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    DELIVERING PROCESS INNOVATIONApril 2004

    Training Material

    Investment Banking

    Valuation

    CONFIDENTIAL

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    1

    DCF Analysis: Overview

    The DCF analysis is based on the premise that ownership is essentially a claim on the cash flows

    generated by a firm's assets.

    The method entails estimating the unlevered free cash flows (FCF) available to all investors and

    discounting these cash flows back to the present using an appropriate cost of capital to arrive at a

    present value for the assets (Enterprise Value).The assets may be financed in a multitude of different ways but because the returns generated by

    these assets are available to all providers of capital, and to avoid distortions caused by a particular

    capital structure, the cash flows should be considered on an unlevered basis, i.e., free from

    financing considerations.

    The company's operations value (prior to adjustments for non-operating assets) can be broken

    down into 2 components:

    PV of free cash flows up to a cut point for terminal value calculation

    PV of terminal value

    The discount rate r is the Weighted Average Cost of Capital (WACC) which reflects the required

    returns by both debt and equity investors for investments with the same risk profile

    Summary Bullet

    Company value = PV(FCF) =

    n

    t=1

    FCFt

    (1+r)t+

    TV

    (1+r)n

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    DCF Analysis: Overview

    Discounted cash flow (DCF) analysis is a theoretical valuation technique which values acompany as the discounted sum of its:

    Unlevered (before financial costs) free cash flows (this is not operating cash flow) over someforecast period (usually 5 years), and

    Terminal value at the end of the forecast period (Year 5)

    Terminal Value

    Terminal value is the projected value of the company at the end of the forecast period. Terminalvalues are most often derived by assuming the business is sold for some multiple of earnings orcash flow. Alternatively, terminal values can be calculated based on the ongoing perpetualvalue of the companys cash flows beyond the forecast period

    Terminal values may be calculated in one of several ways:

    Comparable company multiples of Year 5 cash flow, operating income, net income, etc.

    Comparable acquisition multiples of Year 5 cash flow, operating income, etc.

    Perpetual value of cash flows after Year 5

    f Perpetual value = (final year free cash flow x growth rate)/(discount rate - growth rate)

    The cash flow stream and terminal value are discounted at the companys appropriateweighted average cost of capital

    Discount rates are generally based on the weighted average cost of capital of companies insimilar businesses to reflect the relative riskiness (i.e. variability) of the projected cashflows

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    DCF Analysis: The Process

    Step

    1

    Projections Project the operating results and free cashflows of a business over the forecast period.

    Step2

    Terminal Value Estimate the terminal value of the business,often by using exit multiples, at the end ofthe forecast period.

    Step

    3

    Discount Rate Use the weighted average cost of capitalto determine the appropriate discount raterange.

    Step

    4

    Present Value Determine a range of values for theenterprise by discounting the projected freecash flows and terminal value to the present.

    Step

    5

    Adjustments Adjust your valuation for all assets andliabilities not accounted for in cash flow

    projections.

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    Step 1: Projections

    The free cash flows from a business can be projected using information about the industry

    in which a business operates and information specific to the business.

    DCF analysis is an attempt to look at the companys pure operating results free and clear of

    financial leverage, extraordinary items, discontinued operations, etc.

    f It is also extremely important to look at the historical performance of a company or businessto understand how future cash flows relate to past performance.

    A companys discounted free cash flows represent the cash generating ability of a particular

    company, regardless of its capital structure. As a result, free cash flows are projected on an

    unlevered basis before subtracting interest and financing expense.

    DCF projections should be based on:f Historical performance

    f Company projections

    f Equity research analyst estimates

    f Industry data

    f Common sense

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    Step 1: Projections

    Components of Unlevered Free Cash Flow

    Unlevered Free Cash Flow is the unlevered after-tax cash flow generated by the Company (including the impact

    of any reinvestment). Free Cash Flow is available to all providers of the Companys capital, both creditors and

    shareholders

    Unlevered free cash flow is best determined by considering sources and uses of cash

    f It is free from financing considerations, i.e., it assumes that company is 100% equity financed

    EBIT

    - Taxes on EBIT

    + Depreciation and Amortization

    - Capex

    - Increase / (Decrease) in net working Capital

    - Any other change in the companys financials

    which cause the company to spend cash or to be a

    source of cash= Unlevered free Cash Flow

    Calculation of Unlevered Free Cash Flow

    Net Income

    + After-Tax Interest Expense

    + Deferred Tax Expense

    + Depreciation and Amortization

    - Capex

    - Increase / (Decrease) in net working Capital

    - Any other change in the companys financialswhich cause the company to spend cash or to be a

    source of cash

    = Unlevered free Cash Flow

    Calculation of Unlevered Free Cash Flow

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    Step 1: Projections Sanity Checks on FCF

    Confront sales growth assumptions with underlying market industry dynamics

    Does the increase in sales reflect a constant market share in an expanding market? If so, why

    is the market expanding? Does that assumption agree with industry projections? If it is an

    expanding market, why will the company be able to maintain a constant market share? Or does

    the increase reflect a rising market share in a stagnant market? If yes, why? Are some firmsleaving the industry? Why? etc.

    Check reasonableness of Gross and EBIT margins

    Avoid hockey sticks. Be clear on the required actions which will cause improvement in

    margins (or reasons for decrease in margins). Are the margin levels consistent with structure of

    competition? Any risk of new entrants/substitute products that will drive margins down? etc.

    Capital Expenditures

    Watch out for step-up of production capacity required as sales increase. Is CAPEX level

    sufficient for increase in sales? Factor in impact of industry trends on CAPEX (i.e., increased

    environmental expenditures, technology changes, etc.)

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    Step 1: Projections Sanity Checks on FCF

    Working Capital

    Are inventory and other working capital forecasts consistent with the sales increase?

    What is the pattern in receivable collection period? How is it practically achieved?

    Assess bargaining power of customers (receivable terms) and suppliers (account payables) Are your assumptions in line with industry standards? etc.

    Be Critical About Buyer and Seller's Projections

    Use due diligence/access to seller's management to gain in-depth understanding of company's

    assumptions and challenge them, (if appropriate) on the basis of your analyses

    Compare also for instance company's past record of actual versus budgeted results.

    Add value/ manage client's expectations (both on buy and sell sides) by thorough

    understanding of the company's market dynamics and competitive positioning.

    Be Realistic About Synergies

    When developing a business case, avoid general optimistic statements about synergies. Be as

    specific as possible about nature and level of cost savings.

    Take into account time to implement cost cuttings/achieve synergies

    Consider also costs related to merger such as severance pay, plant shutdown costs that can

    diminish synergy benefits.

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    Step 2: Determination of Terminal Value

    Terminal Value Calculation

    Since DCF analysis is based on a limited forecast period, a terminal value must be used to

    capture the value of the company at the end of the period. The terminal value is added to the

    cash flow in the final year of the projections and then discounted to the present.

    A company value, based on expected FCF, can be separated into two components:

    The second component is the continuing or terminal value.

    The ideal DCF analysis forecasts free cash flows far enough into the future (e.g., 20 years or

    more) so that the present value of the terminal value does not constitute a large percentage

    (e.g., over 40%) of firm value Terminal value can be estimated using exit multiples, cash flow approaches (perpetuity formula)

    or other approaches such as liquidation or break-up value, replacement cost, etc.

    Company

    Value

    Company

    Value

    PV of FCF

    during explicit

    forecast period

    PV of FCF

    during explicit

    forecast period

    PV of FCF

    afterexplicit

    forecast period

    PV of FCF

    afterexplicit

    forecast period= +

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    Step 2: Determination of Terminal Value

    Comparable Multiples Method

    Use multiples that produce an enterprise value.

    Litmus test: Has interest been subtracted before I arrived at this figure?

    f If yes: the multiple gives EQUITY value (for instance, BV)

    f If no: the multiple gives an ENTERPRISE value (Sales, EBITDA, EBIT)

    Exit strategy in final forecast year drives the selection of multiples

    f IPO assumption: Comparable company trading multiples

    f Sale assumption: Comparable acquisition multiples

    Typically final years EBITDA is used

    Commonly used method because conceptually easy to implement and to explain.

    Be aware of circular reasoning (I am putting a value on what I am trying to value!) and theoretical

    difficulties in predicting multiples at the end of the forecast period.

    Provide a range of multiples (i.e., implied valuation for say 6.0x, 7.0x and 8.0x EBITDA) to increase

    reasonableness of results.

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    Step 2: Determination of Terminal Value

    FCF Perpetuity - Growth Rate Method

    Perpetuity formula based calculations implicitly assume that you will own the company and be

    entitled to the FCF to perpetuity (theoretically more correct than multiple approach).

    Assuming that Cash Flow after explicit forecast period grow at a constant rate, the value of the

    terminal value is given by the growing FCF perpetuity formula:

    FCFn: Free Cash Flow in year n

    TVn = FCFn*(1 + g)

    r - g

    r: Discount rateg: Perpetual growth rate of FCF

    n: Forecast horizon (terminal year)

    Perpetual growth rate must be realistic. It can be estimated as the expected long-term rate of

    consumption growth for the industry's products plus inflation (starting point could be forecasted

    nominal GNP growth). Cross check the reasonableness of your terminal value calculation by linking the multiple and

    perpetuity methods (i.e., calculate implied perpetual growth rate for a range of EBITDA multiples

    or conversely check how the perpetual growth rate translates into EBITDA multiples) at different

    discount rates.

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    Step 3: Determination of Discount Rate

    The discount rate is a function of the risk inherent in any business and industry, the degree

    of uncertainty regarding the projected cash flows, and the assumed capital structure.

    In general, discount rates vary across different businesses and industries.

    The greater the uncertainty about the projected cash flow stream, the higher the appropriate

    discount rate.

    Providers of capital (both debt and equity investors) in any given industry require returns

    commensurate with the perceived riskiness of their investment.

    The best measure of the riskiness of projected cash flows and the best way to determine

    the correct range of discount rates is the weighted average cost of capital (WACC) of

    similar businesses. WACC should be thought of as the opportunity cost of capital, the return an investor expects to

    earn in an alternative investment of equivalent risk.

    The WACC to be used in a DCF analysis is specific to the asset being valued, and should

    depend neither on how the asset will be financed nor on the potential buyers or sellers cost of

    capital.

    The relative weights applied to the costs of equity and debt used in computing WACC for

    an asset represent the optimal capital structure for that asset

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    Step 3: Weighted Average Cost of Capital

    (WACC)

    Mathematical Expression of WACC

    Intuitively, we have to pay our equity holders their required rate of return and we have to pay ourdebt holders their required rate of return.

    f Because dividends the theoretical absolute return to an equity holder are not tax-deductible, our true cash cost of equity is reflected as a pre-tax result.

    f Because interest the return to a debt holder is tax-deductible, our true cash cost of debt isreflected as an after-tax result.

    To determine the WACC of a company, one must ascertain for a target capital structure, thecosts of the various sources of capital for the company.

    (1)Assumes capital structure is only debt and equity. Other sources of capital (i.e. preferred stock) would need to be included if present.

    (2)Cost of Equity calculated using the Capital Asset Pricing Model (CAPM).

    (3)Assumes beta of debt is zero.

    Correct formula is: BetaUNLEV EQ = BetaDEBT x (D x [1 t]) / [E + D x (1 t)] + Beta LEV EQ x E / [E+ D x (1-t)].

    WACC(1) = xProportion of Debt

    in Capital Structure +Cost of

    Equity xProportion of Equity

    in Capital Structure

    After-tax

    Cost of Debt;

    ;Cost ofEquity(2) = Risk-FreeRate LeveredBeta+ x Equity Market Risk Premium

    (3)1 + (1 - Tax Rate) x (Debt/Equity Ratio)=

    Unlevered

    BetaxLevered

    Beta

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    Step 3: WACC Target Capital Structure

    Prior to calculating the cost of equity and debt for the company you are valuing, you need to define a

    target capital structure based on the appropriate market value weights (i.e., D/D+E and E/(D+E)) for the

    WACC calculation. The target capital structure should reflect the debt to equity ratio that is expected to

    prevail over the life of the business.

    You can use a combination of the following three approaches:

    Estimate the current market value based capital structure of the company.

    f Estimate the market values of the debt and equity components of the capital structure and review how they

    have changed over time. If a company's common stock is publicly traded and its other source of financing is

    traded corporate bonds, just multiply the number of each type of outstanding security by its respective

    market price. If the debt is not traded, estimate the market value by comparing with publicly traded similar

    debt. If the company is not traded, use the other two approaches.

    Review the structures of comparable companies.

    f Assess the average market capital structure prevailing in the company's sector, which provides a good

    indication of a capital structure for your company.

    Review the management's financing philosophy.

    f When possible, discuss with the management their financing policy and their explicit or implicit target capital

    structure on a normalized basis. If you don't have access to management, look for any statements in press,

    research reports, annual report, etc. that give hints on the company's medium to long term financing

    objectives.

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    Step 3: WACC Conceptual Issues

    Various challenges exist in calculating a cost of capital that is entirelyconsistent with finance theory. In reality most practitioners use judgment andapproximations. Some of the issues one comes across often:

    The Risk Free Rate

    f Theory recommends using a true risk-free rate that has the same term as the cash flowsprojected.

    f Since long bond rates have intrinsic interest rate risk factored in, theorists suggest making aliquidity adjustment to the long bond rate representing the term premium implicit in thoserates. This is, however, rarely done in practice by Wall Street.

    The equity risk premium

    f The equity risk premium must be consistent with the risk-free rate. For example, if your riskfree rate is the 20-year bond, the risk premium must represent return in the equity marketrelative to the 20-year bond.

    f Ibbotson, the most commonly referred-to source, uses actual annual stock market returnssince 1926 to compute the equity risk premium. Some argue that use of this period over-estimates the premium, and that data over a more recent period would suggest a lowerpremium.

    f Equity premia from as low as 3.5% to 8.0% are used on the Street.

    Goldman Sachs Equity Research: 3.5%

    CSFB Equity Research (April 1999): 4.3%

    Ibbotson (long-term, from 19261998): 8.0%

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    Step 3: WACC Conceptual Issues

    Various challenges exist in calculating a cost of capital that is entirelyconsistent with finance theory. In reality most practitioners use judgment andapproximations. Some of the issues one comes across often:

    Beta

    f Beta represents a measure of the systematic (as opposed to unique or diversifiable) risk thatexists in an asset, and is central to the CAPM.

    f Beta = COV[Rasset, Rmarket] / VAR[Rmarket], or equivalently

    = CORR[Rasset, Rmarket] x STDasset / STDmarket

    f Historical betas of publicly traded equity securities can be calculated based on an analysis ofthe actual returns on the security vs. the actual market returns.

    f Unfortunately, historical betas can be poor predictors of expected beta, which is what weneed in our analysis.

    f BARRA, a financial research firm to which CSFB subscribes, computes predicted betas forpublic companies.

    f There are many sources for beta: BARRA, Bloomberg, Value Line.

    Levering / Unlevering Beta

    f Observed betas of companies are by definition levered (to the extent the companies havedebt). Unlevering is required to arrive at the beta of the assets (as opposed to the equity) ofthe company.

    f Increasing leverage will, according to theory, increase the beta of a firms equity and henceits cost of equity. Theorists differ on the most appropriate adjustments to make for theeffects of leverage.

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    Step 3: WACC Unlevering Beta

    The formula presented previously is the one we use at CSFB and is perhaps the most widely recognized(and also the simplest).

    unlevered = U =

    Where: is the tax rate

    Dcomp the market value for the debt and

    Ecomp the market value of the equity

    The comp is based on market returns, not book returns. That is why you should unlever this using themarket value of equity and debt for the comparable.

    If the market value of debt is not easily calculated, use the book value of debt.

    Once you have the u for the company, you have to relever it with the debt to equity ratio you have chosen foryour company or asset:

    f levered=u* (1+(1- ) * D/E)

    f where D/E is our target debt to equity ratio

    + *)-(11

    compE

    compD

    comp

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    The Recommended Way

    In practice we make the following assumptions:

    Risk Free Rate

    f 30 year US Treasury coupon bond yield for US WACC calculation. WACC calculation forinternational assets, particularly emerging market assets, is harder and has to be consideredon a case-by-case basis.

    Tax Rate

    f Marginal tax rate (usually 35%).

    Cost of Debt

    f Risk free rate + current corporate spread over treasury for comparable credits.

    Optimal Debt/Equityf Average of ratio of debt and equity market capitalization of selected comparable companies.

    Beta

    f Simple average of unlevered predicted betas of comparable companies as derived fromBARRA levered predicted betas (available on-line).

    Equity Market Premium

    f Ibbotson equity market premium (approx 8.0%), calculated based on historical return ofequity market relative to 30 year treasury bond.

    In general, WACC calculation is not a science; there are no exact answers, judgment andreality checks are essential

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    Step 4: Present Value

    Time Value of Money A dol lar today is worth more than a do llar tomorrow.

    Discounting The process of finding the present value of a future sum

    Very Simple Example (Assume the WACC is 10%.)

    The total NPV is the sum of the present values of the individual cash flows.

    The NPV calculation assumes that cash flows occur at the end of the period.

    Assuming that cash flows are received at mid year (i.e., spread evenly over the

    year) comes down to moving all cash flows by half a period

    This amounts mathematically to multiplying by (1+WACC) the NPV calculation.

    Mechanicsof

    Discounting

    Mid-YearConvention

    Year 1 2 3 4 5

    Cash Flow $10.0 $15.0 $20.0 $24.0 $30.0

    Discount Rate 10%

    Discount Factor 0.909 0.826 0.751 0.683 0.621

    Disconted Value $9.09 $12.40 $15.03 $16.39 $18.63

    NPV $71.53

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    Step 5: Corporate Adjustments

    DCF analysis calculates the Enterprise Value (Adjusted Market Value) of a company.

    The Equity Value (Market Value) of a company is the Enterprise Value less Corporate

    Adjustments.

    Corporate Adjustments include the companys net debt plus other obligations, less other

    assets not included in the DCF

    The Equity Value per diluted share is the Equity Value divided by the number of fully-diluted

    shares.

    Number of diluted shares = Basic shares + shares underlying in the money exercisableoptions / warrants + shares from the conversion of in the money convertible debt and

    convertible preferred stock

    Incremental common-equivalent shares are typically calculated using the treasury stock

    method.

    Value ofthe Company

    Contingent Liabilities+

    Capitalized Leases+

    Value of other assets not in DCFPreferred Stock+

    Investments in AffiliatesMinority Interest+

    Cash EquivalentsShort Term debt+

    CashLong Term Debt (including current portion)+

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    Conclusions

    The commonly used DCF method consists in estimating the after tax free cash flows available

    to all investors and discount them back to the present at the Weighted Average Cost of Capital

    (WACC)

    The DCF analysis is as good as the projections used. You should step back from the numbers

    by doing repetitively sanity checks and thinking through the implications of your assumptions

    Produce a set of sensitivity analysis on the key model variables to bound the company's

    (intrinsic) value

    Particular care should be given to the last year of the explicit forecast period and the calculation

    to the terminal value as it often represents a significant portion of the total value of the company.

    Terminal value can be calculated using exit multiples and perpetuity approaches. Ideally, you

    should develop the two approaches independently and compare the results obtained

    The WACC reflects the opportunity cost for each type of investors, i.e., the respective rates of

    return these investors could expect to earn on other investments of equivalent risk. The Capital

    Asset Pricing Model (CAPM) establishes a simple relationship between risk and return which

    allow to estimate the cost of equity of a project/company for a given risk level

    The value obtained by discounting the free cash flow and the terminal value should be adjustedfor non-operating assets or liabilities to yield the firm's asset value. The equity value is then

    derived by deducting all non working capital debt and obligations