## Equity Valuation

### -- 2017

### Instructor: Jie

### Brief Introduction

**Topic weight:**

**Study Session 1-2** **Ethics & Professional Standards** ** 10%-15%**

**Study Session 3** **Quantitative Analysis** **5%-10%**

**Study Session 4** **Economics** **5%-10%**

**Study Session 5-6** **Financial Reporting and Analysis** **15%-20%**

**Study Session 7-8** **Corporate Finance** **5%-15%**

**Study Session 9-11** **Equity Valuation** **15%-25%**

**Study Session 12-13** **Fixed Income** **10%-20%**

**Study Session 14** **Derivative Investment** **5%-15%**
**Study Session 15** **Alternative Investment** **5%-10%**
**Study Session 16-17** **Portfolio Management** **5%-10%**
**Weights: 100% **

Brief Introduction
**Content:**

Ø**Study Session 9: **Equity Valuation:Valuation Concepts

• Reading 27: Equity Valuation:Applications and Process

• Reading 28: Return Concepts

Ø**Study Session 10: **Equity Valuation::Industry and Company Analysis and
Discounted Dividend Valuation

• Reading 29: Industry And Company Analysis

• Reading 30:Discounted Dividend Valuation
Ø**Study Session 10: **Equity Investments:Valuation Models

• Reading 31: Free Cash Flow Valuation

• Reading 32: Market-Based Valuation:Orice and Enterprise Value Multiples

• Reading 33: Residual Income Valuation

• Reading 34:Private Company Valuation

Brief Introduction

**Exam-importance ranking:**

• Reading 28: Return Concepts

• Reading 30:Discounted Dividend Valuation • Reading 31: Free Cash Flow Valuation

• Reading 32: Market-Based Valuation:Orice and Enterprise Value Multiples

Brief Introduction

考纲对比:

Ø与2016年相比，2017年考纲删除两个章节(the five competitive forces that shape strategy; your strategy needs a strategy)。其他 考点不变。

### Brief Introduction

学习建议:Ø 本课程系统性地搭建了权益估值的框架，学员应能运用合适的估值概

念和技术对权益证券进行分析和评估，同时要掌握如何评估权益证券 的风险和预期回报

Ø 学习本课程需要一定的财务基础，建议同学开始学习本课程前先完成

财务报表分析学习

Ø 一定要及时做练习，推荐原版教材章节后练习题和历年模考题

### Equity Valuation:Valuation Concepts(1)

**Tasks:**

ØDefine valuation and intrinsic value and explain sources of perceived mispricing

ØExplain the going concern assumption and contrast a going concern value to a liquidation value

ØDescribe definitions of value and justify which definition of value is most relevant to public company valuation

ØDefine applications of equity valuation

Definition of Valuation

**Valuation**

Sources of Perceived Mispricing

**Intrinsic Value (V)**

ØThe value of an asset given a complete understanding of the asset's investment characteristics.

**Perceived Mispricing**

ØThe difference between the estimated intrinsic value ( ) and
the market price (**P**) of an asset

**- P =(V - P) + ( -V)**
** V - P** = true mispricing
- **V **= estimation error

**E**

**V** **VE**

**E**

**V**

**E**

**V**

Going-Concern VS. Liquidation

**Going-Concern Value**

ØThe value under a going-concern assumption that the company will continue its business activties into the foreseeable future

**Liquidation Value**

ØThe value if the company is dissolved and its assets sold individually

Ø**Orderly Liquidation Value: **Assumes adequate time to realize
liquidation value

**Going-concern value > Liquidation value**

Other Defintions of Value

**Fair Market Value**

ØThe price at which a willing, informed, and able seller would
trade an asset to a willing, informed, and able buyer.
**Investment Value**

ØThe value to a specific buyer taking account of potential synergies and based on the investor's requirements and expectations

**Intrinsic value is most relevant to public company valuation**

Applications of Equity Valuation
1. **Stock selection—our focus**

2. Inferring (extracting) market expectations

3. Evaluating corporate event (M&A, divestitures, spin-offs, etc) 4. Fairness opinions for mergers

5. Evaluating business strategies and models 6. Communication with investors and analysts 7. Valuing private business

Ø **Importance: **☆

Ø **Content:**

• Sources of perceived mispricing • definitions of value

• application of equity valuation

Ø **Exam tips: **

• 理解察觉到的错误定价的来源

• 了解不同价值定义

• 理解权益估值的运用

Summary

### Equity Valuation:Valuation Concepts(2)

**Tasks:**

ØDescribe questions that should be addressed in conducting an industry and competitive analysis

Øcontrast abusolute and relative valuation models and describe examples of each type of model

ØDescribe sum-of-the-parts valuation and conglomerate discounts

ØExplain broad criteria for choosing an appropriate approach for valuing a given company

Valuation Process

**1. Understanding** the business
**2. Forecasting** company performance
**3. Selecting** the appropriate valuation model
**4. Converting** forecasts to a valuation
**5. Applying** the valuation conclusions

Issues in Industry and Competitive Analysis

**1. How attractive are the industries in terms of offering **
**prospects for sustained profitability?**

Ø**Porter's Five Forces help characterizing industry structure**
1. Intra-Industry Rivalry

Issues in Industry and Competitive Analysis

**2. What is the company's relative competitive position **
**within its industry, and what is its competitive strategy?**
ØThe level and trend of the company's market share indicates its

relative competitive position

ØPorter's three competitive strategies 1. Cost leadership

2. Differentiation 3. Focus

Issues in Industry and Competitive Analysis

**3. How well has the company executed its strategy and **
**what are its prospects for future execution?**

ØAnalysis of financial reports provides a basis for evaluating a company's performance against its strategic objectives and for developing expectations about irs future performance

ØTwo caveats merit mention:

1. The importance of qualitative factors must be considered (ownership structure, potential consequences of legal disputes, etc)

2. Avoiding simply extrapolating past operating results when forecasting future performance

Issues in Industry and Competitive Analysis

**Quality of Earnings Analysis**
ØSelected quality of earnings indicators

• Recognizing revenue early

• Classification of nonoperating income as part of operations • Recognizing too much or too little reserves in current year • Deferral of expenses by capitalizing expenditures as an

asset

• Use of aggresive estimates and assumptions • Use of off-balance sheet financing

Valuation Models

**Absolute Valuation Models**

ØModels that specify an asset's intrinsic value • Present value model (Discounted cash flow model)

üDDM, FCF, Residual Income
• Asset-based valuation
**Relative Valuation Models**

Valuation of the Total Entity and its Components

**Sum-of-the-Parts Value/Breakup Value/Private Market Value**
ØThe value for a company as a whole obtained by adding up the

values of individual parts of the firm
**Conglomerate Discount**

ØThe market applies a discount to the value of a company operating in multiple and unrelated businesses compared to its sum-of-the-parts value

• Inefficient capital allocation among divisions

• Endogenous factors (poorly performing companies tend to expand by making acquisitions in unrelated businesses) • Research measurement errors

Selection of Appropriate Valuation Approach
Ø** Consistent with characteristics of company**

• Understand the company and how its assets create value

Ø** Based on quality and availability of data **

• DDM problematic when no dividends • P/E problematic with highly volatile earnings

Ø** Consistent with purpose of analysis**

• Free cash flow vs. dividends for controlling interest

Ø **Importance: **☆

Ø **Content:**

• valuation process

• issues in industry and competitive analysis • valuation models

• sum-of-the-part and conglomerate discount • selection of valuation approach

Ø **Exam tips: **

• 了解估值过程，行业与竞争分析中需要考虑的问题，估值

模型，分类加总法和跨业大企业估值折价，以及估值方法 选择要考虑的因素

Summary

### Definitions of Return and

### Equity Risk Premium (ERP)

**Tasks:**

ØDistinguish among realized holding period return, expected holding period return, required return, return from convergence of price to intrinsic value, discount rate, and internal rate of return

Return Concepts

**Holding Period Return (HPR)**

ØThe return earned from investing in an asset over s specified time period

**Realized Return**

ØHistorical return based on observed prices and cash flow

ØEqual to HPR
**Expected Return**

ØReturn based on forecasts of future prices and cash flows yield

ØThe minimum level of expected return that an investor requires over a specified time period, given the asset's riskiness.

ØIt represents the opportunity cost for investment in the asset

ØIt is therefore the issuer's marginal cost of capital (cost of equity)
**Expected alpha = Expected return - Required return**
ØWhen expected alpha is higher than zero, the asset is

undervalued

ØThe rate used in finding the present value of a future cash flow

ØIt reflects the compensation required by investors for delaying consumption and for the risk of the cash flow

ØIt depends on the characteristics of the investment rather than on the characteristics of the investor

**Internal Rate of Return (IRR)**

ØThe discount rate that equates the present value of the asset's expected future cash flows to the asset's price

ØAn IRR coumputed under the assumption of market efficiency equals the required return on equity

Equity Risk Premium

**Equity Risk Premium (ERP)**

ØThe incremental return that investors require for holding equities rather than a risk-free asset.

ØThe risk free rate should be consistent with the investor's investment horizon

• T-Bills for short horizons • T-Bonds for longer holding periods

Approaches to Estimating ERP

**Historical Estimates**

ØThe mean value of the differences between broad-based equity market index returns and government debt returns over the sample period

• **Strength**—objective and simple
• **Weaknesses:**

üAssumes stationary of mean and variance of returns over time

üUpwardly biased due to survivorship bias

üGeometric mean(lower) vs. arithmetic mean(higher)

üWhich risk-free rate to use (T-bond yield or T-bill yield?)

Approaches to Estimating ERP

**Forward-Looking Estimates**

ØEstimating the ERP based on current market conditions and expectations concerning economic and financial variables

• **Strength**—less subject to nonstationarity and data biases
• **Weaknesses:**

ü Requires frequent updates

ü Makes lots of assumptions

Approaches to Estimating ERP

**Forward-Looking Estimates - Gordon Growth Model **

Ø =dividend yield on broad-based equity index based on year-ahead aggregate forecasted dividends and aggregate market value

Ø = Consensus long-term earnings growth rate

Ø = long-term government bond yield
**Multiple Growth Stages Model **
ØEquity index price

=PVFastGrowthStage(r)+PVTransition(r)+PVMatureStage(r)

Approaches to Estimating ERP

**Forward-Looking Estimates - Macroeconomic Model **
ØEstimating the ERP from expected macroeconomic and financial

variables such as inflation, earning growth, P/E growth, etc.
• **Strength**—use of proven models and current information
• **Weakness**—only appropriate for developed counties where

Approaches to Estimating ERP

**Example of Macroeconomic Model - Ibbotson and Chen **
**Model**

**ERP = EDY+[(1+EINFL)(1+EGREPS)(1+EGPE)-1]-E( )**
ØEDY=expected dividend yield

ØEINFL=expected inflation (yield spread between T-bond and TIPS)

ØEGREPS=expected growth rate in real earnings per share (approximately track the real GDP growth rate)

ØEGPE=expected growth rate in the P/E ratio (the baseline value is zero)

Ø =expected risk-free return

f

R

f

R

Approaches to Estimating ERP

**Forward-Looking Estimates - Survey Estimates**

ØAsking a sample of experts about their expectations for ERP
• **Strength**—easy to obtain

• **Weakness**—wide disparity among experts

Ø **Importance: **☆☆

Ø **Content:**

• return concepts • ERP estimation

Ø **Exam tips: **

• 了解不同回报率概念

• 重点掌握权益风险溢价(ERP)评估方法的优缺点和计算。

Summary

### Estimation of Required Return (1)

**Tasks:**

ØEstimate the required return on an equity investment using the capital asset pricing model, the Fama-French model, the Pastor-Stambaugh model, macro-economic multifactor models

ØExplain beta estimation for public companies, thinly traded public companies and nonpublic companies

Models of Required Return

ØThe Capital Asset Pricing Model

ØThe Multifactor Models (APT)

ØThe Build-up Methods

Models of Required Return

**The Capital Asset Pricing Model**

ØInvestors evaluate the risk of an asset in terms of the asset's contribution to the systematic risk of their portfolio

ØThe beta measures the asset's systematic risk

ØIt assumes that equity prices are largely determined by local investors

ØThe assumption that all investors worldwide participate equally in setting prices results in the international CAPM in which risk premium is relative to a world market portfolio

) R R ( R

Ri f*i* *M* *f*

Beta Estimation

**Beta for a Public Company**

ØResulting from regressing the company's returns on the returns
of the market index (**raw beta**, or **unadjusted beta**)

ØBeta Drift: the beta value in future tends to be closer to the mean value of 1

Ø**Adjusted Beta** = (2/3)(Unadjusted beta) +(1/3)(1)

Beta Estimation

**Beta for Thinly Traded stocks or Nonpublic Companies**
Ø**Four-step procedure**

**1. Identify a publicly traded firm **with similar industry
characteristics

**2. Estimate the beta** of the publicly traded firm using
regression -> BE

Models of Required Return

**Multifactor Models**

ØUse multiple factors to explain returns

ØCAPM is a single factor model

Ø**Arbitrage pricing theory (APT) **models are based on a
multifactor representation of the drivers of return

• β = factor sensitivity/factor beta=the asset's sensitivity to a particular factor (holding all other factors constant)

• Factor risk premium=the expected return of a particular factor in excess of the risk-free rate

n

Models of Required Return

**Arbitrage Pricing Theory (APT)**
ØThe Fama-French Model

ØThe Pastor-Stambaugh Model

ØMacroeconomic Multifactor Model(The BIRR Model)

Models of Required Return

**The Fama-French Model (FFM)**

ØRMRF = the return on a market value-weighted equity index in excess of the one-month T-bill rate

ØSMB (small minus big), a size factor = small-cap return premium = the mean return to shorting large-cap shares and investing the proceeds in small-cap shares

ØHML(high minus low), a value factor = value return premium = the mean return from shorting low book-to-market(high P/B) shares and investing the proceeds in high book-to-market shares

Models of Required Return

**The Pastor-Stambaugh Model (PSM)**

ØThe PSM model adds to the Fama-French model a liquidity factor

ØLIQ, a liquidity factor = liquidity return premium = the mean return to shorting high-liquidity shares and investing the proceeds in low-liquidity shares

Models of Required Return

**Macroeconomic Multifactor Model**

ØThe FFM and PSM models are based on multiple fundamental factors that reflect attributes of the stocks or issuers themselves

ØThe macroeconomic factor models are based on multiple macroeconomic factors that affect the expected future cash flows of the stocks or issuers and the discount rate appropriate to determining their present value

Models of Required Return

**Macroeconomic Multifactor Model**

ØA specific example is the five-factor BIRR model (Burmeister, Roll, Ross)

• **Confidence risk**: the unanticipated change in the return
difference between risky corporate bonds and T-bonds
• **Time horizon risk**: the unanticipated change in the return

difference between T-bonds and T-bill

• **Inflation risk**: the unexpected change in inflation rate
• **Business cycle risk**: the unexpected change in the level of

real business activity

• **Market timing risk**: the portion of the total return that
remains unexplained by the first four risk factors

Ø **Importance: **☆☆☆

Ø **Content:**

• capital asset pricing model • beta estimation

• multifactor models(Fama-French, Pastor Stambaugh, BIRR models)

Ø **Exam tips: **

• 重要考点，掌握权益要求回报的各种评估方法的计算及其

特征 Summary

### Estimation of Required Return (2)

**Tasks:**

ØEstimate the required return on an equity investment using the buiild-up method

ØDescribe strengths and weaknesses of methods used to estimate the required return on an quity investment

ØExplain international considerations in required return estimation

Models of Required Return

**Build-Up Method**

ØEstimating the required return as the sum of the risk-free rate and a set of risk premiums

ØIt is useful when beta estimates are “unobtainable”

ØWidely used for closely held companies

scounts)

Models of Required Return

**Build-Up Method for Private Business Valuation**

Ø = required return on average-systematic-risk large-cap public stocks

ØThe size premium is inversely related to the company size

ØUnsystematic risk related to a privately-held company is less easily diversified away

i

Models of Required Return

**Bond Yield Plus Risk Premium**

ØAppropriate for companies with publicly traded debt

Ø**Required return (cost of equity) = YTM on the company's long **
**term debt + risk premium**

ØThe YTM on the company's long term debt include: • a real interest rate and a premium for expected inflation • a default risk premium which captures factors such as

profitability, the sensitivity of profitability to the business cycle, and leverage(operating, financial)

ØThe risk premium compensates for the additional risk of the equity holders compared with the debt holders

Strengths and Weaknesses of Required Return Approaches

Ø**CAPM**—simple, easy to compute, single factor model but
simplicity comes with potential loss of explanatory power

Ø** Multi-factor models**—higher explanatory power but more
complex and expensive

International Considerations in Required Return Estimation

Ø **Exchange rates**—compute the required return in the home
currency and adjust it by the forecast for the change in the
exchange rate

Ø** Country Spread Model**—use a developed market benchmark
and add an emerging market premium

**Equity risk premium for an emerging market = Equity risk **
**premium for a developed market + Country premium**

• Country premium= YTM of emerging market – YTM of developed market

Weighted Average Cost of Capital

Ø(1-tax rate) adjusts the pretax cost of debt downward to reflect the tax duductibility of interest payments

ØUse the target capital structure

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rate)r

Tax 1 ( MVE MVDMVD

WACC _{} d _{}

Discount rate Selection in Relation to Cash Flow

ØFirm value = FCFF, discount at WACC

ØEquity value = FCFE/Dividend, discount at RE

• Use FCFE when capital structure are not volatile • Use FCFF with high debt levels, negative FCFE ØEquity value = firm value – MV of debt

ØNominal (real) discount rate must be used with nominal (real) cash flows

** Important: you must align the discount rate with the cash flows ! **

Ø **Importance: **☆☆

Ø **Content:**

• the build-up method • the international consideration

• WACC

• discount selection

Ø **Exam tips: **

• 重点掌握权益要求回报的叠加法

• 理解不同权益要求回报评估方法的优缺点，以及国际考虑

• 掌握WACC计算，在给定现金流时能选择匹配贴现率

### Industry and Company Analysis (1)

**Tasks:**

ØCompare top-down, bottom-up, and hybrid approaches for developing inputs to equity valuation models

ØCompare “growth relative to GDP growth” and “market growth and market share” approaches to forecasting revenue

ØEvaluate whether economies of scale are present in an industry by analyzing operating margins and sales levels

ØForecast COGS, SG&A, Financing costs and income taxes

Approach for developing inputs to equity valuation models

Ø **Bottom-up analysis**:start with analysis of an individual
company or its business segments

Ø **Top-down analysis**: begins with expectations about a
macroeconomic variable (e.g. GDP)

Ø **Hybrid analysis**: incorporate elements of both top-down
and bottom-up analysis.

Top-Down Approaches to Modeling Revenue
**Growth Relative to GDP Growth**

ØThe relationship between GDP and company sales could be modeled
as “GDP growth plus x%”, or “GDP growth rate times (1+x%)
**Market Growth and Market Share**

ØForecasting growth of industry sales, and how the company's market share is likely to change over time

ØRevenue = market share×market sales

Economies of Scale in an industry

ØSales volume and margins tend to be positively correlated

ØEconomies of Scale are observed when larger companies:

• have larger margin

Forecasting COGS, SG&A, Financing Costs, Income Taxes

**Cost of Goods Sold (COGS)**
ØCOGS has a direct link with sales

Forecasted GOGS = (historical COGS/revenue)*(estimate of future revenue) or

Forecasted COGS = (1 – gross margin)*(estimate of future revenue)

ØBe aware of the impact of the company's hedging strategy on gross margin

ØCompetitors' gross margins can provide a useful cross check

Forecasting COGS, SG&A, Financing Costs, Income Taxes

**Selling, General, and Administrative Expenses (SG&A)**
ØSG&A overall are less closely linked to revenue than COGS

ØSelling and distribution expenses are more variable than others and can be estimated as a percentage of sales

ØOther general and administrative expenses (overhead costs, R&D expenses, etc) are more fixed in nature

Forecasting COGS, SG&A, Financing Costs, Income Taxes

**Financing Costs**

ØGross interest expense depends on the level of debt and market interest rates

**Net debt **= gross debt – cash/cash equivalents – short term
securities

**Net interest expense **= gross interest expense – interest income
on cash and short term debt securities

Forecasting COGS, SG&A, Financing Costs, Income Taxes

**Income Taxes**

Ø**Statutory tax rate**: the tax rate applying to what is considered
to be a company's domestic tax base

Ø**Effective tax rate:** calculated as the reported tax amount on
the income statement divided by pre-tax income

Ø**Cash tax rate**: the tax actually paid divided by pre-tax income

Ø **Importance: **☆☆

Ø **Content:**

• Approaches for developing inputs • Modeling revenues

• Economies of scale

• Forecasting COGS, SG&A, financing costs and income taxes

Ø **Exam tips: **

• 重点掌握预期revenue, COGS, SG&A, financing costs和 income taxes的计算方法

• 能判断行业和公司是否实现规模经济

Summary

### Industry and Company Analysis (2)

**Tasks:**

ØDescribe approaches to balance sheet modeling

ØDescribe the relationship between return on invested capital and competitive advantage

ØExplain how competitive factors affect prices and costs

ØJudge the competitive position of a company based on a Porter’s five forces analysis

ØExplain how to forecast industry and company sales and costs when they are subject to price inflation and deflation

Balance Sheet Modeling

ØMany balance sheet items flow directly from, or very closely linked to income statement.

ØPP&E: determined by depreciation and capital expenditures

ØCapital expenditures include:

• Maintenance capital expenditure necessary to sustain the current business

• Growth capital expenditure needed to expand the business ratio

inventory

365sales

Return on Invested Capital and Compatitive Advantage

Ø**Return on invested capital (ROIC)** measures the profitability of
the capital invested by the company's shareholders and debt
holders

ØInvested capital = operating assets - operating liabilities • ROIC is not affected by financial leverage

Competitive position based on Porter’s model
Ø**Threat of substitute**

• Pricing power and profitability are limited when numerous substitutes exist and switching costs are low.

Ø**Rivalry among incumbent companies**

• Pricing power and profitability are limited when industries are fragmented, have limited growth, high exit barriers, high fixed costs, identical products

Ø**Bargaining power of suppliers**

• Profitability is limited when suppliers have greater ability to increase prices, limit the quality and quantity of inputs

Competitive position based on Porter’s model
Ø**Bargaining power of customers**

• Pricing power and profitability are limited when industries have a concentrated customer base, standardized product, low switching costs for customers

ØThreat of new entrants

• Pricing power and profitability are limited when barriers to entry are low

Industry/Company sales - inflation and deflation

ØCompanies that can pass on inflation through higher prices are likely to have higher and more stable profits and cash flow

• Industry structure is an important factor

• Price-volume trade-off makes accurate revenue projections difficult

ühigher price have a negative impact on volume

üthe decline in volume depend on price elasticity of demand, the reaction of competitors, and availability of substitutes

Industry/Company costs - inflation and deflation ØThe impact of volatility in input costs can be mitigated by:

• long-term price-fixed forward contracts and hedges • access to alternative inputs

• vertically integrated

Ø **Importance: **☆☆

Ø **Content:**

• Balance sheet modeling • return on invested capital • Porter’s model

• Impact of inflation and deflation on sales and costs

Ø **Exam tips: **

• 掌握资产负债表相关科目的预期方法，计算ROIC，利用波

特模型分析行业竞争环境

• 理解通胀和紧缩对销售额和成本的影响

Summary

### Industry and Company Analysis (3)

**Tasks:**

ØEvaluate the effects of technological developments on demand, selling prices, costs, and margins

ØExplain considerations in the choice of an explicit forecast horizon

ØExplain an analyst’s choices in developing projections beyond the short-term forecast horizon

ØDemonstrate the development of a sales-based pro forma company model

Effects of technological developments on demand, price, costs and margin Ø Technological developments can decrease costs of production,

increase profit margins and industry supply and sales

Ø Result in improved substitutes or wholly new products

• Cannibalization factor: the percentage of the market for the existing product that will be taken by the new substitute

Forecast Horizon

Forecast horizon = expected holding period

Ø The horizon for highly cyclical companies should be **long **
**enough **to include the middle of a business cycle.

Ø Use normalized earnings: expected mid-cycle earnings in the absence of any unusual or temporary factors

Forecast Horizon

ØThe difficult part is recognizing inflection points**: **instances when
the future will not be like the past, due to changes in such as:
• Overall economic environment

• Business cycle stage • Government regulations • technology

Methods for projections beyond short term

ØAssume that a trend growth rate of revenue over the previous cycle will continue.

ØUse the earnings/some measure of cash flow over a forecast period, plus the terminal value

ØThe terminal value is can be estimated using either a relative valuation (price multiple) or discounted cash flow approach (DDM)

Sales-based pro forma model

Steps in developing a sales-based pro forma model:
1. Estimate **revenue growth **and **future expected revenue**
2. Estimate **COGS**

3. Estimate **SG&A**
4. Estimate **financing costs**

5. Estimate **income tax expenses **and **cash taxes**

6. Estimate **cash taxes, **taking into account changes in deferred tax
items

7. Model the balance sheet based on items from income statement

8. Estimate **capital expenditure **and **net PP&E **

9. Construct a **pro forma cash flow statement **with the completed
pro forma income statement and balance sheet

Ø **Importance: **☆

Ø **Content:**

• Effects of technological developments • Forecast horizon

• Sales-based pro forma model

Ø **Exam tips: **

• 评估技术发展对需求，价格，成本，和利润的影响

• 了解影响预期长度的因素

• 了解长期预期方法

• 了解基于销售额的预期模型

### Overview of Discounted Cash Flow Models

**Tasks:**

ØCompare dividends, free cash flow, and residual income as inputs to discounted cash flow models

ØIdentify investment situations for which each measure is suitable

ØCalculate and interpret the value of a common stock using the dividend discount model for single and multiple holding periods

Discounted Cash Flow Valuation

ØAn asset’s intrinsic value is the present value of its *expected*

future cash flows

ØMeasures of “**cash flow**”

• Dividends = cash paid to shareholders, used in DDM • Free cash flow = cash “available” to pay shareholders • Residual income = economic profit

•** Key point:** Valuation metric (e.g., divs or FCF) must be
measurable and related to earnings power

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Dividends

Ø**Advantages**

• Dividendsless volatile than other cash flow measures, more stable and predictable

• DCF model is less sensitive to short term fluctuations in underlying value

• Theoretically justified – dividends are what you receive when you buy a stock

• DCF models reflectlong term intrinsic value

• Accounts forreinvested earnings to provide a basis for increased future dividends

Dividends

Ø** Disadvantages**

• Firm maynot pay dividends due to lack of profitability or little cash available for distribution

• Historically many firms arepaying less dividends for tax reasons

Dividends Suitability

ØSituations when appropriate

• Company has history of paying dividends

• Board of directors has a dividend policy that has an understandable andconsistent relationship to profitability • Minority shareholder takes anon-control perspective • Mature firms, profitable but not fast growth

Free Cash Flow (FCF) Definitions

Ø Free cash flow to the firm (FCFF) is cash flow from operations (CFO) minus net capital expenditures, represents firm ownership

Ø Free cash flow to equity (FCFE) is cash flow from operations minus net capital expenditures minus net payments to debt holders (interest and principal), represents returns to equity ownership

Free Cash Flow (FCF)

Ø**Advantages**

• Used with any firm that has different dividend and financing/leverage policies

• FCF can be viewed as what a firm could pay in dividends • Popular with many analysts

Ø**Disadvantages**

• Negative free cash flow, resulting from large capital expenditure demands

• May requirelong forecast periods for CF to turn positive, introducing greater model uncertainty

Free Cash Flow (FCF)

Ø** Situations when appropriate**
• No dividend payment history

• Dividends not related to earnings or dividends and FCF differ significantly

• FCF consistent with profitability within a reasonable time period

Residual Income (RI) Definition

Ø** Residual income is the earnings in excess of the investors’ **
required return on the beginning-of-period investment
(common stockholders' equity)

Ø RI focuses on profitability in relation to all opportunity costs faced by the firm

Ø Intrinsic value equals the book value per share plus the present value of expected future residual earnings, similar to DDM and EVA

Residual Income (RI)

Ø** Advantages**

• Wide applicability, even if FCF < 0 • Used for dividend and non-div paying firms

• Incorporates opportunity cost of capital for both debt and equity holders

• Brings recognition value closer to thepresent by focusing on current book value plus forecasted residual income

• Restated dividend discount model

Residual Income (RI)

Ø** Disadvantages**

•Application of the RI model requires a detailed knowledge of accrual accounting

• The quality of accounting disclosure can make the use of RI valuation less robust and more error prone

Ø** Situations when appropriate**

• Used with firms that haveno dividend history • Used withnegative FCF

• Less horizon dependence

Dividend Discount Models

Ø**The Rule**: Value is present value of all future dividends
discounted at required return

Ø** Problem**: Requires estimation of infinite stream of CFs

###

t###

0 t

t 1

### D

### V

### 1 r

###

###

Single Period DDM

Ø Single-period DDM is the present value of the future dividend and sales price

Ø Notice that there are two cash flows in the final period!

1 1 1 1

Ø For n-period model, the value of a stock is the present value of the expected dividends for the n periods plus the present value of the expected price in n periods

Øthe expected price in n periods depends on the expected dividends after the n periods.

**Example:** Fragrance Ltd. Expects dividends of €1, €1.5, and €2.0
over the next three years. Expected stock price at the end of
year 3 is €80. If the cost of equity is 18%, compute the value of
Fragrance shares today.

If the current market price of Fragrance Ltd is 45.00 euros, then the security is undervalued

###

###

###

3###

31.0 1.5 2.0 80 _{EUR51.83}

1.18 1.18 1.18

To use the DDM, the forecasting problem must be simplified. Two broad approaches exist:

1. Future dividends can be forecast by assuming one of several stylized growth patterns

• constant growth forever (Gordon growth model) • two distinct stages of growth

• three distinct stages of growth

Ø **Importance: **☆☆

Ø **Content:**

• DDM

• FCFE/FCFF models • Residual income models

Ø **Exam tips: **

• 了解DDM，FCF，和residual income模型的优缺点，能判断

每个模型适合的情景

• 能运用单期和多期DDM对权益证券进行估值

Summary

### Gordon Growth Model

**Tasks:**

ØCalculate the value of a common stock using the Gordon growth model and explain the model’s underlying assumptions

ØCalculate and interpret the implied growth rate of dividends using the Gordon growth model and current stock price

ØCalculate and interpret the present value of growth opportunities and the component of the leading price-to-earnings ratio related to PVGO

ØCalculate and interpret the justified leading and trailing P/E using Gordon growth model

Gordon Growth Model

0 1

0 D (1 g) D

V

(r g) (r g)

where

D1 = Dividend expected in one year g = sustainable growth rate r = required return on equity

Gordon Growth Model
**Assumptions:**

1. Dividends grow at constant rate (g) forever
2. Growth rate less than required return (r > g)
**Situations in which model is useful: **

• Mature (late in life cycle) firms • Broad-based equity index

• Terminal value in more complex models • Estimate g, r and PVGO

Gordon Growth Model

Ø The GGM model should reflect long-term growth

expectations – GDP growth, industry life cycle stages and the impact of the five force model

Ø The model’s intrinsic values V0 are very sensitive to the input variables for r and g

Ø Sensitivity analysis may be required to obtain a range of values rather than a specific point estimate of value

Gordon Growth Model

Ø** Example:** A firm paid a dividend yesterday of $1.50 and
dividends are expected to grow at a long term constant rate of
5%. The required return is 10%. Calculate the intrinsic value

Ø Correct answer

V0 = ($1.50 × 1.05) / (0.10 – 0.05) = $31.50

Gordon Growth Model - Implied Growth Rate

Ø Assume:

• Firm just paid $1.20 dividend per share • Required return is 13%

• Market price is $15.75

Ø Implied dividend growth rate is:

###

###

$1.20 1 g $15.75

0.13 g g 0.05 5.0%

Gordon Growth Model - Required Return - r

Ø Point: DDM can be used to find implied *r*
Ø Solving GGM for *r*:

Ø** Example: ** If dividends today are $1.60 and the current price
is $40 with expected growth of 9% the required return is:

1 0

### D

### r =

### + g

### P

% 36 . 13 % 9 40

9%) 1.6(1

Present Value of Growth Opportunities (PVGO)

Ø Increase in shareholder wealth comes when reinvested earnings are directed toward investments which earn greater returns than the opportunity cost of the funds needed to undertake the project (ROE > r or ROIC > WACC)

ØCompanies without positive NPV projects should distribute all earnings in dividends because earnings cannot be reinvested profitably and earnings will be flat in perpetuity, assuming a constant ROE

Present Value of Growth Opportunities (PVGO)

ØStock value is the sum of

• Value of no growth (E1/r)

• Present value of future growth opportunities (PVGO)
**V0 = E1/r + PVGO**

ØComponent of leading P/E related to PVGO

**P0/E1 = 1/r + PVGO/E1**

• 1/r is the P/E1 ratio for a no growth company • PVGO/E1 is the P/E1 component related to growth

Present Value of Growth Opportunities (PVGO)

Ø **Example:** ABV Inc. shares sell for $80 on future earnings per
share of $4.00. If the required return is 20%, compute the
PVGO.

$4.00
$80 _{0.20} *PVGO*

PVGO = $80-$20 = $60

Market assigns 75% of the price ($60/$80) to future growth

Gordon Growth Model - Justified P/E

Ø The Gordon model can also be used to calculate a “justified (or fundamental)” price multiple

ØJustified leading P/E1 ,

• assuming constant dividend payout ratio • define b as the retention rate

1 0

1 0 1 1 D P =

r - g D

P E

justified leading = = E r - g

Gordon Growth Model - Justified P/E

ØJustified trailing P/E0

• assuming constant dividend payout ratio • define b as the retention rate

*g*

• Gordon growth model

• Implied growth rate, required return

• PVGO

• Justified P/E

Ø **Exam tips: **

• 必须掌握戈登增长模型计算和适用前提，能利用戈登增长

模型计算增长率和要求回报率 • 必须掌握PVGO和justified P/E计算 Summary

### Multi-Stage Models (1)

**Tasks:**

ØCalculate the value of a preferred stock

ØExplain the assumptions and justify the selection of the two-stage DDM, the H-model, the three-two-stage DDM

ØDescribe terminal value and explain alternative approaches to determining the terminal value in a DDM

ØCalculate and interpret the value of common shares using the two-stage DDM, the H-model, and three-stage DDM

ØEstimate a required return based on any DDM

Valuation of Non-Callable, Fixed Rate, Perpetual, Preferred Stock

Ø Use the Gordon Growth Model to value preferred stock

Ø The discount or capitalization rate r is often at a positive spread over the firms junior ranking debt yield

Ø Fixed rate level dividends are ranked senior to equity and extend indefinitely into the future

**P0 = Annual fixed Dividend/ Capitalization rate**

Ø**Example:**

• Annual Dividend = $12 • r = 10%

Multi-Stage DDM Models

ØGrowth can fall into three distinct stages:
• **Growth phase**

ü Rapid EPS growth, negative FCF

ü ROE > r, no or low dividend payout
• **Transition phase (transition to maturity)**

ü Sales and EPS growth slow, dividend payout increases

ü ROE approaching r, positive FCF
• **Mature phase**

ü Growth at economy-wide rate, positive FCF

ü ROE = r, high competition, saturation

Multi-Stage DDM Models

Ø Terminal value = forecasted value at beginning of the final mature growth phase

Ø Two estimation methods:

1. Apply a price multiple to a projected terminal value of a fundamental such as P/E, P/B

2. Gordon Growth Model

Ø the terminal value is then discounted back and added to the present value of prior stage dividends

Multi-Stage DDM Models
**Terminal value - Example:**
Postini Ltd had the following data

• D0 = $1.00, payout ratio of 40%, gS = 9.0% for four years and r = 10%

• Trailing P/E for t = 4 is 15.0
**Answer: **Forecasted EPS for year 4 is
• E4 = $1.00(1.09)4 / 0.40 = $3.52

• Apply trailing multiple (P/E) × forecasted EPSt in year t Ø Terminal value in year 4 = 15 × $3.52 = $52.93

Two-Stage DDM Models

ØFirst version of the two-stage DDM assumes:

• the whole of stage 1 represents a period of fixed and abnormal growth

• growth rate is expected to drop suddenly to a mature growth rate at stage 2

08

-L2

-SS

12-S76

Dividend Growth (g)

15%

3%

Stage 1 Stage 2

4 years

Two-Stage DDM Models

ØFirst version of the two-stage DDM assumes: • = the extraordinary growth rate at the first stage

Two-Stage DDM Models

ØSecond version of the two-stage DDM assumes - **H-model**

• the growth rate declines linearly from an abnormal rate to the mature growth rate during the course of stage 1 • constant growth at the mature growth rate in stage 2

Dividend Growth (g)

15%

3%

Stage 1 Stage 2 4 years

Two-Stage DDM Models

Ø**H-model:**

• = the extraordinary growth rate at the first stage • = the mature growth rate at the second stage • H = half-life in years of the high-growth period

• the first term on the right-hand side is the present value of the company if it were to grow at forever

• the second term is an approximation of the extra value accruing to the stock due to its supernormal growth for year 1 to 2H.

*s*

Two-Stage DDM Models

**Example: **BTeam, Inc., currently pays a dividend of $1.30. The
growth rate is 25% and is expected to decline over the next 5 year
horizon to a stable rate of 5% thereafter. The required return is
14%.

Calculate the intrinsic value of BTeam stock using the H-Model.

H-Models - Required Return - r

For H-model, the required rate of return can be derived as:

**Example:** BTeam, Inc., currently pays a dividend of $1.30. The
growth rate is 25% and is expected to decline over the next 5 year
horizon to a stable rate of 5% thereafter. Calculate the implied
expected return for BTeam if the market price is $30.

*L*

• Valuation of preferred stock • Estimation of terminal value • Two-stage DDM (H-model)

Ø **Exam tips: **

### Multi-Stage Models (2)

**Tasks:**

ØCalculate and interpret the value of common shares using the two-stage DDM, the H-model, and three-stage DDM

ØExplain the use of spreadsheet modeling to forecast dividends and to value common shares

ØCalculate and interpret the sustainable growth rate of a company and demonstrate the use of DuPont analysis to estimate a company’s sustainable growth rate

Three-Stage DDM Models Two version of 3-stage model

**1. Three distinct phases**, simply add an additional growth stage
to the two stage model

• Growth, transition, and mature
**1. High-growth phase + H-model pattern **

Three-Stage DDM Models

**Example: **Netweb Inc.’s current annual growth rate of 25% is
expected to last three years and then fall linearly to a sustainable
3% over the following seven years.

The most recent dividend was $0.30 and the required return on equity is 10%.

Calculate the value of Netweb’s shares today.

Three-Stage DDM Models

0 1 2 3

D1 = D2 = D3 =

P3 =

### $12.48

### $0.375

### $0.469

### $15.646

### $0.586 + $15.06

0 $0.375 $0.469 $15.6462 3

P _{1.1} _{1.1} _{1.1} $12.48

$0.30 × 1.251 _{= $0.375 }
$0.30 × 1.252 _{= $0.469 }
$0.30 × 1.253 _{= $0.586 }

###

###

7

$0.586 0.25 0.03

$0.586 1.03 2 _{$15.06}

0.10 0.03 0.10 0.03

_{ }_{ }

_{} _{}

Multi-Stage DDM Models

Ø** Strengths**

• Ability to model many growth patterns • Solve for V, g, and r

Ø**Weaknesses**

• Require high-quality inputs (GIGO)
• Model must be fully understood
• Value estimates sensitive to *g* and *r*
• Model suitability very important

Spreadsheet Modeling

ØCan handle any range of growth assumptions over varying periods

ØThe most flexible method
**Steps:**

• Establish base level cash flows

• Forecast deviations for near future (e.g., supernormal growth for first four years)

SGR: The Sustainable Growth Rate

Ø SGR (g) = sustainable growth rate in earnings and dividends if we assume:

• Growth from internally generated sources • Capital structure remains unchanged • No new equity issued

g = retention rate×ROE

• the lower the earnings retention ratio, the lower the growth rate (dividend displacement of earnings)

SGR: The Sustainable Growth Rate

**Example: **Green, Inc. pays out 25% of it’s $1.00 of earnings as
dividends, BVPS is $10.00 therefore Green earns an ROE of 10%.
Compute SGR.

SGR = Retention rate× ROE SGR = (1 – 0.25) × 10% = 7.5%

SGR: The Sustainable Growth Rate

Ø 3-Part DuPont ROE Decomposition:

• Note: Always use beginning of year balance sheet numbers on exam (unless told otherwise)

g = retention ratio*net profit margin*asset turnover*leverage

net incom e sales assets
ROE _{sales} _{assets} _{equity}

net profit asset equity ROE

m argin turnover m ultiplier

_{} _{}_{} _{}_{} _{}

_{} _{}_{} _{}_{} _{}

Ø **Importance: **☆☆

Ø **Content:**

• Three-stage DDM • Spreadsheet modeling • Sustainable growth rate

Ø **Exam tips: **

• 重点掌握三阶段估值模型

• 理解持续增长率的假设，能利用杜邦系统评估持续增长率

### Introduction to FCFF and FCFE

**Tasks:**

ØCompare the free cash flow to the firm and free cash flow to equity approaches to valuation

ØExplain the ownership perspective implicit in the FCFE approach

Introduction to Free Cash Flows

ØDividends are the cash flows actually paid to stockholders ØFree cash flows are the cash flows available for distribution

after fulfilling all obligations (operating expenses and taxes) and without impacting on the future growth plans of the company (working capital and fixed capital)

Introduction to Free Cash Flows
Ø**FCFF**(**F**reeCash** F**lowtothe** F**irm)

Cash available to shareholders and bondholders after taxes,
capital investment, and WC investment, *pre-levered cash flow*
Ø**FCFE**(**F**ree** C**ash** F**lowto** E**quity)

Cash available to equity holders after payments to and
inflows from bondholders, *post-leverage cash flow*

Not equal to dividends actually paid

Introduction to Free Cash Flows
Ø**Strengths**

• Used with firms that have no dividends

• Functional model for assessing alternative financing policies

• Rich framework provides additional detailed insights into company

• Other measures such as EBIT, EBITDA, and CFO either double count or omit important cash flows

Ø**Limitations**

• If FCF < 0 due to large capital demands

Ownership Perspective
Ø** FCFE = control perspective**

•Ability to change dividend policy

•Used in control perspective

Ø** DDM = minority owner**

•No control

•Used in valuing minority position in publicly traded shares

Ø **Importance: **☆☆

Ø **Content:**

• Strengths and limitations of FCF models • Ownership perspectives of FCF

Ø **Exam tips: **

• 理解自由现金流模型的优缺点

• 理解自由现金流的所有权角度

Summary

### Calculation of FCFF and FCFE (1)

**Tasks:**

ØExplain the appropriate adjustments to net income to calculate FCFF and FCFE

ØCalculate FCFF and FCFE

FCF Formula References

Ø NI = Net income to common shareholders, after preferred dividends but before common dividends

Ø NCC = net non-cash charges Ø Int(1-t) = after tax interest expense

Ø FCInv = net fixed capital investment (capital expenditure less proceeds from sales)

FCFF and FCFE Beginning with Net Income Ø FCFF = NI + NCC + Int(1– t) – WCInv – FCInv

Ø Subtracting after-tax interest and adding back net borrowing from the FCFF equations gives us the FCFE from NI

Ø FCFE = FCFF – Int(1 – t) + Net borrowing ØFCFE = NI + NCC – WCInv – FCInv + Net borrowing

Noncash Adjustment

**Noncash Item** **adjustment to NI **

depreciation added back amortization and impairment of intangibles added back

restructuring expenses added back restructuring charges (income from reversal) subtracted

losses added back gains subtracted amortization of long-term bond discounts added back amortization of long-term premiums subtracted

Investment in Working Capital

ØNet investment in working capital for the purpose of
calculating FCF *excludes*

• changes in cash/cash equivalents

• notes payable

• current portion of L.T. debt

ØThe exclusions are considered financing activities not operating items and therefore not included in WCInv

Investment in Working Capital

ØThere is an inverse relationship between changes in assets and changes in cash flow

ØAn **increase in an asset** account is a **use** (negative/subtraction)
of cash

Investment in Working Capital

ØThere is a direct relationship between changes in liabilities and changes in cash flow

ØAn **increase in a liability** account is a **source **(addition/plus) of
cash

ØA **decrease in a liability** is a **use** (negative/subtraction) of cash

Investment in Working Capital

Increase in WCInv

Decrease ↓FCF Decrease inIncrease ↑_{ FCF}WCInv
Increase in Assets or

Decrease in Liabilities

Decrease in Assets or Increase in Liabilities

↑ Inventory ↓Inventory

↑ Accounts Receivable ↓Accounts Receivable

↓Accounts Payable ↑ Accounts Payable

↓ Accrued Taxes & Expenses ↑ Accrued Taxes & Expenses

Investment in Working Capital

Account 2009 2008 Change Source/Use

Inventory 50 40 10 Use/Subtract

WCInv = –10 Accounting

receivable 25 30 (5) Source/Add_{WCInv = +5}
Accounting

payable 30 10 20 Source/AddWCInv = +20 Accrued

Expenses 5 20 (15) Use/Subtract_{WCInv = }_{–}_{15}

Net FCInv Adjustments

ØInvestments in fixed capital (FCInv) represent a cash out flow necessary to support the company's current and future operations

ØViewed as a capital expenditure (Cap Ex) that reduces both FCFE and FCFF

ØExpenditures can include acquisition of intangible items such as trademarks

Net FCInv Adjustments ØAsset Purchases

• If given **gross PP&E** on the balance sheet, identify the
additions (cap ex) by taking the year over year change in
gross PP&E, only if there wereno disposals during the period,
to identify the capital expenditures for the period

• If given **net PP&E**, use the equation:

**Ending net PP&E = Beginning net PP&E – Depreciation + **
**Assets purchased – Book value of assets sold**

Net FCInv Adjustments

ØIf a company receives cash in disposing/selling of a fixed asset, the analyst must deduct this cash in arriving at the net investment in PP&E (FCInv)

ØGain/Loss on asset sale = Proceeds from sale – book value of asset

ØSubtract gains on sales from NI ØAdd losses on sales to NI

ØDeduct the proceeds from sale in arriving at the net FCInv

Net Borrowing Adjustments

ØNet Borrowings only affect **FCFE**, *they do not affect FCFF*
Ø**Long Term Debt**

• **Add** debt issuances to net income to arrive at FCFE

• **Subtract** debt repurchases from net income to arrive at FCFE

• **Net Borrowings = + new debt issuances – debt repurchases**

Net Borrowing Adjustments
Ø**Notes Payable**

• Incr. in notes payable, add to FCFE

• Decr. in notes payable, subtract from FCFE
Ø**Current Portion of LT Debt**

• Incr. in short-term debt, add to FCFE

Ø **Importance: **☆☆☆

Ø **Content:**

• FCFF and FCFE beginning with net income • Adjustments to net income

Ø **Exam tips: **

• 必须掌握通过net income计算FCFF和FCFE

• 理解计算FCFF和FCFE的各项财务调整

Summary

### Calculation of FCFF and FCFE (2)

**Tasks:**

ØExplain the appropriate adjustments to EBIT, EBITDA, CFO to calculate FCFF and FCFE

FCFF and FCFE Beginning with CFO

Ø Recall, **CFO = NI + NCC – WCInv**

Ø CFO is after-interest under US GAAP

Ø FCFF = CFO + Int(1 – t) – FCInv

Ø Subtracting after-tax interest and adding back net borrowing from the FCFF equations gives us the FCFE from CFO

Ø FCFE = CFO – Inv(FC) + Net borrowing

FCFF and FCFE Beginning with Net Incomehj

**IFRS** **US GAAP **

interest received operating or

investing operating interest paid operating or

financing operating dividends received operating or

investing operating dividend paid operating or

FCFF Beginning with EBIT

Ø To show the relation between EBIT and FCFF, assume that the non-cash charge (NCC) is depreciation (Dep):

Ø FCFF = NI + Dep + Int(1 – t) – WCInv – FCInv

Ø Net income (NI) can be expressed as:

Ø NI = (EBIT – Int)(1 – t), rearranging

Ø NI = EBIT(1 – t) – Int(1 – t)

Ø FCFF = EBIT (1-t) + Dep – WCInv – FCInv

ØFCFE = EBIT(1 – t) – Int (1 – t) + Dep –WCInv – FCInv + Net
**borrowings**

FCFF Beginning with EBITDA

ØTo get FCFF from EBITDA (Earnings*before* Interest, Taxes,
Depreciation, and Amortization):

ØNI = (EBITDA - Dep - Int)(1-t)

Ø**FCFF = EBITDA (1 – t) + Dep(t) – WCInv – FCInv**

ØWe add back the NCC (dep) times the tax because we capture the tax benefit from deducting the depreciation, it represents the cash flow savings from the deduction

Ø**FCFE = EBITDA (1 – t) – Int (1 – t) + Dep(t) – WCInv – FCInv + Net **
**borrowings**

FCFF Formula Review

ØFCFF = NI + NCC + [Int(1 – t)] – WCInv – FCInv ØFCFF = CFO + [Int(1 – t)] – FCInv

ØFCFF = [**EBIT**(1 – t)] + NCC – WCInv – FCInv
ØFCFF = EBITDA(1 – t) + (NCC × t) – WCInv – FCInv

ØNotice: no net borrowings!

FCFE Formula Review

ØFCFE = NI + NCC – WCInv – FCInv + Net borrowings
ØFCFE = **CFO** – FCInv + Net borrowings

ØFCFE = EBIT(1 – t) – Int(1 – t) + NCC – WCInv – FCInv + Net borrowings

ØFCFE = EBITDA(1 – t) – Int(1 – t)+ NCC(t) – WCInv – FCInv + Net borrowings

Example

**Actual **

**1996** **Projected 1997**

**Cash** **$24.0** **$26.0**

**A/R** **17.0** **24.0**

**Inventory** **100.0** **150.0**

**PP&E (FCInv) ** **100.0** **125.0**

**Accumulated Dep** **(30.0)** **(35.0)**

**Total Assets** **$211.0** **$290.0**

Example

**Actual**

**1996** **Projected1997**

**Accounts payable** **$91.0** **$101.0**

**Long-term debt** **20.0** **40.0**

**Common stock** **80.0** **90.0**

**Retained earnings** **20.0** **59.0**

**Total liab. and OE** **$211.0** **$290.0**

Example

**Actual **

**1996** **Projected 1997**

**Sales** **$80.0** **$198.0**

**COGS** **38.0** **90.0**

** Gross profit** **$42.0** **$108.0**

**SG&A** **13.0** **30.0**

**Depreciation** **3.0** **5.0**

** Operating expenses** **$16.0** **$35.0**

Example

**Actual **

**1996** **Projected 1997**
**Interest **

**expense**
**Pre-tax **
**income**
**Income tax **
**expense**
**Net income**

**$4.0**

**22.0**

**(7.0)**

**$15.0**

**$5.0**

**68.0**

**(25.0)**

Example - Solutions
ØFCInv = $125 – $100 = **$25**

ØWC1997 = ($24 + $150) – ($101) = $73
ØWC1996 = ($17 + $100) – ($91) = $26
ØWCInv = $73 – $26 = **$47**

Øt = $25 / $68 ≈ 37%

ØNet borrowing = $40 – $20 = $20

Example - Solutions

Ø**FCFF** =** NI** + NCC + Int(1 – t) – WCInv – FCInv

• –20.85 = 43 + 5 + 5(1 – 0.37) – 47 – 25
Ø**FCFF** = **CFO** + Int(1 – t) – FCInv

• –20.85 = (43 + 5 – 47) + 5(1 – .37) – 25

• Recall, CFO = NI + NCC – WCInv
Ø**FCFF = **[**EBIT**(1 – t)] + NCC – WCInv – FCInv

• –20.85 = 73 (1 – 0.37) + 5 – 47 – 25
Ø**FCFF = EBITDA**(1 – t) + NCC(t) – WCInv – FCInv

• –20.85 = 78 (1 – 0.37) + 5(0.37) – 47 – 25

Example - Solutions

Ø**FCFE = (NI** + NCC – WCInv) – FCInv + Net borrowing
• – 4 = (43 + 5 – 47) – 25 + 20

Ø**FCFE** = **CFO** – FCInv + Net borrowings
• – 4 = (43 + 5 – 47) – 25 + 20

Ø**FCFE = FCFF** – [Int(1 – t)] + net borrowing
• -4 = –20.85 – [5(1 – 0.37)] + 20

Ø**FCFE = EBIT(1 – t)** – Int (1 – t) + NCC – WCInv – FCInv + Net borrowing
• –4 = 73 (1 – 0.37) – 5 (1 – 0.37) + 5 – 47 – 25 + 20

Ø**FCFE = EBITDA**(1 – t)+ NCC(t) – WCInv – FCInv + Net borrowings
• –4 = 78 (1 – 0.37) – 5 (1 - 0.37) + 5(0.37) – 47 – 25 + 20

Ø **Importance: **☆☆_{ }

Ø **Content:**

• FCFF and FCFE beginning with EBIT, EBITDA, CFO

Ø **Exam tips: **

### Forecasting FCFF and FCFE

### Effects of Financial Decisions on FCFF and FCFE

**Tasks:**

ØDescribe approaches for forecasting FCFF and FCFE

ØCompare the FCFE model and dividend discount models

ØExplain how dividends, share repurchases, share issues, and changes in leverage may affect future FCFF and FCFE

FCFF and FCFE on a uses-of-Free-Cash-Flow Basis
ØUses of FCFF =** increases in cash balances + net payment to **

**providers of debt capital + payments to providers of equity **
**capital**

• net payment to providers of debt capital are calculated as: üplus: int*(1-t)

üplus: repayment of principal in excess of new borrowing

• payment to providers of equity capital are calculated as: üplus: cash dividends

üplus: share repurchases in excess of share issuance

FCFF and FCFE on a uses-of-Free-Cash-Flow Basis
ØUses of FCFE =** increases in cash balances + payments to **

**providers of equity capital**

• payment to providers of equity capital are calculated as: üplus: cash dividends

üplus: share repurchases in excess of share issuance

Two Approaches to Forecast FCF
Ø Calculate **historical **FCF:

• Estimate FCF for current period

• Apply a constant growth rate to current FCF: FCF × (1+g)n

• Usually,

Ø** Forecast components** of FCF:

• Forecast each underlying component of free cash flow: net income, FCInv, NCC and WCInv are tied to sales forecast

• Realistic and flexible but time consuming
*FCFE*
*FCFF*

*g*

Sales-Based Forecasting Method for FCFF and FCFE Ø A simple sales-based forecasting method for FCFF and FCFE

assumes:

• (FCInv -Dep) and WCInv both bear a constant relationship to increases in sales

ØSpecially for FCFE forecasting, we assume:

• the capital structure represented by debt ratio (DR) is constant

• DR indicates the percentage of the investment in fixed capital in excess of depreciation and in working capital that will be financed by debt

Ø Assumptions: keeping the following ratios unchanged

Ønet borrowing = DR(FCInv -Dep) +DR(WCInv)

ØFCFE = NI -(FCInv - Dep) - WCInv + DR(FCInv -Dep) +DR(WCInv)

ØFCFE = NI - (1-DR)(FCInv - Dep) - (1-DR)(WCInv) = NI - (1-DR)(FCInv + WCInv - Dep)

Sales-Based Forecasting Method for FCFF and FCFE

*Sales*
*Dep*
*FCInv*

*Sales*
*WCInv*

*D* *E*

*D*
*DR*

ØThe general valuation models are the same but the numerator is different

ØFCFE could be either greater or less than dividends, but the same economic forces that lead to low(high) dividends lead to low(high) FCFE

ØFCFE takes a control perspective that assumes recognition of value should be immediate. While DDM takes a minority perspective that assumes value may not be realized until the dividend policy reflects the firm's long-run profitability

Recognition of Value Between FCFE and DDM Effect of Financing Decisions on FCF

**Statement of Cash Flows** **FCFE/FCFF**
**Net income (NI)** **Net income (NI)**
**+ Non-cash charges (NCC)** **+Non-cash charges (NCC**

**– WCInv** **– WCInv**

** Cash flow operations (CFO)** ** Cash flow operations (CFO)**
**+ Int(1 – tax rate)**

**– FCInv** **– FCInv**

Effect of Financing Decisions on FCF

**Statement of Cash Flows** **FCFE/FCFF**
**Free cash flow to firm (FCFF)**
**+ Net Borrowing ** **+ Net Borrowing **

**– Int(1 – tax rate)**
**Free cash flow to equity **
**(FCFE)**

**– Dividends** **– Dividends**

**+/– Stock issues/repurch** **+/– Stock issues/purch**
** Net change in cash** ** Net change in cash**

Effect of Financing Decisions on FCF

**FCFF** **FCFE**

**Dividends** **None** **None**

**Share repurchase** **None** **None**

**Share issue** **None** **None**

**Change in leverage** **None** _{partially offset*}ST & LT effects

Note: Share repurchase/issueis use of FCF; not determinant

* if leverage increases, FCFE higher in current year (net borrowing) and lower in future years (interest expense)

Ø **Importance: **☆☆☆

Ø **Content:**

• Uses of FCFF and FCFE

• Sales-based forecasting methods of FCFF and FCFE • Comparison of FCFE model and DDM

• Effects of financial decisions on FCFF and FCFE

Ø **Exam tips: **

• 重点掌握预测FCFF和FCFE的方法

• 重点掌握融资决策对FCFF和FCFE的影响

• 理解FCFF和FCFE的用途

• 比较FCFE和DDM模型

Summary

### FCFF and FCFE Valuations

**Tasks:**

ØEvaluate the use of net income and EBITDA as proxies for cash flow in valuation

ØExplain the single-stage, two-stage, and three-stage FCFF and FCFE models and select and justify the appropriate model given a company’s characteristics

ØEstimate a company’s value using the appropriate FCF models

NI is a Poor Proxy for FCFE

ØNI is an accrual concept not cash flow

ØNI recognizes non-cash charges such as depreciation, amortization and gains on sale of equipment, alternatively… ØNI fails to recognize the cash flow impact of investments in

working capital and net fixed assets, and net borrowings

EBITDA is a Poor Proxy for FCFE ØEBITDA doesn’t reflect taxes paid

ØEBITDA ignores effect of depreciation tax shield [Depr (tax)] ØEBITDA does not account for needed investments in working

capital and net fixed assets for going concern viability ØEBITDA is a pre-levered figure so it is pre-interest and before

net borrowings

FCFF vs. FCFE Valuation

ØFirm value = FCF**F** discounted at WACC

ØEquity value = FCF**E** discounted at required return on equity

• Use FCFE when capital structure is stable

• Use FCFF when high or changing debt levels, negative FCFE

Ø**Equity value = firm value – MV of debt**

Single-Stage FCF Model

ØPoint:Analogous to Gordon growth model

•Useful for stable firms in mature industries Ø Two assumptions:

1. Constant growth rate *g* forever

2. Growth rate *g* is less than WACC and r

FCFF 1 g -WACC

FCFF value

Firm

FCFE 1 g -r

Selection of Appropriate Model

Ø **Four major variations:**

1) FCFF or FCFE? 2) Two stages or three?

3) Total FCF or components of FCF? 4) Terminal value via GGM or Multiples?

Ø **Always**: Value = PV of future cash flows discounted at
appropriate required return

Base case: 2-stage, historical growth, FCFE

with the GGM for terminal value

Selection of Appropriate Model

Ø**Single-stage model**

• Income stock (slow, constant growth)

• International setting or volatile inflation rates: use real rates

Ø**Two-stage and three-stage models**

• Competitive advantage will disappear over time
**Match growth pattern or company lifecycle approach to the **

**appropriate model**

FCF Valuation - Example

Ø Calculate the value of the firm given the data forecast in the table. The required return on equity is 15%, the WACC is 12%, and the marginal tax rate is 40%. FCFF is expected to grow at a constant rate of 4% after 3 years.

**Year 1** **Year 2** **Year 3**
**Cash flow from operations****$400** **$500** **$600**

**WCInv****$50** **$60** **$80**

**FCInv****$200** **$250** **$300**

**Interest expense****$15** **$15** **$20**

FCF Valuation - Solution

**Year 1** **Year 2** **Year 3**
*Cash flow from operations*

*+ Int(1 – tax rate)*

$209 $259 $312 $4,056 $3,502.14_{1.12 1.12}
1.12