Investment value: the value of a stock to a particular buyer that depends on the buyer's specific needs and expectations, and perceived synergies with existing buyer assets

Liquidation value; the estimate of what the assets of the firm would bring if sold separately, net of the company's liabilities

大小关系

Liquadation value最小，Investment value最大，其他两个在中间

根据内在价值和市场价值之间的关系，可以判断市场有效性并指导投资决策

Planning: Valuation on individual security is not apply to Indexing strategy but active management

Quantitative and qualitative factors in valuation

Quantitative factors: Key source from company's accounting information and financial disclosures.Including B/S, I/S, CF/S, as well as the footnotes

Qualitative factors: measure industry performance, such as legal and regulatory environment

Quality of the firm's management team

The transparency of its performance

The analyst's confidence in the firm's

Industry's accounting practices

Abnormal return (α)

Ex ante alpha=expected holding period return-required return

Ex post alpha=actual holding period return-contemporaneous required return

Going concern assumption

Going concern: a company will continue to operate as a business, and the valuation models we will cover are all based on this assumption

Non-going-concern: a company will finish operating and all assets will be sold out, which is used to calculate liquadation value

Sum-of-the-parts valuation and conglomerate discount

Sum-of-the-parts value: the value an analyst obtained from individual parts of the firm and add them up to determine the value for the company as a whole. The value is sometimes called breakup value or private market value

Conglomerate discount: the value of a whole company is lower than the sum of its parts

Explanations for conglomerate discounts

Internal capital inefficiency: The company's allocation of capital to different divisions may not have been based on sound decisions

Endogenous (internal) factors: For example, the company may have pursued unrelated business acquisitions to hide poor operating performance

Research measurement errors: Some hypothesize that conglomerate discounts do not exist

Discounted Dividend Valuation

The Gordon Growth model

Assumptions

The firm expects to pay a dividend, D1, in one year

Dividends grow indefinitely at a constant rate, g (which may be less than zero)

3. The growth rate, g, is less than the required return,r

公式

The value of a firm's equity has two components

The present value of a perpetual cash flow of equity

The present value of its present value of growth opportunities(PVGO)

假设：公式将全部净利润用于发放股利

Justified P/E (b=1-dividend payout ratio)

Leading

Trailing

Discount cash flow model

Valuing perferred stock

Multistage dividend discount model

Two-stage DDM

Three-stage DDM

H-model

特点:The growth rate starts out high, and then declines linearly until it reach the long-term growth rate

公式

Spreadsheet modeling

方法：用Excel等软件计算股利变化不规律时的情况

优点

Flexibility

Computational accuracy

Three phases

模型选择

Decline: not valuation; just short

Equity analysis

The sustainable growth rate (SGR)

定义: the rate at which earnings (and dividends) can continue to grow indefinitely

公式: SGR=b*ROE=(1-Dividend payout ratio)*ROE

Expansion (PRAT model)

DuPont model (five-step ROE)

Free Cash Flow Valuation

Introduction

The reasons for using FCF (FCFF/FCFE)

Some companies do not pay dividends

The dividends paid differ significantly from the company's capacity to pay dividends

Free cash flows align with profitability within a reasonable forecast period with which the analyst is comfortable

FCF valuation takes a "control" perspective, while DDM takes a "minority" perspective

The relationship between FCFF and FCFE

FCF 选择的问题（FCFF or FCFE）

FCFE is easier and more straightforward

If a company has negative FCFE, we use FCFF, which is usually positive

Equity value = Firm value - Market value of debt

Different values

The value of the firm

Firm value = FCFF discounted at the WACC

FCFFt= FCFFt-1× (1+g)

The value of equity

Equity value=FCFE discounted at the required return on equity(r)

The methods to estimate return

CAPM

Multifactor model

Build up method

Constant Growth Valuation Model

FCF公式

FCFF

From EBIT (核心公式)

From NI

From EBITDA

From CFO

FCFE

核心公式

From NI

注：这里计算NI时用的FCFE公式中的Int(1-t)实际上是债券利息支付，等于票面利率*面值，而FCFF中的Int(1-t)是利息费用，等于实际负债*市场利率，只有当债券账面价值与市场价值相等，即平价发行，二者相等，公式才成立，因此题目中通常会做出该假设

From EBIT

From EBITDA

From CFO

From target debt ratio (DR)

计算公式中的项目

NCC(Non-cash charges) adjustments

WCInv

WC=CA (exclude cash) - CL (exclude debt, e.g., notes payable)

FCInv

核心公式: FCInv = capital expenditures − proceeds from sales of long-term assets

不同情况计算

If no long-term assets were sold during the year

基于GV

基于BV

If long-term assets were sold during the year

基于GV

基于BV

Net borrowing (NB)

net borrowing=debt1- debt0

注: debt包含long and short-term(note payable)

特殊情况： Free Cash Flow With Preferred Stock

FCFF=NI(total) + Int * (1-T) + NCC – WCInv- FCInv

FCFE=NI(common stock) + NCC – WCINV– FCINV +NB

NI(total)=NI(common stock)+preferred dividends

根据财务报表计算FCF

用FCF折现（模型与DDM中相同）

Single-stage

Two-stage: The value is the present value of the first stage's FCF plus the present value of the terminal value of the FCF

Three-stage: The value is the present value of the high-growth and transitional period's FCF plus the present value of the terminal value of the FCF

Sensitivity analysis: Some variables have a greater impact on valuation results than others. The importance of various forecasting errors can be assessed through this approach

Market-Based Valuation: Price And Enterprise Value Multiples

Introduction

The method of comparables values a stock based on the average price multiple of the stock of similar companies

The economic rationale: Law of One Price

Price multiple

P/E

Advantages

Earnings power (EPS) is the primary determinant of investment value

The P/E ratio is popular in the investment community

Disadvantages

Earnings can be negative, which produces a meaningless P/E ratio

The volatile, transitory portion of earnings makes the interpretation of P/Es difficult for analysts

Management discretion within allowed accounting practices can distort reported earnings, and thereby lessen the comparability of P/Es across firms

计算

Methods of normalizing EPS

Historical average EPS

The normalized EPS is estimated as the average EPS over some recent period,

The method ignores size effects

Average return on equity

Normalized EPS is estimated as the average return on equity (ROE) multiplied by the current book value per share (BVPS)

The reliance on BVPS reflects the effect of firm size changes

average EPS and ROE are often measured over the most recent business cycle

P/E-to-growth ratio (PEG)

公式

The implied valuation rule is that stocks with lower PEGs are more attractive than stocks with higher PEGs

Disadvantages

The relationship between P/E and g is not linear, which makes comparisons difficult

The PEG ratio doesn't reflect the duration of the high-growth period for a multistage valuation model, especially if the analyst uses a short-term high growth forecast

P/B

计算

定义: P/B=P/BVPS

The computation of BVPS

Common shareholders' equity = shareholders' equity - prefer shareholders' equity

BVPS= common shareholders' equity / number of common stock shares

计算式

P/B0=(ROE-g) / (r-g)

The P/B increases as

ROE increases

as the spread between ROE and r increases

Rationales for using P/B ratio in valuation

Book value is a cumulative amount that is usually positive, even when the firm reports a loss and EPS is negative. Thus, a P/B can typically be used when P/E cannot

Book value is more stable than EPS and it is an appropriate measure of net asset value for firms that primarily hold liquid assets

Disadvantages

P/Bs can mislead when there are significant size differences

Different accounting conventions can obscure the true investment in the firm made by shareholders

Inflation and technological change can cause the book and market value of assets to differ significantly

P/Bs do not recognize the value of nonphysical assets

P/S

Rationales for using price-to-sales (P/S) ratio

P/S is meaningful even for distressed firms

Sales revenue is not as easy to manipulate or distort as EPS and book value

P/S ratios are not as volatile as P/E multiples

P/S ratios are particularly appropriate for valuing stocks in mature or cyclical industries and start-up companies with no record of earnings

Disadvantages

Higher sales do not necessarily indicate higher operating profits

P/S ratios do not capture differences in cost structures across companies

Revenue recognition practices can still distort sales forecasts

P/S calculation

变形

P/CF

Advantages

Cash flow is harder for managers to manipulate than earnings

Price to cash flow is more stable than price to earnings

Reliance on cash flow rather than earnings handles the problem of differences in the quality of reported earnings

Disadvantages

Items affecting actual cash flow from operations are ignored when the EPS plus noncash charges estimate is used

From a theoretical perspective, free cash flow to equity (FCFE) is preferable to operating cash flow. However, FCFE is more volatile than operating cash flow, so it is not necessarily more informative

EV/EBITDA

公式

Enterprise value (EV) = market value of common stock + market value of preferred equity +market value of debt + minority interest – cash and investments

EBITDA = recurring earnings from continuing operations + interest + taxes + depreciation + amortization

Situations when EV/EBITDA is useful

Comparing firms with different degrees of financial leverage

Value capital-intensive businesses with high levels of depreciation and amortization

EBITDA is usually positive even when EPS is not

Dividend yield

Compare price multiple with benchmark

For P/E P/B P/S P/CF EV/EBITDA

If multiples < benchmark: the stock is undervalued

If multiples > benchmark, the stock is overvalued

For dividend yield

If multiples < benchmark, the stock is overvalued

If multiples > benchmark, the stock is undervalued

技术分析

Momentum valuation indicators

Unexpected earnings (earnings surprise) = reported EPS − expected EPS

存在问题：只考虑收益（EPS），没有考虑风险（标准差）

解决: standardized unexpected earnings (SUE)

Relative strength indicator (RSTR): compare a stock's price or return performance during a given time period with benchmark

Its own historical performance

Some group of peer stocks

计算 portfolio P/E

Residual Income Valuation

Concept and calculation of residual income

定义

Resisual income (RI) = NI – Equity capital * cost of equity

Economic value added (EVA) = NOPAT* (WACC- cost of capital)=EBIT*(1-t)-WACC

Market value added (MVA)= market value of equity + market value of debt − total capital

计算

RI = Equity0* (ROE - re)

RI 的递推计算公式（基于 clean surplus relation）

Residual income valuation model

Introduction

The two elements of residual income valuation model

Current book value of equity

Present value of expected future residual income

b0=current book value of equity

Difference with DDM & FCFE: a large portion of the estimated intrinsic value comes from the present value of the expected terminal value

Single-stage

公式

The relation with justified price-to-book ratio

ROE > r

The present value of residual income >0

Market value > book value

The justified P/B ratio > 1

Continuing residual income (Two-stage model)

Three components: V0= B0+ (PV of interim high-growth RI) + (PV of continuing residual income)

Steps

Calculate the current book value per share

Calculate residual income in each year 1 to T − 1 during the interim high-growth period and discount them back to today at the required return on equity

Calculate continuing residual income that begins at the end of the high-growth period starting in year T, and then calculate the present value of continuing residual income as of the end of year T − 1

Assumptions

Assumption #1: Residual Income Persists at the Current Level Forever

Assumption #2: Residual Income Drops Immediately to Zero

Assumption #3: Residual Income Declines Over Time to Zero (market price=book value)

persistence factor(ω): The projected rate at which residual income is expected to fade over the life cycle of the firm, which is between zero and one

Assumption #4: Residual Income Declines to Long-Run Level in Mature Industry

Issues in applying residual income models

Clean Surplus Violations

Foreign currency translation gains and losses that flow directly to retained earnings under the current rate method

Certain pension adjustments

Gains/losses on certain hedging instruments

Changes in revaluation surplus (IFRS only) for long-lived assets

Changes in the value of certain liabilities due to changes in the liability's credit risk (IFRS only)

Changes in the market value of debt and equity securities classified as available-for-sale

Variations from Fair Value

Operating leases

Special purpose entities (SPEs)

Inventory

Deferred tax liabilities

Private Company Valuation

Compare public and private company

Company-Specific Factors

Stage of lifecycle: Private companies are typically less mature than public firms

Size: Private firms typically have less capital, fewer assets and employees and can be riskier

Quality and depth of management: Smaller private firms may not be able to attract as many qualified applicants as public firms

Management/shareholder overlap: In most private firms, management has a substantial ownership position

Short-term investors : management may take a shorter-term view compared to private firms where managers are long-term holders of significant equity interests

Quality of financial and other information: A potential creditor or equity investor in a private firm will have less information and reduces private firm valuations

Taxes: Private firms may be more concerned with taxes than public firms due to the impact of taxes on private equity owners/managers

Stock-Specific Factors

Liquidity: Private company equity typically has fewer potential owners and is less liquid

Restrictions on marketability: Private companies often have agreements that prevent shareholders from selling

Concentration of control: The control of private firms is usually concentrated in the hands of a few shareholders

Definitions of Value

Fair market value

Fair value for financial reporting

Fair value for litigation

Market value:

Investment value

Intrinsic value

Liquidation value

Valuation process

Issues for financial statement adjustments

Estimating Normalized Earnings

Exclude nonrecurring and unusual items

Artificially low earnings may also be the result of excessively high owner compensation or of personal expenses charged to the firm

Any real estate owned by the firm may merit treatment separate from that of firm operations

Strategic and Nonstrategic Buyers

In a strategic transaction, valuation of the firm is based in part on the perceived synergies with the acquirer's other assets

A financial transaction assumes no synergies, as when one firm buys another in a dissimilar industry

Estimating Cash Flow

FCFF is usually more appropriate when the significant changes in the firm's capital structure are anticipated

the FCFF valuation is less sensitive to the degree of financial leverage assumed in the analysis than the FCFE valuation

Factors that require adjustment (when estimating the discount rate for private companies)

Size premiums: Size premiums are often added to the discount rates for small private companies

Availability and cost of debt

Projection risk: Because of the lower availability of information from private firms and managers who are inexperienced at forecasting

Lifecycle stage

Acquirer versus target: When acquiring a private firm, some acquirers will incorrectly use their own (lower) cost of capital, rather than the higher rate appropriate for the target, and arrive at a value for the target company that is too high

Valuation approaches

Income approach

Free Cash Flow Method (a two-stage model)

Capitalized Cash Flow Method (single-stage model): capitalization rate = required rate of return - growth rate

Excess Earnings Method

Excess earnings = firm earnings - the earnings required to provide the required rate of return on working capital -earnings of fixed assets

excess earnings=value of intangible assets

Market-based valuation

Market multiple

Large private firm: is usually based on EBIT or EBITDA multiples

Small private companies with limited assets: net income multiples

The three methods

guideline public company method (GPCM): 要考虑 control premium

The guideline transactions method (GTM)：不考虑 control premium

The prior transaction method (PTM)

Valuation discounts

Discount for Lack of Control (DLOC)

公式

Premiums (discounts) for controlling interest

Discount for Lack of Marketability(Liquidity) (DLOM)

Asset-based approach

计算: value of firm equity = fair value of assets - fair value of liabilities

The approach might be appropriate in these circumstances

Firms with minimal profits and little hope for better prospects

Finance firms where their asset and liability values can be based on market prices and factors

Investment companies where the underlying assets values are determined using the market or income approaches

Small companies or early stage companies with few intangible assets

Natural resource firms where assets can be valued using comparables sales

Three models used to estimate the required rate of return

CAPM

Expanded CAPM: includes additional premiums for size and firm-specific (unsystematic) risk

Build-up method: When it is not possible to find comparable public firms for beta estimation