CONSTRUCTION OF FREE CASH FLOWS A PEDAGOGICAL NOTE.

This is the first part of a paper where the construction of the free cash flow is studied. Usually a great deal of effort is devoted in typical financial textbooks to the mechanics of the calculations of time value of money equivalencies: payments, future values, present values, etc. This is necessary. However less or no effort is devoted to how to arrive at the figures required to calculate a NPV or Internal Rate of Return, IRR. In Part I, pro forma financial statements (Balance Sheet (BS), Profit and Loses Statement (P &L) and Cash Budget (CB) are presented.

From the CB, the Free Cash Flow FCF, the Cash Flow to Equity CFE and the Cash Flow to Debt CFD, are derived. Emphasis is done to the reasons why some items included in the P&L and CB are no included in the FCF. Also, the FCF and the CFD are calculated with the typical approach found in the literature: from the P&L and it is specified how to construct them. In doing this, working capital is redefined: the result is that it has to include and exclude some items that are not taken into account in the traditional methods.

In Part II a comparison between the proposed method to construct the above-mentioned cash flows and the ones found in the current and typical textbooks is presented. KEYWORDS Free cash flow, cash flow to equity, cash flow to debt, project evaluation, firm valuation, investment valuation, Net Present Value NPV assumptions. JEL Classification: D92, E22, E31, G31 1 This paper is based on chapter 6 of Velez-Pareja, Ignacio, Decisiones de inversion, Una aproximacion al analisis de alternativas, CEJA, 1998. Available on line at http://www. javeriana. edu. co/decisiones/libro_on_line INTRODUCTION

This is the first part of a paper where the construction of the free cash flow is studied. Usually a great deal of effort is devoted in typical financial textbooks to the mechanics of the calculations of time value of money equivalencies: payments, future values, present values, etc. This is necessary. However less or no effort is devoted to how to arrive at the figures required to calculate the Net Present Value NPV or Internal Rate of Return, IRR. In Part I, pro forma financial statements (Balance Sheet (BS), Profit and Loses Statement (P&L) and Cash Budget (CB) are presented.

From the CB, the Free Cash Flow FCF, the Cash Flow to Equity CFE and the Cash Flow to Debt CFD, are derived. From the CB, the Free Cash Flow FCF, the Cash Flow to Equity CFE and the Cash Flow to Debt CFD, are derived. Also, the FCF and the CFD are calculated with the typical approach found in the literature: from the P&L and it is specified how to construct them. In doing this, working capital is redefined: the result is that it has to include and exclude some items that are not taken into account in the traditional methods.

In Part II a comparison between the proposed method to construct the above-mentioned cash flows and the ones found in the current and typical textbooks is presented. MODELS AND THEIR USE Models simplify reality in order to deal with it and to understand the basics of the problem. For this reason some strong assumptions are generally stipulated. A good analyst has to know very well not only the model she constructs, but also the reality she desires to simulate. This is very important because conditions in reality have to be checked in order to define if the model complies with them or not.

On the other hand, a good model should include as many elements from reality as possible, in order to confirm or predict the studied behavior. The model should recognize all the variables and their inter relationships, even if it is not possible to include or measure them in the model. The analyst should take into account all the measurable variables and should try to predict or determine the possible results from not taking into account some elements of the reality. After the model has been built, and only then, some assumptions or restrictions can be dropped out.

Done this the estimation of the consequences over the behavior of the model can be studied. This leads to the idea of two classes of models. Models for explanation and models for application. The first class is related to the explanation of an idea or concept. In doing that, the model has to be simple, schematic and with many conditions, simplifying assumptions and restrictions. This kind of models is good to fix and define concepts. The second class is related to the application of an explanatory model in a given reality.

This kind of model has to include many of the variables and/or conditions that were disregarded in the explanatory model. Great effort has to be done to include as 3 many as real conditions as possible in order to make the model approximate the reality. Many failures attributed to some traditional models are due to the wrong selection or utilization of the model. This is, an explanatory model has been used without the proper adjustment to convert it to an application model. Many assumptions are hidden or implicit in a model. In some cases this is due to the time when the model was formulated.

When computational resources were scarce or non-existent. But today, it might be unacceptable to include some implicit or explicit simplifying assumptions. The speed of the computers, the computing ability, their high storage capacity and precision allows us to include more variables and interrelationships among them at reasonable cost. A very good example is the Net Present Value, NPV, and its formulae (including those available in any spreadsheet). This model starts from some assumptions that are not real, e. g. : 1. The discount rate is constant through the life of a project. . The reinvestment rate is the same as the discount rate. 3. The intermediate free cash flows are reinvested at the above-mentioned rate. 4. When dealing with mutually exclusive alternatives, the difference between the largest initial investment and the initial investment of the other alternatives is invested at the discount rate. The purpose of this paper is to show how to take advantage of the power of spreadsheets to project pro forma financial statements, including cash budget CB and from them, deduct the free cash flow FCF of the project.

In doing that, some of the implicit assumptions of the NPV will be examined. A SHORT REVIEW To understand the procedure to construct the FCF, it is important to review some basic concepts. First, the discount rate. It is an interest rate that measures the cost of money for the firm. It is the cost that the firm pays for the resources received from creditors or bondholders and from the stockholders. Usually it is known as the Weighted Average Cost of Capital, WACC. A second concept is the idea of investment: any sacrifice of resources, ? oney, time and assets? with the expectation to receive some benefits in the future. A third one is the distinction between the project (or firm), the stockholders and the creditors. Last, but not least, it is convenient to review some elementary ideas from basic accounting. 4 FINANCIAL STATEMENTS AND CASH FLOWS Let us make a very brief review of the most common financial statements utilized in the firm: The Balance Sheet and the Profit and Losses Statement (P&L) and the Cash Budget CB (not the free cash flow).

The Balance Sheet states and tries to measure the amount of wealth owned by stockholders. Always equilibrium is expected: Assets – Liabilities = Equity Each of the elements of this equilibrium equation has associated some cash flows: • Assets (the amount invested in the firm) have the capacity to generate benefits to the firm. • Liabilities have associated inflows and outflows, this is, the proceeds from new debts and the payment of principal and interest charges. • Equity has associated the inflows and outflows from stockholders investment and dividends paid.

Eventually, the stockholders will receive the residual after all liabilities are paid. From these ideas it is easy to suggest that in the same way the elements keep an equilibrium relationship, the associated cash flows will behave in the same manner. This proposal will be studied below. The Profit and Losses Statement tries to measure the net profit earned by the firm in a given period. Both financial statements are constructed on the basis of the accrual concept and the assignation of costs. This means that some income (i. e. ccounts receivables) or costs (accrued payments) are registered when the situation or fact that generates the income or expense occurs and not when the income is received or the expense is paid. On the other hand, cost assignation apportions some cost incurred in the past to future periods (i. e. depreciation). The cash budget CB is related to the inflows and outflows of money (the checkbook movements). It measures the liquidity of the firm for each period. Usually, this is a projected or pro forma financial statement. In this financial statement all the expected inflows and outflows are registered when they are expected to occur.

It is better to analyze the liquidity situation of the firm with this pro forma statement rather than with the traditional financial ratios. Usually what is known as financial analysis is a kind of autopsy of the firm. They look at the past, assuming that the past will be repeated in the future. Cash budget CB is one of the most, if not the most important tool to control and follow up the liquidity of the firm. For investment analysis or project evaluation, it is important to know how is the performance of the firm or project in terms of liquidity.

A careful examination of the cash budget CB will allow the decision maker to choose a given financing alternative or, on the other hand, a good investment of cash surplus decision. 5 The elements of the cash budget CB are the inflows and the outflows of cash. The difference between these two figures result in the cash balance of the period and from it, the cumulative cash balance can be calculated. This cash balance is the clue to decide if the firm should borrow or invest funds. Typical items included in a pro forma cash budget CB are: Inflows |Outflows | |Accounts receivables recovery |Accounts payable payments | |Loans received |Salaries and fringe benefits | |Equity invested |Interest charges | |Sale of assets |Principal payments | |Return on short or long term investment |Rent | |Short term investment recovery |Overhead expenses | |Customers’ in advance payments |Promotion and publicity | |Repayments of cash lent |Asset acquisition | | |Social Security payments | | |Earnings distributed or dividends paid | | |Taxes | | |Short term investment of cash surpluses | And last, but not least, the free cash flow (FCF). The FCF measures the expected operating benefits and costs of an activity (firm or project). In contrast with the cash budget CB, some cash inflows or outflows are excluded from the FCF. More, some items included in the FCF of a project might not be a real cash inflow or inflow (i. e. he opportunity cost of some resource: remember the definition of investment: a sacrifice of resources). With the FCF, the NPV and IRR are calculated. Along with the FCF two other cash flows are constructed: the financing cash flow or cash flow to debt CFD and the owner or stockholder cash flow or cash flow to equity CFE. THE WEIGHTED AVERAGE COST OF CAPITAL The WACC reflects the cost of debt and the opportunity cost of equity. This means that the payments for interest charges and the dividends paid to stockholders are implicit in the WACC. Let us remember a basic concept in accounting: Assets = Liabilities + Equity This shows the origin of all the resources the firm has in order to make any investment.

The assets the firm possesses have been acquired because there are some third parties (creditors and stockholders) that have provided for the funds to buy those assets. Every actor, creditors and stockholders, has the right to receive some return for the funds provided to the firm. Hence, the cost of capital of the firm can be visualized in this chart: 6 Cost debt (liabilities) Cost of capital Cost of funds provided by stockholders (equity) When calculating the cost of debt, interest charges and principal payments are taken into account. The cost of debt might include the cost of rent and lease as well2. These expenses are related to what might be called cuasi debt. These costs are part of the WACC.

The resulting interest rate has implicit the value paid for interest charges. And these are deductible from income taxes. This means that there is a subsidy from the government for having debt and paying interest. This subsidy is equal to TxI, where T is the marginal tax rate and I is the interest payment. The net effect is a tax shield that reduces the cost of debt. A shortcut to estimate the after tax cost of debt is to calculate ibt(1-T), where ibt is the cost of debt before taxes. This shortcut implies that taxes are paid in the same period as interest is paid. The cost of funds provided by the stockholders might be calculated in a variety of ways.

From a simple one as the well known dividend growth model up to the Capital Asset Pricing Model (CAPM). In any case, the dividends paid are taken into account in the estimation. With these two costs (debt and equity) and the expected proportions of debt and equity, the WACC can be estimated. THE CASH FLOW CALCULATION There are two ways to get the FCF: Directly from the Profit and Losses statement P&L and from the Cash Budget. From the P&L it starts from the Earnings before Interest EBIT adding depreciation and amortization charges and subtracting taxes o EBIT and changes in non-cash working capital. This method is widely used and is found in any financial textbook. However, it might be the source of potential errors.

As it subtracts the tax on EBIT directly, it may be possible Earnings before Taxes EBT is zero or negative and then taxes are not paid; hence, the tax payment and the correspondent tax savings might never occur. A simple example will illustrate this idea. Assume that EBIT is 100 and the tax rate is 40%. If taxes are calculated as usual, directly from EBIT, they will amount to 40 and if interest charges are 150 the tax saving will be accounted as 60. However, if interest charges are 150 taxes will be zero, but there exists a tax savings of only 40 and not of 60. 2 This idea implies that the investment should include the market value of leased or rented assets. 7 Tax savings calculations |Levered |Unlevered | |EBIT |100 |100 | |Interest charges |150 |0 | |EBT |-50 |100 | |Tax |0 |40 | |Net profit |-50 |60 | On the other hand, it is the indirect calculation of FCF. Financial statements (Balance sheet, P&L and Cash Budget CB) are projected and from the CB, the FCF is derived. It is important to know how is the performance of the firm or project in terms of liquidity. A careful examination of the cash budget CB will allow the decision maker to choose a given financing alternative or, on the other hand, a good investment of cash surplus decision. The cash balance is the clue to decide if the firm should borrow or invest funds.

WHAT IS INCLUDED IN THE FCF In the cash budget CB are included all the inflows and outflows. Among them are found some items such as, equity investment, proceeds from loans, principal payments, interest charges, earnings distributed or dividends and implicit in the tax payments, the tax shield for interest payments. These above-mentioned items should not be included in the FCF, as follows. 1. Equity payment 2. Loans received 3. Loans paid These are not included in the FCF because they are not the result of the operating activity of the firm or the project. For instance, the inflow of a loan is not a benefit produced by the firm in its operations.

The idea is to measure the value generated by the firm or project. 4. Interest charges paid 5. Tax shield for interest payments 6. Distributed earnings or dividends These items are not included in the FCF because they are embodied in the cost of capital. Including these items would result in a double counting of the cost of the money for the firm or project. The FCF must be discounted with the WACC in order to calculate the NPV and the IRR is compared to the WACC in order to know if the project is accepted or rejected. 8 The FCF is called free because it must be clean from any financing effect, including the effect from the tax payment (the tax shield).

The financing effects are embodied in WACC. 3 INTEREST PAYMENTS AND EARNINGS PAID When applying the discounted cash flow analysis (DCF) the idea behind it is to determine if there exists value added. This value added comes from the operating net benefits and any other operations performed by the firm. In order to accept a project it has to be able to pay back the amount invested plus the cost of money (the discount rate or WACC). (See Velez-Pareja, 1999) The discounting process (P=F/(1+i)n) discounts the interest paid at the discount rate. As it was mentioned above, the WACC is calculated taking into account the interest and earnings or dividends paid.

This means that if the cost of debt or cuasi debt (interest, rent and leases charges) and part of the cost of equity (earnings or dividends paid) are included in the FCF as an outflow and besides the NPV is calculated (P=F/(1+i)n), the cost of money would be counted twice. Hence, there would be an underestimation of the value added (NPV) by the alternative analyzed. For the same reason, the tax shield has to be excluded from the FCF: it has been measured in the cost of debt after taxes and is implicit in the WACC. A simple example will clarify the idea. EXAMPLE 1 Assume an investment of $1,000 and $1,500 are received in a year. |Year |Free cash flow | |0 |-1. 000 | |1 |1. 500 | If the WACC is 30%, then the $1,500, might be decomposed as follows: Investment $ |1,000 | |Cost of money $ |300 | |Value added $ |200 | When discounted, the present value of $1,500 is $1,153. 85. This figure can be decomposed as, | |Cash flow |Present |Cumulated | | |in year 1 $ |value $ |value | |Investment $ |1,000 |769. 23 |769. 23 | |Cost of money $ |300 |230. 77 |1,000 | |Value added $ |200 |153. 85 |1,153. 85 |

Investment plus the cost of money (the interest charged to the project) are equivalent to $1,000 in year zero. This means that the discounting process discounted (subtracted) the interest charged for the investment (the cost of money or WACC. The 3 There is a debate upon the suitability of WACC to evaluate an investment alternative. Alternate methods are the Adjusted Present Value APV (Myers, 1974) and the Generalized Adjusted Present Value GAPV (Gallo and Pecatti, 1993 and Prina della Tallia and Pattison, 1996) 9 remaining, when discounted is precisely the NPV. And this value ? $153. 85? at year zero means that it is a good project and should be accepted. On the other hand if the interest (the $300) is subtracted in the FCF, the cash flow would be. |Y| | |FCF | | |Interest | | |e| | | | | | | | |a| | | | | | | | |r| | | | | | | |1 | |1,500 |-300 |1. 200 | | When discounted at 30%, the NPV will be -76. 92 and the project has to be rejected. Again, if the interest payments are subtracted in the FCF and the NPV is calculated, the cost of money will be counted twice. And with this approach we could reject a good project. LOANS AND EQUITY

If the loans are included as an inflow and later as an outflow, the resulting cash flow is not the free cash flow of the project. The investment in a project is the total value of all the resources sacrificed in it, no matter where they come from. On the other hand, loan or equity inflows are not part of the free cash flow of the project because they are not a benefit produced by the operation of the project. By the same token, the loan payments are not an expense of the operation of the project. It is necessary to recall that the idea is to evaluate how good is the project. How much value it aggregates from the operation to the firm. TAXES All taxes have to be included in the free cash flow.

This means local taxes, capital gains taxes, income tax, etc. The best way to determine the taxes paid by the project is to calculate the taxes of the firm with and without the project. The taxes attributable to the project are the difference between the taxes paid by the firm with the project and the taxes paid by the firm without the project. In countries where adjustments for inflation are applied to the financial statements, the only adjustment to be done in the FCF is the one related to taxes paid after adjustments for inflation. It has to be remembered that adjustments for inflation do not create wealth, they only try to approximate to reality.

The net effect of taxes on the firm is that an expense after taxes is equal to the same expense minus the tax shield or tax savings. A deductible expense (i. e. interest payments) implies tax shield or tax savings of T times I, where T is the marginal tax rate and I is the interest charges paid. 10 CONSTRUCTION OF THE FREE CASH FLOW FCF In the case of the discounted free cash flow approach ( DCF) for project evaluation there are many oversimplifying assumptions or shortcuts. These shortcuts were valid 35 or 100 years ago. However, they can be found today in finance and engineering economy textbooks, and among teachers, analysts, managers and practitioners. For the projection of pro forma financial statements a great variety of “”methods”” exist.

The typical methodology found in many respected textbooks is to express the items of the last balance sheet and P&L statement as a percentage of net sales, make a lineal regression for sales with a few data and apply the percentages to the projected sales figures. How to balance the figures? Easy, they say, use cash and current liabilities or dividends as the checking or balancing account! 4 When a project is planned (to start a business, for instance) it is necessary to construct the initial (year 0) Balance Sheet and gather some information about the market, sales volume, price-demand elasticity, unit sales price, unit input price, increase in the level of sales, price increases, etc. With this information pro forma financial statements are projected.

From the P&L statements and the plans and policies for collecting receivables and paying accounts payable, inventories, dividends or earnings payment, etc. the cash budget (CB) can be constructed. These are managerial tools for follow up and control a project or firm. The CB figures are the closest to the FCF figures of a project because the CB registers the inflows and outflows at the time they occurs. Hence, it is from this financial statement where the FCF should be derived. THE FREE CASH FLOW (FCF) OF A PROJECT In order to accept or reject an alternative, it is necessary to measure if the projected cash flows are enough to generate aggregated value to the firm. This is done with the free cash flow (FCF) of the project. The FCF can be deducted from the pro forma financial statements.

As was studied above, it is necessary to eliminate from the CB some items that should not be included in the FCF. These items are loans received and paid, equity invested by stockholders, dividends paid to stockholders, interest charges paid and the tax shield from interest payments. Then, for year 1 to n: Net cash gain (loss) after financing and reinvestment from the CB (NCG) Minus investment from stockholders (IS) Minus proceeds from loans received (LR) Plus principal payments (PP) Plus interest, rent and lease charges paid (I) Minus tax shield for interest, rent and lease payments (TSI) Plus dividends or earnings paid (D) Minus investment in the project (IP) Equal free cash flow 4 Van Horne 1998, p. 742, Gallaher and Andrew 2000, p. 129 and Brealey, Myers and Marcus, 1995, p. 521 in the Spanish version 11 At period n, the present value of future FCF beyond the period n, has to be added. Copeland et. al. (1995) and Weston and Copeland (1992), call it continuing value. Damodaran (1996) calls it terminal value5. For year 0 the opportunity cost of the resources engaged in the project. In other words, total assets. With the FCF the NPV is calculated at the weighted average cost of capital WACC. It should be remembered that the WACC includes the cost of debt and the cost of equity. EXAMPLE 2 Assume a new commercial business is planned.

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