV/EBITDA multiple} - \text{Net debt}_{\text{exit}}

PE invests in unlisted firms or takes listed firms private by buying all shares

4 pitfallsquiz

Advanced & Applied

advanced

Venture Capital Valuation and the VC Method

\text{Ownership} = \dfrac{\text{Investment} \times (1 + ROR)^{n}}{\text{Exit equity value}}

VC is a subset of PE for early-stage, high-growth startups

4 pitfallsquiz

Advanced & Applied

advanced

Real Options in Valuation

\text{Expanded NPV} = \text{Static NPV} + \text{Value of real options}

A real option is the right, not the obligation, to act once uncertainty resolves

4 pitfallsquiz

Advanced & Applied

advanced

Options to Expand, Abandon and Delay

\text{Abandonment value} = \max(\text{Salvage value} - \text{PV of continuing}, \; 0)

The three core real options are expand, abandon and delay

4 pitfallsquiz

Advanced & Applied

intermediate

The Control Premium

\text{Control premium \%} = \dfrac{\text{Price per share paid for control}}{\text{Unaffected market price}} - 1

A control premium is paid above market price to acquire a controlling stake

4 pitfallsquiz

Advanced & Applied

intermediate

The Illiquidity and Marketability Discount

V_{\text{illiquid}} = V_{\text{liquid}} \times (1 - \text{DLOM})

An illiquidity discount lowers the value of assets that cannot be sold quickly

4 pitfallsquiz

Advanced & Applied

advanced

Applied Company Valuation: The Analyst’s Verdict

\text{Margin of safety} = \dfrac{\text{Intrinsic value} - \text{Market price}}{\text{Intrinsic value}}

The workflow runs from information gathering to a buy, hold or sell verdict

4 pitfallsquiz

Advanced & Applied

intermediate

ESG, Non-Financial Information and the Limits of Valuation

V_0 = \sum_{t=1}^{n} \dfrac{FCF_t(\text{ESG})}{(1 + r(\text{ESG}))^t} + \dfrac{TV_n}{(1 + r)^n}

Traditional valuation rests on uncertain forecasts and a discount rate

4 pitfallsquiz

Financial Forecasting

intermediate

Pro-Forma Financial Statements

\text{Statements} \to \text{pro-forma IS and BS} \to FCFF_t \to \text{terminal value}

Pro-forma projects the income statement, balance sheet and cash-flow statement together

4 pitfallsquiz

Financial Forecasting

beginner

Percent-of-Sales Forecasting

X_t = \left(\dfrac{X_0}{Sales_0}\right) \times Sales_t

Forecasts each variable line as a fixed historical fraction of sales

4 pitfallsquiz

Financial Forecasting

intermediate

Sales-Driven Forecasting

Revenue_t = \text{Volume}_t \times \text{Price}_t

The sales forecast is the most important single assumption in a valuation

4 pitfallsquiz

Financial Forecasting

intermediate

Forecasting Working Capital and Capex

NWC = (AR + Inv) - AP

Growth ties up cash in working capital and demands capex

4 pitfallsquiz

Financial Forecasting

advanced

The Financing Plug

\text{Plug} = \text{Total assets} - (\text{Spontaneous liabilities} + \text{Equity} + \text{Existing debt})

A pro-forma balance sheet seldom balances after the operating forecast

4 pitfallsquiz

Financial Forecasting

advanced

Earnings Normalization

EBIT_{norm} = EBIT_{reported} - \text{One-off items} - \text{Non-operating income}

Normalization strips reported profit to a recurring, maintainable base

4 pitfallsquiz

Financial Forecasting

advanced

Cyclical and Through-the-Cycle Adjustment

\overline{m} = \dfrac{1}{n}\displaystyle\sum_{t=1}^{n} \dfrac{EBIT_t}{Sales_t}

Cyclical firms should be forecast from a mid-cycle, not a peak or trough, base

4 pitfallsquiz

Financial Forecasting

intermediate

Sustainable Growth Rate

g = b \times ROE

Sustainable growth is the rate financeable from retained earnings alone

4 pitfallsquiz

Relative Valuation

beginner

Comparable Companies Analysis

\text{Value} = \text{Peer multiple} \times \text{Target metric}

Comparables apply a peer multiple to the target’s own metric

4 pitfallsquiz

Relative Valuation

beginner

Price-to-Earnings Multiple

\text{P/E} = \dfrac{\text{Price per share}}{\text{EPS}}

P/E is price per share divided by earnings per share

4 pitfallsquiz

Relative Valuation

intermediate

EV/EBITDA Multiple

\text{EV/EBITDA} = \dfrac{\text{Enterprise value}}{\text{EBITDA}}

EV/EBITDA divides enterprise value by pre-interest operating earnings

4 pitfallsquiz

Relative Valuation

intermediate

Price-to-Book Multiple

\text{P/B} = \dfrac{\text{Market value of equity}}{\text{Book value of equity}}

P/B is market value of equity over book value of equity

4 pitfallsquiz

Relative Valuation

intermediate

Price-to-Sales Multiple

\text{P/S} = \dfrac{\text{Market value of equity}}{\text{Revenue}}

P/S is market value of equity over revenue

4 pitfallsquiz

Relative Valuation

intermediate

PEG Ratio

\text{PEG} = \dfrac{\text{P/E}}{g}

PEG divides the P/E by the expected earnings growth rate

4 pitfallsquiz

Relative Valuation

intermediate

Precedent Transactions

\text{Deal value} = \text{Standalone value} \times (1 + \text{Control premium})

Precedent transactions use multiples paid in past acquisitions

4 pitfallsquiz

Relative Valuation

advanced

Multiples versus DCF

V_0 = \sum_{t=1}^{n} \dfrac{\text{FCF}_t}{(1 + r)^t} + \dfrac{\text{TV}_n}{(1 + r)^n}

Multiples are fast, market-based and a transparent reality check

4 pitfallsquiz

Cost of Capital

intermediate

Weighted Average Cost of Capital (WACC)

WACC = w_d\,k_d\,(1 - t) + w_p\,k_p + w_e\,k_e

WACC blends after-tax costs of debt, preferred and equity by market-value weights

4 pitfallsquiz

Cost of Capital

intermediate

Cost of Equity and the CAPM

k_e = k_{rf} + \beta_e\,(k_m - k_{rf})

Cost of equity is the hardest WACC input, since equity holders are residual claimants

4 pitfallsquiz

Cost of Capital

intermediate

Cost of Debt

k_d^{after\text{-}tax} = k_d\,(1 - t)

Cost of debt is the YTM on the firm’s traded bonds, not the coupon

4 pitfallsquiz

Cost of Capital

intermediate

Capital Structure Weights

w_d = \dfrac{D}{D + P + E}, \quad w_p = \dfrac{P}{D + P + E}, \quad w_e = \dfrac{E}{D + P + E}

Weights are each source’s share of total invested capital

4 pitfallsquiz

Cost of Capital

advanced

Levered and Unlevered Beta

\beta_U = \dfrac{\beta_e}{1 + (1 - t)\,\frac{D}{E}}

Equity beta equals business risk plus financial leverage risk

4 pitfallsquiz

Cost of Capital

advanced

Debt Beta and the Asset Beta

\beta_U = \beta_e\,\dfrac{E}{D + E} + \beta_d\,\dfrac{D}{D + E}

Hamada’s simple form assumes a zero debt beta, that is, risk-free debt

4 pitfallsquiz

Cost of Capital

intermediate

Risk-Free Rate, Equity and Country Risk Premiums

k_e = k_{rf} + \beta_e\,(k_m - k_{rf}) + CRP

Risk-free rate is the safe base return, matched to the cash-flow horizon

4 pitfallsquiz

Cash Flows & DCF

intermediate

Free Cash Flow: FCFF versus FCFE

\text{Revenue} - \text{COGS} - \text{OpEx} = \text{EBIT}, \quad \text{EBIT} + \text{D\&A} = \text{EBITDA}

Free cash flow is a cash measure, deliberately distinct from accounting Net Income

4 pitfallsquiz

Cash Flows & DCF

beginner

Incremental and Relevant Cash Flows

\text{Incremental CF} = \text{Cash flow}_{\text{with project}} - \text{Cash flow}_{\text{without project}}

Count only cash flows that change with the decision, with minus without

4 pitfallsquiz

Cash Flows & DCF

beginner

Sunk Costs and Opportunity Costs

\text{Relevant cost of a resource} = \max(\text{value in next-best use})

A sunk cost is already spent and unrecoverable, so it is irrelevant

4 pitfallsquiz

Cash Flows & DCF

beginner

NPV and Value Additivity

\text{NPV} = -\,\text{CF}_0 + \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t}

NPV is the present value of future cash flows minus the cash invested today

4 pitfallsquiz

Cash Flows & DCF

beginner

Discounting and the Time Value of Money

\text{PV} = \frac{\text{CF}_t}{(1 + r)^t}

A dollar today beats a dollar tomorrow because it can be reinvested

4 pitfallsquiz

Cash Flows & DCF

intermediate

The Mid-Year Convention

\text{PV}_{\text{mid}} = \frac{\text{CF}_t}{(1 + r)^{\,t - 0.5}} \;>\; \frac{\text{CF}_t}{(1 + r)^{t}} = \text{PV}_{\text{end}}

Year-end discounting assumes cash arrives in one lump at the period end

4 pitfallsquiz

Cash Flows & DCF

intermediate

Terminal Value: Perpetuity and Growing Perpetuity

\text{TV}_n = \frac{\text{CF}}{r}

Terminal value captures all cash beyond the explicit forecast horizon

4 pitfallsquiz

Cash Flows & DCF

advanced

Equivalent Annual Cost

\text{AF}(r, n) = \frac{1 - (1 + r)^{-n}}{r}

Raw NPV unfairly favours longer projects with more years to accrue value

4 pitfallsquiz

Enterprise Valuation

intermediate

Enterprise Value vs Equity Value

\text{Equity value} = \text{Enterprise value} - \text{Net debt} - \text{Minority interest} + \text{Associates}

Enterprise value is the value of the operating business to all capital providers

4 pitfallsquiz

Enterprise Valuation

intermediate

The Equity Bridge

\text{Equity value} = \text{EV} - \text{Net debt} - \text{Minority interest} - \text{Preferred} + \text{Associates} + \text{Non-operating assets}

The bridge crosses from enterprise value to equity value

4 pitfallsquiz

Enterprise Valuation

advanced

DCF Enterprise Valuation with FCFF

\text{EV} = \displaystyle\sum_{t=1}^{n} \dfrac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \dfrac{\text{TV}_n}{(1 + \text{WACC})^n}

Three steps: forecast FCFF, discount at WACC, add terminal value

4 pitfallsquiz

Enterprise Valuation

advanced

Adjusted Present Value (APV)

\text{APV} = V_{\text{unlevered}} + \text{PV(financing side effects)}

APV is unlevered value plus the value of financing side effects (Myers 1974)

4 pitfallsquiz

Enterprise Valuation

intermediate

The Interest Tax Shield

\text{Tax shield}_t = \tau_c \times r_d \times D_t

Interest is tax-deductible, so debt creates a tax saving

4 pitfallsquiz

Enterprise Valuation

intermediate

Two-Stage and Three-Stage DCF

\text{EV} = \displaystyle\sum_{t=1}^{n} \dfrac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \dfrac{\text{FCFF}_{n}(1 + g)}{(\text{WACC} - g)} \cdot \dfrac{1}{(1 + \text{WACC})^{n}}

Two-stage: explicit planning period then a stable terminal stage

4 pitfallsquiz

Enterprise Valuation

intermediate

Terminal Value Cross-Check

\text{TV}_n = \dfrac{\text{FCFF}_{n}(1 + g)}{\text{WACC} - g}

Terminal value dominates a DCF, so compute it two ways

4 pitfallsquiz

Enterprise Valuation

advanced

Non-Operating Assets and NOLs

\text{Equity value} = \text{Operating EV} - \text{Net debt} + \text{Excess cash} + \text{Associates} + \text{Non-operating assets}

The operating DCF excludes anything outside operations

4 pitfallsquiz

Applied Cases

intermediate

Case: Valuing Vinamilk (VNM)

\text{TV}_n = \dfrac{\text{FCFF}_{n+1}}{\text{WACC} - g} = \dfrac{\text{FCFF}_n\,(1 + g)}{\text{WACC} - g}

Vinamilk (VNM) is a stable dairy staple, revenue about VND 62 trillion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing Hoa Phat (HPG)

\overline{m} = \dfrac{1}{n}\displaystyle\sum_{t=1}^{n} \dfrac{\text{EBIT}_t}{\text{Sales}_t}, \qquad \text{EBIT}_{\text{norm}} = \overline{m} \times \text{Sales}_{\text{mid}}

Hoa Phat (HPG) is a cyclical steelmaker, revenue about VND 140 trillion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing FPT Corporation

V_0 = \displaystyle\sum_{t=1}^{n} \dfrac{\text{FCFF}_t}{(1 + \text{WACC})^t} + \dfrac{1}{(1 + \text{WACC})^n}\cdot\dfrac{\text{FCFF}_{n+1}}{\text{WACC} - g_{\text{stable}}}

FPT is a high-growth IT-services group, revenue about VND 62 trillion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing Masan Group (MSN)

\text{EV}_{\text{SOTP}} = \displaystyle\sum_{i} \text{EV}_i

Masan (MSN) is a consumer and retail conglomerate, revenue about VND 84 trillion (FY2024)

4 pitfallsquiz

Applied Cases

intermediate

Case: Valuing Mobile World (MWG)

\text{Revenue}_t = \text{Store count}_t \times \text{Revenue per store}_t

Mobile World (MWG) is a sales-driven retailer, revenue about VND 134 trillion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing Commonwealth Bank (CBA)

\dfrac{P}{B} = \dfrac{\text{ROE} - g}{r_e - g}

Commonwealth Bank (CBA) is the largest ASX bank, cash profit about A$9.8 billion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing CSL Limited (CSL)

V_{\text{total}} = V_{\text{base DCF}} + \displaystyle\sum_{i} \text{Option value}_i

CSL is an ASX-listed plasma and biotech group reporting in US dollars, revenue about US$14.8 billion and R&D about US$1.4 billion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: Valuing Transurban (TCL)

V_0 = \displaystyle\sum_{t=1}^{T} \dfrac{\text{CF}_t}{(1 + r)^t} + \dfrac{\text{Handback}_T}{(1 + r)^T}

Transurban (TCL) is an ASX toll-road operator, proportional toll revenue about A$3.5 billion (FY2024)

4 pitfallsquiz

Applied Cases

advanced

Case: The Newmont and Newcrest acquisition

\text{Control premium} = \dfrac{P_{\text{offer}}}{P_{\text{unaffected}}} - 1

Newmont acquired Newcrest in an all-scrip deal completed 6 November 2023

4 pitfallsquiz