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Valuation. Contents. Introduction – Fundamentals of Where Value Comes From Discounting and IRR Review Overview of Alternative Valuation Methods Valuation Using Multiples Valuation Using Discounted Free Cash Flow Valuation Using Projected Earnings and Equity Cash Flow Case Studies.

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Presentation Transcript
  • Introduction – Fundamentals of Where Value Comes From
  • Discounting and IRR Review
  • Overview of Alternative Valuation Methods
  • Valuation Using Multiples
  • Valuation Using Discounted Free Cash Flow
  • Valuation Using Projected Earnings and Equity Cash Flow
  • Case Studies
valuation decision making and risk
Valuation, Decision Making and Risk

Every major decision a company makes is in one way or another derived from how much the outcome of the decision is worth. It is widely recognized that valuation is the single financial analytical skill that managers must master.

  • Valuation analysis involves assessing
    • Future cash flow levels, (cash flow is reality) and
    • Risks in valuing those cash flows, whether it be the cash flow from assets, debt or equity
  • Measurement value – forecasting and risk assessment -- is a very complex and difficult problem.
  • Intrinsic value is an estimate and not observable

Reference: Chapter 4

market value of debt credit spreads and par value
Market Value of Debt, Credit Spreads and Par Value
  • Before thinking about valuation of a company, consider the value of debt
    • The par value or the value on the balance sheet does not determine the value of debt
    • Rather the value depends on the future level of cash flows (par value x coupon rate) and the risk applied to cash flows
    • Credit spreads are driven by the risk and can be measured by the One of the few things we know is that there is a tradeoff between risk and return.
  • Key idea is to use future cash flows and incremental discount rate in measuring market value

Reference: Folder on Yield Spreads

measurement of risk in financial models
The fundamental issue in any valuation problem is how to assess the risk of future cash flow projections.

Financial theory

Financial theory dictates that the CAPM should be used to compute the WACC, that the un-levered beta should be used to estimate equity returns, that options pricing models should be used for credit spreads, debt capacity and covenants.

Mathematical Models

Mathematical models include beta adjustments for the CAPM, statistical models for credit analysis, Monte Carlo simulation and value at risk.

Practical Market Information

Practical market information can be used to gauge required equity returns, required credit spreads, required financial ratios to achieve investment grade rating and other issues.

Consider Investment Alternatives A and B, where A has a higher project IRR than B. Assume A has a return of 11% and B has a return of 9%.

Project A or Project B would be selected through assessing the return on the projects relative to the weighted average cost of capital for each project. If the WACC for A is 10% and for B is 9.5% then A is selected. One must computed beta for each investment.

Compute the distributions in cash flow of project A and project B to equity holders. If the standard deviation is lower for project B, then assess the risk relative to the return.

Compute the achieved rate of return from the ability to raise debt and then assess the return earned on equity. If the return on equity is greater for B then A, select project A.

Measurement of Risk in Financial Models
problems with capm
Problems with CAPM
  • Ke = Rf + Beta x EMRP
  • Difficulty in establishing Rf
  • Can’t find Betas
  • Betas performed horribly during financial crisis
  • EPRM cannot be measured and changes with perceptions over time
capm post financial crisis
CAPM Post Financial Crisis
  • The cost of equity was calculated using the capital asset pricing model, which is a theoretical financial model that estimates the cost of equity capital based on a company’s “beta” which is a measure of a company’s volatility relative to the overall market, a 6% market risk premium and a relevant predicted beta and risk-free rate. The public market trading price targets published by securities research analysts do not necessarily reflect current market trading prices for Wyeth’s and Pfizer’s common stock and these estimates are subject to uncertainties, including the future financial performance of Wyeth and Pfizer and future financial market conditions.
  • Academic studies – 2-3%
  • Pre-Crisis Bankers – 4-5%
  • Historical U.S. premium pre-crisis 6-8%
problems with growth
Problems with Growth
  • Typical assumption that growth equals inflation means world economy would stop
  • Time period before which reach stable growth is impossible to estimate
  • Evidence that sell-side analysts chronically over-estimate short-term growth rates
example of method 1 financial theory
Example of Method 1: Financial Theory

Fundamental parameters are almost impossible to measure

Differences in Beta, Rm and Terminal Growth have an Immense Effect on the Value of the Investment

method 2 stochastic mathematics
Method 2: Stochastic Mathematics

If only we could measure these things

Case 1: 15% Volatility; 40% Mean Reversion; 4.5 Long-run Marginal Cost

Case 2: 25% Volatility; 10% Mean Reversion; 4.0 Long-run Marginal Cost

The probability of earning below the risk free rate is about 5%

The probability of earning below the risk free rate is about 55%

example of method 3 debt capacity
Example of Method 3: Debt Capacity

Let Bankers Assess the Risk – That is Their Job

comparison of approaches which investment would you select
Project A

Project B

Comparison of Approaches: Which Investment would you Select

Project A has a higher rate of return relative to its cost of capital, but Project B has a higher equity return

valuation diagram dcf from free cash flow
Valuation Diagram – DCF from Free Cash Flow
  • Valuation using discounted cash flows requires forecasted cash flows, application of a discount rate and measurement of continuing value (also referred to as horizon value or terminal value)

Continuing Value

Cash Flow

Cash Flow

Cash Flow

Cash Flow

Discount Rate is WACC

Enterprise Value

Net Debt

Reference: Private Valuation; Valuation Mistakes

Equity Value

equity cash flow debt cash flow free cash flow and cost of equity cost of debt and wacc
Equity Cash Flow, Debt Cash Flow, Free Cash Flow andCost of Equity, Cost of Debt and WACC

Equity Cash Flow and Value of Equity :

Dividends less Equity Issued

Value of Equity

PV of Cash Flows at

Cost of Equity



Debt Cash Flow and Market Value of Debt :

Net Interest plus Net Debt Payments

Value of Debt

PV of Cash Flows at

Incremental Cost of Debt



Free Cash Flow:

EBITDA – Op Taxes – Cap Exp – WC Chg

Value of Enterprise

PV of Cash Flows


valuation overview
Valuation Overview

Despite that fact that all we have to do is forecast cash flow and then determine the risk associated with those cash flows, valuation is a huge topic. Some Key issues in valuation analysis include:

  • Cost of Capital in DCF or Discounted Earnings for Measuring Risk
  • Selection of Market Multiple and Adjustment that implicitly accounts for growth in cash flow and risk
  • Determination of Growth Rates in Earnings and Cash Flow Projections
  • How to Compute Terminal Value when Cash Flow Lasts for an Indefinite Period
tools for valuation
Tools for Valuation
  • There is no magic answer as to whether one valuation approach is better than others. But virtually all valuation analyses involve the following work:
  • Financial Models:
    • Valuation model used to project earnings or cash flows
  • Statistical Data:
    • Industry Comparative Data to establish Multiples and Cost of Capital
  • Industry, company knowledge and judgment
    • Knowledge about risks and economic outlook to assess risks and value drivers in the forecasts
problems with traditional finance and discounted free cash flow
Problems with Traditional Finance and Discounted Free Cash Flow
  • The entire process is dependent on WACC and the CAPM
    • Rm is one of the most debated issues in finance
    • Beta is difficult to measure
    • The model doesn’t work
  • Valuation is highly dependent on terminal values and growth rates
    • Often zero real growth is used, implying that if all companies had zero growth, economies around the world would be stagnant
  • If multiples are used, they can be very subjective
    • Comparable companies are not comparable at all
    • Arbitrary adjustments are made to the P/E and EV/EBITDA valuation ratios
valuation and cash flow
Valuation and Cash Flow
  • Ultimately, value comes from cash flow in any model:
    • DCF – directly measure cash flow from explicit cash flow and cash flow from selling after the explicit period
    • Multiples – The size of a multiple ultimately depends on cash flow in formulas
      • FCF/(k-g) = Multiple
        • They still have implicit cost of capital and growth that must be understood
    • Replacement Cost – cash from selling assets
  • Growth rate in cash flow is a key issue in any of the models

Investors cannot buy a house with earnings or use earnings for consumption or investment

reasonable estimates of growth is this graph reasonable
Reasonable Estimates of Growth – Is this Graph Reasonable

The short term

Based on best estimate of likely outcome

  • The medium term transition to tranquillity
  • Assessment of industry outlook and company position
  • ROIC fades towards the cost of capital
  • Growth fades towards GDP
  • The long run – tranquillity and equilibrium
  • Long run assumptions:
  • ROIC = Cost of capital
  • Real growth = 0%

Much of valuation involves implicitly or explicitly making growth estimates – High P/E comes from high growth

Reference: Level and persistence of growth rates

how long will growth last
How Long will Growth Last
  • Some Theoretical Issues with Growth:
    • The greater the current growth rate in earnings of a firm, relative to the stable growth rate, the longer the high growth period; although the growth rate may drop off during the period. Thus, a firm that is growing at 40% should have a longer high-growth period than one growing at 14%.
    • The larger the size of the firm, the shorter the high growth period. Size remains one of the most potent forces that push firms towards stable growth; the larger a firm, the less likely it is to maintain an above-normal growth rate.
    • The greater the barriers to entry in a business, e.g. patents or strong brand name, should lengthen the high growth period for a firm.
    • Look at the combination of the three factors A,B,C and make a judgment. Few firms can achieve an expected growth period longer than 10 years
terminal value and growth
Terminal value is reached when a company has reached maturity – it grows at the overall rate of the economy. This should be nominal growth in the economy since all of the currency in models is in nominal terms.

For immature companies, the reaching of equilibrium will exceed the standard five year forecast

Extending the forecast forces one to make assumptions for more than one year which become very speculative

Some suggest a fade growth period to address this issue

Terminal Value and Growth
fade period
Fade Period
  • The fade period is the length of time it takes for the long-term growth rate to be reached after from the growth in the last year of the forecast.
  • For example, the last year growth is 10%
  • The terminal growth is 3%
  • The time to get from 10% to 3% is 5 years
  • You can use the formula
  • Growth = Growtht-1 x [(Long term/Short term)]^(1/Fade)
  • Note: This does not work with negative growth rates
growth when companies are earning more than their cost of capital
Growth When Companies are Earning More than their Cost of Capital
  • It is a lot more difficult to maintain growth when you are earning 40% return on investment than when you are earning 10% in the terminal period
      • Competition tends to compress margins and growth opportunities, and sub-par performance spurs corrective actions.
      • With the passage of time, a firm’s performance tends to converge to the industry norm.
      • Consideration should be given to whether the industry is in a growth stage that will taper down with the passage of time or whether its growth is likely to persist into the future.
      • Competition exerts downward pressure on product prices and product innovations and changes in tastes tend to erode competitive advantage. The typical firm will see the return spread (ROIC-WACC) shrink over time.

A study by Chan, Karceski, and Lakonishok titled, “The Level and Persistence of Growth Rates,” published in 2003. According to this study, analyst “growth forecasts are overly optimistic and add little predictive power.”

growth issues
Growth issues include

Growth is difficult to sustain

Law of large numbers means that it is more difficult to maintain growth after a company becomes large

Investment analysts overestimate growth

Examine sustainable growth formulas from dividend payout and from depreciation rates

Growth Issues
valuation basics inclusion of returns
Valuation Basics – Inclusion of Returns
  • The future cash flow of a company and the risk of that company’s cash flow can be measured by:
    • Return on Invested Capital
    • Ability to Grow
    • Weighted Average Cost of Capital
      • It is in the formula: Cash Flow (ROIC x Inv)/(k-g) which is the basis for multiples
  • All of the other ratios – gross margins, effective tax rates, inventory turnover etc. are just details.


EBIT x (1-tax rate) (NOPLAT)


analytical framework for valuation combine forecasts of economic performance with cost of capital
Analytical framework for Valuation – Combine Forecasts of Economic Performance with Cost of Capital

Competitive position such as pricing power and cost structure affects ROIC

In financial terms, value comes from ROIC and growth versus cost of capital

P/E ratio and other valuation come from ROIC and Growth

practical discounting issues in excel
Practical Discounting Issues in Excel
  • NPV formula assumes end of period cash flow
  • Growth rate is ROE x Retention rate
  • If you are selling the stock at the end of the last period and doing a long-term analysis, you must use the next period EBITDA or the next period cash flow.
  • If there is growth in a model, you should use the add one year of growth to the last period in making the calculation
  • To use mid-year of specific discounting use the IRR or XIRR or sumproduct
valuation and sustainable growth
Valuation and Sustainable Growth
  • Value depends on the growth in cash flow. Growth can be estimated using alternative formulas:
    • Growth in EPS = ROE x (1 – Dividend Payout Ratio)
    • Growth in Investment = ROIC x (1-Reinvestment Rate)
    • Growth = (1+growth in units) x (1+inflation) – 1
  • When evaluating NOPLAT rather than earnings, a similar concept can be used for sustainable growth.
    • Growth = (Capital Expenditures/Depreciation – 1) x Depreciation Rate
  • Unrealistic to assume growth in units above the growth in the economy on an ongoing basis.
gordon s model and valuation
Gordon’s Model and Valuation
  • Gordon’s model is
  • P0 = D1/(k-g)
  • Example
value comes from economic profit and growth
Value Comes from Economic Profit and Growth

Economic profit is the difference between profit and opportunity cost

This implies that there are three variables – return, growth and cost of capital that are central to valuation analysis

Once you have a good thing, you should grow

the value matrix stock categorisation
The Value Matrix - Stock Categorisation

What is the economic reason for getting here and how long can the performance be maintained

Throwing good money after bad

Give the money to investors

Try to get out of the business

microsoft value creation and earnings
Microsoft Value Creation and Earnings

Earnings are a good indicator of value; but not always as shown by the recent increases which resulted from share buybacks

microsoft return and revenue growth
Microsoft Return and Revenue Growth

Strong Returns plus growth resulted in increased price; when return fell, the price fell

general motors slow growth and low roe
General Motors – Slow Growth and Low ROE

GM had low growth and low returns and the stock price did not increase.

roic issues
Issues with ROIC include

Will the ROIC move to WACC because of competitive pressures

Evidence suggests that ROIC can be sustained for long periods

Consider the underlying economic characteristics of the firm and the industry

What is the expected change in ROIC

When ROIC moves to sustainable level, then can move to terminal value calculation

Examine the ROIC in models to determine if detailed assumptions are leading to implausible results

Migration table

ROIC Issues
practical growth rate issues growth rate estimation vs roe and retention rate
Practical Growth Rate Issues: Growth Rate Estimation vs. ROE and Retention Rate
  • What we really need to estimate are reinvestment rates and marginal returns on equity and capital in the future (the change in income over the change in equity).
  • Those who use analyst’s or historical growth rates are implicitly assuming something about reinvestment rates and returns, but they are either unaware of these assumptions or do not make them explicit. This means, look at the ROE and the dividends to make sure that the growth is consistent.
  • Future ROE depends on changes in economic variables affecting the existing investment and new projects with incremental returns.
valuation ranges
Valuation Ranges
  • Do not claim to derive a single number – unrealistic to derive one number
    • Forecasting uncertainty
    • Cost of capital uncertainty
    • Bigger ranges for growth companies and for emerging economies
general valuation approaches
General Valuation Approaches
  • Typical Valuation Approaches are Differentiated According to:
    • Relative Valuation
      • Multiples, Comparative Transactions
    • Absolute Valuation
      • DCF, APV, Risk Neutral Valuation, Option Pricing
  • We Differentiate by
    • Direct Valuation
      • DCF, Multiples etc.
    • Indirect Valuation
      • Equity IRR from LBO Multiples, Accretion/Dilution in EPS from integrated merger analysis, IRR and debt capacity in project finance
direct valuation models
Direct Valuation Models
  • There are many valuation techniques for assets and investments including:
    • Income Approach
      • Discounted Cash Flow
      • Venture Capital method
      • Risk Neutral Valuation
    • Sales Approach
      • Multiples (financial ratios) from Comparable Public Companies of from Transactions or from Theoretical Analysis
      • Liquidation Value
    • Cost Approach
      • Replacement Cost (New) and Reproduction Cost of similar assets
    • Other
      • Break-up Value
      • Options Pricing
  • The different techniques should give consistent valuation answers

See the appraisal folder in the financial library

indirect valuation from modelling transactions
Indirect Valuation from Modelling Transactions
  • Instead of using DCF or multiples, back into the value of a company:
    • Leveraged buyout
      • Entry and exit multiples, debt capacity and EBITDA Growth. See how much you can pay an finance and obtain an equity rate or return consistent general benchmarks such as 20%.
    • Project Finance
      • Given contracts and assumptions about cash flows over the life of the asset and debt capacity, see how much investment can be made to generate and equity rate of return.
    • Merger Integration
      • Given assumptions about financing and accounting in a mergers, see how much you can afford to pay and still achieve accretion in earnings per share.
sum of the parts analysis
Sum of the Parts Analysis
  • Morgan Stanley performed a sum of the parts analysis, which is designed to imply a value of a company based on the separate valuation of the company’s business segments. Morgan Stanley calculated ranges of implied equity values per share for Wyeth, assuming a hypothetical disposition of Wyeth’s Nutrition, Consumer and Animal Health divisions.
  • Morgan Stanley valued Wyeth’s divisions using multiple ranges derived from comparable precedent transactions.
  • Morgan Stanley used a 3.5x to 4.5x multiple of aggregate value to estimated 2008 revenue for Wyeth’s Nutrition and Consumer divisions, and
  • 11.0x to 13.0x multiple of aggregate value to estimated 2009 EBITDA for the Animal Health division.
  • The Pharmaceutical division was valued at a public market trading multiple range of 9.0x to 11.0x estimated 2009 P/E multiple.
  • Based on the multiple ranges described above, and including the net present value of the step-up in the tax basis of the assets which would result from such a theoretical transaction, this analysis implied a range for Wyeth’s common stock of approximately $33 to $40 per share. Morgan Stanley noted that the merger consideration had an implied value of $50.19 per share.
risk neutral valuation
Risk Neutral Valuation
  • Theory – If one can establish value with one financial strategy, the value should be the same as the value with alternative approaches
  • In risk neutral valuation, an arbitrage strategy allows one to use the risk free rate in valuing hedged cash flows.
  • Forward markets are used to create arbitrage
  • Risk neutral valuation does not work with risks that cannot be hedged
  • Use risk free rate on hedged cash flow
  • Example
    • Valuation of Oil Production Company
    • Costs Known
    • No Future Capital Expenditures
practical implications of risk neutral valuation
Practical Implications of Risk Neutral Valuation
  • Use market data whenever possible, even if you will not actually hedge
  • Use lower discount rates when applying forward market data in models

Valuation with high

discount rates


Uncertain cash


Valuation with


Markets and

Low Discount


examples of risk neutral valuation
Examples of Risk Neutral Valuation
  • Risk neutral valuation means that one attempts to remove the risk from the cash flow and then discount the adjusted cash flow at the risk free rate. (This is how options pricing models were developed.)
  • There are various examples of risk neutral valuation that can be applied in valuation:
    • If there is a construction contract that includes a premium – say 20% to eliminate cost over-run and delay risk; this verifies the risk rather than attempts to simulate the risk or use of a high discount rate.
    • If there is a long-term contract that fixes the price, the project can be financed with a lower discount rate.
    • If a project can secure political risk insurance to eliminate political and currency conversion risk, a lower discount rate can be used rather than attempting to measure political risk.
    • Other examples …
venture capital method
Venture Capital Method
  • Two Cash Flows
    • Investment (Negative)
    • IPO Terminal Value (Positive)
      • Terminal Value = Value at IPO x Share of Company Owned
  • Valuation of Terminal Value
    • Discount Rates of 50% to 75%
      • Risky cash flows
      • Other services

See the article on private valuation

valuation diagram venture capital
Valuation Diagram – Venture Capital
  • Valuation in venture capital focuses on the value when you will get out, the discount rates and how much of the company you will own when you exit.

Continuing Value

Cash Flow

Cash Flow

Cash Flow

Cash Flow

  • In the extreme, if you have given away half of your company away, and the cash flow is the same before and after your give away, then the amount you would pay for the share must account for how much you will give away.

Discount Rates

Enterprise Value

Evaluate how much of the equity value that you own

Net Debt

Equity Value

venture capital method1
Venture Capital Method
  • Determine a time period when the company will receive positive cash flow and earnings.
    • e.g. projection of earnings in year 7 is 20 million.
  • At the positive cash flow period, apply a multiple to determine the value of the company.
    • e.g. P/E ratio of 15 – terminal value is 20 x 15
  • Use high discount rate to account for optimistic projections, strategic advice and high risk;
    • e.g. 50% discount rate – [20 x 15]/[1+50%]^7 = 17.5 million
  • Establish percentage of ownership you will have in the future value through dividing investment by total value
    • e.g. 5 million investment / 17.5 million = 28.5%
  • You make an investment and receive shares (your current percent). You know the investment and must establish the number of shares
venture capital method continued
Venture Capital Method Continued
  • In the venture capital method, there are only two cash flows
    • The investment
    • The value when the company is sold
  • The value received when the company is sold depends on the percentage of the company that is owned. If there is dilution in ownership, the value is less.
  • Therefore, an adjustment must be made for dilution and the percent of the company retained. See the Cost of Capital folder for and example
    • e.g. Share value without dilution = 17.5/700,000 = 25 per share
    • If an additional 30% of shares is floated, the value per share must be increased by 30% to maintain the value.
    • Value per share = 17.5/((500,000+VC shares) x 1.3)
    • VC Shares: (25 x 1.3)/17.5-500,000 = 343,373
replacement cost
Replacement Cost
  • First a couple of points regarding replacement cost theory
    • In theory, one can replace the assets of a company without investing in the company. If you are valuing a company, you may think about creating the company yourself.
    • If you replaced a company and really measured the replacement cost, the value of the company may be more than replacement cost because the company manages the assets better than you could.
    • By replacing the assets and entering the business, you would receive cash flows. You can reconcile the replacement cost with the discounted cash flow approach
measuring replacement cost
Measuring Replacement Cost
  • Replacement cost includes:
    • Value of hard assets
    • Value of patents and other intangibles
    • Cost of recruiting and training management
  • Analysis
    • Begin with balance sheet categories, account for the age of the plant
    • Add: cost of hiring and training management
  • If the company is generating more cash flow than that would be produced from replacement cost, the management may be more productive than others in managing costs or be able to realize higher prices through differentiation of products.
  • The ratio of market value to replacement cost is a theoretical ratio that measures the value of management contribution
replacement value and tobin s q
Replacement Value and Tobin’s Q
  • Recall Tobin’s Q as:
    • Q = Enterprise Value / Replacement Cost
  • Buy assets and talent etc and should receive the ROIC. Earn industry average ROIC.
    • If the ROIC > industry average, then Q > 1.
    • If the ROIC < industry average, then Q < 1
real options in investment decisions
Real Options in Investment Decisions
  • Example of real options in many investments
    • the right to abandon an asset in the research and development phase;
    • the right to abandon the plant during construction;
    • the right to delay construction of the facility;
    • the right not to dispatch the plant when prices below short-run marginal cost;
    • the right to retire or mothball the plant before the end of its physical life;
    • the right to extend the life of the plant instead of retiring it at the end of its planned life; and
    • the right to expand the asset
real options and problems with dcf
Real Options and Problems with DCF
  • The DCF model has many conceptual flaws, the most significant of which is assuming that cash flows are normally distributed around the mean or base case level.
  • For many investments, the cash flows are skewed:
    • When an asset is to be retired, there is more upside than downside because the asset will continue to operate when times are good, but it will be scrapped when times are bad.
    • An investment decision often involves the possibility to expand in the future. When the expansion decision is made, it will only occur when the economics are good.
    • During the period of constructing an asset, it is possible to cancel the construction expenditures and limit the downside if it becomes clear that the project will not be economic.
real options and dcf problems continued
Real Options and DCF Problems - Continued
  • Problems with DCF because of flexibility in managing assets:
    • In operating an asset, the asset can be shut down when it is not economic and re-started when it becomes economic. This allows the asset to retain the upside but not incur negative cash flows.
    • When developing a project, there is a possibility to abandon the project that can limit the downside as more becomes known about the economics of the project.
    • In deciding when to construct an investment, one can delay the investment until it becomes clear that the decision is economic. This again limits the downside cash flows.
  • In each of these cases, management flexibility provides protection in the downside which means that DCF model produces biased results.
simulation exercise
Simulation Exercise
  • To demonstrate how options affect valuation, consider a simple simulation exercise
  • Enter the following inputs
  • Volatility is the standard deviation of the percent change in a variable over time.
fundamental valuation
Fundamental Valuation
  • What was behind the bull market of 1980-1999
    • EPS rose from 15 to 56
    • Nominal growth of 6.9% -- about the growth in the real economy (the real GDP)
    • Keeping P/E constant would have large share price increase
    • Long-term interest rates fell – lower cost of capital increases the P/E ratio
  • Real Market
    • Value by ROIC versus growth
    • Select strategies that lead to economic profit
    • Market value from expected performance
three primary methods discussed in remainder of slides
Three Primary Methods Discussed in Remainder of Slides
  • Market Multiples – Relative Valuation
  • Discounted Free Cash Flow
  • Discounted Earnings and Dividends
  • Warning: No method is perfect or completely precise
  • Use industry expertise and judgment in assessing discount rates and multiples
  • Different valuation methods should yield similar results
  • Bangor Hydro Case
debt bond valuation

Bt = It +1 + It +2 + It +3 + ... + It +n + F

(1+r)1 (1+r)2 (1+r)3 (1+r)n (1+r)n

Debt (Bond) Valuation
  • Bt is the value of the bond at time t
  • Discounting in the NPV formula assumes END of period
  • It +n is the interest payment in period t+n
  • F is the principal payment (usually the debt’s face value)
  • r is the interest rate (yield to maturity)

Case exercise to illustrate the effect of discounting (credit spread) on the value of a bond

risk free discounting
Risk Free Discounting
  • If the world would involve discounting cash flows at the risk free rate, life would be easy and boring
equity dividend discount valuation and gordon s model

Vt = E(Dt +1)+ E(Dt +2) + E(Dt +3) + ... + E(Dt +n)+ ...

(1+k)1 (1+k)2 (1+k)3 (1+k)n

Equity – Dividend Discount Valuation and Gordon’s Model
  • Vt is the value of an equity security at time t
  • Dt +n is the dividend in period t+n
  • k is the equity cost of capital – difficult to find (CAPM)
  • E() refers to expected dividends
  • If dividends had no growth the value is D/k
  • If dividends have constant growth the value is D/(k-g)
  • Terminal Value is logically a multiple of book value per share
example of capitalization rates
Example of Capitalization Rates
  • Proof of capitalization rates using excel and growing cash flows
equity valuation free cash flow model

Vt = E(FCFt +1) + E(FCFt +2) + E(FCFt +3) + ... + E(FCFt +n) + ...

(1+k)1 (1+k)2 (1+k)3 (1+k)n

Equity Valuation - Free Cash Flow Model
  • FCFt+n is the free cash flow in the period t + n [often defined as cash flow from operations less capital expenditures]
  • k is the weighted average or un-leveraged cost of capital
  • E(•) refers to an expectation
  • Alternative Terminal Value Methods
setting up the model to reflect period discounting with terminal value and transaction dates
Setting-Up the Model to Reflect Period Discounting with Terminal Value and Transaction Dates
  • The example shown accounts for mid-year discounting and terminal value at the end of the period. The discount rate assumes annual discounting using the formula:
  • The terminal value must use the last mid year value multiplied by (1+g)^1.5

Terminal value is after the last period cash flow and must use mid year period x (1+g)^1.5

Precise discounting with mid year period

advantages and disadvantages of multiples

Objective – does not require discount rate of terminal value

Simple – does not require elaborate forecast

Flexible – can use alternative multiples and make adjustments to the multiples

Theoretically correct – consistent with DCF method if there are stable cash flows and constant growth – FCF/(k-g).


Valuation depends on opinions of others and not the underlying drivers of value.

Too simple: Does not account for prospective changes in cash flow

Accounting Based: Depends on accounting adjustments in EBITDA, earnings

Timing Problems: Changing expectations affect multiples and using multiples from different time periods can cause problems.

Advantages and Disadvantages of Multiples

There are reasons similar companies in an industry should have different multiples because of ROIC and growth – this must be understood

equity analysis target prices
Equity Analysis – Target Prices
  • Equity Research Analyst Price Targets Analysis
  • Morgan Stanley reviewed and analyzed future public market trading price targets for Wyeth’s common stock and Pfizer’s common stock prepared and published by equity research analysts. These targets reflect each analyst’s estimate of the future public market trading price of Wyeth’s common stock and Pfizer’s common stock. Morgan Stanley noted that the range of equity analyst price targets of Wyeth’s common stock was between approximately $33 and $48 per share. Morgan Stanley further calculated that using a cost of equity of 8.5% and a discount period of one year, the present value of the equity analyst price target range for Wyeth’s common stock was approximately $30 to $44 per share, with a mean target price of $40.82 and a median target price of $40.00. Morgan Stanley noted that the merger consideration had an implied value of $50.19 per share of Wyeth’s common stock based upon $17.45 per share of Pfizer common stock, the closing price of Pfizer’s common stock on January 23, 2009, the last trading day prior to announcement of the proposed merger.
example of problems with relative valuation housing prices
Example of Problems with Relative Valuation – Housing Prices
  • During the housing bubble, appraisers would use the value of similar transactions to estimate the value of properties
    • Appraisers would have a lot of tricks and make biased estimates by using houses with relatively high value and ignoring those with lower value (if they did not make high estimates, they would not be hired)
    • The fundamentals of housing value from evaluating the income levels relative to the house price, the trends in housing or the demand and supply of housing were ignored.
    • This lead to absurd valuations.
valuation from multiples
Valuation from Multiples
  • Valuation from multiples is known as relative valuation because valuation is compared to other companies and not to fundamental cash flows.
  • A measure of value is standardized by earnings or something else
    • Financial Multiples
      • P/E Ratio
      • EV/EBITDA
      • Price/Book
    • Industry Specific
      • Value/Oil Reserve
      • Value/Subscriber
      • Value/Square Foot
    • Issues
      • Where to find the multiple data and comparable companies
      • What income or cash flow base to use
      • Discounts for lack of marketability
mechanics of multiples
Mechanics of Multiples
  • Find market multiple from comparable companies
    • Rarely are there truly comparable companies
    • Understand economics that drive multiples (growth rate, cost of capital and return)
  • P/E Ratio (forward versus trailing)
      • Value/Share = P/E x Projected EPS
      • P/E trailing and forward multiples
  • Market to Book
      • Value/Share = Market to Book Ratio x Book Value/Share
      • Value/Share = (EV/EBITDA x EBITDA – Debt) divided by shares
  • P/E and M/B use equity cash flow; EV/EBITDA uses free cash flow

In the long-term P/E ratios tend to revert to a mean of 15.0

more valuation examples adjustments to multiples
More Valuation Examples – Adjustments to Multiples
  • Here the multiple is adjusted for risk and the dividends are accounted for in computing the rate of return
relate multiples to growth in a crude way
Relate Multiples to Growth in a Crude Way
  • The multiples depend on assessment of growth as illustrated by the quote below

Theory of growth and multiples – depends on long-term growth more than short-term growth. Also depends greatly on the cost of capital.

real world examples of bad practice
Real World Examples of Bad Practice

Comparison of equity value (P) to EBITDA compares value after debt to income before interest – favors companies with less debt

  • Invalid comparable companies
  • Logical comparisons

Sample should have similar WACC and growth rates and therefore be in the same industry and have the same kind of risks. Note difference in size and difference in company profile.

examples of valuation with multiples from analyst reports
Examples of Valuation with Multiples from Analyst Reports
  • Note how the industry multiples are used and then adjusted for risk and growth. The multiple is adjusted for growth, risk and rate of return.
use of multiples in valuation
Use of Multiples in Valuation

The red bars from the DCF valuation are compared to market date

  • Should be able to explain difference from:
  • Growth
  • 2. WACC
  • 3. ROIC
illustration of some multiples
Illustration of Some Multiples
  • Multiples for a couple companies are shown below

Which multiple best reflects value for the various companies – note the EV/EBITDA is most stable

which multiple to use
Which Multiple to Use
  • Valuation from multiples uses information from other companies
  • It is relevant when the company is already in a steady state situation and there is no reason to expect that you can improve estimates of EBITDA or Earnings
  • One of the challenges is to understand which multiple works in which situation:
    • Leveraged Buyout
      • EV/EBITDA is used
        • Changes in the common equity ratio
        • Intangible assets make book value inappropriate
        • Different leverage makes P/E difficult
    • Banks/Insurance
      • Market/Book may be best
        • Not many intangible assets, so book value is meaningful
        • Book value is the value of loans which is adjusted with loan loss provisions
        • Cost of capital and financing is very important because of the cost of deposits
multiples summary
Multiples - Summary
  • Useful sanity check for valuation from other methods
  • Use multiples to avoid subjective forecasts
  • Among other things, well done multiple that accounts for
    • Accounting differences
    • Inflation effects
    • Cyclicality
  • Use appropriate comparable samples
  • Use forward P/E rather than trailing
  • Comprehensive analysis of multiples is similar to forecast
  • Use forecasts to explain why multiples are different for a specific company

When you compute the terminal value using

CF x (1+g)/(k-g)

Compute the implied

EV/EBITDA from the data

Also compute the implied P/E and the implied EV/EBITDA when computing the DCF

p e ratio growth and reconciliation to cash flow
P/E Ratio, Growth and Reconciliation to Cash Flow
  • P = D1/(k-g)
  • g = ROE * (1-DPO) or DPO = 1 - g/ROE
  • P/E = D/E/(k-g)
  • Substituting for D/E = DPO
  • P/E = (1-g/r)/(k-g)
    • g -- long term growth rate in earnings and cash flow
    • r -- rate of return earned on new investment
    • k -- discount rate
  • (k-g) = (1-g/r)/(P/E)
  • k = (1-g/r)/(P/E) + g
  • Example: if r = k than the formula boils down to 1/(k)
  • If the g = 0, the formula is P/E = 1/k
price to earnings and other statistics
Price to Earnings and Other Statistics

Market crashed after very high PE in 2000

Low P/E when long-term interest rates where high

understanding the p e ratio

1/PE = 6.6%

Understanding the P/E Ratio
  • Corporations as a whole, typically reinvests about 50 percent of its profits every year to achieve this profit growth, leaving the other half to pay to shareholders as dividends and share repurchases. This translates to a cash yield to shareholders of about 3 to 3.5 percent at the long-term average P/E ratio of 15.1 Adding the annual 3 to 3.5 percent increase in share prices to the cash yield of 3 to 3.5 percent results in total real shareholder returns of about 6 1/2 percent per year.
  • Between 1980 and 1999, earnings per share for the S&P 500 rose from $15 to $56. If the forward P/E ratio had remained constant, earnings growth alone would have boosted the index by 302 points. This nominal annual growth in earnings of 6.9 percent equals 3.2 percent in real terms, close to the long-term average growth in real profits for the economy. Simultaneously, U.S. interest rates and inflation fell dramatically. Long term U.S. government bond yields peaked at nearly 15 percent in 1981 and then fell, more or less steadily, to 5.7 percent in 1999. The decline in inflation and interest rates drove P/E ratios back up to more typical levels. This occurred because during the high-inflation years, companies were unable to increase returns on capital commensurate with the rise in cost of capital, leading to extremely low P/E ratios.
example of valuation with multiples comparison of different transactions
Example of Valuation with Multiples – Comparison of Different Transactions

Note how multiples cover the cycle in a commodity business

Demonstrates that the multiple in the merger is consistent with other transactions

example of computation of multiples from comparative data
Example of Computation of Multiples from Comparative Data
  • JPMorgan also calculated an implied range of terminal values for Exelon at the end of 2009 by applying a range of multiples of 8.0x to 9.0x to Exelon's 2009 EBITDA assumption.

Note that the median is presented before the mean

adjustments to multiples
Adjustments to Multiples
  • Process
    • Find multiples from similar public companies
    • Adjust multiples for
      • Liquidity
      • Size
      • Control premium
      • Developing country discount
    • Apply adjusted multiples to book value, earnings, and EBITDA
  • There is often more money in dispute in determining the discounts and premiums in a business valuation than in arriving at the pre-discount valuation itself. Discounts and premiums affect not only the value of the company, but also play a crucial role in determining the risk involved, control issues, marketability, contingent liability, and a host of other factors.
adjustments to multiples marketability and liquidity discount
Adjustments to Multiples – Marketability and Liquidity Discount
  • If the entity were closely held with no (or little) active market for the shares or interest in the company, then a non-marketability discount would be subtracted from the value.
  • Non-marketabiliy Discounts – ranges from 10% to 30%
  • …represents the reduction in value from a marketable interest level of value to compensate an investor for illiquidity of the security, all else equal.
  • The size of the discount varies base on:
    • relative liquidity (such as the size of the shareholder base);
    • the dividend yield, expected growth in value and holding period;
    • and firm specific issues such as imminent or pending initial public offering (IPO) of stock to be freely traded on a public market.
studies of liquidity discount
Studies of Liquidity Discount
  • Private and public transactions
    • Attempt to compute EV/EBITDA in public and private transactions
    • Adjust so that the transactions are comparable
    • Compute the ratio in pubic and private transactions
    • Discount of 20 to 28 percent for US firms
    • Discount of 44 to 54 percent for non-US firms
  • Other studies
    • Value in IPO versus value of private trades before IPO
    • High liquidity in 40-50% range, but selection bias
    • Theory involves control by public board
adjustments to multiples controlling interest premium
Adjustments to Multiples – Controlling Interest Premium
  • Controlling interest value …the value of the enterprise as a whole assuming that the stock is freely traded in a public market and includes a control premium.
    • Control premium …reflects the risks and rewards of a majority or controlling interest.
    • A controlling interest is assumed to have control power over the minority interests.
  • Minority interest value …represents the value of a minority interest “as if freely tradable” in a public market.
    • Minority interest discount …represents the reduction in value from an absence of control of the enterprise.
private companies sell at a small discount
Private Companies Sell At A Small Discount

Median P/E Multiples: Public vs. Private Deals


Source: Mergerstat (U.S. Only)

Disclaimer: Data is continually updated and is subject to change

liquidity determines valuation premium
Liquidity Determines Valuation Premium

Median Transaction Multiples by Deal Size


Source: Mergerstat (U.S. Only)

Disclaimer: Data is continually updated and is subject to change

p e analysis use of p e ratio in valuation
P/E Analysis – Use of P/E Ratio in Valuation
  • J.P. Morgan performed an analysis comparing Exxon's price to earnings multiples with Mobil's price to earnings multiples for the past five years.
  • The source for these price to earnings multiples was the one and two year prospective price to earnings multiple estimates by I/B/E/S International Inc. and First Call, organizations which compile brokers' earnings estimates on public companies. Such analysis indicated that Mobil has been trading in the recent past at an 8% to 15% discount to Exxon.
  • J.P. Morgan's analysis indicated that if Mobil were to be valued at price to earnings multiples comparable to those of Exxon, there would be an enhancement of value to its shareholders of approximately $11 billion.
  • Finally, this analysis suggested that the combined company might enjoy an overall increase in its price to earnings multiple due to the potential for improved capital productivity and the expected strategic benefits of the merger. According to J.P. Morgan's analysis, a price to earnings multiple increase of 1 for Exxon Mobil would result in an enhancement of value to shareholders of approximately $10 billion.
p e ratio growth and reconciliation to cash flow1
P/E Ratio, Growth and Reconciliation to Cash Flow
  • P/E = (1-g/r)/(k-g)
    • g -- long term growth rate in earnings and cash flow
    • r -- rate of return earned on new investment
    • k -- discount rate
  • (k-g) = (1-g/r)/(P/E)
  • k = (1-g/r)/(P/E) + g
  • Example: if r = k than the formula boils down to 1/(k)
  • If the g = 0, the formula is P/E = 1/k
  • P = E/(k-g) x (1-g/r)
    • If, for some reason, g = r, then the Gordon model could be applied to compute k.
company profile in website

Company Profile in website
price earnings ratio
Price Earnings Ratio
  • The price earnings ratio is obviously very important in stock evaluation. Therefore, I describe some background related to the ratio and some theory with regards to the P/E ratio. Subjects related to the P/E ratio include:
    • Dividend growth Model
    • Theory of price earnings ratio and growth
    • P/E ratio and the EV/EBITDA ratio
      • The PE ratio depends more on accounting
      • The PE is affected by leverage
      • The EV/EBITDA ignores depreciation and capital expenditure
    • Case exercise on P/E and EV/EBITDA
p e ratio versus ev ebitda
P/E Ratio versus EV/EBITDA
  • Use the EV/EBITDA when the funding does not make much difference in valuation
    • Many companies in an industry with different levels of gearing and companies do not attempt to maximize leverage
    • Very high levels of gearing and wildly fluctuating earnings
    • When the earnings are affected by accounting policy and account adjustments
  • Use the P/E ratio when cost of funding clearly affects valuation and/or when the level of gearing is stable and similar for different companies
    • Debt capacity can provide essential information on valuation
    • EBITDA does not account for taxes, capital expenditures to replace existing assets, depreciation and other accounting factors that can affect value.
p e ratio
P/E Ratio
  • If you use the P/E ratio for valuation, the ratio implies that only this year or last years earnings matter
  • Cash matters to investors in the end, not earnings (different lifetime of earnings)
  • When earnings reflect cash flow, P/E is reasonable for valuation
  • High P/E causes treadmill and does not necessary imply that companies are performing well
  • Earnings can be managed and manipulated
use of p e ratio formula to compute the required return on equity capital
Use of P/E Ratio Formula to Compute the Required Return on Equity Capital
  • It will become apparent later that one cannot get away from estimating the cost of equity capital and the CAPM technique is inadequate from a theoretical and a practical standpoint.
  • The following example illustrates how the formula can be used in practice:
    • k = (1-g/r)/(P/E) + g
p e notes
P/E Notes
  • High ROE does not mean high PE – Hence the existence of high ROE stocks with low PEs
  • Growth and value are not always positively correlated
  • Growth from improvement will always be value enhancing whereas growth from reinvestment depends upon the return against the benchmark return
  • Reinvestment should also include “ Cash hoarding”
  • PB is better at differentiating ROE differences than PE
relationship between multiples
Relationship Between Multiples
  • The P/E, EV/EBITDA and Cash Flow Multiples should be consistent and you should understand why one multiple gives you a different answer than another multiple.
  • Each of the multiples is affected by
    • The discount rate – the risk of the cash flow
    • The ability of the company to earn more than its cost of capital
    • The growth rate in cash flow or earnings
  • Differences in the ratios are a function of
    • Leverage, Depreciation Rates, Taxes, Capital Expenditures relative to cash flow
relationship between multiples1
Relationship Between Multiples
  • Enterprise Value = NOPLAT x (1-g/ROIC)/(WACC – g)
  • NOPLAT = Investment x ROIC
  • NOPLAT = EBIT x (1-t)
  • EBITDA = EBIT + Depreciation
  • EBT = EBIT – Interest
  • NI = EBT x (1-t)
    • NI/Market Cap
  • Market Cap = EV – Debt
    • MB = Market Cap/Equity
relationship between multiples illustration
Relationship Between Multiples - Illustration
  • Assume
    • Value = NOPLAT x (1-g/ROIC)/(WACC –g)
    • This is the EVA Formula
  • Assume
    • No Taxes
    • No Leverage
    • No Depreciation
    • No Growth Rate
    • ROIC = 10%
comparative multiples
Comparative Multiples
  • With the simple assumptions, each of the multiples is the same as shown below

Exercise: Data table with alternative parameters to investigate P/E and EV/EBITA

comparative multiples1
Comparative Multiples
  • Once taxes, leverage and depreciation are added, the multiples diverge as shown on the table below:
advantages and disadvantages of dcf

Theoretically Valid – value comes from free cash flow and assessing risk of the free cash flow.

Operating and Financial Values – explicitly separates value from operating the company with value of financial obligations and value from cash

Sensitivity – forces an understanding of key drivers of the business and allows sensitivity and scenario analysis

Fundamental – not biased by optimism or pessimism in the market


Assumptions: Requires WACC assumptions and residual value assumptions. There are major problems with WACC estimation and the long-term growth assumption.

Forecasting Problems: Complex forecasting models can easily be manipulated

Growth: The residual value depends on a number of assumptions which can easily distort value

Real Options: Discussed above

Advantages and Disadvantages of DCF
problems with dcf range in values
Problems with DCF – Range in Values
  • Note the range in values in the analyst report
  • The range is less when a terminal value is used, but the range is still very high
  • The high range exists even though there is a tight range in discount rates
discounted cash flow morgan stanley example
Discounted Cash Flow – Morgan Stanley Example
  • Morgan Stanley performed a discounted cash flow analysis, which is designed to imply a value of a company by calculating the present value of estimated future cash flows of the company.
  • Morgan Stanley calculated ranges of implied equity values per share for Wyeth, based on discounted cash flow analyses utilizing Wall Street analyst estimates compiled by Thomson First Call and Wyeth management projections for the calendar years 2009 through 2013. In arriving at the estimated equity values per share of Wyeth’s common stock, Morgan Stanley calculated a terminal value by applying a range of perpetual free cash flow growth rates ranging from (0.5)% to 0.5%.
  • Such rate range was derived, based on Morgan Stanley’s judgment, after considering a number of factors, including growth of the overall economy, projected earnings expectations for comparable pharmaceutical companies and Wyeth’s upcoming patent expiration profile.
  • Morgan Stanley observed that this range implied P/E multiples for Wyeth that were consistent with the P/E multiples of the comparable companies studied by Morgan Stanley and identified above under “— Comparable Companies Analysis.” The unlevered free cash flows and the terminal value were then discounted to present values using a range of weighted average cost of capital from 7.0% to 9.0%.
  • Morgan Stanley selected this range using the capital asset pricing model. The weighted average cost of capital is a measure of the average expected return on all of a given company’s equity securities and debt based on their proportions in such company’s capital structure.
discounted cash flow general discussion
Discounted Cash Flow – General Discussion
  • Executives and investors alike can draw reassurance from an important trend that has gained momentum even through years of the market's twists and turns. More and more investors, analysts, and investment bankers are turning to fundamental financial analysis and sophisticated discounted cash flow (DCF) models as the touchstone of corporate valuation.
  • Recent accounting scandals and inappropriate calculation of revenues and capital expenses give DCF new importance. With heightened concerns over the quality of earnings and reliability of standard valuation metrics like P/E ratios, more investors are turning to free cash flow, which offers a more transparent metric for gauging performance than earnings. It is harder to fool the cash register. Developing a DCF model demands a lot more work than simply dividing the share price by earnings or sales. But in return for the effort, investors get a good picture of the key drivers of share value: expected growth in operating earnings, capital efficiency, balance sheet capital structure, cost of equity and debt, and expected duration of growth. An added bonus is that DCF is less likely to be manipulated by aggressive accounting practices.
discounted flow
Discounted Flow
  • Use the discounted cash flow when you know something more about the company that can be obtained with a forecast
  • Any cash flow forecast involves:
    • Value =
      • Cash flow during explicit forecast period +
      • Present of cash flow after explicit forecast period
  • The second item generally involves some kind of growth projection.
  • Value of Equity = Value of Enterprise – Value of Net Debt
step by step valuation with free cash flow
Step by Step Valuation with Free Cash Flow
  • Step by Step valuation using free cash flow:
    • Step 1: Compute projected free cash flow over the explicit forecast period and discount the free cash flow at the WACC
    • Step 2: Make adjustments to free cash flow in the last forecast year
    • Step 3: Add terminal value to cash flow to establish enterprise value
    • Step 4: Make other balance sheet adjustments for balance sheet liabilities and assets that are not in cash flow but affect value
    • Step 5: Subtract current value of debt net of surplus cash to establish the total equity value.
    • Step 6: Divided the equity value by the current outstanding shares to establish value per share
dcf discussion
DCF Discussion
  • DCF models are powerful, but they do have shortcomings. DCF is merely a mechanical valuation tool, which makes it subject to the axiom "garbage in, garbage out". Small changes in inputs can result in large changes in the value of a company. Investors must constantly second-guess valuations; the inputs that produce these valuations are always changing and susceptible to error.
  • DCF analysis shows that changes in long-term growth rates have the greatest impact on share valuation. Interest rate changes also make a big difference. Example: Sun Microsystems, which recently traded on the market at $3.25, is valued at almost $5.50, which makes its price of $3.25 a steal. The model assumes a long-term growth rate of 13.0%. If we cut the growth rate assumption by 25%, Sun's share valuation falls to $3.20. If we raise the growth rate variable by 25%, the shares go up to $7.50. Similarly, raising interest rates by one percentage point pushes the share value to $3.55; a one percent fall in interest rates boosts the value to about $7.70.
discounted cash flow
Discounted Cash Flow
  • Why would you make a cash flow forecast of more than one year
    • If the company is stable and you know the stable level of earnings and cash flow, then a cash flow forecast does not add anything to the valuation analysis
    • If you do not know what the future earnings will be, then a cash flow forecast is helpful as long as you have information to make the forecast
    • If you know earnings and cash flow will fluctuate and then reach a stable amount, then discounted cash flow will be better than multiple analysis
dcf valuation length of forecast
DCF Valuation – Length of Forecast
  • Short-run
    • Forecast all financial statement items
      • Gross-margin, selling expenses, Etc.
  • Further out
    • Individual line items more difficult
    • Focus on key drivers
      • Operating margin, tax rate, capital efficiency
  • Continuing Value
    • When ROIC and growth stabalise
growth rate and discount rate
Growth Rate and Discount Rate
  • A stable growth rate is a growth rate that can be sustained forever. Since no firm, in the long term, can grow faster than the economy which it operates it - a stable growth rate cannot be greater than the growth rate of the economy.
  • It is important that the growth rate be defined in the same currency as the cash flows and that be in the same term (real or nominal) as the cash flows.
  • Most models use inflation as a growth rate with no new real growth. If this were true, all existing firms would decline as a proportion to the GDP.
  • In theory, this stable growth rate cannot be greater than the discount rate because the risk-free rate that is embedded in the discount rate will also build on these same factors - real growth in the economy and the expected inflation rate.
DCF Example to Compute Equity Value from Free Cash Flow – Net Debt is Bank and Minority Interest minus Cash and Listed Investments

Treatment of other investments depend on definition of free cash flow. Here, income from other investments must not be in free cash flow

Note how investments are added and debt is deducted in arriving at equity value

example of dcf
Example of DCF
  • Lehman Brothers and Evercore calculated per share equity values by:
    • first determining a range of enterprise values of BellSouth by
      • adding the present values of the after-tax unlevered free cash flows and
      • terminal values for each EBITDA terminal multiple and discount rate scenario
    • then subtracting from the enterprise values the net debt (which is total debt minus cash) and
    • dividing those amounts by the number of fully diluted shares of BellSouth.
discounted cash flow example
Discounted Cash Flow Example
  • JPMorgan conducted a discounted cash flow analysis to determine a range of estimated equity values per diluted share for Exelon common stock.
  • JPMorgan calculated the present value of the Exelon cash flow streams from 2005 through 2009, assuming it continued to operate as a stand-alone entity, based on financial projections for 2005 through 2007 and extensions of those projections from 2008 through 2009 in each case provided by Exelon's management.
  • JPMorgan also calculated an implied range of terminal values for Exelon at the end of 2009 by applying a range of multiples of 8.0x to 9.0x to Exelon's 2009 EBITDA assumption.
  • The cash flow streams and the range of terminal values were then discounted to present values using a range of discount rates from 5.25% to 5.75%, which was based on Exelon's estimated weighted average cost of capital, to determine a discounted cash flow value range.
  • The value of Exelon's common stock was derived from the discounted cash flow value range by subtracting Exelon's debt and adding Exelon's cash and cash equivalents outstanding as of December 31, 2004.
example of discounted cash flow analysis
Example of Discounted Cash Flow Analysis
  • For the Exelon discounted cash flow analysis, Lehman Brothers calculated terminal values by applying a range of terminal multiples to assumed 2009 EBITDA of 7.72x to 8.72x. This range was based on the firm value to 2004 estimated EBITDA multiple range derived in the comparable companies analysis. The cash flow streams and terminal values were discounted to present values using a range of discount rates of 5.43% to 6.43%. From this analysis, Lehman Brothers calculated a range of implied equity values per share of Exelon common stock.
  • PSE&G: For PSEG's regulated utility subsidiary, Morgan Stanley calculated a range of terminal values at the end of the projection period by applying a multiple to PSE&G's projected 2009 earnings and then adding back the projected debt and preferred stock amounts in 2009. The price to earnings multiple range used was 14.0x to 15.0x and the weighted average cost of capital was 5.5% to 6.0%.
dcf model issues and problems
DCF Model Issues and Problems
  • The basic structure of a DCF model is simple; more complex issues include:
    • How to precisely discount including mid-year cash flows, terminal values, and transaction periods
    • How to make terminal growth consistent with multiples and inflation in the WACC
    • How to account for deferred taxes, net operating loss, unfunded pension plans, derivatives, stock option plans, minority interest, asset retirement obligations and other liabilities
    • How to account for high cost debt that has been issued by the company being valued
example of bad dcf
Example of Bad DCF
  • In valuing a bank in Tanzania:
    • The WACC used included country premium that produced a WACC of 22%
    • The assets of the bank are not loans, but are government securities
    • The terminal growth rate was 2%
    • To make the valuation consistent with multiples in Kenya and Nigeria, liquidity and other discounts that reduced the PE multiple from about 20 to about 8.
common errors in discounted cash flow model
Common Errors in Discounted Cash Flow Model
  • Discounted cash flow models have assumptions about net capital expenditures and growth that are strongly linked. When capital expenditures change, then the growth rate should change. There are two types of errors that show up in these valuations.
    • First, high growth firms with high net capital expenditures are assumed to keep reinvesting at current rates, even as growth drops off. Not surprisingly, these firms are not valued very highly in these models.
    • Second, the net capital expenditures are reduced to zero in stable growth, even as the firm is assumed to grow at some rate forever. Here, the valuations tend to be too high.Avoid errors and make the assumptions about reinvestment a function of the growth and the return on capital. As growth changes, the reinvestment rate must change.
three issues that can add complexity
Three Issues that Can Add Complexity
  • Deferred Taxes
  • Employee Stock Options and Diluted Shares
  • Minority Interest
  • Derivatives Valued on Balance Sheet
  • Asset Retirement Obligations
  • High Interest Rate Debt
  • Over-funded or Under-Funded Defined Pension Obligations
  • The key is to understand how these items affect the value in theory and be able to work through examples
deferred tax
Deferred Tax
  • There are two ways to consider deferred tax:
    • Option 1:
      • Ignore deferred tax in the calculation of free cash flow and either add or subtract deferred tax assets or liabilities
    • Option 2:
      • Model deferred tax as part of free cash flows and explicitly model the net operating loss
    • Option 1 has problems
      • Models future liability even though the future capital expenditures create new cash flows
      • Does not consider the timing of NOL
deferred tax1
Deferred Tax
  • Simulation (see Deferred Tax Example.xls) on CD, shows
    • If stable growth in capital expenditures, growth in deferred tax is the same as growth in overall capital expenditures
    • Should subtract deferred tax changes from cash flow and not make other adjustments to value
    • If use EBITDA – EBIT x Tax without considering deferred tax, will understate value by the PV of deferred tax
    • Deferred tax as a percent of capital stays constant and does not vary much for different growth rates
adjustments to dcf for employee stock options
Adjustments to DCF for Employee Stock Options
  • If options issued to employees are deducted when computing net income:
    • Adjust EBITDA so it is the same with and without the option
    • The option means more cash or less debt is on the balance sheet
  • Consider two companies that are identical except that one pays employees with stock options
    • The enterprise value of the two companies should be the same
    • One company has more cash which becomes a reduction in net debt
    • The second company in the future will have to dilute the existing equity ownership
    • The future dilution should be a reduction in the equity value of the company
option example
Option Example
  • We apply the intrinsic value method of accounting for employee stock-based compensation and expense it ratably over the vesting period. We recognize compensation cost for awards on the grant-date fair value of those awards.
minority interest
Minority Interest
  • Minority interest should be deducted in computing the value of common equity
  • The issue is whether the minority interest should be subtracted at market value or at book value
  • If the minority interest is significant, the market value should be used rather than the book value.
  • Example:
    • Minority interest is 49% of the value of the company
    • The market value of the company is three times the book value
    • The minority interest should also be three times the book value
derivatives on the balance sheet
Derivatives on the Balance Sheet
  • The treatment of derivatives on the balance sheet depends on the manner in which the derivatives are treated in the cash flow.
  • Derivatives measure the costs or benefits signing contracts that lock in prices, interest rates or other costs.
  • If the derivatives are related to operating flows, the treatment depends on how the contracts are treated in the cash flows.
    • If the contracts are included in the cash flows, the value of the derivatives is in the free cash flow and no adjustment should be made.
    • If the contracts are not included in cash flows, the value should be added or subtracted from the enterprise value
  • If the derivatives are related to locking in interest rates, the value of the derivatives is analogous to valuing debt at market value and it should be include in the DCF
high interest rate debt
High Interest Rate Debt
  • Without adjustments high interest rate debt from being a low rated company would:
    • Increase the WACC
    • Result in high value of debt to be subtracted if the valuation is for a M&A transaction where the new owner will have a lower cost of debt
  • Theory
    • If the cost of debt is higher because of a higher probability of default, the equity holders are receiving this value because they own a call option. If two companies have the same cash flow and one has more leverage, the enterprise value should not be reduced. Thus, in theory, the cost of equity should be lower. The APV where all-equity cost of capital is computed solves this problem.
  • Practice
    • Do not use the high cost of debt in the WACC and do not adjust the cost of equity
high coupon debt
High Coupon Debt
  • If the WACC does not have the cost of the high coupon debt (and it should not) then the market value of debt should be subtracted and not the book value
  • If two companies have the same free cash flow and one has higher leverage then the other, then the value of the enterprise and the value of the debt and equity together should be the same.
  • If the value of debt is reduced for the risk premium, then the value of the equity should be increased to compensate.
assets and liabilities that escape dcf valuation
Assets and Liabilities that Escape DCF Valuation
  • Any asset or liability that has no cash flow consequences
  • Carefully Analyze the Balance Sheet::
    • Assets  Add to Enterprise Value
      • Un-utilized Land
      • Un-utilized Equipment
      • Legal Claims
    • Liabilities  Subtract From Enterprise Value
      • Environmental
      • Contract Provisions
      • Unrecorded unfunded Liabilities
      • Net Pension Liabilities not Funded
unfunded pension liabilities
Unfunded Pension Liabilities
  • Defined benefit versus defined contribution
    • No issue with defined contribution since contribution covers future obligations and there is no future obligation that is not covered
    • Defined benefit plan can lead to requirements to fund that are not included in investment reserves
    • Difference between investment reserves and pension requirements is unfunded liability or asset
    • Unfunded liability is like debt – it will have to be replaced by getting cash through issuing debt or equity
      • If a company runs a defined-benefit pension plan for its employees, it must fund the plan each year. If the company funds its plan faster then expenses dictate, the company can recognise a portion of the excess assets on the balance sheet.

If the liability is included in operating expenses, then no adjustment may be necessary

under funded or over funded pension obligations example
Under-Funded or Over-Funded Pension Obligations - Example
  • Balanced
    • Accrue expense as deposit into fund and accumulate pension fund sufficient to pay all obligations
      • Deposits to pension fund equal the accrued expense
      • Pension liability for future payments equals pension fund
over funded pension obligations example
Over-Funded Pension Obligations - Example
  • Establish a fund before obligations arise
      • No need to make cash deposits into fund
      • Pension liability for future payments still is operating expense in EBITDA but not requiring cash deposits
under funded pension obligations example
Under-Funded Pension Obligations - Example
  • Revise example to include current obligations
      • Fund has not been established for obligations
      • Need to use cash to pay for obligations; this cash not a part of EBITDA
terminal value in corporate model
Terminal Value in Corporate Model

Year after explicit period to establish stable cash flows


CFt x (1+g)/



Terminal Value

Explicit Forecast Period

EV/EBITDA that Reflects

Long-term Growth Rate and ROIC

PV of Cash

Year t


Step 2: PV from Year t to current year

Step 1: PV to year t – End of period t, so Gordon’s method must use t+1 cash flows

Market to Book Ratio that Reflects Long-term ROE

Make sure Cash Flow in period t reflects realistic ROIC, Working Capital that reflects long-term growth and realistic capital expenditures

Valuation Date

estimating continuing value
Estimating Continuing Value
  • Continuing value is important aspect of valuation
  • In actual valuations compiled by McKinsey, the terminal value is – 56% to 125% of valuation
  • High terminal values are reasonable if cash flow in early years is offset by outflows for capital spending that should generate higher cash flows in later yearsThe terminal value should reflect cash flow and earnings that is at the middle of the business cycle, or in the case of commodities, where prices reflect long-run marginal production cost, or in the case of high growth companies, when the market is saturated
continuing value to add to free cash flow
Continuing Value to Add to Free Cash Flow
  • Terminal or continuing value is analogous to dividends and capital gains. Free cash flow is dividends, residual value is capital gain.
  • A few methods of computing residual value include:
    • Perpetuity
    • EBITDA Multiple
    • P/E Ratio
    • Market to Book Ratio
    • Replacement Cost
    • NOPLAT
  • Present value of residual amount to add to present value of cash flow to establish enterprise value

First, high growth firms with high net capital expenditures are assumed to keep reinvesting at current rates, even as growth drops off. Not surprisingly, these firms are not valued very highly in these models.

Second, the net capital expenditures are reduced to zero in stable growth, even as the firm is assumed to grow at some rate forever. Here, the valuations tend to be too high.

capital expenditures and depreciation in terminal period
Capital Expenditures and Depreciation in Terminal Period
  • Cash Flow can not be maintained if a company does not make investments that support the cash flow – the cash flow may be the result of earlier investments.
  • Some simply set the capital expenditures equal to depreciation.
    • This is not correct if a company grows and experiences inflation.
    • The long-term stable relationship depends on the growth rate, and the depreciation rate.
    • With a higher growth rate and a longer depreciation life, the stable rate of Capital Expenditures/Depreciaiton increases.
some terminal value issues
Some Terminal Value Issues
  • Should you grow from a company that is already earning a high ROIC (is the ROIC sustainable)
  • Should the capital expenditures in the last year be equal to the depreciation expense (if not, what should be the ratio of capital expenditures to depreciation).
  • Should deferred taxes be included in the terminal year (how should the deferred taxes correspond to the depreciation assumptions)
  • If multiples are used rather than a perpetuity formula, should the multiples be adjusted for prospective growth or returns
  • How long should a fade period be in achieving the long-term growth
formulas for continuing value
Formulas for Continuing Value
  • A common method for computing cash flow is using the final cash flow in the corporate model and assuming the company is sold at the end of the
    • Perpetuity Value at beginning of final year = FCF/WACC
    • Perpetuity Adjusted for Growth = FCF(1+g)/(WACC - g)
    • Perpetuity using investment returns =
    • NOPLAT x (1-g/ROIC)/(WACC - g)
  • Once the Perpetuity Value is established for in the last year, it must be discounted to the current value:
    • Current Perpetuity Value = PV(Perpetuity Value that occurs at beginning of final year)
  • NPV in excel assumes flows occur at the end of the year. Adjustments can be made to assume that flows occur in the middle of the year.
    • In this case, the discounting of the residual is different from discounting of the individual cash flows
sustainable growth and plowback rate
Sustainable Growth and Plowback Rate
  • In the P/E ratio, the sustainable growth of earnings per share is:
    • g = ROE x (1 – dividend payout ratio)
    • This depends on assumptions with respect to constant payout and constant ROE. It also assumes that either there are no new share issues, or if new share issues occur, the market to book ratio is one.
  • Growth in free cash flow:
    • g = Dep Rate x [(Cap Exp/Dep) – 1]
    • Capital expenditures can be greater than depreciation because historic depreciation is low from historic accounting or because company has opportunities for growth.
example with terminal growth
Example with Terminal Growth
  • Goldman Sachs also performed an illustrative discounted cash flow analysis to determine indications of implied terminal value multiples for FPL Group based upon projected 2008 EBITDA as provided by Constellation’s management.
  • In performing the illustrative discounted cash flow analysis, Goldman Sachs applied discount rates ranging from 5.25% to 7.25% to the projected cash flows of FPL Group for calendar years 2006 through 2008.
  • Goldman Sachs also applied perpetuity growth rates ranging from 2.50% to 3.50%.
  • Goldman Sachs derived illustrative implied equity values for Constellation’s implied 40% share of the combined company ranging from $6,822 million to $25,326 million and illustrative implied equity values ranging from $37.76 to $140.16 per share of the common stock of the combined company. Applying the mid-point discount rate of 6.75% and the mid-point perpetuity growth rate of 3.25%, Goldman Sachs derived an illustrative implied equity value for Constellation’s implied 40% share of the combined company of $12,139 million and an illustrative implied equity value of $67.18 per share of the common stock of the combined company.
example of terminal value in telecommunications
Example of Terminal Value in Telecommunications
  • “Terminal value” refers to the value of all future cash flows from an asset at a particular point in time.
  • Lehman Brothers and Evercore estimated a range of terminal values in 2015 based on AT&T management estimates, in 2010 based on consensus research estimates, and in 2008 based on BellSouth management estimates calculated based on selected free cash flow perpetuity growth rates of 1.0% to 2.0% for AT&T management estimates and 1.5% to 2.5% for BellSouth management estimates and consensus research estimates.
  • For BellSouth’s Wireline segment, Citigroup and Goldman Sachs calculated a range of estimated terminal values by multiplying the BellSouth Wireline segment’s calendar year 2008 EBITDA by selected multiples ranging from 4.75x to 5.25x.
  • For BellSouth’s 40% interest in Cingular, BellSouth’s Wireless business segment, Citigroup and Goldman Sachs calculated a range of estimated terminal values by multiplying Cingular’s calendar year 2008 estimated EBITDA by selected multiples ranging from 5.75x to 6.25x.
reasons for multiplying by 1 g in perpetuity method
Reasons for Multiplying by (1+g) in Perpetuity Method
  • Assume
    • Company is sold on last day in the cash flow period
    • Valuation is determined from cash flow in the year after the residual period
    • This cash flow is final year x (1+g)
  • Discounting
    • Since the value is brought back to final period, the discount factor should be the final year period
    • Without growth, the value is the cash flow (cf x 1+g)) divided by the discount growth
    • The discounting should also reflect the growth rate
  • Formula
    • 1. Cash Flow for Valuation – CF x (1+g)
    • 2. Value at Last Day of Forecast – CF x (1+g)/(WACC –g)
    • 3. PV of the Value -- discount rate must be at last day of forecast, not mid year
problems with use of multiples and growth rates in dcf
Problems with Use of Multiples and Growth Rates in DCF
  • Multiples can cause problems
    • Sustainable growth once stable period has been reached is probably less than the growth used in the explicit forecast period. This means that the multiple should be less as well.
    • The multiples for evaluating a merger transaction may include synergies and other current market items. The use of similar multiples in terminal value is highly inappropriate.
  • Constant growth rates can also cause problems
    • Using FCF x (1+g)/(k-g) requires the assumption that growth is constant forever, and that the cost of capital will not change over time.
continuing cash flow from noplat and roic
Continuing Cash Flow from NOPLAT and ROIC
  • Using a multiple of NOPLAT has a couple of advantages
    • It is not distorted by large of small capital expenditures
    • Continuing value directly relates to assumptions about ROIC
    • For companies with low leverage, the NOPLAT multiplier is similar to the P/E ratio
  • Formulas for Computing Continuing Value with NOPLAT
    • Free Cash = NOPLAT – Capital Expenditure + Depreciation
    • Free Cash = ROIC x Investment – Capital Expenditure + Depreciation
    • The equation becomes:
    • Free Cash = (1-Real Growth/Real ROIC) x NOPLAT
      • In this formulation
      • G = ROIC x Plowback Rate
      • Similar to ROE x Retention Rate
drivers in terminal value
Drivers in Terminal Value
  • Rather than using growth from final year, use value drivers:
    • Return on Invested Capital
    • WACC
    • Capital Expenditures to Depreciation
      • Natural growth from inflation
      • Real growth
  • Formula for Sustainable Growth
    • Cap Exp/Investment – Depreciation/Investment
    • Cap Exp/Depreciation x Depreciation – Depreciation
  • Implied EV/EBITDA can be established
depreciation and capital expenditures in terminal cash flow
Depreciation and Capital Expenditures in Terminal Cash Flow
  • Some assume that capital expenditures equal depreciation in the final period
    • This would make sense if:
      • No past inflation
      • No past growth
    • To replace assets will have to pay current costs rather than historic costs that were affected by inflation.
    • If the company has grown, the stable cash flows will reflect current state of the company.
  • Address with simple simulations to derive equilibrium level of capital expenditures relative to depreciation
detailed discounting issues
Detailed Discounting Issues
  • In excel, the NPV formula assumes that cash flows occur at the end of the year.
  • It is more reasonable to assume that cash flows occur in the middle of the year.
  • You can use discount factors that use mid-year discounting
  • If the last year cash flow occurs at the middle of the year and it is assumed that the company is sold at the end of the last year, then you should use (1+g)^1.5 rather than (1+g) in discounting
  • If you use XNPV it is equivalent to computing a daily discount rate with the formula (1+r)^(1/365)-1 and then using the number of days in the discounting process
valuation from projected earnings and dividends
Valuation from Projected Earnings and Dividends
  • Earnings Valuation
    • PV of EPS over forecast horizon discounted at the equity discount rate
    • Add the present value of the perpetuity EPS value reflecting the growth rate
  • Dividend Valuation
    • PV of Dividend per share over the forecast horizon
    • Add present value of book value per share rather than perpetuity of earnings because book value grows when dividends are not paid
    • Can multiply the book value per share by market to book multiple
price earnings and gordon model
Price Earnings and Gordon Model

Gordon Dividend Discount Model.

P = D1/(K – G)

  • P = the "correct" share price
  • D = dividend payment for the next period (recall from discounting exercise that the next period must be used)
  • K = Required rate of return (based largely on market interest rates a adjusted for equity risk)
  • G = anticipate rate of dividend growth

The model can be used to compute the cost of capital where:

R = D/P + G

Problem: D is not EPS and G is affected by payout ratio

use of relationship between multiples and financial ratios in residual value
Use of Relationship between Multiples and Financial Ratios in Residual Value
  • The financial model projects the return on equity and the relationship between ROE and the Market to book ratio can be used to make projections of multiples
valuation issues
Valuation Issues
  • 1. How do you choose between firm and equity valuation (DCF valuation versus Earnings Growth)
  • Done right, firm and equity valuation should yield the same values for the equity with consistent assumptions. Choosing between firm (DCF) and equity valuation (PE x EPS forecasts) boils down to the pragmatic issue of ease.
  • For banks, firm valuation does not work because small differences in WACC can have dramatic effects on valuation while and if the market value of debt differs from the book value, firm value can cause distortions.
firm versus equity valuation
Firm versus Equity Valuation
  • From the perspective of convenience, it is often easier to estimate equity than the DCF, especially when leverage is changing significantly over time (for example, in project finance and in leveraged buyouts where equity IRR is used).
  • Equity value measures a real cash flow to owners, rather than an abstraction (free cash flows to the firm exist only on paper).
  • Free cash flow is affected to a large extent by capital expenditures which can cause problems.
  • Equity cash fllow brings to light potential cash shortfalls (and the likelihood of bankruptcy) much more directly
measurement of expected growth rate
Measurement of Expected Growth Rate
  • While there are many who use historical (past) growth as a measure of expected growth, or choose to trust analysts (with their projections), try using fundamentals.
  • Think about the two factors that determine growth - the firm's reinvestment policy and its rate of return.
    • For expected growth in earnings = Retention Ratio * ROE, where Retention Ratio is 1 – Dividend Payout
    • For expected growth in EBIT = Reinvestment Rate * ROC, where reinvestment rate is Cap Exp/Depreciation
estimation of terminal value
Estimation of Terminal Value
  • Terminal value refers to the value of the firm (or equity) at the end of the high growth period. Estimate terminal value, with DCF, by assuming a stable growth rate that the firm can sustain forever. If we make this assumption, the terminal value becomes:
  • Terminal Value in year n = Cash Flow in year n+1 / (r - g)
  • This approach requires the assumption that growth is constant forever, and that the cost of capital will not change over time.
exit multiple in dcf valuation
Exit multiple in DCF valuation
  • In some discounted cash flow valuations, the terminal value is estimated using a multiple, usually of earnings. In an equity valuation model, the exit multiple may be the PE ratio. In firm valuation models, the exit multiple is often of EBIT or EBITDA.
  • Analysts who use these multiples argue that it saves them from the dangers of having to assume a stable growth rate and that it ties in much more closely with their objective of selling the firm or equity to someone else at the end of the estimation period.
  • Problems arise if the PE assumes a higher growth than is sustainable after the holding period.
exit multiples and dcf valuation
Exit multiples and DCF valuation
  • On the contrary, exit multiples may introduce relative valuation into discounted cash flow valuation, and that you create a hybrid, which is neither DCF nor relative valuation. These exit multiples use the biggest single assumption made in these valuation models.
  • It seems foolish to assume that current multiples will remain constant as the industry matures and changes and that investors will continue to pay high multiples, even if the fundamentals do not justify them. If there is stable growth, the P/E multiple in the terminal value should be lower.
valuation of firms that are losing money
Valuation of Firms that are Losing Money
  • There are a number of reasons why a firm might have negative earnings, and the response will vary depending upon the reason:- If the earnings of a cyclical firm are depressed due to a recession, the best response is to normalize earnings by taking the average earnings over a entire business cycle.
    • - Normalized Net Income = Average ROE * Current Book Value of Equity- Normalized after-tax Operating Income = Average ROC * Current Book Value of Assets- Once earnings are normalized, the growth rate used should be consistent with the normalized earnings, and should reflect the real growth potential of the firm rather than the cyclical effects.
valuation of a firm that is losing money
Valuation of a firm that is Losing Money
  • - If the earnings of a firm are depressed due to a one-time charge, the best response is to estimate the earnings without the one-time charge and value the firm based upon these earnings. - If the earnings of a firm are depressed due to poor quality management, the average return on equity or capital for the industry can be used to estimate normalized earnings for the firm. The implicit assumption is that the firm will recover back to industry averages, once management has been removed.- Normalized Net Income = Industry-average ROE * Current Book Value of Equity- Normalized after-tax Operating Income = Industry-average ROC * Current Book Value of Assets
valuation of a firm that is losing money1
Valuation of a firm that is losing money
  • - If the negative earnings over time have caused the book value to decline significantly over time, use the average operating or profit margins for the industry in conjunction with revenues to arrive at normalized earnings. Thus, a firm with negative operating income today could be assumed to converge on the normalized earnings five years from now. - If the earnings of a firm are depressed or negative because it operates in a sector which is in its early stages of its life cycle, the discounted cash flow valuation will be driven by the perception of what the operating margins and returns on equity (capital) will be when the sector matures.
  • - If the equity earnings are depressed due to high leverage, the best solution is to value the firm rather than just the equity, factoring in the reduction in leverage over time.
valuation of a private firms
Valuation of a private firms
  • The valuation of a private firm is more difficult than stock in a publicly traded firm. In particular,
    • A. The information available on private firms will be sketchier than the information available on publicly traded firms.
    • B. Past financial statements, even when available, might not reflect the true earnings potential of the firm. Many private businesses understate earnings to reduce their tax liabilities, and the expenses at many private businesses often reflect the blurring of lines between private and business expenses.
valuation of a private firm
Valuation of a private firm
  • C. The owners of many private businesses are taxed on the salary they make and the dividends they take out of the business; often do not try to distinguish between the two.The limited availability of information does make the estimation of cash flows impossible; past financial statements might need to be restated to make them reflect the true earnings of the firm. Once the cash flows are estimated, the choice of a discount rate might be affected by the identity of the potential buyer of the business. If the potential buyer of the business is a publicly traded firm, the valuation should be done using the discount rates based upon market risk
eps measures establishing a reliable starting point
EPS Measures – Establishing a reliable starting point
  • Reported EPS – EPS reported by the company using generally accepted accounting principles. Therefore includes earnings from recurring and non-recurring items
  • Recurring EPS – Reported EPS adjusted to exclude non-recurring items
  • Fully diluted EPS – EPS adjusted to reflect dilution to existing shareholders as a result of future increases in equity shares
share buy back
Share buy back
  • Redeem Ltd made earnings of $ 33 million dollars for the year ended March 2004. The number of shares issued at the start of the year was 200 million. In September 2003 Redeem Ltd bought back 20 million shares at market price.

EPS = $33 million/ 190 million = 17. 3 CENTS

dilution factors and treatment
Dilution – Factors and treatment
  • Contingently issuable shares - Include shares in the calculation of basic EPS if the contingency has been met.
  • Options or warrants in existence over as yet un-issued shares – Assume exercise of outstanding dilutive options and warrants
  • Loan stock or preference shares convertible into equity shares in the future – Assume that instruments are converted therefore saving interest but increasing the number of shares in issue
diluted shares
Diluted Shares
  • If you have agreed to give away shares to someone, then your claim to the cash flow of the company is reduced.
  • In the extreme, if you have given away half of your company away, and the cash flow is the same before and after your give away, then the amount you would pay for the share must account for how much you will give away.
  • In this extreme example, you should reduce the value by ½.
  • This can be accomplished by using diluted shares rather than basic shares.
option dilution
Option dilution
  • Calculation of the number of shares in the dilution calculation is illustrated below:
multiple listings
Multiple Listings
  • Fungible shares listed on different exchanges – EPS calculated on the basis of total shares - Value equity based on shares held by the investor group to whom your research is directed
employee stock options latest developments
Employee Stock options – Latest developments
  • IFRS 2 – Requires companies to measure the fair value of share-based payments at the grant date and expense over the vesting period
  • FAS 123 – The above treatment is optional
  • A company grants 100 options to 200 employees. The estimated fair value is $ 50 per option. The options are contingent on the employees working at the Company in 3 years time. The company estimates that 25% of the employees Will leave over the 3 year period. No employees leave in year 1 and 2 but 10% leave In year 3.
issues in the application of pes
Issues in the application of PEs
  • Accounting Policy differences – Particularly significant for cross border comparisons where companies may follow local, international or US GAAP
  • Loss making companies – No earnings therefore no PE
  • Cyclical companies – PEs volatile through the cycle and therefore difficult to benchmark
  • Finding a suitable benchmark – Difficult to find companies that are perfect matches in all determinants of a PE
  • Growth – As discussed value and growth are not always the same
  • Capital market conditions – The cost of equity will vary depending on underlying interest rate environment that is likely to be different in different countries
  • Financing – The greater the gearing of a company the greater the cost of equity and therefore, all other things being equal, the lower the value and the lower the PE
valuation of subsidiary companies in different countries
Valuation of Subsidiary Companies in Different Countries
  • How would things differ if we are valuing companies from different countries, different sectors etc.
  • The basic rule is:
    • Cash flows should be nominal
    • Cash flows should be stated in the currency where the subsidiary is located
      • If there are multiple currencies, use the future expected spot exchange rates to translate cash flows
    • Cash flows should be discounted at cost of capital that reflects the interest rates where the country is located
      • This means that the risk free rate in the country where the subsidiary is located should be used.
    • Once the value is established, translate the amount to the home country at the spot exchange rate
valuation of subsidiary companies in different countries1
Valuation of Subsidiary Companies in Different Countries
  • How would things differ if we are valuing companies from different countries, different sectors etc.
    • Example:
      • Subsidiary is located in Malaysia
      • Parent Company is in Hong Kong
      • Subsidiary company sells in Malaysia and Thailand
      • Subsidiary company produces in Malaysia and Thailand
    • Exchange Rates and Interest Rates
      • Spot Exchange Rates
        • HK Dollars to Ringet
        • Baht to Ringet
valuation of subsidiary companies in different countries2
Valuation of Subsidiary Companies in Different Countries
  • How would things differ if we are valuing companies from different countries, different sectors etc.
  • Cash flows should be stated in the currency where the subsidiary is located (Malaysian Ringgit)
    • Compute prices and costs in Baht and Ringgit and then translate the revenues and costs in Baht to Ringgit
    • To convert the Baht to Ringgit, use the expected future spot Ringet/Baht exchange rates
    • Since, as a practical matter, forward exchange rates are not available beyond 18 months, compute future spot rates from interest rate parity
    • Interest rate parity means that if you invest in risk free securities of different currencies, the spot exchange rate must reflect the future values.
valuation of subsidiary companies in different countries3
Valuation of Subsidiary Companies in Different Countries
  • How would things differ if we are valuing companies from different countries, different sectors etc.
  • Example of future expected spot exchange rates:
free cash flow
Free Cash Flow

We often talk about free cash flow, sometimes, it is challenging to assess what is "free“ cash flow or not, may wish to elaborate on that rather than just defining free cash flow in a text book term.

The basic point is to keep things consistent. If you define FCF as EBITDA without other income, then the valuation does not include other investments.

On the other hand if FCF is defined using Cash B/4 Financing that includes other income, the other investments are included in the valuation

in the money options and convertibles
In-the-money Options and Convertibles
  • Can the trainer also cover dealing with in-the money options and convertibles?
  • Convertibles can trade as straight debt if it is unlikely that the convertibles will be converted to common shares, or if the conversion option is in the money, it is clear that the convertibles will be switched into common shares. In this case, the ownership share of current shareholders is diluted.
  • If you buy the current shares, you are not really getting the whole company because you will have to give a share of the cash flow to the convertible bondholders.
in the money convertibles
In the Money Convertibles
  • Can the trainer also cover dealing with in-the money options and convertibles?
terminal value1
Terminal Value

Terminal value, and the use of a stable growth rate. How do you determine that, what is the rule of thumb and how do you determine which year onwards should be terminal year (i.e. how long should your forecasted period be).

On how to calculate a WACC, rather than just providing the formula of WACC, it would be useful to give instructions on where to find the market premium data, betas and what is the best method vs the most practical method.

  • Should we include country risk, exchange rate risks etc and how to get them.

Also there is no mentioning of cash revolver and how to calculate it.

lbo valuation
LBO Valuation
  • How can LBO’s be valued by making an assumption on target IRRs for the venture cap / private equity investor.
  • Recall the very first simple case that was developed in the class. In this case the equity IRR was driven by the level of leverage and the structure of the debt.
  • Valuation is realistically driven by the equity IRR criteria of developers and not free cash flow or WACC
  • The risk metric boils down to the debt capacity of the LBO and the value of the investment depends on the debt structure.
  • In this case, risk is driven by bankers outside of the company rather than the management or advisors to the company.
example of multiples to check valuation
Example of Multiples to Check Valuation

Used multiples to demonstrate that the valuation is not plausible

signals that you should sell
Signals that you should sell
  • Does the CEO have other board seats?
  • Has the company made takeovers of more than $250 million in the last 3 years?
  • Did the auditor grow up with the company?
  • Do finance writers call the CEO:

- ‘Whiz-kid’

- Dynamo

- Takeover King

- Breath of fresh air in the ‘old’ boardroom

  • Does the company sponsor the highest level of performing arts in the country?
  • Does the Chairman speak at more than 4 seminars a year?
  • Did the share price rocket because of some new technological breakthrough?
  • Has the company recently moved into a luxurious head office?
  • Is the company installing a state-of-the-art computer system?
  • Is the company diversifying into media, resources, high-tech?
  • Has the chief executive been praised by finance writers for innovative financings?
  • Has the chief executive been involved with a previous corporate collapse?
  • Does the Chairman have a private sauna in his office?

Source: Pierpont (Trevor Sykes) Australian Financial Review, 24 May 2002

finance professor
Finance Professor
  • A finance professor received a call from a large financial institution in New York, asking him to interview for a position on their scientific advisory committee. He agreed to go up and interview, knowing that such a position would be prestigious and with the extra income we would be able to purchase more consumer durables. As all of you know, interviews are a long and painful process. The interviews lasted two days and at the end of the last day the professor was interviewing with the chief executive who would ultimately be making the hiring decision. At the very end of the interview, the executive asked him, “what is 7 times 3?” The finance professor confidently responded, “22.”
  • When he got home from New York his family, for once, was eagerly awaiting his return… with lists of consumer durables in their hands. “How did it go?” they asked. “Good,” he said, “except in the last interview they asked me 7x3 and I said 22.” “Ohh! Dad!!!” they cried, “it’s 21!” They threw out their lists of consumer durables, knowing he would never get the job.
  • Much to his surprise he got a call 2 weeks later saying he’d gotten the position and the firm was having a reception in his honor. At the reception he found the executive and went up to him. “Do you remember our interview?” the professor asked. “Yes,” said the executive. “And do you remember when you asked me 7x3 and I said 22.” “Yes,” replied the executive, “I wrote down your answer.” “Well the correct answer is 21,” said the professor, “why did I get the job?” “Well,” said the executive, “of all the finance professors we interviewed… you were the closest.”
  • The moral of the story is, if I can do this, you can do this: pricing bonds and non-American options using monte carlo simulation to replicate the results achieved explicitly using decision trees.
finance professors
Finance Professors
  • A medical doctor, an engineer, and a finance professor are at a cocktail party.
    • The medical doctor pompously asserts that the medical profession is the oldest profession. He cites a passage from the Bible, in Genesis where god creates man and woman. “Surely,” he says, “this was the first medical act.”
    • The engineer jumps in and says, “I remember a passage prior to that, which says, out of the chaos and confusion, God created the earth. Surely, this was the first act of engineering and predates the first medical act.”
    • “Aha!” says the finance professor, “who created the confusion?!”
resources and contacts
Resources and Contacts
  • My contacts
    • Ed Bodmer
    • Phone: +001-630-886-2754
    • E-mail:
  • Other Sources
    • -- financial documents
    •;; -- stock prices and financial ratios
    •; – credit rating and other information
    • – credit spreads