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    ONCE MORE, THE CORRECT DEFINITION FOR THE CASH FLOWS TO VALUE A FIRM

    (FREE CASH FLOW AND CASH FLOW TO EQUITY)

    Ignacio Vlez-Pareja

    Master ConsultoresCartagena, [email protected]

    I wish to thank the comments received from

    Hugo Berlingeri ([email protected]), Ricardo Botero ([email protected]), Edinson Caicedo([email protected], [email protected]), Juan Carlos Gutirrez ([email protected]) y Eduardo

    Petracca ([email protected]).Any mistake is my entire responsibility.

    First version: January 3, 2004This version: August 5, 2013

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    ABSTRACT

    This paper is an extension of a previous one untitled The Correct Definition for the CashFlows to Value a Firm (Free Cash Flow and Cash Flow to Equity) 1. We have added a comparativeanalysis between the current practice of including as cash flows amounts that belong to the Balance Sheetand the proposed approach to include only as cash flows those elements that in fact are cash flows and

    hence are not listed in the Balance Sheet. Differences are significant.Surprisingly there is a wide range of interpretations on how to calculate the cash flows forvaluation purposes. This ample definition of what the cash flows are is shared by academicians and

    practitioners. Some of the definitions openly contradict the essential and basic concepts of cash flowand time value of money.

    This work analyzes the definition of cash flows for valuation (free cash flow and cash flow toequity). We examine the empirical evidence in the recent literature and we present a comparative analysis

    between the current practice of including as cash flows amounts that belong to the Balance Sheet and theproposed approach to include only as cash flows those elements that in fact are cash flows and hence arenot listed in the Balance Sheet. Differences are significant.

    We analyze the evidence reported in the literature that liquid assets items in the balancesheet (potential dividends) do not contribute to value creation and hence should not be included in

    the cash flows. This fact reinforces previous arguments on the inconvenience of adding the changein liquid assets as part of the cash flows for firm valuation. Tham and Vlez-Pareja (2004), Vlez-

    Pareja (1994, 1997, 1998, 1999, 2004a, 2004b y 2006)have asserted that liquid assets items found inthe Balance Sheet (BS) should not be considered as cash flows for firm valuation. On the otherhand, some respected authors (Copeland, et al, 1995, 2000, Benninga et al. 1997, and Damodaran,2004, Jensen, 1986, Brealey et al, 2003, Copeland and Weston, 1988, among many others) supportthe idea that the CFE has to include potential dividends. This definition openly contradict the

    essential and basic concepts of cash flow and time value of money. Pinkowitz, Williamson andStulz, (2007) and Pinkowitz and Williamson (2002) present findings related to firms in developedand emerging countries where there is some minor relationship of cash holdings with the MV/BV

    ratio.

    In this work we specify very clearly what has to be included in those cash flows and the

    reasons why they should be included.The main issue is related to the inclusion or exclusion of some items in the working capitaland the current practice to consider that funds that appear in the Balance Sheet (cash and marketsecurities and the like) belong to the free cash flow FCF and the cash flow to equity CFE. In thesame line of reasoning, the idea is that cash flows have to be consistent with financial statements.With a hypothetical example we show the implicit financial facts reflected in the financialstatements behind the practice of including as cash flow items that appear in the Balance Sheet.

    KEY WORDS

    Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cashbudget.

    JELCLASSIFICATION

    M21, M40, M46, M41, G12, G31, J33

    1 Available at www.ssrn.com

    ii

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    ONCE MORE,THE CORRECT DEFINITION FOR THE CASH FLOWS TO VALUE A FIRM(FREE CASH FLOW AND CASH FLOW TO EQUITY)

    INTRODUCTION

    This paper is an extension of a previous one untitled The Correct Definition for the

    Cash Flows to Value a Firm (Free Cash Flow and Cash Flow to Equity)2. We have added a

    comparative analysis between the current practice of including as cash flows amounts that

    belong to the Balance Sheet and the proposed approach to include only as cash flows those

    elements that in fact are cash flows and hence are not listed in the Balance Sheet.

    Differences are significant.

    Surprisingly there is a wide range of interpretations on how to calculate the cash flows

    for valuation purposes. This ample definition of what the cash flows are is shared by

    academicians and practitioners. Some of the definitions openly contradict the essential and

    basic concepts of cash flow and time value of money.

    In this note we specify very clearly what has to be included in those cash flows and the

    reasons why they should be included.

    The main issue is related to the inclusion or exclusion of some items in the working

    capital and the current practice to consider that funds that appear in the Balance Sheet (cash

    and market securities and the like) belong to the free cash flow FCF and the cash flow to

    equity CFE. In the same line of reasoning, the idea is that cash flows have to be consistent

    with financial statements. With a hypothetical example we show the implicit financial facts

    2 Available at www.ssrn.com

    3

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    reflected in the financial statements behind the practice of including as cash flow items that

    appear in the Balance Sheet.

    We analyze the evidence found in the recent literature and it shows that liquid assets

    in the Balance Sheet (BS), called by some "potential dividends", do not contribute to the

    creation of value and therefore should not be included in the cash flows. This reinforces

    arguments discussed by some authors about the inconvenience of adding the change in

    liquid assets to cash flows for firm valuation. Tham and Vlez-Pareja (2004), Vlez-Pareja

    (1994, 1998, 1999, 2004) have claimed that the liquid assets that are in the BG should not

    be regarded as cash flows and that the most straightforward approach to derive the cash

    flows is starting from the cash budget3. On the other hand, some highly respected authors

    (Copeland, et al, 1995, 2000, Benninga et al. 1997 and Damodaran, 2004, Jensen, 1986,

    Brealey et al, 2003, Copeland and Weston, 1988, among others) argue the idea that the

    equity cash flow should be included as "potential dividends". This definition contradicts the

    basics and essentials of what a cash flow and the concept of the value of money over time.

    Pinkowitz, Williamson and Stulz (2007) and Pinkowitz and Williamson (2002) present

    empirical evidence on developed and emerging countries where there is a relatively minor

    relationship between holdings of liquid assets and the ratio MV/BV or Tobin's Q.

    The literature shows that holding liquid assets destroys value or at most do not

    create a significant amount of value. Schwetzler and Reimund (2003) report that in

    Germany persistent excessive cash holdings lead to a significant operating

    underperformance [] in line with expectations of the agency theory (p. 25).4 Harford

    3The cash budget is a financial statement where every inflow and outflow is listed and the difference is the period

    net cash flow. The accumulated balance resulting form the net cash flow has to match with the cash on hand found

    in the Balance Sheet.4 Italics ours from now on, unless otherwise specified.

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    (1999)5 finds that cash-rich bidder destroys seven cents of firm value for every dollar of

    excess cash held (p. 1983) and says that the stock market appears to partially anticipate

    this behavior, as evidenced by the negative stock market reaction to cash stockpiling. (p.

    1972). Finally, he says that one might expect that stockpiling cash would be greeted

    negatively by the market (p. 1992). Opler, Pinkowitz, Stulz and Williamson (1999) say

    that holdings of liquid assets can make shareholders worse offin some circumstances (p.

    2). Finally, they write that investing in cash can therefore have an adverse effect on firm

    value. To put it another way, increasing firms holdings of liquid assets by one dollarmay

    increase firm value by less than one dollar (p. 11). Faulkender and Wang (2004) find that the

    marginal value of cash declines with larger cash holdings (p. 2).

    On the other hand, Mikkelson (2003) concludes that persistent large holdings of

    cash and equivalents have not hindered corporate performance, (p. 2) and that there is no

    evidence that large firms with lower insider stock ownership, higher inside board

    composition, or a controlling founder perform differently than other large cash firms (p.

    20).

    This said, it is counter evident that what destroys value (keeping cash) by some

    manipulation, ends up creating value as when cash flows are inflated assuming full

    distribution when the firm keeps cash and quasi cash in its Balance Sheet.

    It is important to say that the context of this paper is for nontraded firms. When the

    firms are traded, and the assumptions of a perfect market are met, it could be shown, using

    arbitrage arguments, that the value is the same if the firm distributes or not the cash excess.

    5 Quotations from this author are taken from the SSRN version, 1997.

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    SOME CONSIDERATIONSREGARDING THE TYPICAL PRACTICE

    Some respected authors (Copeland, et al, Benninga et al.6 and Damodaran) support

    the idea that the CFE has to include potential dividends.7 On the other hand, professor

    Damodaran has, in some slides found at his website, excellent arguments to favor the idea that

    the CFE has to include just what the stockholders actually receive, however, he

    disregards those arguments and keep using the idea that CFE is what is available (even if it is not

    paid to the equity holder).8

    Our position is very simple: cash flow implies movement of cash (except when we

    consider the opportunity cost of some asset and then we include that value as a cash flow)

    hence funds tied to the balance sheet cannot be considered a cash flow. Hence, the strict

    definition of CFE is dividends plus repurchase of stock and minus equity investment.

    Some other arguments to reinforce this idea are:

    1. To consider as cash flow items that are listed in the balance sheet is to denythe basic concept in valuation: the time value of money. We discount cash

    flows when they are received. It is a contradiction to say that an item is at

    the same time a line in the balance sheet and a line in the cash flow.

    2. The use of potential dividends is in clear contradiction with the CapitalAsset Pricing Model, CAPM. When the CAPM is used to estimate the cost

    of equity, Ke, we use dividends paid; we never use potential dividends. We

    never add to the dividends use to calculate the return of a stock the items in

    6 Benninga says: [] Free Cash Flow (FCF) a concept that defines the amount of cash that the firm candistribute to security holders. [] Cash and marketable securities are the best example of working capital items

    that we exclude from our definition of [change in net working capital] adjustment.7 Professor Tom Copeland in a private correspondence says: If funds are kept within the firm you still own them -

    - hence "potential dividends" are cash flow available to shareholders, whether or not they are paid out now or in the

    future.8 See the transcription of the relevant slides in the Appendix

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    the balance sheet listed as cash in hand and marketable securities. More. If to

    estimate the cost of capital we depart from the betas found in the market,

    they capture the risk of the stock using paid dividends and the value the

    market assign to the stock discounting the future dividends.

    It is argued that when cash excess is invested in market securities, then we

    are facing cash flows with net present value of zero because those flows are

    discounted at the same rate of return the securities earn. This is not

    reasonable because precisely the beta coefficient captures the risk of paid

    dividends, and the dividends are a function of the net income, that includes

    the return received from those market securities investments; hence in the

    beta coefficient we are counting the larger or smaller risk associated to the

    market securities.

    3. The same idea of Miller y Modigliani, M&M, 1961, about the irrelevance of

    dividends should deter that practice. Even if dividends are not paid the value

    is captured in the terminal value, TV. Then it is not clear at all why we

    should insist on using as CF what it is not. For traded firms it is possible to

    use arbitrage arguments to show that it is the same to distribute or not the

    cash excess and even to invest them at higher or lower rates of return.

    4. Our position is that there should be a complete consistency between cash

    flows and financial statements. If we say that every penny available belongs

    to the cash flow to the equity holder (CFE), then that fact should be reflected

    at the financial statement. Below we show what might happens in a simple

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    example when the payout ratio is 100% and any excess cash is distributed

    instead of being invested in market securities, for instance.

    5. When including the excess cash invested in marketable securities and cash

    as part of the CFE we are distorting the taxes. In fact we are. Instead of

    generating an explicit return (usually very low) that is taxed in the income

    statement, we generate a virtual return at the cost of equity, Ke, that is not

    taxed in reality. Here we understand as virtual return that return obtained

    implicitly when the cash flows are paid to the owners of the capital (euity or

    debt). This virtual or implicit return is one of the implicit assumptions when

    we discount cash flows. This is an old proposal from Lorie and Savage (see

    Lorie and Savage (1955)). When we assume that some funds are invested at

    a rate that usually is lower than the discount rate, and yet we incluye those

    funds in the cash flow, we are assuming implicitly that those cash flows are

    reinvested at the same discount rate we use to discount them, but those

    implicit returns never are taxed.

    Here it is important to say take into account the following: cash flows are

    what the firm pays to the owners of capital, be it debt or equity. When those

    cash flows are in the hands of the equito or debt holders it is ASSUMED that

    they invest at their own required rate of returns (it is possible that they invest

    those cash flows in investment with higher rates than the required ones). The

    problem arises when THE FIRM DOES NOT PAY the cash flows to the

    equity holders the funds that are tied either to cash in hand or to market

    securities. If those funds are in the cash flows, it is as if the equity holders

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    have received them, but they have not, and when we discount the flows at

    the discount rate be it the cost of levered equity, Ke, or the weighted average

    cost of capital (WACC), the implicit assumption is that the equity holders

    invest the cash flows at their required cost of capital and it is not true

    because they have not received those funds. (the funds are investid in market

    securities). It might sound as a paradox but, the firm is worth because the

    capital owners withdraw funds from the firms. The value of the firm is in the

    cash flows that go out of it and not in the funds that remain within the firm.

    The outflows (the CFD and the CFE adjusted by tax savings) from the firm

    are the free cash flow!

    6. When we add the cash in hand and the marketable securities listed in the

    balance sheet we are concealing a potential wrong financial management

    practice. This is to say that if we model a firm as we expect as it will happen in

    the future and if in that future it is expected that excess cash is invested and

    low rates (even at zero interest if the funds are kept at hand) and at the same

    time we include the invested funds in the CFE we are concealing a financial

    malpractice. In other words, it would mean that it would be the same to have

    the excess cash invested at high or low rates.

    There is some empirical evidence that dividends and not cash in hand or invested in

    market securities is what increases firm value. Data from Pinkowitz, Williamson and Stulz,

    (2007) present evidence of this fact. Data cover ten years with some exceptions such as

    India, Philippines, Turkey and Peru. Market Value to Book Value (MV/BV) is the sum of

    market equity value plus book value of debt divided by book value of assets. Dividends and

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    Cash and market securities is the percent of those items in the Balance Sheet on total assets. We

    have run a simple linear regression between MV/BV, Cash and market securities and

    dividends. See table and statistical analysis below.

    The values in the table are the mean of the medians for each variable for each

    country.

    Table 1a. Dividends, Cash & market securities and MV/BV by country

    Country Dividends Cash MV/BV

    Argentina 0.013 0.065 0.769

    Australia 0.023 0.044 1.013

    Austria 0.009 0.066 0.758

    Belgium 0.013 0.089 0.809

    Brazil 0.006 0.047 0.586

    Canada 0.007 0.026 0.967Chile 0.045 0.046 1.125

    Denmark 0.009 0.138 0.889

    Finland 0.009 0.08 0.817

    France 0.008 0.085 0.711

    Germany 0.011 0.056 0.822

    Greece 0.026 0.037 1.164

    Hong Kong 0.029 0.102 0.834

    India 0.014 0.025 1.301

    Ireland 0.014 0.094 0.947

    Italy 0.01 0.089 0.655

    Japan 0.005 0.16 1.014Korea (South) 0.004 0.064 0.783

    Malaysia 0.014 0.055 1.344

    Mexico 0.007 0.057 0.972

    Netherlands 0.014 0.048 0.813

    New Zealand 0.024 0.015 0.969

    Norway 0.006 0.119 0.897

    Peru 0.011 0.048 1.046

    Philippines 0.003 0.076 1.29

    Portugal 0.009 0.025 0.763

    Singapore 0.013 0.138 1.013

    South Africa 0.025 0.056 0.893

    Spain 0.014 0.039 0.808Sweden 0.013 0.092 0.861

    Switzerland 0.011 0.108 0.821

    Thailand 0.021 0.026 1.174

    Turkey 0.042 0.094 1.389

    UK 0.024 0.062 0.997

    USA 0.008 0.044 1.151

    Source: Pinkowitz, Williamson and Stulz, (2007)

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    The regression with MV/BV as dependent variable and the other two variables as

    independent variables, Cash and market securities leaves the model for statistic

    significance. When the regression is run with only dividends and MV/BV the result is

    Table 1b. Coefficient and significance of MV/BV dependent variable

    Coefficients Probability

    Intercept 0,83040682 4,7122E-16

    Dividends 7,97813497 0,01806838Critical value for F is 0.01806838

    In other words, cash in hand or invested in market securities do not increase the firm

    value. What increase that value are dividends paid to equity holders. Potential dividends

    does not mean more value for equity holders although including them in the analysis as

    cash flows for valuation the resulting value is greater than when they are not included.

    Tham and Vlez-Pareja (2004) propose explicitly to include in the CFE only the

    cash that is received or distributed to the equity holder. The approach departs from the cash

    budget, CB statement. In this financial statement they present four modules or sections.

    Two of these sections include the transactions with debt and equity holders. From there the

    CFE and the cash flow to debt, CFD can be derived straightforward. The financial

    statements and the cash flows are completely integrated. This allows the analyst to see

    what is going on. As can be seen below in a simple example, when total excess cash is

    distributed then initial equity could be reduced and eventually reach negative values.

    Would a financial analyst dare to present a financial model where equity becomes

    negative? We are sure she will not.

    AN EXAMPLE9

    This is an example where the book value leverage D% affects the growth of the firm

    and the accounts payable conditions. The higher the D% the lower the growth and the

    9 This example is available directly from the author, but titles are in Spanish.

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    stringent accounts payable conditions (when D% is higher than a given value, (for instance, the

    average in the industry) the suppliers require payment more quickly and customers fear that

    the firm will not honor its delivery and might go to the competition).

    Next we show the Balance Sheet and the Cash Budget. We indicate the derivation of the

    CFE and the cost of equity, Ke, as well.

    Table 2a. Cash Budget, CB when payout ratio is 100% and any excess cash in invested in

    market securities.Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Taxes 0.0 121.7 1,161.0 2,298.6 3,683.5 2,242.6

    Operating net cash flow -46,680.0 15,461.6 16,080.6 16,906.8 -38,026.1 22,253.5

    Module 2: External financing

    Loan 1 LT 16,632.7Loan 3 LT 29,961.0

    Loan 2 ST 0.0 0.0 0.0 0.0 1,955.4

    Loan in foreign exchange 16,632.7

    Payment of loans

    Loan 1 LT 3,326.5 3,326.5 3,326.5 3,326.5 3,326.5

    Loan 3 LT 0.0 0.0 0.0 0.0 5,992.2

    Loan 2 ST 0.0 0.0 0.0 0.0 0.0

    Loan in foreign exchange 3,457.0 3,547.8 3,684.0 3,784.9 3,881.5

    Interest paid 0.0 3,654.2 3,003.2 2,154.9 1,465.8 4,158.0

    Net cash flow after financialtransactions -13,414.6 5,023.9 6,203.1 7,741.4 -16,642.2 6,850.7

    Module 3: Transactions with the

    equity holderEquity investment 15,000.0

    Payment of dividends 0.0 226.0 2,156.2 4,268.8 6,840.7

    Repurchase of shares 0.0 0.0 0.0 0.0 0.0

    Net cash flow after Transactions with

    the equity holder 1,585.4 5,023.9 5,977.1 5,585.2 -20,911.0 10.0

    Module 4: Discretional transactions

    Market securities recovery 0.0 0.0 6,509.3 12,971.7 19,534.1 0.0

    Interest from market securities 0.0 0.0 495.4 987.1 1,386.9 0.0

    Investment in market securities 6,509.3 12,971.7 19,534.1 0.0 0.0

    Net cash flow after discretional

    transactions 1,585.4 -1,485.4 10.0 10.0 10.0 10.0

    Net cash balance at the of year 1,585.4 100.0 110.0 120.0 130.0 140.0

    We have listed the taxes paid in order to compare how taxes change when one or

    another method is used.

    Now we show the Balance Sheet

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    Table 2b. Balance Sheet, BS when payout ratio is 100% and any excess cash is invested in

    market securities.

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Assets

    Cash on hand 1,585.4 100.0 110.0 120.0 130.0 140.0

    Accounts receivable 0.0 2,440.8 2,617.6 2,835.0 3,055.9 3,294.5Inventory 1,680.0 1,937.9 2,094.1 2,228.6 2,311.1 2,425.9

    Market securities 0.0 6,509.3 12,971.7 19,534.1 0.0 0.0

    Current assets 3,265.4 10,988.0 17,793.5 24,717.7 5,497.0 5,860.3

    Net fixed assets 45,000.0 33,750.0 22,500.0 11,250.0 56,193.2 42,144.9

    Total 48,265.4 44,738.0 40,293.5 35,967.7 61,690.2 48,005.2

    Liabilities and equity

    Accounts payable 0.0 2,377.9 2,514.3 2,678.0 2,777.0 2,916.2

    Short term debt ST 0.0 0.0 0.0 0.0 0.0 1,955.4

    Current liabilities 0.0 2,377.9 2,514.3 2,678.0 2,777.0 4,871.5

    Debt in domestic currency 16,632.7 13,306.1 9,979.6 6,653.1 33,287.6 23,968.8Debt in foreign currency 16,632.7 13,828.0 10,643.4 7,367.9 3,784.9 0.0

    Total Liabilities 33,265.4 29,511.9 23,137.3 16,699.0 39,849.5 28,840.3

    Equity 15,000.0 15,000.0 15,000.0 15,000.0 15,000.0 15,000.0

    Retained earnings 0.0 226.0 2,156.2 4,268.8 6,840.7 4,164.9

    Total 48,265.4 44,738.0 40,293.5 35,967.7 61,690.2 48,005.2

    D% (book value) 68.92% 60.65% 51.18% 38.98% 60.09% 54.00%

    Check 0.0 0.0 0.0 0.0 0.0 0.0

    From Module 3 at the CB we construct the CFE:

    Table 3. CFE with 100% payout reinvestment of excess cash in market securities

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Equity investment 0.0 0.0 0.0 0.0 0.0

    Payment of dividends 0.0 226.0 2,156.2 4,268.8 6,840.7

    Repurchase of shares 0.0 0.0 0.0 0.0 0.0

    CFE 0.0 226.0 2,156.2 4,268.8 6,840.7

    TV debt 32,112.0

    CFE with TV for CFE 0.0 226.0 2,156.2 4,268.8 38,952.7

    Ke 19.90% 17.99% 16.96% 15.70% 16.83%

    Levered equity 21,109.0 25,310.0 29,636.9 32,506.8 33,342.5

    Observe that the CFE is derived directly from Module 3 in the CB (except the

    terminal value at year 5 and Ke, calculations not shown).

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    The values for equity and firm (calculation not shown) are: equity value is 21,109.0

    and firm value is 54,374.4 that is equal to equity value plus debt.

    Table 4. Cash Budget, CB when layout ratio is 100% and any excess cash is paid to theequity holder.

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Taxes 0.0 121.7 987.7 1,953.1 3,198.0 1,446.3

    Operating net cash flow -46,680.0 14,556.7 15,051.9 17,042.6 -38,880.0 20,839.5

    Module 2: External financing

    Loan 1 LT 16,632.7

    Loan 3 LT 49,745.0

    Loan 2 ST 0.0 0.0 0.0 0.0 6,479.5

    Loan in foreign exchange 16,632.7

    Payment of loans

    Loan 1 LT 3,326.5 3,326.5 3,326.5 3,326.5 3,326.5

    Loan 3 LT 0.0 0.0 0.0 0.0 9,949.0

    Loan 2 ST 0.0 0.0 0.0 0.0 0.0

    Loan in foreign exchange 3,457.0 3,547.8 3,684.0 3,784.9 3,881.5Interest paid 0.0 3,654.2 3,003.2 2,154.9 1,465.8 6,433.1

    Net cash flow after financial transactions -13,414.6 5,023.9 6,376.5 8,086.9 3,627.1 5,939.2

    Module 3: Transactions with the

    equity holder

    Equity investment 15,000.0

    Payment of dividends 0.0 226.0 1,834.2 3,627.1 5,939.2

    Repurchase of shares 6,609.3 6,150.5 6,252.7 0.0 0.0

    Net cash flow after Transactions with theequity holder 1,585.4 -1,585.4 0.0 0.0 0.0 0.0

    Module 4: Discretional transactions

    Market securities recovery 0.0 0.0 0.0 0.0 0.0 0.0

    Interest from market securities 0.0 0.0 0.0 0.0 0.0 0.0

    Investment in market securities 0.0 0.0 0.0 0.0 0.0Net cash flow after discretional

    transactions 1,585.4 -1,585.4 0.0 0.0 0.0 0.0

    Net cash balance at the of year 1,585.4 0.0 0.0 0.0 0.0 0.0

    Observe the taxes paid in this case and in the previous one. For instante, taxes for

    years 3, 4 and 5 are 2,298.6, 3,683.5 y 2,242.6 in the first case; in the second case they are

    1,953.1, 3,198.0 y 1,446.3 respectively. This indicates a very important variation in taxes.

    Next we show the Balance Sheet

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    Table 5. Balance Sheet, BS when payout ratio is 100% and any excess cash is paid to the

    equity holder

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Assets

    Cash on hand 1,585.4 0.0 0.0 0.0 0.0 0.0

    Accounts receivable 0.0 2,440.8 2,617.6 2,835.0 3,055.9 3,294.5Inventory 1,680.0 1,937.9 2,094.1 2,228.6 2,311.1 2,425.9

    Market securities 0.0 0.0 0.0 0.0 0.0 0.0

    Current assets 3,265.4 4,378.7 4,711.8 5,063.7 5,367.0 5,720.3

    Net fixed assets 45,000.0 33,750.0 22,500.0 11,250.0 56,193.2 42,144.9

    Total 48,265.4 38,128.7 27,211.8 16,313.7 61,560.2 47,865.2

    Liabilities and equity

    Accounts payable 0.0 2,377.9 2,514.3 2,678.0 2,777.0 2,916.2

    Short term debt ST 0.0 0.0 0.0 0.0 0.0 6,479.5

    Current liabilities 0.0 2,377.9 2,514.3 2,678.0 2,777.0 9,395.7

    Debt in domestic currency 16,632.7 13,306.1 9,979.6 6,653.1 53,071.5 39,796.0Debt in foreign currency 16,632.7 13,828.0 10,643.4 7,367.9 3,784.9 0.0

    Total Liabilities 33,265.4 29,511.9 23,137.3 16,699.0 59,633.4 49,191.6

    Equity 15,000.0 8,390.7 2,240.2 -4,012.4 -4,012.4 -4,012.4

    Retained earnings 0.0 226.0 1,834.2 3,627.1 5,939.2 2,686.0

    Total 48,265.4 38,128.7 27,211.8 16,313.7 61,560.2 47,865.2

    D% (book value) 68.92% 71.16% 75.79% 85.95% 92.36% 96.68%

    Check 0.0 0.0 0.0 0.0 0.0 0.0

    Observe the net equity in the Balance Sheet. When cash flows are calculated using the

    traditional approach, the analyst do not even realize Chat is going on!

    Who dares to submit a financial statement like this one?

    From Module 3 in the CB, we construct the next table to derive the CFE:

    Table 6. CFE with 100% payout total distribution of excess to equity holders

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Equity investment 0.0 0.0 0.0 0.0 0.0

    Payment of dividends 0.0 226.0 1,834.2 3,627.1 5,939.2

    Repurchase of shares 6,609.3 6,150.5 6,252.7 0.0 0.0CFE 6,609.3 6,376.5 8,086.9 3,627.1 5,939.2

    TV debt 11,620.8CFE with TV for CFE 6,609.3 6,376.5 8,086.9 3,627.1 17,560.0Ke 15.65% 15.10% 15.10% 14.56% 14.01%

    Levered equity 24,010.8 22,056.5 19,741.7 15,186.6 14,143.0

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    Again, observe that the CFE is derived directly from Module 3 in the CB (except the

    terminal value at year 5 and Ke, calculations not shown).

    Values for equity and firm (the calculation is not shown) are: equity value is

    24,010.8 and firm value, 57,276.1 and it is equal to equity value plus debt.

    Observe the BS and look at the equity and retained earnings together. Equity has

    been reduced steadily from year 1 to year 5. The sum of the 2 items is positive in some

    years, but we have to pay the retained earnings just the next year. Then we can say that

    equity is in fact negative for the last 3 years.

    The relevant issue here is that when the FCF or the CFE is derived from the Income

    Statement and the Balance Sheet, and it is assumed that all excess cash is distributed, the

    analyst does not even realize what is happening with the equity in the Balance Sheet.

    We are sure that no analyst will dare to present a business plan or forecasted

    financial statements with the behavior for the equity as it is shown in this example.

    Now we will examine what occurs when the common practice is used, that is,

    calculating the cash flows from the Income Statement and not including the cash in hand

    and the market securities in the working capital.

    As a first step we calculate the working capital without including the cash in hand and

    the market securities and assuming that the financial statement do not reflects the fact that all

    the cash excess is distributed, this is, that cash is held in the bank and there is investment

    in market securities.

    Now we calculate the cash flows from the Income Statement and cash in hand and

    market securities will not be included in the working capital.

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    Table 7: Calculation of the change in working capital (cash excess invested)

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Accounts receivable 0.0 2,440.8 2,617.6 2,835.0 3,055.9 3,294.5

    Inventory 1,680.0 1,937.9 2,094.1 2,228.6 2,311.1 2,425.9

    Current assets 1,680.0 4,378.7 4,711.8 5,063.7 5,367.0 5,720.3

    Accounts payable 0.0 2,377.9 2,514.3 2,678.0 2,777.0 2,916.2

    Short term debt 0.0 0.0 0.0 0.0 0.0 1,955.4

    Unpaid taxes 0.0 0.0 0.0 0.0 0.0 0.0

    Current liabilities 0.0 2,377.9 2,514.3 2,678.0 2,777.0 4,871.5

    Working capital 1,680.0 2,000.8 2,197.4 2,385.7 2,590.0 848.8

    Change in Working capital 320.8 196.6 188.3 204.3 -1,741.2

    Now we calculate the FCF and the CFE departing from the Income Statement.

    Table 8: Calculation of cash flows and value (cash excess invested)Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Earnings Before Taxes and Interest(EBIT) 0,0 4.654,2 6.188,3 8.143,6 10.804,8 10.662,1

    Taxes on EBIT 0,0 -1.629,0 -2.165,9 -2.850,3 -3.781,7 -3.731,7

    Depreciation 0,0 11.250,0 11.250,0 11.250,0 11.250,0 14.048,3

    Minus change in working capital 0,0 -320,8 -196,6 -188,3 -204,3 1.741,2

    Minus investment -45.000,0 0,0 0,0 0,0 -56.193,2 0,0

    FCF -45.000,0 13.954,4 15.075,8 16.355,1 -38.124,3 22.719,8

    Tax savings (TS = T Interest) 1.507,3 1.178,2 897,2 583,7 1.489,1

    Capital Cash Flow CCF = FCF +

    TS 15.461,6 16.254,0 17.252,3 -37.540,6 24.208,9

    TV (calculation not shown) 58.036,2

    CCF + TV 15.461,6 16.254,0 17.252,3 -37.540,6 82.245,1

    Firm value = FV 56.554,5 49.941,4 41.228,8 30.202,3 72.138,9

    Equity value (FV debt) 23.289,1

    CFE = FCF + TS CFD10 5.023,9 6.376,5 8.086,9 -16.156,8 40.918,1

    Ke 19,5% 18,3% 17,8% 16,9% 16,7%

    Equity value 23.289,1 22.807,3 20.605,8 16.181,3 35.066,4

    Now we calculate the same items calculated above but assuming that the financial

    statements reflect the fact that all the available cash is distributed: nothing left as cash in

    hand, no investment in market securities.

    10CFD is derived from module 2 in the CB.

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    In the same manner we calculate the cash flows from the Income Statement and

    working capital will not include cash in hand nor market securities (in fact, now they are at

    zero, except for year 0).

    Table 9: Calculation of the change in working capital (cash excess not invested)

    Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Accounts receivable 0.0 2,440.8 2,617.6 2,835.0 3,055.9 3,294.5

    Inventory 1,680.0 1,937.9 2,094.1 2,228.6 2,311.1 2,425.9

    Current assets 1,680.0 4,378.7 4,711.8 5,063.7 5,367.0 5,720.3

    Accounts payable 0.0 2,377.9 2,514.3 2,678.0 2,777.0 2,916.2Short term debt 0.0 0.0 0.0 0.0 0.0 6,479.5

    Unpaid taxes 0.0 0.0 0.0 0.0 0.0 0.0

    Current liabilities 0.0 2,377.9 2,514.3 2,678.0 2,777.0 9,395.7

    Working capital 1,680.0 2,000.8 2,197.4 2,385.7 2,590.0 -3,675.3Change in Working capital 320.8 196.6 188.3 204.3 -6,265.3

    As before, now we calculate the FCF and the CFE departing from the Income

    Statement.

    Table 10: Calculation of cash flows and value (cash excess not invested)Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

    Earnings Before Taxes and Interest

    (EBIT) 0.0 4,654.2 6,188.3 8,143.6 10,804.8 10,662.1

    Taxes on EBIT 0.0 -1,629.0 -2,165.9 -2,850.3 -3,781.7 -3,731.7

    Depreciation 0.0 11,250.0 11,250.0 11,250.0 11,250.0 14,048.3Minus change in working capital 0.0 -320.8 -196.6 -188.3 -204.3 6,265.3

    Minus investment -45,000.0 0.0 0.0 0.0 -56,193.2 0.0

    FCF -45,000.0 13,954.4 15,075.8 16,355.1 -38,124.3 27,243.9

    Tax savings (TS = T Interest) 1,507.3 1,178.2 897.2 583.7 2,285.4Capital Cash Flow CCF = FCF +

    TS 15,461.6 16,254.0 17,252.3 -37,540.6 29,529.3

    TV (calculation not shown) 57,896.2

    CCF + TV 15,461.6 16,254.0 17,252.3 -37,540.6 87,425.6

    Firm value = FV 59,143.5 52,935.4 44,674.9 34,168.8 76,682.7

    Equity value (FV debt) 25,878.1

    CFE = FCF + TS CFD11 5,023.9 6,376.5 8,086.9 3,627.1 24,039.5

    Ke 19.1% 17.9% 17.4% 16.4% 21.3%

    Equity value 25,878.1 25,801.3 24,052.0 20,147.8 19,826.3

    11CFD is derived from module 2 in the CB.

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    Now we can compare the different results. We take as reference the firm and equity

    values calculated when excess cash is invested in all cases (second line versus first line). In the

    same way, we compare the values calculated according the common practice of not

    including cash and market securities in the working capital against the proposed approaches

    (columns 4 and 5 against columns 2 and 3).

    Table 11: Differences between methodsFirm value Equity value Firm value Equity value Difference Difference

    using qith current in firm in equity

    current practice value value

    practice

    With cash excess

    invested 54,374.4 21,109.0 56,554.5 23,289.1 4.01% 10.33%

    All cash excess is

    distributed and

    reflected in the

    financial statements 57,276.1 24,010.8 59,143.5 25,878.1 3.26% 7.78%

    Difference 5.34% 13.75% 4.58% 11.12%

    Now we compare all the values obtained with the value calculated making explicit the

    investment of the excess cash and listing as a cash flow only what the equity and debt holders

    effectively receive.

    Table 12: Differences against proponed approach to calculate cash flows (shaded cells)Firm value Valor del patrimonio Valor de la Valor del

    firma con la patrimonio con la

    prctica prctica

    corriente

    54,374.4 21,109.0 56,554.5 23,289.1

    With cash excess invested 0.00% 0.00% 4.01% 10.33%

    All cash excess is distributed

    and reflected in the financial 57,276.1 24,010.8 59,143.5 25,878.1

    statements 5.34% 13.75% 8.77% 22.59%

    In tables 11 and 12 we can observe that the differences when calculating cash flows

    according to the current practice against to calculate the value based on the actual cash that

    is listed as a cash movement (not potential dividends, for instance) are relevant, mainly

    when we observe the amounts related to the equity value. (and this is what finally we are

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    looking for) In the case of the firm value these differences are 4.01% and 8.77%; in the

    case of equity differences are 10.33% and 22.59%. These differences are significant.

    CONCLUDING REMARKS

    We have shown some arguments against the current practice of including in the

    CFE items that are not cash flows. In fact, they belong to the BS. We have shown with a

    simple example what might happen when the payout ratio is 100% and when all the excess

    cash is distributed to the equity holder. In that case, the financial statements show how that

    practice distorts the financial statements and in many cases the analyst do not even realize

    what is happening with the financial statements. In summary: the CFE should reflect

    exactly what is paid to the equity holders. In case that it is decided to distribute all the

    available cash, that fact should be reflected in the financial statements.

    On the other hand, we have shown how when considering amounts that are not cash

    flows we overvalue the firm value and specially, the equity value.

    BIBLIOGRAPHIC REFERENCES

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    visited on Octubre 30.

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    Vol. 54, No. 6, p. 1969-1997. Available at SSRN: http://ssrn.com/abstract=2109 or

    DOI: 10.2139/ssrn.2109, (January 30, 1997).

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    Mikkelson, Wayne H., 2003, "Do Persistent Large Cash Reserves Lead to Poor

    Performance?", Journal of Financial and Quantitative Analysis Vol. 38, n 2, June,

    p. 275-294. Available at SSRN: http://ssrn.com/abstract=186950 or

    DOI: 10.2139/ssrn.186950

    Miller, M. H. and F. Modigliani, 1961, Dividend Policy, Growth and the Valuation ofShares, The Journal of Business, V. 34, No. 4, P. 411-433 (Oct).

    Opler, Tim C., Pinkowitz, Lee Foster, Stulz, Ren M. and Williamson, Rohan G., 1999,

    "The Determinants and Implications of Corporate Cash Holdings", Journal ofFinancial Economics, Vol. 52, Iss. 1, p: 3-46. as NBER Working Paper No.W6234. Available at SSRN (October 1997): http://ssrn.com/abstract=225992

    Pinkowitz, Lee Foster, Stulz, Ren M. and Williamson, Rohan G., 2003, "Do Firms in

    Countries with Poor Protection of Investor Rights Hold More Cash?" (November).

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    http://ssrn.com/abstract=476442 or DOI: 10.2139/ssrn.476442

    Pinkowitz, Lee, Rohan Williamson and Ren M. Stulz, 2007, Cash Holdings, DividendPolicy, and Corporate Governance: A Cross-Country Analysis,Journal of AppliedCorporate Finance, Vol. 19 N. 1, Winter.

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    Value of Cash Holdings" (October). Available at SSRN:http://ssrn.com/abstract=355840 or DOI: 10.2139/ssrn.355840

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    Holdings: Evidence from Germany". HHL Working Paper. Available at SSRN:

    http://ssrn.com/abstract=490262

    Tham, Joseph y Vlez-Pareja, Ignacio, 2004, Principles of Cash Flow Valuation, Academic

    Press.

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    I" (December). http://ssrn.com/abstract=196588.

    Vlez-Pareja, Ignacio, 1998. Decisiones de Inversin, una aproximacin al anlisis de

    alternativas. CEJA.

    Vlez-Pareja, Ignacio, Decisiones de Inversin. Enfocado a la Valoracin de Empresas,

    4ed 2004, CEJA.

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    APPENDIX

    Explanation of Professor Damodaran regarding the items to be included in the CFE

    Aswath Damodaran 95Slides 94 to 97

    Dividends and Cash Flows to Equity In the strictest sense, the only cash flow that an investor will receive from an equity

    investment in a publicly traded firm is the dividend that will be paid on the stock.

    Actual dividends, however, are set by the managers of the firm and may be muchlower than the potential dividends (that could have been paid out)

    o managers are conservative and try to smooth out dividendso managers like to hold on to cash to meet unforeseen future contingencies

    and investment opportunities

    When actual dividends are less than potential dividends, using a model that focusesonly on dividends will under state the true value of the equity in a firm.

    Measuring Potential Dividends

    Some analysts assume that the earnings of a firm represent its potential dividends.This cannot be true for several reasons:

    o Earnings are not cash flows, since there are both non-cash revenues andexpenses in the earnings calculation

    o Even if earnings were cash flows, a firm that paid its earnings out asdividends would not be investing in new assets and thus could not grow

    o Valuation models, where earnings are discounted back to the present, willover estimate the value of the equity in the firm

    The potential dividends of a firm are the cash flows left over after the firm has madeany investments it needs to make to create future growth and net debt repayments(debt repayments - new debt issues)

    o The common categorization of capital expenditures into discretionary andnon-discretionary loses its basis when there is future growth built into the

    valuation.

    Estimating Cash Flows: FCFE

    Cash flows to Equity for a Levered FirmNet Income

    - (Capital Expenditures - Depreciation)

    - Changes in non-cash Working Capital12

    - (Principal Repayments - New Debt Issues) =

    Free Cash flow to Equity

    I have ignored preferred dividends. If preferred stock exist, preferred dividends willalso need to be netted out

    12 From slide 92 (Damodaran 95): In accounting terms, the working capital is the difference between current assets(inventory, cash and accounts receivable) and current liabilities (accounts payables, short term debt and debt due within

    the next year)

    A cleaner definition of working capital from a cash flow perspective is the difference between non-cash current assets

    inventory and accounts receivable) and non-debt current liabilities (accounts payable). Observe that investment of excess cash

    is not included in the definition of working capital.

    22