Xay dung cua dong tien xet lai E0

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Xay dung cua dong tien xet lai E0

  1. 1. Construction of Free Cash Flows Revisited CONSTRUCTION OF CASH FLOWS REVISITED Ignacio Vélez-Pareja ivelez@poligran.edu.co School of Industrial Engineering Politécnico Grancolombiano Bogotá, Colombia First version: 5-Jun-05 This version: 13-Sep-05 Ignacio Vélez-Pareja
  2. 2. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja CONSTRUCTION OF CASH FLOWS REVISITED Never do with more, what you can do with less. Anonymous ABSTRACT 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 the paper, pro forma financial statements (Balance Sheet (BS), Income Statement (IS) 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 CFE are calculated with the typical approach found in the literature: from the IS and it is specified how to construct them. In doing this, working capital is redefined: the result is that it has to include some items that are not taken into account in the traditional methods. An example is presented to illustrate the procedure to calculate the cash flows. Keywords Free cash flow, cash flow to equity, cash flow to debt, project evaluation, firm valuation, investment valuation, Net Present Value NPV. JEL Classification: D92, E22, E31, G31
  3. 3. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja INTRODUCTION 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 the paper, pro forma financial statements (Balance Sheet (BS), Income Statement (IS) 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 CFE are calculated with the typical approach found in the literature: from the IS and it is specified how to construct them. In doing this, working capital is redefined: the result is that it has to include some items that are not taken into account in the traditional methods. 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. An example is presented to illustrate the procedure to calculate the cash flows. 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, money, 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 equity holders and the debt holders. Last, but not least, it is convenient to review some elementary ideas from basic accounting. We will spend a little more time reviewing these concepts. 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 (1) 3
  4. 4. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja 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: Cost debt (financial debt) 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 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 under some restrictive conditions. This subsidy is equal to T×I, 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 Kdt(1-T), where Kdt is the cost of debt before taxes. This shortcut implies that taxes are paid in the same period as accrued and the only source of tax shields is interest payments. 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, both at market value1, the WACC can be estimated. The most common expression for the WACC is WACCt = Kd(1−T)D%t−1 + Ke E%t−1 (2)2 Where WACCt is the weighted average cost of capital, Kd is the cost of debt, T is the corporate tax rate, D%t−1 is the leverage based on the market value of the firm, Ke is the cost of levered equity and E%t−1 is the weight of equity based on the market value of the firm. (See Appendix B) As can be expected from the previous paragraphs, this means that there is a circularity problem: the WACC requires to know the market value of the firm or project and to know the market value of the firm requires knowing the WACC3. 1 For market value we understand the present value of the FCF discounted at the WACC. This creates circularity. This is a well known expression for the WACC and it is found in most financial textbooks and literature; however, it is valid under restrictive conditions. For a general expression for the WACC see Taggart 1989, Velez-Pareja and Tham 2001 and Tham and Velez-Pareja, 2004, Velez-Pareja and Burbano 2005, and Tham and Velez-Pareja, 2002. 3 The solution of this problem is surprisingly easy and can be found at Velez-Pareja and Tham 2001 and Tham and Velez-Pareja, 2004. 2 4
  5. 5. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja 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 Income Statement (IS) 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. The basic accounting equation is: Assets - Liabilities = Equity (3) 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. This is known as double entry accounting. In the next table we show an example (that we will use throughout this paper) that illustrates the Balance Sheet. Table 1 Pro forma Balance sheet Year 0 Assets Cash Accounts receivable Inventory Investment in marketable securities Current assets Net fixed assets Total assets Liabilities and equity Accounts payable Short term debt Unpaid taxes Current liabilities Debt in local currency Debt in foreign currency Total liabilities Equity Retained earnings Total liabilities and equity Year 1 Year 2 Year 3 Year 4 Year 5 1,553.1 0.0 1,680.0 0.0 3,233.1 45,000.0 48,233.1 100.0 2,404.2 1,933.0 5,516.9 9,954.0 33,750.0 43,704.0 110.0 2,577.8 2,191.1 11,034.3 15,913.2 22,500.0 38,413.2 120.0 2,791.9 2,222.5 19,170.6 24,304.9 11,250.0 35,554.9 130.0 3,009.4 2,365.7 0.0 5,505.1 56,193.2 61,698.3 140.0 3,244.3 2,453.5 78.7 5,916.5 42,144.9 48,061.4 0.0 0.0 0.0 0.0 16,616.6 16,616.6 33,233.1 15,000.0 0.0 48,233.1 1,716.6 0.0 0.0 1,716.6 13,293.2 13,814.5 28,824.4 15,000.0 -120.3 43,704.0 1,936.7 0.0 0.0 1,936.7 9,969.9 10,633.0 22,539.7 15,000.0 873.6 38,413.2 2,670.6 0.0 0.0 2,670.6 6,646.6 7,360.8 16,678.0 15,000.0 3,876.9 35,554.9 2,842.7 0.0 0.0 2,842.7 32,842.1 3,781.2 39,466.0 15,000.0 7,232.3 61,698.3 2,949.4 0.0 0.0 2,949.4 23,615.0 0.0 26,564.4 15,000.0 6,497.0 48,061.4 The Income Statement measures the net profit earned by the firm in a given period. 5
  6. 6. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Both financial statements are constructed on the basis of the accrual concept and the assignation of costs. This means that some income (i. e. accounts 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 and amortization ). In the next table we show an Income Statement that is consistent with the previous Balance Sheet. Table 2 Pro forma Income Statement Sales Cost of goods sold Gross profit Selling and administrative expenses Depreciation and amortization Earnings before interest and taxes Other income (interest received) Other expenses (interest expenses in domestic currency) Other expenses (interest expenses in foreign currency) Loss in Foreign Exchange Total financial expenses Earnings before taxes Taxes Net profit Dividends to be paid next year Accumulated retained earnings Year 1 Year 2 Year 3 Year 4 Year 5 48,083.8 51,555.1 55,837.1 60,188.1 64,885.8 23,443.9 26,049.1 26,674.4 28,283.6 29,405.8 24,640.0 25,505.9 29,162.7 31,904.5 35,480.0 9,208.0 9,848.4 10,500.6 11,203.9 11,957.9 11,250.0 11,250.0 11,250.0 11,250.0 14,048.3 4,181.9 4,407.6 7,412.1 9,450.6 9,473.8 0.0 419.8 839.7 1,361.1 0.0 2,165.1 1,664.3 1,248.2 798.3 3,776.8 1,485.5 1,335.9 904.5 666.1 329.6 651.6 362.8 408.2 201.7 96.5 4,302.3 3,363.1 2,560.9 1,666.0 4,202.9 -120.3 1,464.3 5,690.9 9,145.7 5,270.9 0.00 470.39 1,991.81 3,201.00 1,844.80 -120.3 993.9 3,699.1 5,944.7 3,426.1 0.0 695.7 2,589.4 4,161.3 2,398.2 -120.3 873.6 3,876.9 7,232.3 6,497.0 Notice that in year 1 there are losses and that there exists losses carried forward, LCF. This can be seen when we calculate the effective tax rate. This effective tax rate can be calculated as taxes divides by Earnings before taxes. In this example for all years, exception made for year 2, the tax rate is 35%. For year 2 it is 32.12% due to the losses carried forward mechanism. 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 the performance of the firm or project is 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 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 6
  7. 7. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja 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: Table 3a Typical Items in a CB 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 long term investment Rent Short term investment recovery Overhead expenses Customers' in advance payments Promotion and advertising Repayments of principal for cash lent Asset acquisition Value Added Tax (VAT) collection Social Security payments Income for interest from market Earnings distributed or dividends paid and repurchase of securities equity Sale of fixed assets Taxes Sale of current assets Short term investment of cash surpluses Return on short term investment VAT payment By convenience s, (below we will explain the convenience of this structure) the CB has been constructed with several modules with their respective net cash balance, as follows: 1. Module 1: Operating Module. This module lists the inflows and outflows related with the operation of the firm and it includes taxes paid. Some of the items we include in this module are Accounts receivables recovery, Sale of assets, Customers' in advance payments, Accounts payable payments, Salaries and fringe benefits, Overhead expenses, Promotion and advertising, etcetera. If we consider that the forecasted cost of debt will be the same as the cost we have estimated for the forecasting period, when we discount the Net Cash Balance from this module we obtain the maximum debt capacity of the firm. (See Appendix A) 1.1. Operative inflows (accounts receivable and similar items) 1.2. Operative outflows (raw material, labor costs, and any payments to the work force, taxes, overhead expenses, sales expenses, etc.) 1.3. Net Cash Balance before investment in assets 2. Module 2: 2.1. Initial investment in assets 2.2. Investment in assets in other periods 2.3. Net Cash Balance after investment in assets 3. Module 3: Financing Module. This module lists the inflows and outflows related to the financing operations. It includes Interest charges, Principal payments and Loans received. In Module 2 we derive the Net Cash Balance after transactions with debt holders. From this module we can derive a cash flow: the Cash Flow to Debt, CFD. The CFD is the amount received and supplied by the debt holders to the firm. 7
  8. 8. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja 3.1. Inflows due to loans received in domestic or foreign currency (converted to local currency). 3.2. Payment of principal in domestic or foreign currency (converted to domestic currency) 3.3. Interest charges in domestic or foreign currency (converted to domestic currency) 3.4. Net Cash Balance after financing activities. 4. Module 4: Equity Module. This module lists the Equity investment by equity holders, Earnings distributed or dividends paid to them and any Repurchase of equity. From this module we can derive another cash flow: the Cash Flow to Equity, CFE. The CFE is the amounts received and supplied by the equity holders to the firm. It list the following: 4.1. Equity investment 4.2. Dividend payments 4.3. Repurchase of equity 4.4. Net Cash Flow after transactions with equity holders 5. Module 5: Discretionary Module. This module lists the operations the management performs with the excess of cash the firm generates. The financial manager has among her goals to maximize value even with non operating cash flows. In this case, the managers invest the excess of liquidity on market securities. The items listed in this module are Short term investment of cash surpluses, Return on short investment and Short term investment recovery. 5.1. Sale of market securities 5.2. Return from market securities 5.3. Investment in market securities 5.4. Net Cash Flow alter discretionary transactions 5.5. Cumulated Net Cash Balance for the period In the next table we find a Cash budget that completes the three financial statements. 8
  9. 9. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table 3b Pro forma cash budget CB Year 0 Module 1. Operating Module Cash inflows Cash collection of sales Total cash inflows Cash outflows Total Payments Overhead Payroll payments Royalties Advertising and promotion Taxes Total cash outflows Net cash balance before investment in assets Module 2. Investing module Initial investment in fixed assets Investment in assets at year 4 Net cash balance after investing in assets Module 3: Financing Module Proceeds from LT loan 1 Proceeds from LT loan 3 Proceeds from ST loan 2 Proceeds from loan in foreign exchange Principal payments LT loan 1 LT loan 3 ST loan 2 Loan in foreign exchange Interest charges NCB after transactions with debt holders Module 4: Equity Module Equity investment Dividend payments Repurchase of equity NCB after transactions with equity holders Module 5: Discretionary Module Recovery of short term investments4 Interest on short term investment Investment of surplus Net cash Balance after discretionary transactions Cumulative cash balance at end of year Year 1 Year 2 Year 3 Year 4 Year 5 0.0 45,679.7 51,381.5 55,623.0 0.0 45,679.7 51,381.5 55,623.0 59,970.6 59,970.6 64,650.9 64,650.9 1,680.0 21,980.3 26,087.2 25,971.8 0.0 2,326.6 2,466.9 2,615.5 0.0 2,582.2 2,765.0 2,969.9 0.0 2,856.7 3,069.8 3,240.0 0.0 1,442.5 1,546.7 1,675.1 0.0 0.0 470.4 1,991.8 1,680.0 31,188.3 36,406.0 38,464.3 -1,680.0 14,491.4 14,975.5 17,158.7 28,254.8 2,760.1 3,186.7 3,451.5 1,805.6 3,201.0 42,659.6 17,310.9 29,386.9 2,913.1 3,410.2 3,688.0 1,946.6 1,844.8 43,189.6 21,461.3 45,000.0 0.0 0.0 0.0 0.0 -46,680.0 14,491.4 14,975.5 17,158.7 56,193.2 -38,882.2 0.0 21,461.3 16,616.6 0.0 0.0 0.0 0.0 0.0 0.0 29,518.8 0.0 0.0 0.0 3,323.3 0.0 0.0 3,453.6 3,650.6 4,063.8 3,323.3 0.0 0.0 3,544.3 3,000.2 5,107.6 3,323.3 0.0 0.0 3,680.4 2,152.8 8,002.2 3,323.3 0.0 0.0 3,781.2 1,464.3 -17,932.3 3,323.3 5,903.8 0.0 3,877.7 4,106.4 4,250.0 0.0 0.0 695.7 2,589.4 4,161.3 4,063.8 5,107.6 7,306.5 -20,521.7 88.7 0.0 5,516.9 11,034.3 0.0 419.8 839.7 5,516.9 11,034.3 19,170.6 19,170.6 1,361.1 0.0 0.0 0.0 78.7 10.0 130.0 10.0 140.0 16,616.6 0.0 -13,446.9 15,000.0 1,553.1 0.0 0.0 1,553.1 -1,453.1 1,553.1 100.0 10.0 110.0 10.0 120.0 Notice that dividends are paid the following year after the net income is accrued, that in the first year the tax shield is not earned in full because EBIT plus Other income do not fully offset the interest charges and that there are losses carried forward. This means that TS for year 1 4 Some authors such as Copeland et.al. (2000, Damodaran (1995)) and Weston and Copeland (1992) say that the cash flows associated to the investment of cash surplus and its returns must be discounted at a different discount rate. 9
  10. 10. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja is earned part in year 1 and part in year 2. Remind that TS are received only at the time taxes are paid. 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) that can be distributed and effectively is distributed among the owners of equity and debt. 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. the 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 debt cash flow or cash flow to debt CFD and the owner or stockholder cash flow or cash flow to equity CFE. THE MODIGLIANI AND MILLER APPROACH TO THE FCF CONSTRUCTION In their pioneering work, Modigliani and Miller (M&M), 1958, 1963, recognized a relationship between several cash flows, namely, the cash flow to debt, CFD, the cash flow to equity, CFE, the tax savings or tax shields TS, and the free cash flow, FCF. The CFD and the CFE are constructed from the point of view of the debt and equity holders. This relationship might be named as conservation of cash flows or equilibrium among cash flows. It states that FCF + TS = CFD + CFE = CCF (4a) Where CCF stands for Capital Cash Flow. And hence, FCF = CFD + CFE − TS = CCF − TS (4b) This conservation of cash flows has to be valid for every period. Along with this conservation of cash flows there is another major relationship: the conservation of value, as follows: VL = VUn + VTS = VD + VE (4c) L Un TS Where V is the levered value, V is the unlevered value, V is the value of the TS, VD is the value of debt and VE is the levered value of equity. THE CASH FLOW CALCULATION There are two ways to get the cash flows for valuation: from the Income statement IS (the indirect method) and from the Cash Budget (the direct method). Both approaches if properly done, give identical results. In any case, the purpose is to arrive to the amount available and effectively distributed to the owners of debt and equity adjusted by the tax savings. If we use the direct method we pick out those amounts from the CB; if we use the indirect method we depart from the Income Statement and the Balance Sheet and make some adjustments to convert a 10
  11. 11. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja number (say EBIT or Net Income) based on accrual operations to cash flow available and effectively distributed. If we use the direct method we use the modules 3 and 4 from the CB and derive the TS from module 3, complying with some rules that we will show below. Vélez-Pareja, 1999 used the direct method departing from a Net Cash Balance that included some financial transactions and then it was necessary to undo some of them (related to the financing activity and equity holders transactions). This method should provide identical results as the one we will show in this paper. However, they included the cash in hand as part of the cash flows, which is inconsistent. In Vélez-Pareja, 2005a and 2005b shows the reasons of this inconsistency. When we use the indirect method we start from the IS and the BS and roughly we start from the Earnings Before Interest and taxes EBIT or Net Income and we add depreciation and amortization charges (and subtracting taxes from EBIT) and subtract the change in working capital. When we use the indirect method care has to be taken not to include some of the items we wish to arrive to. This is, we have to be careful and exclude those items associated with the financing of the firm or project, be it equity or debt. This method is widely used and is found in any financial textbook. However, it might be the source of potential errors. In the next pages we will show how to derive de different cash flows using the direct and indirect methods. THE CASH FLOW TO DEBT, CFD This cash flow is simply the inflows for debt borrowed to the firm and the outflows for interest and principal payments paid to the debt holder. These items are listed in the CB and can be put together to derive the CFD. The CFD is constructed from the point of view of the debt holder. This means that the inflows or proceeds from new loans are outflows for the debt holders and the outflows of payments are inflows for the debt holders as well. In the example: Table 6a Module 3 from the CB Module 3: Financing Module Proceeds from LT loan 1 Proceeds from LT loan 3 Proceeds from ST loan 2 Proceeds from loan in foreign exchange Principal payments LT loan 1 LT loan 3 ST loan 2 Loan in foreign exchange Interest charges Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 16,616.6 0.0 0.0 0.0 0.0 0.0 0.0 29,518.8 0.0 0.0 0.0 3,323.3 0.0 0.0 3,453.6 3,650.6 3,323.3 0.0 0.0 3,544.3 3,000.2 3,323.3 0.0 0.0 3,680.4 2,152.8 3,323.3 0.0 0.0 3,781.2 1,464.3 3,323.3 5,903.8 0.0 3,877.7 4,106.4 16,616.6 0.0 The derivation of the CFD from the module 3 is straightforward. 11
  12. 12. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table 6b CFD from the CB Year 0 Proceeds from LT loan 1 (1) Proceeds from LT loan 3 (2) Proceeds from ST loan 2 (3) Proceeds from loan in foreign exchange (4) Principal payments (5) LT loan 1 (6) LT loan 3 (7) ST loan 2 (8) Loan in foreign exchange (9) Interest charges (10) CFD (11) Debt outflow (12) (lines 1+2+3+4) Principal payments (13) (lines 6+7+8+9) Interest charges (14) (line 10) CFD (14) (lines 12+13+14) Year 1 Year 2 Year 3 Year 4 Year 5 0.0 0.0 0.0 0.0 0.0 0.0 −29,518.8 0.0 0.0 0.0 0.0 3,323.3 0.0 0.0 3,453.6 3,650.6 3,323.3 0.0 0.0 3,544.3 3,000.2 3,323.3 0.0 0.0 3,680.4 2,152.8 3,323.3 0.0 0.0 3,781.2 1,464.3 3,323.3 5,903.8 0.0 3,877.7 4,106.4 −33,233.1 0.0 0.0 −33,233.1 0.0 6,776.9 3,650.6 10,427.6 0.0 6,867.7 3,000.2 9,867.9 0.0 7,003.7 2,152.8 9,156.5 −29,518.8 7,104.5 1,464.3 −20,949.9 0.0 13,104.8 4,106.4 17,211.2 −16,616.6 −16,616.6 As can be seen from the BS, there is a debt balance outstanding in year 5 of 23,615.0. This debt outstanding is the present value of the CFD from year 6 up to infinity. Let us call this value the terminal value of the CFD. Now we show the CFD with its terminal value. Table 6c CFD from the CB with terminal value Year 0 CFD Terminal value for CFD CFD with terminal value Year 1 Year 2 Year 3 Year 4 Year 5 −33,233.1 10,427.6 9,867.9 9,156.5 −20,949.9 −33,233.1 10,427.6 9,867.9 9,156.5 −20,949.9 17,211.2 23,615.0 40,826.2 THE CASH FLOW TO EQUITY (CFE) From the stockholders point of view, the cash flow associated to them are the equity invested by them, the dividends or earnings paid and any repurchase of equity. Repurchase of equity is any effectively paid funds to the equity holder in excess to Net Income. As the CFE is constructed from the point of view of the equity holder, what the firm receives as equity investment is an outflow of cash for the equity holder and what the firm pays is an inflow. When discounting the CFE the problem of circularity arises. When the CFE is discounted at the cost of levered equity, Ke, we obtain the equity market value. The Net Present Value of this cash flow is the same NPV of the firm or project. (This is true when the market value of debt is the same as its book value. (See Appendix B). In our example, we depart from Module 4 where the equity investment, payment of dividends and repurchase of equity. The Module 4 in our example is 12
  13. 13. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table 7a Module 4 Equity Module from the CB Equity investment Dividend payments Repurchase of equity Year 0 Year 1 Year 2 Year 3 15,000.0 0.0 0.0 695.7 Year 4 Year 5 2,589.4 4,161.3 We have to remind that the CFE considers an outflow what is an inflow for the firm and vice versa. Then, the CFE is Table 7b CFE from the CB Equity investment (1) Dividend payments (2) Repurchase of equity (3) CFE (1) + (2) + (3) Year 0 Year 1 Year 2 Year 3 −15,000.0 0.0 0.0 695.7 −15,000.0 0.0 0.0 Year 4 2,589.4 4,161.3 2,589.4 695.7 Year 5 4,161.3 5 Let us assume we have a terminal value of the FCF at the end of year 5. This terminal value is the present value of the free cash flows at perpetuity beginning at year 6. Let it be 75,101.9. As we said above, the conservation of value has to be valid at any period. As we have a debt balance of 23,615.03, then the equity terminal value is the difference between the terminal value of FCF and the debt balance at year 5. Hence, the terminal value for equity is 51,486.89. The CFE with terminal value is Table 7c CFE from the CB with terminal value Year 0 Year 1 Year 2 Year 3 −15,000.0 0.0 0.0 695.7 Equity investment (1) Dividend payments (2) Repurchase of equity (3) CFE (1) + (2) + (3) −15,000.0 Terminal value CFE with terminal value −15,000.0 0.0 0.0 695.7 0.0 0.0 695.7 Year 4 Year 5 2,589.4 4,161.3 2,589.4 4,161.3 51,486.9 2,589.4 55,648.2 THE CAPITAL CASH FLOW, CCF The Capital Cash Flow is what effectively the debt and equity holders receive. When the CCF is discounted at the proper discount rate, we obtain the market value of the firm or project. The NPV of the CCF is the NPV of the firm or project and it is identical to the NPV for the equity when the market value of the debt is the same as its book value. Under some assumptions, the discounting process does not present the problem of circularity. (See Appendix B). As we can see in equation 4a once we have the CFD and the CFE we can calculate the CCF as CCF = CFD + CFE (4c) 5 The calculation of the terminal value has some complexities that we do not want to deal with in this paper. See Tham and Vélez-Pareja, 2004. 13
  14. 14. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja In our example Table 8a CCF from the CB CFD CFE CCF Year 0 -33,233.1 −15,000.0 −48,233.1 Year 1 10,427.6 0.0 10,427.6 Year 2 9,867.9 0.0 9,867.9 Year 3 9,156.5 695.7 9,852.2 Year 4 −20,949.9 2,589.4 −18,360.6 Year 5 17,211.2 4,161.3 21,372.5 With the CCF we can calculate the value of the firm or project. Table 8b CCF from the CB with terminal value CFD with terminal value CFE with terminal value CCF with terminal value Year 0 −33,233.1 −15,000.0 −48,233.1 Year 1 10,427.6 0.0 10,427.6 Year 2 9,867.9 0.0 9,867.9 Year 3 9,156.5 695.7 9,852.2 Year 4 −20,949.9 2,589.4 −18,360.6 Year 5 40,826.2 55,648.2 96,474.4 THE FREE CASH FLOW (FCF) OF A FIRM OR PROJECT The FCF is the amount of cash available and effectively distributed to the owners of debt and equity. It looks as a paradox, but FCF is not what remains in the firm but what leaves the firm as cash payments to the debt and equity holders. It is not what is left for investment and distribution, but only what is left for distribution after investment is done. This means that if the firm requires some investment, it is financed by funds provided by debt or equity, in the case the firm does not generate enough cash. More, if that were the case, the FCF might be negative, which implies that either the debt holder or the equity holder or both will have to invest additional funds and the cash flows (CFD, CFE or FCF) might be negative. When we calculate the present value of the FCF at the WACC we obtain the firm or project value. The NPV of the FCF is the NPV of the firm or project and it is identical to the equity NPV given that the market value of debt is the same as its book value. When calculating the present value of the FCF with the WACC, the circularity problem arises. (See Appendix B) Using (4b) we can calculate the FCF. However, we need the TS. A simple example will illustrate this idea. Assume that EBIT is 100 and the tax rate is 40%. The TS can be calculated as the difference between the taxes with and without debt. However, the TS depend on the size of EBIT compared with interest charges. Table 9 Tax savings calculations Levered A Levered B Unlevered EBIT 100 100 100 Interest charges 150 70 0 EBT -50 30 100 Tax 0 12 40 Net profit -50 18 60 If interest charges are 70 (Levered B), taxes will be 12 and the tax savings will be 28. If interest charges are 150 (Levered A) taxes will be zero, but there exists a tax savings of 40. In the 14
  15. 15. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja first case the TS are calculated as T×Interest charges, this is 28 (40%×70). In the second case the TS are not T×Interest (40%×150=60) but T×EBIT (40%×100=40). In our example we have something similar. The calculation of the TS is as shown in the next table. Table 10 Calculation of TS Tax rate Financial expenses Earnings before interest and taxes (EBIT) AI earned (T×Interest or T×EBIT) Tax savings based on T×Financial expenses Pending TS Recovery of TS Total TS Year 1 Year 2 Year 3 Year 4 Year 5 35.0% 35.0% 35.0% 35.0% 35.0% 3,650.6 3,000.2 2,152.8 1,464.3 4,106.4 4,407.6 7,412.1 9,450.6 9,473.8 4,181.9 1,463.67 1,177.08 896.32 583.10 1,471.02 1,505.79 1,177.08 896.32 583.10 1,471.02 42.12 0.00 0.00 0.00 0.00 0.00 42.12 0.00 0.00 0.00 1,463.67 1,219.20 896.32 583.10 1,471.02 On the other hand, is the direct calculation of FCF. Financial statements (Balance sheet, IS and Cash Budget CB) are projected and from the CB, the FCF is derived. It is important to know how the performance of the firm or project in terms of liquidity is. 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. With the TS calculated now we can calculate the FCF as FCF = CFD + CFE − TS (5) In our example we have Table 11a. Calculation of the FCF from the CB CFD CFE TS FCF = CFD + CFE − TS Year 0 -33,233.1 −15,000.0 0 -48.233,10 Year 1 Year 2 Year 3 Year 4 10,427.6 9,867.9 9,156.5 −20,949.9 0.0 0.0 695.7 2,589.4 1,463.67 1,219.20 896.32 583.10 8.963,91 8.648,70 8.955,90 -18.943,66 Year 5 17,211.2 4,161.3 1,471.0 19,901.5 Now we calculate the FCF with the terminal value. Table 11b. Calculation of the FCF from the CB FCF = CFD + CFE − TS Terminal value FCF with terminal value Year 0 -48.233,10 Year 1 Year 2 Year 3 Year 4 8.963,91 8.648,70 8.955,90 -18.943,66 Year 5 19,901.5 -48.233,10 8.963,91 8.648,70 8.955,90 -18.943,66 95,003.4 75,101.9 ADVANTAGES OF USING THIS APPROACH This approach of working with the three financial statements including the cash budget, has some advantages: 15
  16. 16. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja It provides managerial tools. The approach that suggests the construction of the different financial statements provides managerial tools for control and follow-up. It allows for immediate checking for consistency. The Balance Sheet and the relationship between cash flows provide a checking point to guarantee that the different cash flows and pro forma financial statements are correct. It is simple. The adjustments made refer to “real” figures found at the cash budget CB, except a “virtual” adjustment to the taxes paid (the tax shield). It is a better approach to what happens in reality. In the model, different real assumptions can be introduced, i.e. the reinvestment of cash surpluses. It provides a tool for sensitivity analysis and scenario analysis. The spreadsheet where these figures come from includes all the relationships between basic variables such as, prices, increases in prices, volume, increase in volume, price-demand elasticity, accounts receivable, accounts payable and inventory policies, cash cushion policy, etc. It provides means to calculate debt capacity. When constructing the CB the way we propose in this paper, we can estimate the maximum debt capacity for the firm discounting the Net Cash Balance from the operating module with the expected cost of debt. THE INDIRECT CALCULATION THE CASH FLOWS The cash flows can be deducted from the Income Statement (IS) either departing from the earnings before interest and taxes (EBIT) or the Net Income (NI). This is called the indirect method. Before any arithmetic to derive the cash flows we have to derive the working capital and its change. 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 WORKING CAPITAL Working capital is defined as current assets minus current liabilities. It is the result of some policies adopted by the firm: i.e. the account receivable and payable policy, the inventory policy and the excess cash investment policies. In our example we have Table 12. Working capital and Change in Working Capital Year 0 Cash Accounts receivable Inventory Investment in marketable securities Year 1 Year 2 Year 3 Year 4 Year 5 1,553.10 0.00 1,680.00 0.00 100.00 2,404.19 1,932.97 5,516.87 110.00 2,577.75 2,191.14 11,034.35 120.00 2,791.85 2,222.48 19,170.56 130.00 3,009.41 2,365.72 0.00 140.00 3,244.29 2,453.51 78.74 16
  17. 17. Construction of Free Cash Flows Revisited Current assets Accounts payable Current liabilities Working capital = Current assets − Current liabilities Change in working capital Ignacio Vélez-Pareja 3,233.10 0.0 0.0 9,954.03 1,716.6 1,716.6 15,913.25 1,936.7 1,936.7 24,304.89 2,670.6 2,670.6 5,505.13 2,842.7 2,842.7 5,916.55 2,949.4 2,949.4 3,233.1 3,233.1 8,237.4 5,004.3 13,976.5 5,739.1 21,634.3 7,657.8 2,662.4 -18,971.9 2,967.2 304.7 WHAT IS INCLUDED IN THE FCF WHEN USING THE INDIRECT METHOD In the IS some items are defined using the accrual principle and others include the financial effects of the financing decisions. This is the payment of interest and the tax savings derived from that. On the other hand, in the CB appear some other financing related items such as the principal payments, loans received, equity investments and distributed earnings. Those above-mentioned items should not be included in the FCF when using the indirect method, as follows. 1. Equity investment 2. Loans received 3. Loans paid 4. Interest charges paid 5. Tax shield for interest payments 6. Distributed earnings or dividends These are not included in the FCF because they are the items we are looking for: this is what is available for distribution and effectively distributed to the owners of debt and equity. In addition, 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. The FCF is called free because it is the cash flow not committed (free) for any other operating activity and that can be distributed and effectively distributed among owners of debt and equity adjusted by the tax savings TS. 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. In fact what we do is to compare what the debt and equity holders receive with what they expect to receive. The debt holder receives the interest expenses, the equity holder 17
  18. 18. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja receives the distributed dividends or distributed net income and all this is adjusted by the TS. All this is compared with what they expect to receive: the debt holder expects to receive the contractual interest (Kd×Dt−1), the equity holder expects to receive his return based on his expected cost of equity (Ke×Et−1) and the expected TS which is based in the expected interest to be received by the debt holder, (T×Kd×Dt−1). When we discount the cash flows what we do is to eliminate the expected cost of the resources received from the owners of debt and equity. Hence, in the indirect method we exclude items such as interest payments, dividends and TS; if not 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 $ Cost of money $ Value added $ 1,000 300 200 When discounted, the present value of $1,500 is $1,153.85. This figure can be decomposed as, Cash flow in year 1 $ Present value $ Cumulated 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 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. Year 0 1 FCF $ -1,000 1,500 Interest payments $ -300 18 Net FCF $ -1.000 1.200
  19. 19. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja When discounted at 30%, the NPV will be -76.92 and the project has to be rejected. Again, when calculating the cash flows with the indirect method, 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 the project is or what the same, how much value is created 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. However, for determining the TS the only tax rate to be taken into account is the corporate income tax. 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 income taxes paid by the firm with the project and the income 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. In particular, we have to be aware that in non-adjusted financial statements there are some costs related with the adjusted for inflation capital that generates tax savings. 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. DERIVING THE FCF FROM THE IS The free cash flow -FCF- can be deducted from the Income Statement (IS). This what they call indirect method. 19
  20. 20. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja DERIVING THE FCF FROM EBIT The right arithmetic for it is, starting from EBIT (for periods 0 to n): For year 0: total assets. For years 1 to n: Earnings before interest and taxes (EBIT) minus taxes on EBIT plus depreciation and amortization charges minus change in working capital plus returns on short term investment x (1-Tax rate) minus investment in the project For year n, add terminal value (or market value or continuing value). As we depart from the EBIT that is obtained from accrual operations, we need to “undo” some accruals made when EBIT is calculated (see Vélez-Pareja, 2005). The aim is to calculate what is available for distribution and effectively distributed to the equity and debt holders. Hence, we will “undo” any accrual or non-cash charges. When we add depreciation and amortization charges we are recognizing that these two items are not a cash movement and when we subtract the CWC we are adjusting EBIT that is based on accrual accounting, by those items that appear in the IS as if they have been totally received in cash (in particular, sales revenues and cost of goods sold because there exist accounts receivable and accounts payable). In the example: Table 8. FCF from EBIT Year 0 Year 1 Year 2 EBIT EBIT×T Depreciation and amortization charges Return on excess cash investments Tax on return on excess cash investments Change in working capital Investment Terminal Value FCF Year 3 Year 4 Year 5 0.0 0.0 4,181.9 -1,463.7 4,407.6 -1,542.6 7,412.1 -2,594.2 9,450.6 -3,307.7 9,473.8 -3,315.8 0.0 11,250.0 11,250.0 11,250.0 11,250.0 14,048.3 0.0 419.8 839.7 1,361.1 0.0 0.0 -5,004.3 0.0 0.0 8,963.9 -146.9 -5,739.1 0.0 0.0 8,648.7 -293.9 -7,657.8 0.0 0.0 8,955.9 -476.4 18,971.9 -56,193.2 0.0 -18,943.7 0.0 -304.7 0.0 75,101.9 95,003.4 -3,233.1 -45,000.0 0.0 -48,233.1 DERIVING THE FCF FROM NET INCOME We can derive the FCF from Net income. In this case we have to take into account not only the change in working capital and depreciation and amortization but have to include some adjustment related to the debt financing (remember that the Net Income results after the firm has 20
  21. 21. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja paid the interest charges. If calculated from Net Income, (for periods 1 to n) we have the following arithmetic: Net Income Plus Depreciation and amortization charges minus change in working capital plus interest charges(financial expenses) minus tax shield minus investment in the project For year n, add terminal value (market value or continuing value). In the example: Table 9 Deriving the FCF from Net Income Year 0 Net Income Depreciation and amortization Change in working capital CWC Financial expenses Tax shield from interest payments Investment in fixed assets Terminal value FCF Year 1 Year 2 -45,000.0 -120.3 11,250.0 -5,004.3 4,302.3 -1,463.7 0.0 993.9 11,250.0 -5,739.1 3,363.1 -1,219.2 0.0 3,699.1 5,944.7 11,250.0 11,250.0 -7,657.8 18,971.9 2,560.9 1,666.0 -896.3 -583.1 0.0 -56,193.2 -48,233.1 8,963.9 8,648.7 8,955.9 -18,943.7 -3,233.1 Year 3 Year 4 Year 5 3,426.1 14,048.3 -304.7 4,202.9 -1,471.0 0.0 75,101.9 95,003.4 In both cases, working capital is defined as current assets minus current liabilities […]. Cash and investment in marketable securities have to be included in the current assets because otherwise they would appear as cash flows (in the CFE) while they are in the BS. This would be a clear violation of the concept of cash flow. Cash flow is a movement of cash and hence it cannot appear as cash flow and as an item in the BS. DERIVING THE CFE FROM THE IS The cash flow to equity CFE can be derived from the IS. We can depart either from EBIT or from Net Income. In both cases, as above, we need to “undo” some accrual items and non-cash items that are listed when we calculate EBIT or Net Income. DERIVING THE CFE FROM EBIT The arithmetic for deriving the CFE from EBIT is as follows: Earnings before interest and taxes EBIT minus taxes on EBIT plus depreciation and amortization charges minus change in working capital plus returns on short term investment ×(1-Tax rate) plus proceeds from new debt 21
  22. 22. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja minus principal payments minus interest charges Plus tax shield for interest paid previous year (n-1) minus investment in the project For year n, add terminal value (or market value or continuing value). In our example we have, Table 10. Deriving the CFE from EBIT Year 0 EBIT Taxes on EBIT Depreciation and amortization charges Change in working capital Principal payment of debt Loss in foreign Exchange already considered either in the debt balance or the principal payment. Proceeds from new debt Investment in fixed assets Returns on short term investment Tax on Returns on short term investment Financial expenses TS Terminal Value CFE Year 1 Year 2 Year 3 Year 4 Year 5 0.0 0.0 0.0 −3,233.1 0.0 4,181.9 -1,463.7 11,250.0 −5,004.3 −6,776.9 4,407.6 -1,542.6 11,250.0 −5,739.1 −6,867.7 7,412.1 -2,594.2 11,250.0 −7,657.8 −7,003.7 9,450.6 -3,307.7 11,250.0 18,971.9 −7,104.5 9,473.8 -3,315.8 14,048.3 −304.7 −13,104.8 0.0 33,233.1 −45,000.0 0.0 0.0 0.0 651.6 0.0 0.0 0.0 0.0 −4,302.3 1,463.7 0.0 0.0 362.8 0.0 0.0 419.8 −146.9 −3,363.1 1,219.2 0.0 0.0 408.2 0.0 0.0 839.7 −293.9 −2,560.9 896.3 0.00 695.7 201.7 29,518.8 −56,193.2 1,361.1 −476.4 −1,666.0 583.1 0.0 2,589.4 96.5 0.0 0.0 0.0 0.0 −4,202.9 1,471.0 51,486.9 55,648.2 0.0 −15,000.0 DERIVING THE CFE FROM NET INCOME The arithmetic for deriving the CFE from Net Income is: Net Income plus depreciation and amortization and amortization plus proceeds from new debt minus change in working capital minus principal payments minus investment in the project In the example 22
  23. 23. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table 11. Year 0 Net Income Depreciation and amortization Change in working capital principal payments Loss in foreign Exchange already considered either in the debt balance or the principal payment. Proceeds from new debt Investment in the project Terminal value CFE Year 1 Year 2 Year 3 0.00 −120.35 993.92 3,699.07 0.00 11,250.00 11,250.00 11,250.00 −3,233.10 −5,004.34 −5,739.10 −7,657.78 −6,776.95 −6,867.66 −7,003.71 Year 4 Year 5 5,944.72 11,250.00 18,971.88 −7,104.54 3,426.06 14,048.29 −304.75 −13,104.78 96.48 0.00 0.00 51,486.89 55,648.2 33,233.10 −45,000.00 651.63 0.00 0.00 362.83 0.00 0.00 408.16 0.00 0.00 201.67 29,518.79 −56,193.16 −15,000.0 0.0 0.0 695.7 2,589.4 Observe that in the case of deriving the CFE from the IS we have to make some ad-hoc adjustments such as avoiding the double counting of loss in foreign exchange. When we pay the principal payment there is a loss in exchange embedded in that payment and it is listed in the IS as loss in exchange as well and is included in the financial expenses. This is one of the drawbacks of using the indirect method compared with the direct method: the analyst has to be aware of the peculiarities of the situation and has to include them in the “general” formulation to arrive to the cash flow. In the direct method all theses specific situations are included in the Module 4 of the CB. For checking purposes: Table 12 Cash flows derived from IS statement and the CB FCF (IS) CFE (IS) CFD CFD +CFE =CCF (IS) TS CFE (CB) CFD (CB) CFD +CFE =CCF (CB) FCF (CB)= CFD +CFE−TS Year 1 8,963.9 0.0 10,427.6 10,427.6 1,463.67 0.0 10,427.6 10,427.6 8.963,91 Year 2 8,648.7 0.0 9,867.9 9,867.9 1,219.20 0.0 9,867.9 9,867.9 8.648,70 Year 3 8,955.9 695.7 9,156.5 9,852.2 896.32 695.7 9,156.5 9,852.2 8.955,90 Year 4 -18,943.7 2,589.4 −20,949.9 −18,360.6 583.10 2,589.4 −20,949.9 −18,360.6 -18.943,66 Year 5 95,003.4 55,648.2 17,211.2 96,474.4 1,471.0 55,648.2 40,826.2 96,474.4 95,003.4 Notice that the FCF, CCF and CFE calculated from IS statement are identical to the ones calculated from cash budget. These last approaches from IS are conceptually right, but they have to be carefully done, trying to include any credit received or given to customers and any other item as mentioned above. However, they disregard possibility to construct and use the cash budget CB the project or firm. This is a very useful tool for the management and should be used as much as possible. Some teachers, analysts and practitioners do not include the change in working capital. Others subtract the principal and interest payments. More, some of them do not distinguish 23
  24. 24. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja between the cash budget CB and the free cash flow FCF. Others, (i.e. Blank and Tarquin6, 1998) do not make a difference between the free cash flow and the cash flow to equity. Some others define the working capital as current assets (not including cash and/or not including market securities) minus current liabilities. A very relevant issue in this paper is the inclusion of cash on hand (not considered in Velez-Pareja 1999) and this paper is a rectification/clarification of that 1999 paper. In general, it has to be said-, the cash in hand and cash-like items such as the investment of cash excess have to be included in the working capital. Otherwise, they will be considered as cash flows (in the CFE, and hence, in the FCF) even if they are not a cash flow (in fact they are listed in the BS and hardly can be considered as cash flows). In Velez-Pareja 2005a and 2005b very good arguments are posited to support this position. Additional to the violation of the concept of cash flow (just mentioned) arguments supporting this position include the inconsistency with the Capital Asset Pricing Model, CAPM and the implicit assumption of NPV identical to zero for the excess cash investment. This last assumption would lead to an indifferent position of the financial management when seeking for value in excess cash investment. If the NPV of those excess cash investments is zero, then they do not create value and hence, it is the same to keep that excess cash in hand or to invest it with a high return. And this makes no sense. SUMMARY In this paper we have shown how, when properly done, the direct and indirect method to calculate cash flows produce identical results. A method to calculate the FCF from the CB is presented. Methods to calculate the FCF from the IS statement are presented as well. These methods leads to the same FCF if careful done. As was shown in the body of the paper, when using the indirect method some ad-hoc items have to be taken into account to properly calculate the cash flows. Specifically we showed how this happens when deriving the CFE from the IS and when there are exchange losses due to a foreign exchange debt. In comparison, with the direct method that detail is taken into account straightforward when we use the CFD, the CFE and the TS derived from the CB. We leave the reader the decision to use the most simple and error proof method, remembering that “one should not do with more what can be done with less”. Finally, arguments are presented to support the idea of not including as cash flows items that are listed in the balance sheet, such as cash on hand and investment in marketable securities. BIBLIOGRAPHIC REFERENCES Blank, Leland T. and Anthony J. Tarquin, 1998, Engineering Economy, 4th edition, McGraw-Hill. Spanish version: Ingeniería económica, McGraw-Hill, 1999. Brealey, Richard A., Stewart C. Myers and Alan J. Marcus, 1995, Fundamentals of Corporate Finance, McGraw-Hill 6 This book is of great acceptance in the academic and practitioner’s world in Colombia. 24
  25. 25. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Copeland, Thomas E., T. Koller and J. Murrin, 1995, Valuation: Measuring and Managing the Value of Companies, 2nd Edition, John Wiley & Sons. Damodaran, Aswath, 1996, Investment Valuation, John Wiley. Gallagher, Timothy J. and Joseph D. Andrew, jr., 2000, Financial Management, 2nd ed., Prentice Hall, Modigliani, Franco and Merton H. Miller, 1958, The Cost of Capital, Corporation Taxes and the Theory of Investment, The American Economic Review. Vol XLVIII, pp 261-297 Modigliani, Franco and Merton H. Miller, 1959, The Cost of Capital, Corporation Finance, and the Theory of Investment: Reply, The American Economic Review, XLIX, pp. 524-527. Modigliani, Franco and Merton H. Miller, 1963, Corporate Income Taxes and the Cost of Capital: A Correction, The American Economic Review. Vol LIII, pp 433-443. Myers, Stewart C. 1974, “Interactions of Corporate Financing and Investment Decisions. Implications for Capital Budgeting”, Journal of Finance, March, pp. 1-25. Taggart, Jr, Robert A. 1989, Consistent Valuation and Cost of Capital Expressions with Corporate and Personal Taxes, National Bureau of Economic Research, August. Tham, Joseph and Ignacio Velez–Pareja, 2002, An Embarrassment of Riches: Winning Ways to Value with the WACC, Working Paper in SSRN, Social Science Research Network Tham Joseph and Ignacio Vélez Pareja, 2004, Principles of Cash Flow Valuation. An Integrated Market Based Approach, Academic Press. Van Horne, J.C. 1998, Financial Management and Policy, 11th Ed., Prentice Hall Inc., Englewood Cliffs, New Jersey. Vélez–Pareja, Ignacio and Joseph Tham, 2001, A Note on the Weighted Average Cost of Capital WACC, Working Paper in SSRN, Social Science Research Network, In Spanish as Nota sobre el costo promedio de capital in Monografías No 62, Serie de Finanzas, La medición del valor y del costo de capital en la empresa, de la Facultad de Administración de la Universidad de los Andes, Jul. 2002, pp. 61–98. Both versions are posted as working papers in SSRN, Social Science Research Network. Velez-Pareja, Ignacio, 1999, Construction of free cash flow: a Pedagogical note. Part I, Social Science Research Network, Corporate Finance Abstracts: Valuation, Capital Budgeting and Investment Policy, http://papers.ssrn.com/paper.taf?ABSTRACT_ID=196588 Velez-Pareja, Ignacio, 1999, Construction of free cash flow: a Pedagogical note. Part II, Social Science Research Network, Corporate Finance Abstracts: Valuation, Capital Budgeting and Investment Policy, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=199752 Velez-Pareja, Ignacio, 2004, Decisiones de inversión, Una aproximación al análisis de alternativas, CEJA, Available on line at http://www.javeriana.edu.co/decisiones/libro_on_line Velez-Pareja, Ignacio, 2005a, "Once More, the Correct Definition for the Cash Flows to Value a Firm (Free Cash Flow and Cash Flow to Equity)" (January 3, 2005). http://papers.ssrn.com/sol3/papers.cfm?abstract_id=199752 Velez-Pareja, Ignacio, 2005b, "The Correct Definition for the Cash Flows to Value a Firm (Free Cash Flow and Cash Flow to Equity)" (January 3, 2005). http://ssrn.com/abstract=597681 Velez Pareja, Ignacio, 1999, Value Creation and its Measurement: A Critical Look at EVA, Social Science Research Network, Financial Accounting (WPS) Vol.3 No.17 May 24, http://papers.ssrn.com/paper.taf?ABSTRACT_ID=163466 Velez-Pareja, Ignacio, 2005c Why We Subtract the Change in Working Capital when Defining Cash Flows? A Pedagogical Note, Social Science Research Network, Why We Subtract the 25
  26. 26. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Change in Working Capital when Defining Free Cash Flows? A Pedagogical Note Weston, J. Fred and T.E. Copeland, 1992, Managerial Finance, 9th ed. The Dryden Press. 26
  27. 27. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja APPENDIX A In this appendix we show how to calculate the maximum debt capacity of the firm departing from the Net cash balance before investment in assets in Module 1. Table A1. Calculation of maximum debt capacity Year 0 Net cash balance before investment in assets Forecasted interest rates Maximum debt capacity Year 1 Year 2 Year 3 Year 4 Year 5 14,491.4 14,975.5 17,158.7 17,310.9 21,461.3 13.03% 12.52% 12.52% 12.01% 11.50% 59,393.8 52,641.4 44,256.6 32,638.8 19,247.8 When we have non constant discount rates we use the following expression: PVt +1 + CFt +1 PVt = 1 + DR t +1 (A1) Where PVt is the present value at time t, PVt+1 is the present value at time t+1, CFt+1 is the cash flow at time t+1 and DRt+1 is the discount rate at time t+1. For instance, for year 4 the present value is PV5 + CF5 0 + 21,461.3 PV4 = = = 19,247.8 1 + DR 5 1 + 11.50% For year 3 the present value is PV4 + CF4 19,247.8 + 17,310.7 PV3 = = = 32,638.8 1 + DR 4 1 + 12.01% APPENDIX B In this appendix we show how to calculate the firm value with the CCF, FCF and CFE. The discount rate for the CCF is Ku; the discount rate for the FCF is WACC but in this case we have to use a different expression for it because the restrictive conditions for using equation (2) in the body of the paper are not met; the discount rate for CFE is Ke. In these cases we apply the same formulation for the present value shown at (A1). The calculation of the present value for the CCF is straightforward because in this case we do not find the circularity problem. The first step we do is to inflate the real Ku defined for year 0. We include the inflation for each year in the value of nominal Ku, using the well know Fisher relationship. 27
  28. 28. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table B1. Calculation of nominal Ku Inflation year 0 Nominal Ku observed at year 0 Ku real at year 0 Inflation rate Ku nominal for each year Year 0 5.01% 14.5659100% 9.10% Year 1 Year 2 Year 3 6.00% 15.65% 5.50% 15.10% 5.50% 15.10% Year 4 5.00% 14.56% Year 5 4.50% 14.01% For year 4 we have Ku4 = (1+9.1%)×(1+5.0%)−1 = 14.56%. Table B2. Calculation of value with the CCF Year 0 CCF Ku (nominal) PV(CCF at Ku) 60,613.3 Year 1 10,427.6 15.65% 59,669.3 Year 2 9,867.9 15.10% 58,811.8 Year 3 9,852.2 15.10% 57,840.4 Year 4 -18,360.6 14.56% 84,619.7 Year 5 96,474.4 14.01% For year 4 the present value is PV5 + CF5 0 + 96,474.4 PV4 = = = 84,619.7 1 + DR 5 1 + 14.01% For year 3 the present value is PV3 = PV4 + CF4 84,619.7 − 18,360.6 = = 57,840.4 1 + DR 4 1 + 14.56% In the case of the FCF we have to apply the WACC as discount rate. However, as we said above we cannot use (2) but a different expression for WACC as follows: TS WACC t = Ku t − t (B1) Vt -1 This formulation presents circularity. We have to iterate. The first iteration is calculated with any value for WACC, say 0%. Table B3a. Temporary calculation of value with the FCF Year 0 TS FCF WACC = Ku-TS/V V Year 1 1,463.7 8,963.9 Year 2 1,219.2 8,648.7 Year 3 896.3 8,955.9 Year 4 583.1 -18,943.7 102,628.3 93,664.4 85,015.7 76,059.8 Year 5 1,471.0 95,003.4 95,003.4 Once we have an initial value (temporary) we can construct the WACC for this case. 28
  29. 29. Construction of Free Cash Flows Revisited Ignacio Vélez-Pareja Table B3a. Final calculation of value with the FCF Year 0 TS FCF WACC = Ku-TS/V V 60,613.3 Year 1 1,463.7 8,963.9 13.23% 59,669.3 Year 2 1,219.2 8,648.7 13.06% 58,811.8 Year 3 896.3 8,955.9 13.58% 57,840.4 Year 4 583.1 -18,943.7 13.55% 84,619.7 Year 5 1,471.0 95,003.4 12.27% Observe that the value V is identical with the obtained with the CCF. When calculating the market equity value we have the same problem of circularity. We have to determine the value of Kd, the cost of debt and we calculate it as the financial expenses divided by the value of debt at the beginning of the period (end of previous period). Table 4. Calculation of Kd Year 0 Debt Financial expenses Kd=Gast Fin t/Saldo deuda t-1 Year 1 Year 2 Year 3 Year 4 Year 5 33,233.10 27,107.79 4,302.27 12.95% 20,602.97 3,363.08 12.41% 14,007.42 2,560.93 12.43% 36,623.33 1,666.00 11.89% 23,615.03 4,202.93 11.48% Now we proceed to calculate the temporary the market value of equity. Table B3 Table 5a. Temporary calculation of equity market value with the CFE Year 0 CFE Ke = Ku +(Ku-Kd)D/E PV(CFE at Ke) Year 1 0.0 Year 2 0.0 Year 3 695.7 Year 4 2,589.4 Year 5 55,648.2 58,933.3 58,933.3 58,933.3 58,237.5 55,648.2 0.0 Once we have the initial (temporary) value of the market equito value we can proceed to introduce the formulation of Ke. Table 5b. Final calculation of equity market value with the CFE Year 0 CFE Ke = Ku +(Ku-Kd)D/E PV(CFE at Ke) Debt V 27,380.2 33,233.1 60,613.3 Year 1 0.0 18.92% 32,561.5 27,107.8 59,669.3 Year 2 0.0 17.34% 38,208.8 20,603.0 58,811.8 Year 3 695.7 16.54% 43,833.0 14,007.4 57,840.4 Year 4 2,589.4 15.41% 47,996.3 36,623.3 84,619.7 Year 5 55,648.2 15.94% 0.0 Observe that the value V is identical with the obtained with the CCF and the FCF. In valuation all the methods (more than 10) should give identical results. 29

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