• Selected
• Entire List

Abstract:
SUBJECT AREAS: Corporate Finance, Valuation, Capital Budgeting, Investment Policy, Economic Value Added, EVA, Market Value Added, MVA, Net Present Value, NPV, cash flows, free cash flows real free cash flows

This technical note studies Economic Value Added, EVA. First, a conceptual framework regarding Net Present Value, NPV, is presented. Second, the note presents an approach for calculating the free cash flow of a project starting from the periodic net cash flows. Third, a procedure for calculating the real free cash flow is developed. Fourth, the EVA is presented and contrasted to NPV. EVA starts from accounting figures (profit) and NPV starts from net cash flows. The coincidence between MVA and NPV is examined. Four examples are presented which reveal some inconsistencies between the two measurement. The four examples show circumstances where EVA underestimates the value generated by a project or firm as compared with the NPV. An approach for calculating the real EVA is presented. The note offers reflections upon figures that should be employed in order to calculate the cost of the invested capital or equity to be included in EVA calculation. Finally, different approaches to calculate EVA and MVA are compared with NPV results.

Abstract:
Most finance textbooks (See Benninga and Sarig, 1997, Brealey, Myers and Marcus, 1996, Copeland, Koller and Murrin, 1994, Damodaran, 1996, Gallagher and Andrew, 2000, Van Horne, 1998, Weston and Copeland, 1992) present the Weighted Average Cost of Capital WACC calculation as:

WACC = d(1-T)D% eE% (1)

Where d is the cost of debt before taxes, T is the tax rate, D% is the percentage of debt on total value, e is the cost of equity and E% is the percentage of equity on total value. All of them precise (but not with enough emphasis) that the values to calculate D% y E% are market values. Although they devote special space and thought to calculate d and e, little effort is made to the correct calculation of market values. This means that there are several points that are not sufficiently dealt with: Market values, location in time, occurrence of tax payments, WACC changes in time and the circularity in calculating WACC. The purpose of this note is to clear up these ideas and emphasize in some ideas that usually are looked over.

Also, some suggestions are presented on how to calculate, or estimate, the equity cost of capital.

Published as "Market Value Calculation and the Solution of Circularity between Value and the Weighted Average Cost of Capital".

Weighted Average Cost of Capital, WACC, firm valuation, capital budgeting, equity cost of capital

Abstract:
In Velez-Pareja and Tham (2001), we presented several different ways to value cash flows. First, we apply the standard after-tax Weighted Average Cost of Capital, WACC to the free cash flow (FCF). Second, we apply the adjusted WACC to the FCF, and third we apply the WACC to the capital cash flow. In addition, we discount the cash flow to equity (CFE) with the appropriate returns to levered equity. We refer to these four ways as the "discounted cash flow (DCF)" methods.

In recent years, two new approaches, the Residual Income Method (RIM) and the Economic Value Added (EVA) have become very popular. Supporters claim the RIM and EVA are superior to the DCF methods. It may be case that the RIM and EVA approaches are useful tools for assessing managerial performance and providing proper incentives. However, from a valuation point of view, the RIM and EVA are problematic because they use book values from the balance sheet. It is easy to show that under certain conditions, the results from the RIM and EVA exactly match the results from the DCF methods.

Velez-Pareja 1999 reported that when using relatively complex examples and book values to calculate Economic Value Added (EVA), the results were inconsistent with Net Present Value (NPV). Tham 2001, reported consistency between the Residual Income Model (RIM) and the Discounted Cash Flow model (DCF) with a very simple example. Fernandez 2002 shows examples where there is consistency between DCF, RIM and EVA. He uses a constant value for the cost of levered equity capital and in another example constant debt. Young and O'Byrne, 2001, show simple examples for EVA but do not show the equivalence between DCF and EVA. Ehrbar (1998) uses a very simple example with perpetuities and shows the equivalence between EVA and DCF. Lundholm and O'Keefe, 2001, show this equivalence with an example with constant Ke. Tham 2001, commented on their paper. Stewart, 1999, shows the equivalence between DCF and EVA with an example using a constant discount rate. Copeland, et al, show an example with constant WACC and constant cost of equity even with varying debt and assuming a target leverage that is different to the actual leverage.

In general, textbooks do not specify clearly how EVA should be used to give consistent results.

In this teaching note using a complex example with varying debt, varying leverage and terminal (or continuing value), we show the consistency between DCF, RIM and EVA. We stress what Velez-Pareja 1999 and Fernandez 2002 said: for a single period, RI or EVA does not measure value. We have to include expectations and market values in the calculation of discount rates and hence values.

Economic Value Added, EVA, Market Value Added, MVA, Net Present Value, NPV, cash flows, free cash flows, market value of equity, market value of the firm

Abstract:
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 that serve 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, it is necessary to redefine working capital: 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.

Free cash flow; Cash flow to equity; Cash flow to debt; Project evalaution; Firm valuation; Investment valuation; Net Present Value, NPV assumptions

Abstract:
Most finance textbooks (See Benninga and Sarig, 1997, Brealey, Myers and Marcus, 1996, Copeland, Koller and Murrin, 1994, Damodaran, 1996, Gallagher and Andrew, 2000, Van Horne, 1998, Weston and Copeland, 1992) present the Weighted Average Cost of Capital WACC calculation as:

WACC = d(1-T)D% eE% (1)

Where d is the cost of debt before taxes, T is the tax rate, D% is the percentage of debt on total value, e is the cost of equity and E% is the percentage of equity on total value. All of them precise (but not with enough emphasis) that the values to calculate D% y E% are market values. Although they devote special space and thought to calculate d and e, little effort is made to the correct calculation of market values. This means that there are several points that are not sufficiently dealt with: Market values, location in time, occurrence of tax payments, WACC changes in time and the circularity in calculating WACC. The purpose of this note is to clear up these ideas and emphasize in some ideas that usually are looked over.

Also, some suggestions are presented on how to calculate, or estimate, the equity cost of capital.

Weighted Average Cost of Capital, WACC, firm valuation, capital budgeting, equity cost of capital

Abstract:
In this short teaching note I explain why we subtract the change in working capital from the proper item (Earnings before interest and taxes (EBIT) or Net income) in the Income Statement. I show in detail how departing from the sales revenues and the cost of goods sold we have to subtract the change in working capital. This explanation might be seen as unnecessary given it is a common practice. However, my experience in teaching this subject indicates that some additional explanations are needed.

Cash flows, free cash flow, cash flow to equity, working capital

Abstract:
This is the second part of a paper where the construction of the free cash flow is studied. Usually a great deal of effort is given 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 the Internal Rate of Return, IRR. In Part I, a procedure for projecting pro forma financial statements (Balance Sheet (BS), Profit and Loses Statement (P&L) and Cash Budget (CB) is 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 found 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. Textbooks studied include Blank and Tarquin, 1998, Brealey, Myers and Marcus 1995, Copeland et.al. 1995, Damodaran, 1996, Gallaher and Andrew, 2000, and Weston and Copeland, 1992.

Abstract:
Usually in financial textbooks and courses the theory of portfolio selection is taught in a strictly theoretical way. There is a model (Markowitz) that stipulates that an investor has preferences and that she will choose the best portfolio, given her preference curves and an efficient frontier. On the other hand, the Capital Asset Pricing Model (CAPM) is presented as it is: a genial idea that served to simplify and to make operative the Markowitz setup.

Most students and practitioners conclude that those models are just inapplicable theory. This is the most rational behavior one can expect. What can an investor do with the textbook recipes to configure an optimal portfolio? Very little.

My purpose with this note is to rescue a simple procedure presented by Black (1972), Merton (1973) and later by Levy and Sarnat (1982), Elton and Gruber (1995) and Benninga (1997). They just propose that the optimal portfolio can be found maximizing the slope of the line that joins the point of risk-free return and the efficient frontier. When this maximum tangent is reached, that line is the capital market line (CML) (it is tangent to the efficient frontier). This is a simple procedure that does not require one to calculate the efficient frontier and is an easy task with Excel Solver. It is just one point of the efficient frontier. An example is presented.

Keywords CAPM, efficient frontier, porfolio selection, capital market line, optimal portfolio

Abstract:
In Velez-Pareja, (1999b and 1999c), some difficulties of EVA as an approach for the measurement of economic added value were considered. In those papers, the use of real economic value added based on the real free cash flow was suggested. This means the real cash flow calculated from the immediately previous period. In Velez-Pareja (1999a and 2000), a methodology was presented to determine and to construct the free cash flow of a firm. The present article studies based on the previous works, an indicator of value added derived from the real free cash flow.

Free cash flow, firm evaluation, firm valuation, investment valuation, Net Present Value (NPV), Economic Value Added (EVA)

Abstract:
This short paper studies the Economic Profit, a different label for the Economic Value Added, EVA. Copeland et al. (1995) show that the present value of the free cash flow and the present value of EVA (Market Value Added MVA) are not the same, unless the present value of future EVA (they call it economic profit) be added to the initial capital invested. This present value includes, in both of them, the continuing value, which is the present value of the perpetuity for the cash flow and for the economic profit. For both of them, they end up with the Entity Value and the Equity Value. They present an extensive example and it will be analyzed in this paper. In that example they show that both, Entity and Equity Value are the same when calculated through the free cash flow or the economic profit. In this paper that assertion is examined in detail. It will be shown with the same example presented by them, that it holds true only under very restrictive assumptions. This is, when WACC assumes a given value.

Abstract:
When creating a firm or when we intend to value an ongoing concern it is very important to have reliable and consistent financial statements in order to make the proper decisions not only for the starting of a new firm but for the following up and monitoring that firm or simply an ongoing concern. In this guide we show a very clear and simple step by step procedure to construct proforma financial statements. From these financial statements we will derive the cash flows necessary to calculate the market value and net present value (NPV) for the firm. We calculate the traditional break even points and what we call the dynamic break even points. We present some complexities and show a simple sensitivity analysis that includes the determination of critical variables and scenario analysis.

Financial statements, forecasting, net present value (NPV), firm valuation, equity valuation, cost of capital, break even analysis, sensitivity analysis, cash flow valuation

Abstract:
Practitioners and teachers very easily break some consistency rules when doing or teaching valuation of assets. In this short and simple note we present a practical guide to call the attention upon the most frequent broken consistency rules. They have to do firstly with the consistency in the matching of the cash flows, this is, the free cash flow (FCF), the cash flow to debt (CFD), the cash flow to equity (CFE) and the tax savings or tax shield (TS). Secondly, they have to do with the proper expression for the cost of unlevered equity with finite cash flows and perpetuities. Thirdly, they have to do with the consistency between the terminal value and growth for the FCF and the terminal value and growth for the CFE, when there is a jump in the CFE due to the adjustment of debt to comply with the leverage at perpetuity. And finally, the proper determination of the cost of capital either departing from the cost of unlevered equity (Ku) or the cost of levered equity (Ke). In the Appendixes we show some algebraic derivations and an example.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity

Abstract:
In cash flow valuation (CFV), there are two main categories of mistakes: derivation of the appropriate cash flows and estimation of the cost of capital. A simple-minded view of the world would suggest that with near perfect capital markets, the presence of arbitrage would severely punish wrong valuations and eradicate such mistakes in the derivations of cash flows and estimations of the cost of capital. Nonetheless, to the dismay of academics, such mistakes continue to exist and thrive. It is not clear why such mistakes persist in practice.

In this paper we present our list of the top nine mistakes in cash flow valuation. In the age of the computer these mistakes are both unnecessary and avoidable. In the usual triumph of hope over experience, we are attempting to persuade analysts that they would benefit from paying attention to these mistakes. Ultimately, the (un)importance of the mistakes is an empirical question and depends on the considered judgment of practitioners.

Cost of capital, WACC, valuation

Abstract:
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 reflected in the financial statements behind the practice of including as cash flow items that appear in the Balance Sheet.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cash budget

Abstract:
Vélez-Pareja and Tham (2001), presented several different ways to valor cash flows. First, we apply the standard after-tax Weighted Average Cost of Capital, WACC to the free cash flow (FCF). Second, we apply the adjusted WACC to the FCF, and third we apply the WACC to the capital cash flow. In addition, we discount the cash flow to equity (FCA) with the appropriate returns to levered equity. We refer to these four ways as the "discounted cash flow (DCF)" methods.

In recent years, two new approaches, the Residual Income Method (RIM) and the Economic Valor Added (EVA) have become very popular. Supporters claim the RIM and EVA are superior to the DCF methods. It may be case that the RIM and EVA approaches are useful tools for assessing managerial performance and providing proper incentives. However, from a valuation point of view, the RIM and EVA are problematic because they use book values from the balance general. We refer to these methods as valor added methods. It is easy to show that under certain conditions, the results from the RIM and EVA exactly match the results from the DCF methods.

Velez-Pareja 1999 reported that when using relatively complex examples and book values to calculate Economic Valor Added (EVA), the results were inconsistent with Net Present Valor (NPV). Tham 2001, reported consistency between the Residual Income Model (RIM) and the Discounted Cash Flow model (DCF) with a very simple example. Fernandez 2002 shows examples where there is consistency between DCF, RIM and EVA. He uses a constant valor for the cost of levered equity capital and in another example constant debt. Young and O'Byrne, 2001, show simple examples for EVA but do not show the equivalence between DCF and EVA. Ehrbar (1998) uses a very simple example with perpetuities and shows the equivalence between EVA and DCF. Lundholm and O'Keefe, 2001, show this equivalence with an example with constant Ke. Tham 2001, commented on their paper. Stewart, 1999, shows the equivalence between DCF and EVA with an example using a constant discount rate. Copeland, et al, show an example with constant WACC and constant cost of equity even with varying debt and assuming a target leverage that is different to the actual leverage.
In general, textbooks do not specify clearly how EVA should be used to give consistent results.

In this teaching note using a complex example with varying debt, varying leverage and terminal (or continuing valor), we show the consistency between DCF, RIM and EVA. We stress what Velez-Pareja 1999 and Fernandez 2002 have said: for a single period, RI or EVA does not measure valor. We have to include expectations and market values in the calculation of discount rates and hence values.

Economic Value Added, EVA, Market Value Added, MVA, Net Present Value, NPV, cash flows, free cash flows, market value of equity, market value of the firm

Abstract:
In this teaching note I explain a method to obtain consensus among the members of a group. This method is the well known Delphi Method. This method is useful to close the gap between the total ignorance regarding a fact or situation and a disciplined guess. I present the origin of the name, that is associated to the Delphos Oracle in Greece and I define the origin and operational procedure as well. I mention the advantages, the basic elements and the most common critiques and objections found in the literature. Finally, I present the most common uses of the method. In the last section I conclude. This note is not intended to present something really new. It is just an actualized bibliographic review.

Uncertainty, consensus, group decisions, decisions under uncertainty, Delphi method, group of experts, impact matrices, committee work

Abstract:
This paper is a Spanish version of two previous papers published at Social Science Research Network: Value Creation and its Measurement: A Critical Look at EVA and Economic Value Measurement: Investment Recovery and Value Added - IRVA. The first section is an introduction. In section 2 a conceptual framework regarding the Net Present Value, NPV, is presented. The NPV is a method for financial decision-making based on value maximization. In section 3, the need to measure value is presented. Section 4 studies the Economic Value Added, EVA. EVA is presented as it pursues to measure the same concept as the NPV does. However, EVA starts from accounting figures (profit) and NPV starts from net cash flows. In this section it is shown the correlation between the stock value for Coca Cola and some other indicators, including Economic Profit -EP- and some examples are presented where it is shown that EVA and EP do not measure value. In section 4 some adjustments for EVA and EP are mentioned. The concept of Market Value Added is studied and the coincidence between MVA and NPV is examined. Examples are presented where some inconsistencies between the two measurements are found. In section 5 an alternative to the measurement of value is presented: Investment Recovery and Value Added. It is based on free cash flows, implies the investment recovery schedule and the discounted payback period. A procedure to calculate the real cash flow is presented. In section 6, we conclude.

English versions of two previous papers are also at SSRN: Value Creation and its Measurement: A Critical Look at EVA http://papers.ssrn.com/abstract=163466 and Economic Value Measurement: Investment Recovery and Value Added - IRVA http://papers.ssrn.com/abstract_id=223429
cash flows

Economic Value Added; EVA; Market Value added, MVA; Net Present Value; NPV; Cash flows; Free cash flows; Real free

Abstract:
Subject Areas: project evaluation, capital budgeting, investment, constant and nominal prices, valuation analysis, NPV and NPV assumptions, cash flows, cash flows construction, sensitivity analysis, pro-forma financial statements. Example Setting: Hypothetical firm in an inflationary environment. In this example it is shown how the usual procedure for evaluating a project (i.e., assuming constant prices or constant dollars and a deflated or real rate of discount) could give an inappropriate investment recommendation.

Situation:

This is a technical note, useful for supporting a lecture, class discussion, or case analysis. The example of a hypothetical firm illustrates how to construct a free cash flow based on given parameters (inflation rate, real interest rate, risk premiums, prices, price increases, elasticity function, accounts receivable and accounts payable policies, etc.) and then value the firm.

This technical note has six objectives:

* illustrate how to construct a pro-forma financial statement, such as Balance Sheet, Profit and Loss Statement, and cash flow forecast for the new firm.

* show how the financial evaluation of the firm as a project made with constant prices and/or constant dollar and real or deflated interest rates might differ from the evaluation of the same project with current or nominal prices.

* suggest the conditions or assumptions that have to be met in order for the two approaches (the constant price approach and the current or nominal price approach) to give equal results (this is, identical NPV).

* show which problems in the follow up and monitoring of a project might be present when working with the constant price approach.

* illustrate why NPV calculated at constant prices and real or deflated rate of interest is, in general, different to the NPV calculated at current or nominal prices and discounted at nominal rates of interest, contrary to what is written in many financial textbooks.

* describe how a spreadsheet might be utilized to make a more sophisticated analysis and avoid unnecessary, but widely-used oversimplifications. An Excel spreadsheet accompanies the note and allows students to conduct sensitivity analysis on the project's NPV and other results.

Abstract:
In order to value a firm or a project, it is necessary to construct estimated financial statements and free cash flows. In this teaching note we will present a spreadsheet model - EXCEL© - for forecasting financial statements in a consistent way and without using what is known as plugs. The simplest and coarse form of a plug in forecasting financial statements is to match the financial statements (in particular the Balance Sheet) creating a line or item to account for any difference that arises between total assets and liabilities plus debt in order to make the Balance Sheet to check. If total assets are greater than total liabilities plus equity, then the plug is a new line in the liabilities side. If lower, the plug is a line in the assets side. This is no only inappropriate, but it can hide mistakes when working with complex models such as those used by valuation analysts.

We illustrate the procedure with an example that has some complexities. These complexities are explained in Section One. The purpose of this note is that the reader, following the instructions, could complete the example. Then, the readers are encouraged to read actively by constructing the financial statements for themselves on a spreadsheet. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from policies and/or targets (i.e. accounts receivable policy or target) and input data that is specific for the firm or from the macroeconomic environment. With these targets or policies and data we can construct the financial statements. For valuation purposes, the balance sheet and the income statements are important but may be insufficient if we wish to construct the cash flow using the direct method. For that reason we construct the CB.

From the table of parameters we construct tables that will be used in the construction of the main financial statements. In the main text we describe some complexities such as price-demand elasticity, the effect of book value leverage on the real growth and on accounts payable policy. We introduce the effect of accounts receivable policy on growth as well.

We reproduce Excel© spreadsheet and in the last two columns we include the formulation than the reader should replicate and copy for the forecasting period. There are a few exceptions, but they will be announced.

Financial statements, forecasting, net present value (NPV), firm valuation, equity valuation, cost of capital, break even analysis, sensitivity analysis, scenario analysis, cash flow valuation

Abstract:
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) and available at SSRN. 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 reflected in the financial statements

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cash budget

Abstract:
Velez-Pareja and Tham, 2003a, Velez-Pareja and Tham, 2003b and Tham and Velez-Pareja, 2004 showed the matching between discounted cash flow (DCF) methods and value added methods. They departed from the net operating profit less adjusted taxes NOPLAT and net income when using market values to calculate the weighted average cost of capital (WACC) and the cost of levered equity, Ke. In those previous works they assumed that the proper discount rate for the tax savings is the unlevered cost of equity, Ku. We assume the same discount rate in this paper. The previous procedures implied circularity between the cost of capital and the levered values. In this paper we show that the same firm values can be obtained using the cost of unlevered equity, Ku and the net income and the interest charges. No circularity is found using this procedure.

EVA, economic value added, cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cost of levered equity, cost of unlevered equity, tax savings

Abstract:
We discuss some ideas useful when forecasting financial statements that are based on historical data.

The chapter is organized as follows: First we discuss the relevance of prospective analysis for non traded firms. In a second section we a basic reviews of subjects that will be needed for forecasting financial statements. We discuss the use of plugs for financial forecasting. We show an alternate approach to avoid such popular practice. The approach we propose follows the Double Entry Principle. This principle guarantees consistent and error free financial statements. We show with a simple example how the plug works and its limitations and problems that arise when using it.

Next, the reader will find what information is needed for the forecasting of financial statements and where and how to find it. We present the procedure to identify policies that govern the ongoing of a firm such as accounts receivable and payable, inventories, dividend payout, and identify price increases and other basic variables. We also deal with the real life problem of a firm with multiple products and/or services.

We start with historical financial statements. We include inflation rates, real increases in prices and volume and policies in order to construct intermediate tables that make very easy the construction of the pro forma financial statements. We use a detailed example to illustrate the method.

We derive the cash flows that will be used in the book to value a firm. This type of models might be used by non traded firm for a permanent assessment of the value creation. Finally we show some tools to perform sensitivity analysis for financial management and analysis.

Financial statements forecasting, sensitivity analysis, cash flows, plug, financial statement balancing

Abstract:
The purpose of this paper is twofold: the first purpose is to tell a naive history of an experience in constructing knowledge. In this first part I tell how I approached the process to solve the inconsistency between the net present value, NPV, the internal rate of return, IRR and the benefit-cost ratio B/CR or profitability index. There are improvements and drawbacks, mistakes and successes. I think this is important for our students because sometimes they might believe that discovering new ideas or new approaches is an insurmountable job. Sometimes it is, but they have to learn that this is a cumulative process with advances and drawbacks and sometimes it is necessary to start again and start from scratch. The second purpose is to study the development of a procedure to include the implicit assumptions of NPV in the IRR and the profitability index (benefit-cost ratio B/CR). The resulting indicators are named the weighted IRR (WIRR) and the expanded B/CR (EB/CR). These two desirability measures have the property to coincide with the NPV ranking for investment analysis and hence, will maximize value. Examples are presented.

Net present value, NPV, internal rate of return, IRR, benefit-cost ratio, B/CR, profitability index, NPV assumptions, overall rate of return, modified internal rate of return, MIRR.

Abstract:
In this teaching note I make a short review of the major statistics regarding the non traded firms in the U.S. and in Colombia as an example of an emerging market. I show some alternatives to estimate the cost of equity capital when there is not enough trading information. Some of them use the Capital Assets Pricing Model (CAPM), some of them use accounting information or simply, subjective estimation of risk.

The note is organized as follows: In Section One I present some relevant statistics regarding the non traded firms in the U. S. and in Colombia. In Section Two I mention the importance of the emerging markets mostly composed of non-trading firms and the relevance of popular approaches to the estimation of cost of equity capital. In Section Three I distinguish between total and systematic risk and present methods to estimate the cost of equity capital with systematic risk and total risk. When using Accounting Risk Models (ARM) I use data from a well known firm in the Colombian stock market. In Section Four I present some concluding remarks.

stocks, stock markets, Colombia, Colombian stock market, nominal returns on stocks, Colombian firms, CAPM, cost equity capital, levered cost of equity capital, unlevered cost of equity capital, non-trading firms, risk free rate of return, risk premium, Accounting Risk Models (ARM), Asset Pricing, Capital Budgeting, Investment Policy

Abstract:
In this teaching note I make a short review of the major statistics regarding the non traded firms in the U.S. and in Colombia as an example of an emerging market. I show some alternatives to estimate the cost of equity capital when there is not enough trading information. Some of them use the Capital Assets Pricing Model (CAPM), some of them use accounting information or simply, subjective estimation of risk.

The note is organized as follows: In Section One I present some relevant statistics regarding the non traded firms in the U. S. and in Colombia. In Section Two I mention the importance of the emerging markets mostly composed of non trading firms and the relevance of popular approaches to the estimation of cost of equity capital. In Section Three I distinguish between total and systematic risk and present methods to estimate the cost of equity capital with systematic risk and total risk. When using Accounting Risk Models (ARM) I use data from a well known firm in the Colombian stock market. In Section Four I present some concluding remarks.

Stocks, stock markets, Colombia, Colombian stock market, nominal returns on stocks, Colombian firms, CAPM, cost equity capital, levered cost of equity capital, unlevered cost of equity capital, non trading firms, risk free rate of return, risk premium, Accounting Risk Models (ARM), Asset Pricing, Ca

Abstract:
In this teaching note the reader finds a simplified financial model. In reality, financial models are huge and cumbersome. This is a very simplified model compared with what is found in practice.

We present some basic principles for constructing the financial statements needed for valuation. The reader is encouraged to construct the financial statements for herself on a spreadsheet. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements.

The first table to be constructed is the table of parameters. This table organizes all of the relevant information. The subsequent tables are linked to the table of parameters via formulas. We construct other supplementary tables that will be used in the construction of the main financial statements. We indicate the formulas that have to be utilized in the construction of the financial model. In the first line and in the first column the reader finds the letters and numbers corresponding to the Excel spreadsheet in order to make it easier the localization and the construction of the formulas. In the last two columns we have written those formulas. Usually they correspond to the year 0 and/or year 1. When necessary, we show the formulas for other years and we indicate it. Shaded cells are for the input data. If the reader wishes to construct the model exactly as we did, she will be able to do that step by step.

The contribution of this work is double: one is to show that we can construct financial statements without the use of plugs and circularity and the second is that we can use a very simple approach to construct cash flows and to value them.

The model shown has two parts. One is the proper financial statements forecast. The second one is a simple cash flow calculation and valuation exercise using the Capital Cash Flow and assuming the risk of the tax savings equal to Ku, the cost of unlevered equity.

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem, cash flows, firm valuation, cost of unlevered equity

Abstract:
Usually in financial textbooks and courses the theory of portfolio selection is taught in a strictly theoretical way. There is a model (Markowitz) that stipulates that an investor has preferences and that she will choose the best portfolio, given her preference curves and an efficient frontier. On the other hand, the Capital Asset Pricing Model (CAPM) is presented as it is: a genial idea that served to simplify and to make operative the Markowitz setup.

Most students and practitioners conclude that those models are just inapplicable theory. This is the most rational behavior one can expect. What can an investor do with the textbook recipes to configure an optimal portfolio? Very little.

My purpose with this note is to rescue a simple procedure presented by Black (1972), Merton (1973) and later by Levy and Sarnat (1982), Elton and Gruber (1995) and Benninga (1997). They just propose that the optimal portfolio can be found maximizing the slope of the line that joins the point of risk-free return and the efficient frontier. When this maximum tangent is reached, that line is the capital market line (CML) (it is tangent to the efficient frontier). This is a simple procedure that does not require one to calculate the efficient frontier and is an easy task with Excel Solver. It is just one point of the efficient frontier. An example is presented.

CAPM, efficient frontier, porfolio selection, capital market line, optimal portfolio

Abstract:
Our students, at least in some countries in Latin America, are taught that one of the most important (if not the most important one) is the effective interest rate per period and how to derive it. For some of our teachers in Finance that is all a good student should know. If she does not know to convert from nominal interest rate per period to effective interest rate per period, she is lost in the world of Finance. More, most people in the finance industry work, make decisions and induce others (their customers) to make decisions (this is to choose among investment alternatives) on the basis of an effective interest rate per period. For instance, when deciding to invest in a bond, they recommend that if the effective interest rate is the same for different ways to liquidate the payments for the bond, they should be indifferent to them. This is wrong and we show it with a very simple and real example. In this teaching note we show with very simple examples the risk of giving excessive relevance to the effective interest rate per period. In one of the examples we show that we should look at the tax savings earned for the payment of interest charges. The tax savings contribute to value creation in a firm.

Weighted average cost of capital, WACC, interest rates, nominal interest rate per period, effective interest rate per period, capitalized interest rate

Abstract:
This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversion. Para la valoracion financiera de proyectos y empresas.

Chapter 5 deals with how to prepare and use information to make forecasts to be used in forecasting financial statements. In this chapter we show step by step how to proceed to make proper forecasts in order to have the future financial statements. In Chapter 6 we deal with the construction of the forecasted financial statements based on the tables calculated in Chapter 5.

Forecasting, input data for financial statements

Abstract:
Unquestionably, before the advent of the personal computer, modeling the impacts of inflation in investment appraisal was an enormous task. Currently, with the widespread availability of personal computers, conducting investment appraisal by constructing financial statements with nominal prices is a straightforward and simple task.

In this paper, we would like to persuade the reader (if indeed there is need for persuasion) that conducting investment appraisal based on financial statements with real prices is potentially misleading and under certain circumstances, the adverse effects of inflation could result in the selection of 'bad' projects.

The paper is organized as follows. In Section One, we discuss some of the apparent reasons why the real prices approach persists in investment appraisal. In Section Two, we review briefly some of the main impacts of inflation and use simple numerical examples to illustrate the ideas.

In Section Three, we combine all of the previous examples into a single numerical example and use sensitivity and scenario analyses to examine the impacts of inflation on the NPV of the project. First, we conduct a simple sensitivity analysis of the NPV of the project with the expected inflation rate. Second, we conduct a detailed sensitivity analysis of the PV of each line item in the FCF statement and identify the specific effects of inflation. We show clearly why the results from the real prices approach are incorrect and explain the reasons for the inadequacy of the real prices method.

Note that the sensitivity analysis is unrealistic because it assumes that the same inflation rate will occur for all the years. In Section Four, we redo the analysis with different scenarios for the expected inflation rates. Scenario analysis is extremely flexible. For example, for one scenario, we can specify that the expected inflation rate is 8% for two years and 10% for the next three years.

Project evaluation; Impacts of inflation

Abstract:
In this teaching note I list some suggestions that might be useful to take into account when forecasting financial statements departing from historical data. The ideas presented in this note are the result of advising undergraduate and graduate students in the course Econ 195.96/295.96 (Crosslisted: PubPol 264.96): Cash Flow Valuation (CFV): A Basic Introduction to an Integrated Market-Based Approach at Duke University during the Fall of 2005 and my previous experience of teaching the subject at Politécnico Grancolombiano in Bogotá, and other universities in Colombia.

The note is divided in four sections: Section One, Analyzing the Historical Financial Statements, is related to the analysis and use of historical information from the financial statements. In Section Two I mention some tips related to the construction of forecasted financial statements. In Section Three I present a list of tips related to the proper way to valuate the cash flows. In Section Four a brief summary is presented.

Financial statements, forecasting, net present value (NPV), firm valuation, equity valuation, cost of capital, cash flow valuation

Abstract:
A large percentage of companies use the discounted cash flow (DCF) approach as the primary technique of investment/project evaluation and capital budgeting process. This approach requires forecasting detailed cash flow of the project under evaluation and then discounting the resulting cash flow to the present value (Net Present Value - NPV) using an appropriate discount rate.

The discount rate commonly used represents the Weighted Average Cost of Capital (WACC) of the firm. There is no scarcity of literature on this subject as the concept has been around for the last 50 years or so. Although most analysts believe the concept is simple and very well known, the irony is that its misinterpretation and misuse prevails. There are many versions of the WACC equation and each is specific to a certain cash flow. Therefore, using the classic WACC relationship in all cases may result in calculation of overly optimistic NPV. Depending on the cash flow pattern, the investment may show positive NPV at the classic WACC but it will actually be loosing on equity.

This paper highlights the (a) pitfalls and misuse of the WACC, (b) interdependence between type of cash flow and WACC, (c) assumptions behind the WACC and whether these assumptions are realistic, and (d) shows alternative approaches to arrive at the correct net present value (NPV). The company CEOs, management, analysts, and other investors using WACC for investment decisions need to be fully aware of its pitfalls and misuse.

Cost of capital, Cash flows

Abstract:
Practitioners and teachers very easily break some consistency rules when doing or teaching valuation of assets. In this short and simple note we present a practical guide to call the attention upon the most frequent broken consistency rules. They have to do firstly with the consistency in the matching of the cash flows, this is, the free cash flow (FCF), the cash flow to debt (CFD), the cash flow to equity (CFE), the capital cash flow (CCF) and the tax savings or tax shield (TS). Secondly, they have to do with the proper expression for the cost of levered equity, Ke and different formulations for the weighted average cost of capital, WACC, with finite cash flows and perpetuities. And finally, they have to do with the consistency between the terminal value and growth for the FCF and the terminal value and growth for the CFE. We illustrate the consistency using a simple example. In the Appendix we show some algebraic derivations

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity

Abstract:
In the recent writings on valuation, there is no consensus about the correct formulas for calculating the relevant cost of capital in an M & M world. The proliferation of alpha number of methods and omega number of theories for the calculation of the cost of capital is puzzling because in the derivation of the original M & M result, the use of the no-arbitrage argument would suggest that there should only be a single result.

In this non-technical, introductory teaching note, we would like to present a simple, general and unified approach to valuation in an M & M world. The Holy Grail in the Quest for Value (with alpha methods and omega theories) is rho, the required return to unlevered equity.

Cost-Benefit Analysis, Capital Budgeting, Project evaluation

Abstract:
This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversión. Para la valoración financiera de proyectos y empresas.

In this second chapter we deal with the Basic concept in Finance: the time value of Money. A dollar today is worth more than a dollar tomorrow. This concept allows us to find equivalent amounts of Money in different periods of time. This will enable us to compare different cash flow profiles. In the last part of the chapter we study the different structures of a debt schedule. We use intensively the spreadsheet.

Time value of money, interest, discount process, annuities, real interest rate, discount rate, debt schedule

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this ninth chapter we present the Markowitz portfolio analysis and the Capital Asset Pricing Model CAPM. We also present a procedure to derive the optimum portfolio.

Portfolio analysis, CAPM, Capital Asset Pricing Model, optimum portfolio

Abstract:
This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversión. Para la valoración financiera de proyectos y empresas.

Chapter Three includes the study of different method for financial decision making. This includes the Net Present Value, NPV, Internal Rate of Return, IRR, and the Benefit - Cost Ratio. We study the implicit assumptions in each of the methods, the limitations and advantages in using each method. The selection of projects with capital rationing is included in this chapter. As a complement, we study in this chapter other methods that do not take into account the time value of money.

NPV, IRR, Cost-Benefit Ratio, present value, capital rationing, payback period

Abstract:
Using no-arbitrage arguments in an M & M world, we show that in the N-period case, the appropriate discount rate for the tax shield is rho, the return to unlevered equity. We make no assumption about the appropriate discount rate for the tax shield. Instead, the appropriate discount rate for the tax shield is deduced from the no-arbitrage arguments. Furthermore, it is shown that the appropriate discount rate for the tax shield does not depend on whether the value of the debt is a fixed amount or is a fixed proportion of the levered value of the firm. The analysis begins at the end of the penultimate period N-1. First, we assume that the value of the levered cash flow is higher than the sum of the value of the unlevered cash flow and the value of the tax shield. It is shown that the inequality cannot hold because arbitrage opportunities exist. The equality only holds if the discount rate for the tax shield is rho, the return to unlevered equity.

Second, we assume that the value of the levered cash flow is lower than the sum of the value of the unlevered cash flow and the value of the tax shield. Again, it is shown that the inequality cannot hold because arbitrage opportunities exist. The equality only holds if the discount rate for the tax shield is rho, the return to unlevered equity. Using an iterative process, the argument can be extended period by period backwards to period zero.

In conclusion, in the N-period case, the appropriate discount rate for the tax shield is rho, the return to unlevered equity.

Value of Tax Shield

Abstract:
In this teaching note I list some suggestions that might be useful to take into account when forecasting financial statements departing from historical data. The ideas presented in this note are the result of advising undergraduate and graduate students in the course Econ 195.96/295.96 (Crosslisted: PubPol 264.96): Cash Flow Valuation (CFV): A Basic Introduction to an Integrated Market-based Approach at Duke University during the Fall 2005 and my previous experience of teaching the subject at Politécnico Grancolombiano in Bogotá, and other universities in Colombia.

The note is divided in four sections: In Section One, Analyzing the Historical Financial Statements, is related to the analysis and use of historical information from the financial statements. In Section Two I mention some tips related to the construction of forecasted financial statements. In Section Three I present a list of tips related to the proper way to valuate the cash flows. In Section Four a brief summary is presented.

Financial statements, forecasting, net present value (NPV), firm valuation, equity valuation, cost of capital, break even analysis, sensitivity analysis, scenario analysis, cash flow valuation

Abstract:
If the forecast period is short, then the specification of the assumption for the calculation of the terminal may be an important element of the valuation exercise. To be specific, with respect to the reference year 0, the (present) value of the terminal value may be more than fifty percent of the total levered value.

In this teaching note, we present a numerical example that values consistently a finite stream of cash flows with a terminal value from three different points of view: the Adjusted Present Value (APV) approach, the Capital Cash Flow (CCF) method and the traditional after-tax Weighted Average Cost of Capital that is applied to the Free Cash Flow (FCF). We assume an M & M world.

Abstract:
For the practitioner, making sense of the bewildering number of theories on the cost of capital must be a truly challenging and daunting task. In a perfect world without taxes, the cost of capital formula for a finite stream of free cash flows, with debt and equity financing, is elegant, simple and eminently sensible. The cost of capital is a weighted average of the cost of debt and the cost of equity, where the weights are the market values of debt and equity as percentages of the levered market value. In a perfect world with taxes, complications abound.

What criteria should we use to select the best expression for the cost of capital from all the available formulations? Fundamentally, the cost of capital is a question about how to properly account for the tax benefits (if any) from the interest deduction with debt financing. In other words, what are the appropriate risk-adjusted discount rates for the tax shield? At last count, there were 23 theories!

In this note, we briefly describe two methods for estimating the cost of capital: the traditional after-tax WACC applied to the free cash flow (FCF) and the alternative WACC applied to the capital cash flow (CCF). Using three criteria, simplicity, flexibility and correctness, we assess the strengths and weaknesses of the two different methods for calculating the cost of capital. Based on these criteria, we select the best expression for the cost of capital for a finite stream of cash flows.

WACC; Cost of capital; Free cash flow (FCF); Capital cash flow (CCF); Cash flow to equity (CFE)

Abstract:
This is a teaching material for a module of Financial analysis at Universidad Tecnologica de Bolivar. The educational material was developed with Professor Ricardo Davila from Universidad Javeriana, Bogota, Colombia. The written material has been modified several times, but the basic content is the same we developed many years ago. This material is an unpublished one.

This chapter is a detailed presentation of different financial ratios commonly used in financial management. However, we make some changes to the traditional way of measuring ratios and many of them are related to items from current and previous period. The usual formulation is to compare all items with other items of the same period. This is not correct for some ratios (i.e. for measuring return of equity and/or total assets. We give detailed examples for each case.

Accounting, financial management, financial statements, balance sheet, Income Statement, financial ratios, Dupont analysis

Abstract:
In this note we show with a simple example the proper way to use the adjusted WACC , the Cash Flow to Equity and the Capital Cash Flow, CCF to calculate the levered value of a firm when it has debt in foreign currency (FC). In this note we assume we are valuating the firm in the context of the domestic currency. We calculate the levered value of a firm using four approaches: the WACC for the Free Cash Flow, FCF, the adjusted WACC (that takes into account the tax savings, TS in absolute terms), the Capital Cash Flow discounted with the unlevered cost of equity and the independent calculation of the levered equity. Except for the calculation with CCF, all of them have to solve the circularity that arises between the cost of capital and the levered value. All the approaches match. However, the WACC for FCF takes into account the effect of tax savings through the factor (1-T) and the other approaches need to consider not only the tax savings related to the interest charges, but the tax savings associated with the losses in exchange for the debt.

Weighted Average Cost of Capital, WACC, Capital Cash Flow, CCF, firm valuation, capital budgeting, equity cost of capital, foreign exchange, purchasing parity power, cost of debt, tax shield, tax savings.

Abstract:
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). 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 reflected in the financial statements behind the practice of including as cash flow items that appear in the Balance Sheet.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cash budget

Abstract:
In this paper we find restrictions for the value of a parameter used in defining the cost of capital for perpetuities and terminal values: the growth rate for the free cash flow. When defining the growth rate for the free cash flow the usual warning is to set it below the growth of the economy or the industry because in the long run the firm would be larger than the economy or the industry. This approach might be considered somewhat standard in the sense that usually they either take the growth of NOPLAT (mathematically) and/or check that it complies with the previous statement. However, in this paper we propose to find another objective limits deriving them from the formulation for the cost of capital in perpetuity and the traditional formula for the terminal value in a world where the discount rate for the tax savings is Kd, the cost of debt. These limits give additional criteria for determining the value of g. The limits are calculated in terms of real rate of growth. We use an example to show the effects of violating these limits.

Calculating these limits is very important in valuation because usually the terminal value is a substantial portion of the levered value of the firm.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity, tax savings, cost of capital for growing perpetuities, growth rate for the free cash flow

Abstract:
This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversión. Para la valoración financiera de proyectos y empresas.

In this first chapter we present a conceptual framework on decision making. We mention the ethical implications of financial decisions. We point out the three major areas of financial management and corporate finance: investment decision making; capital structure and dividend policy.

G31

Abstract:
There are many different ways to calculate the Weighted Average Cost of Capital (WACC) and for the beginner the plethora of possibilities may be very confusing. We present a general framework for classifying the WACCs that are applied to the FCF and the CCF. For the moment, we avoid complexities. To facilitate the discussion, we classify the menagerie of WACCs along three dimensions. We hope that the structured framework assists the reader in making the correct decision with respect to the calculation of the cost of capital in practice. First, we present a qualitative discussion on the dimensions of the framework. Second, we specify the appropriate formulas and calculations for the cells in the framework.

At the outset, it is important to stress that this paper is concerned only with finite cash flows. In our judgment, it is best to discuss expressions for the cost of capital that are relevant to finite cash flows and this needs no further justification. In valuation, the continued use of cost of capital formulas (derived from cash flows in perpetuity), which are inappropriate for finite cash flows, is inexplicable and incomprehensible.

From a practical point of view, free cash flows are derived from financial statements, which are not constructed in perpetuity. At best, expressions for the cost of capital that are derived from cash flows in perpetuity may be reasonable approximations for finite cash flows. At worst, the results could be misleading.

multi-period WACC, cost of capital

Abstract:
Typical textbooks on corporate finance and forecasting and budgeting recommend "closing" and matching the financial statements using what is known as a plug. A plug is a formula to match the Balance Sheet using differences in some items listed in it in such a way that the accounting equation holds. This is a very easy way to do it but it encompasses some risks. The risks are that certain numbers in the financial statements could be in error and still the plug would indicate that everything is correct because the Balance Sheet matches.

In this work we show how to construct financial statement without plugs and circularity.

The basic learning objective of this work is to develop the students' and practitioners' abilities for constructing a proper financial model to forecast financial statements without plugs and without circularity.

We explain how the plug works and which its drawbacks are. We present a detailed example that can be used by any student, teacher or practitioner to properly construct consistent financial statements. The example shows how to relate different cells in the spreadsheet and the reader is encouraged to develop the example by herself.

We present some criticisms received against the no plug, no circularity approach and we discuss them. Finally, as a conclusion we suggest that the use of plugs should be discontinued when teaching forecasting financial statements and budgeting.

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem

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 little 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, the Cash Flow to Debt CFD and the Capital Cash Flow 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. In the Appendixes we show how to arrive to the levered equity and firm value.

Free cash flow, cash flow to equity, cash flow to debt, project evaluation, firm valuation, investment valuation, Net Present Value NPV

Abstract:
Usually financial textbooks present the financial ratio analysis. Many courses are taught in financial analysis and teachers spend lot of efforts teaching how to calculate financial ratios. Most of them are used to analyze historical financial statements. These analyses are very useful in identifying historical policies and targets. It is useful to analyze a posteriori, the consequences of a given decision and in general the performance of the firm management. Also, they can be used as predictors of the performance of a firm using the proper discriminant analysis technique. However, examining historical financial statements is a kind of necropsy that does not help very much to reach optimal financial decisions.

The most important management function is to increase the value of the firm. In this paper we present how the future decisions can be evaluated in terms of measuring the behavior of the firm value, given a decision to be analyzed. We also show the limitations of the traditional financial ratio analysis in reaching the target of maximizing the firm value.

Financial ratios, vertical analysis, horizontal analysis, firm valuation, firm value

Abstract:
This is a course material (slides in pdf format) for the chapter Financial Analysis and Control Financial Ratio Analysis already in SSRN. The chapter is originally in Spanish. In these slides we present a detailed explanation of different financial ratios commonly used in financial management. We introduce some examples in the slides and they serve more as quick review for the written material of the main chapter than a summarized (bulleted) guide for conducting a lecture. However, we use them as a guide for our lectures. The original slides are available on request.

Accounting, financial management, financial statements, balance sheet, Income Statement, financial ratios, Dupont analysis

Abstract:
In this note we present the basic legal concepts regarding intellectual property and its different versions. We offer a gentle summary of the major intangible valuation methods, as well. It includes the basic concepts on time value of money and accounting. A brief explanation of the discounted cash flow for valuation approach is presented. Each method is presented with advantages and disadvantages and limitations.

Intangible advantages, intangible assets, brands, patents, royalties

Abstract:
Practitioners and teachers in finance usually treat the most important issues in project appraisal and cash flow valuation is at least light. One is the construction of cash flows; in the other hand is the cost of capital that is intrinsically related to the valuation of the cash flows.

The problem with the cash flows relies on the difficulty of that construction mainly when some real life complexities are present. When this happens the analyst is prone to incur in mistakes because it is very easy to forget some items.

On the other hand, the determination of the cost of capital many times is tackled selecting the discount rate (cost of capital) from the thin air, perhaps adding some percent points to the cost of debt or similar. Some other times a weighted average is calculated using initial book values and keeping that average constant during the period of analysis.

Facing this reality we intend to approach this problem in a very simple and easy but correct way to discount cash flows taking into account the market values to determine the correct discount rate (the weighted average cost of capital WACC). Although we know that the determination of the cost of capital might be biting off more than what one can chew and it is one of the most difficult problems in corporate finance we will try.

In this paper we show a very simple approach to construct the cash flows to value a firm. In particular, we show the Capital Cash Flow, CCF used by Ruback, 2000. We present a simple methodology to determine the cost of capital used to discount the CCF. In order to create a proper context, we present at the very beginning the most common mistakes in cash flow valuation. In the body of the paper we show how to avoid these mistakes.

Financial statements, forecasting, net present value (NPV), firm valuation, equity valuation, cost of capital, break even analysis, sensitivity analysis, scenario analysis, cash flow valuation

Abstract:
This is a course material (slides in pdf format) from the book Investment Decision Making. For Firm and Project Valuation. The book is originally in Spanish and is untitled as Decisiones de inversión. Para la valoración financiera de proyectos y empresas.

In this chapter 4 we study some special problems that we find when using the methods studied in chapter 3. We introduce the idea of non constant discount rates, a method to solve the discrepancy among the methods studied in chapter 3. This method solves the problem of the inconsistency that sometimes is present when we use the NPV and the IRR.

Non constant discount rates, inequal time period, contradictions between NPV, IRR and R B/C

Abstract:
In this short teaching note I explain why we subtract the change in working capital from the proper item (Earnings before interest and taxes (EBIT) or Net income) in the Income Statement. I show in detail how departing from the sales revenues and the cost of goods sold we have to subtract the change in working capital. This explanation might be seen as unnecessary given it is a common practice. However, my experience in teaching this subject indicates that some additional explanations are needed.

Cash flows, free cash flow, cash flow to equity, working capital.

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this seventh chapter we introduce the reader to the simulation tools. First we use very simple examples and finally we isllustrate the results of a complex example. We discuss the proper discount rate to use when we introduce explicitly the risk in the analysis. We use intensively the spreadsheet.

Risk analysis, Montecarlo Simulation, decisions under risk

Abstract:
In this teaching note we show how to use sensitivity analysis to consider uncertainty in the valuation of cash flows. We illustrate in a very simple way the use of the traditional identical percent change in the variables and an approximate approach that considers the probability of occurrence of the changes using the standard deviation as the change instead of the relative change expressed as a percent. Two variables and scenario analysis is shown to illustrate the sensitivity of multiple variables.

Uncertainty, sensitivity analysis, probabilistic sensitivity analysis, cash flow valuation.

Abstract:
This article explores the behavior of the stock market in Colombia with the information given by the Bolsa de Bogota Index (Indice de la Bolsa de Bogota, IBB). The index is analyzed from January, 1930 to December, 1998. The inflation rate covers the same period; the inflation rate is measured by the Consumer Price Index. However, as the available monthly data for CPI is recorded since 1954, we analyzed the behavior of annual rates only for the period 1930-1998. When possible, monthly returns were analyzed. This exploratory paper does not intend to present conclusive remarks: in fact, there more questions than answers. They are just ideas to work on. The trends of this analysis show that monthly and per annum return - nominal and real - are well below from the expected return of any financial investor. A first hypothesis to explain this is that the investor and entrepreneurs receive benefits that are non-measurable in terms of economic return. Also it can be said that inflation is negative to the return at the stock market, thus: the larger the inflation rate, the smaller the real return. It is shown that the market does not anticipate the future inflation, and of course it is not included in the actual price. Probabilities for selected real return values are presented. The probability to obtain a real return greater than 0% and other values (5%, 10%. 12% and 18%) as well, is much less than 50%. This might show that investing at the stock market is just gambling.

Abstract:
This article explores the behavior of the stock market in Colombia with the information given by the Bolsa de Bogota Index (Indice de la Bolsa de Bogota, IBB). The index is analyzed from January, 1930 to December, 1998. The inflation rate covers the same period; the inflation rate as measured by the Consumer Price Index. This exploratory paper does not intend to present conclusive remarks: in fact, there more questions than answers. They are just ideas to work on. The trends of this analysis show that monthly and per annum return -nominal and real- are well below from the expected return of any financial investor. A first hypothesis to explain this is that the investor and entrepreneurs receive benefits that are non- measurable in terms of economic return. Also it can be said that inflation is negative to the return at the stock market, thus: the larger the inflation rate, the smaller the real return. It is shown that the market does not anticipate the future inflation, and of course it is not included in the actual price. Probabilities for selected real return values are presented. The probability to obtain a real return greater than 0% and other values (5%, 10%. 12% and 18%) as well, is much less than 50%. This might show that investing at the stock market is just gambling.

Abstract:
This is a course material for an introductory course in Probability and Statistics for Engineering and Management. It is part of some course notes for my courses in Spanish on that subject. The draft of the book is Apuntes de Probabilidad y Estadística para Ingeniería y Administración (Notes for Probability and Statistic for Engineering and Management) and this part is Métodos de pronóstico (Forecasting Methods).

Humankind has pursued the knowledge of the future. Remember the sybil in the Delphi oracle. In this chapter we present and describe the most known forecasting methods. We show in detail how to use the decomposition method to make forecasting when there are several components in the data. This is, trend, seasonality, cycle and error. We take a set of real monthly data and keep the last 12 months to test how good the forecast was and compare several methods. All these methods are studied using intensively the spreadsheet.

Forecasting methos, smoothing methods, decomposition methods

Abstract:
This is a course material for an introductory course in Probability and Statistics for Engineering and Management. It is part of some course notes for my courses in Spanish on that subject. The draft of the book is Apuntes de Probabilidad y Estadística para Ingeniería y Administración (Notes for Probability and Statistic for Engineering and Management) and this part is Análisis de regresión (Basic Regression Analysis).

In this chapter we present the basic tools for regression analysis. With linear regression analysis we can find models that relate variables linked by causal relationships between given variables. The idea is to use this tool to predict the behavior of some independent variable and other dependent variables.

Before performing any statistical analysis we should examine if there is a logical relationship between independent and dependent variables. This effort is of utmost importance. Calculations are easily made using the computing and inexpensive power of software and computers. To find the possible relationships between variables is a delicate work of observation, intelligent, experience and intuition. All these methods are studied using intensively the spreadsheet.

Linear Regression analysis, independent variables, dependent variables

Abstract:
Velez-Pareja and Tham (2003) presented a method to match the value added approaches (Residual Income Method, RIM and Economic Valor Added, EVA) with the discounted cash flow, DCF methods. There they used a relatively complex example, but yet, far away from reality. In this note we use a real life case from an emerging country to illustrate the same procedure, but with additional and real life complexities such as unpaid taxes, losses carried forward, foreign exchange debt, presumptive income and inflation adjustments to the financial statements. In all methods we use market values to calculate the discount rates.

We stress what Velez-Pareja 1999 and Fernandez 2002 have said: for a single period, RI or EVA does not measure valor. We have to include expectations and market values in the calculation of discount rates and hence values.

Economic Value Added, EVA, Market Value Added, MVA, residual income model, utilidad, economica, valor presente neto (VPN), flujos de cja, flujos de caja libre, valor de Mercado del patrimonio, valor de la firma, perdidas amortizadas, losses carried forward, perdida en cambio, deuda en moneda etanjera, foreign exchange loss, foreign exchange debt, renta presuntiva, presumptive income, ajustes por inflacion a los estados financieros, inflation adjustments to the financial statements

Abstract:
Although perpetuities are somewhat artificial in the sense that in practice they do not exist, they are relevant because no matter how detailed and complex a forecasted financial plan for a firm or project could be terminal value usually is calculated as perpetuity. This terminal value might be a growing or a non growing perpetuity. On the other hand, usually terminal value is a substantial part of the firm value.

In this note we examine in detail the proper discount rate for cash flows in perpetuity, the present value of tax savings and the calculation of terminal value. The findings contradict what is generally accepted in the literature.

WACC, perpetuities, terminal value, tax savings

Abstract:
This is a summary of the basic ideas on valuation depicted as a conceptual map. Under the assumption that Capital Asset Pricing Model, CAPM, works and that the discount rate for the tax savings is Ku, I show the sequence of calculations and interactions among the variables, beta, values, cash flows and discount rates. We might consider that Ku is the origin of everything.

WACC, valuation methods, cash flows

Abstract:
In the latest edition of Principles of Corporate Finance (Brealey, Myers and Allen, 2006) the authors use a finite cash flow example to illustrate the valuation procedure for using the Discounted Cash Flow (DCF) method with the free cash flow (FCF) and the Adjusted Present Value (APV). The two firm values obtained are different. They say that the "... difference [...] is not a big deal considering all the lurking risks and pitfalls in forecasting [...] cash flows".

In this teaching note we show that the two methods give identical values when the proper discount rates are used.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, Adjusted Present Value, APV, Discounted Cash Flow, DCF, weighted average cost of capital, WACC, cost of unlevered equity, tax savings

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this eigth chapter we analyse the problem of sequencial decisions. In particular we use the decision tree approach. We illustrate the tool with a relatively complex example.

Sequential decisions, decision trees

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this sixth chapter we present the idea of sensitivity analysis. We illustrate the different ways to do sensitivity analysis with one, two and more variables. We include what if analysis with and without probabilities, reverse engineering, one and two way tables, scenarios, and Montecarlo Simulation (MCS). We use intensively the spreadsheet.

Sensitivity analysis, one way table, two way table, montecarlo simulation, scenarios, solver

Abstract:
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 reflected in the financial statements behind the practice of including as cash flow items that appear in the Balance Sheet.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cash budget

Abstract:
This is a course material for an introductory course in Probability and Statistics for Engineering and Management. It is part of some course notes for my courses in Spanish on that subject. The draft of the book is Apuntes de Probabilidad y Estadística para Ingeniería y Administración (Notes for Probability and Statistic for Engineering and Management) and this part is Conceptos básicos de estadística (Basic Concepts in Statistics). Statistics is an analytical scientific method used in the social and natural sciences. Its main use is the statistic inference. This is, from the information of a simple, we infer values of the universe where it comes from.

In this chapter we study the basic statistical concepts and the descriptive statistics tools. We present the most common probability distribution functions and some test of hypothesis. We present some typical test for non-parametric statistics. Random sampling is presented in a very simple way. All these methods are studied using intensively the spreadsheet.

Statistics, non parametric statistics, descriptive statistics

Abstract:
This is a summary of the basic ideas on valuation depicted as a conceptual map. Under the assumption that Capital Asset Pricing Model, CAPM, works and that the discount rate for the tax savings is Ku, I show the sequence of calculations and interactions among the variables, beta, values, cash flows and discount rates. We might consider that Ku is the origin of everything.

WACC, valuation methods, cash flows

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this third chapter we deal with the idea of uncertainty (not having a probability distribution assigned to the events). We use the basic ideas of game theory to introduce the reader into the strategies when dealing with uncertainty. We illustrate the different approaches in game theory: minimax, maxmax, minimum regret, Laplace method, etc. We also present a simple method to estimate the probability of an outcome and one method to estimate a subjective probability distribution.

Uncertainty, game theory, subjective probability distributions

Abstract:
Most popular corporate finance textbooks (See Benninga and Sarig, 1997, 2007 Brealey, Myers and Marcus, 1996, Brealey, Myers and Allen, 2006, Brealey and Myers, 2000, 2003 and previous editions, Copeland, Koller and Murrin, 1995 and 2000, Damodaran, 1996, Gallagher and Andrew, 2000, Van Horne, 1998, Weston and Copeland, 1992) and practitioners (see World Bank, 2002) present the Weighted Average Cost of Capital WACC calculation as independent from the Free Cash Flow.

It is a common use that practitioners calculate a WACC a priori and use it independently from the firm value (this is, from FCF). In this teaching note we show that FCF affects WACC and that this interrelationship creates circularity, but it can be solved in a very easy way.

There are two appendixes: one explaining the circularity issue and another one for deriving the proper formulation of the cost of equity.

Weighted Average Cost of Capital, WACC, firm valuation, capital budgeting, equity cost of capital, circularity

Abstract:
In this note we analyze the tutorial based on the McKinsey methodology for valuing companies. We have found that the McKinsey methodology has one of the most common mistakes mentioned in Tham and Vélez-Pareja (2004a and b): valuing cash flows with a constant cost of capital when the leverage is not constant. We calculate the proper firm and equity values by assuming the free cash flow, FCF calculated in the tutorial, and deriving the cash flow to equity, CFE. We develop the proper calculations of firm and equity values for constant leverage as well.

For both calculations we calculate the deviations from the values calculated in the tutorial.

Valuation, free cash flow, discounting, accounting data

Abstract:
Financial textbooks offer multiple options to value a firm. However, few of them show the practical aspects related to negotiating a firm (selling or buying a firm).

In this note we present some suggestions to be taken into account when selling or buying a firm. At the same time we present a brief review of different valuation methods. At the same time we present a summary of the COMPASS methodology to assess the productivity of a firm.

It might seem at first sight, that there is a symmetric mirroring between the seller and buyer of a firm. However, there exist some specific activities to be carried out by each of them.

Business plans, selling a firm, buying a firm, negotiation

Abstract:
In this work we explore the effect of book value leverage upon some financial indexes, such as real growth, payment terms from suppliers and gross and operating margins. We explore if there is statistical evidence on the influence of the book value leverage level in the financial distress or bankruptcy costs that appear as measured by the worsening of those indexes. Four dependent variables were explored: gross margin, operating margin, real growth in sales and payment terms from suppliers. In order to estimate the financial distress and bankruptcy costs associated with each dependent variable, logarithmic and semi-logarithmic models were constructed using data panel. We used a balanced sample composed by 644 firms from the commercial Colombian industry, provided by the Superintendence of Societies of Colombia. We also examined an unbalanced sample of 683 firms with Ordinary Least Squares (OLS) analysis. We found that there exists a relationship between book value leverage perceived by the market and gross margin. This allows us to explore the possibility to introduce the financial distress costs in the cash flows. The aim of the study is to explore a model that allows the analyst to include this effect in the forecasted financial statements. When this effect is included in the financial statements the free cash flows will be affected and hence the interaction of cash flows, cost of capital (weighted average cost of capital) and firm value calculated with the cash flows will eventually allow determining an optimal capital structure.

Cash flows, forecasted financial statements, cost of capital, bankruptcy costs, financial distress costs

Abstract:
When estimating future or pro forma financial statements and free cash flows we need to estimate future prices. In doing this we must estimate nominal increases in prices of many items, for instance selling prices, inputs prices (raw material, labor, overhead, etc.), cost of future debt, and others. If we set nominal price increases without a proper link to inflation we might end up with price increases independent of the inflation rate. The purpose of this teaching note is to present an approach to estimate nominal price increases examining historical nominal prices and inflation rates. This way we can "discover" which policy, if any, the decision maker used to fix prices assuming that she has a fair estimate of immediate future inflation rate.

This approach can be used to asses the risk premium a debt holder (in case it is a bank loan) is applying to the cost of debt. This way we could estimate the cost of future debt, given an estimation of future inflation rate.

We present an appendix where the formal assumptions that has to be met for robust econometric analysis.

inflation, nominal price increase estimation, inflationary environment, price level, project evaluation, firm valuation, capital budgeting, project evaluation

Abstract:
Vélez-Pareja and Tham, 2003a, Vélez-Pareja and Tham, 2003b and Tham and Vélez-Pareja, 2004 showed the matching between discounted cash flow (DCF) methods and value added methods. They departed from the net operating profit less adjusted taxes NOPLAT and net income when using market values to calculate the weighted average cost of capital (WACC) and the cost of levered equity, Ke. In those previous works they assumed that the proper discount rate for the tax savings is the unlevered cost of equity, Ku. We assume the same discount rate in this paper. The previous procedures implied circularity between the cost of capital and the levered values. In this paper we show that the same firm values can be obtained using the cost of unlevered equity, Ku and the net income and the interest charges. No circularity is found using this procedure. This article is based upon Vélez-Pareja and Tham 2004.

EVA, economic value added, cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, cost of levered equity, cost of unlevered equity, tax savings

Abstract:
It is a well known problem the interactions between the market value of cash flows and the discount rate (usually the weighted average cost of capital, WACC) to calculate that value. This is mentioned in almost all textbooks in corporate finance. However, the solution adopted by most authors is to assume a constant leverage D%, and hence assume that the leverage gives raise to an optimal capital structure and the discount rate is constant.

On the other hand, most authors use the definition of the Ke, the cost of leveraged equity for perpetuities even if the planning horizon is finite. Among these authors we find the work of Wood and Leitch W&L 2004.

In this paper we wish to analyze the claim made by W&L 2004 in the sense to have found an iterative solution to the problem of circularity that results in a near matching with the Adjusted Present Value APV, proposed by Myers, 1974. They use as the basic principle the fact that there is a near constant relation between Ke the cost of equity and Kd the cost of debt. They consider as well that the cost of debt Kd is not constant and changes proportionately with the leverage D%.

We propose a very simple and precise approach to solve the above mentioned circularity problem.

Adjusted Present Value, APV, weighted average cost of capital, circularity problem, discounted cash flow, DCF equity value, cost of equity

Abstract:
It is a well known problem the interactions between the market value of cash flows and the discount rate (usually the weighted average cost of capital, WACC) to calculate that value. This is mentioned in almost all textbooks in corporate finance. However, the solution adopted by most authors is to assume a constant leverage D%, and hence assume that the leverage gives raise to an optimal capital structure and the discount rate is constant.

On the other hand, most authors use the definition of the Ke, the cost of leveraged equity for perpetuities even if the planning horizon is finite. Among these authors we find the work of Wood and Leitch W&L 2004.

In this paper we wish to analyze the claim made by W&L 2004 in the sense to have found an iterative solution to the problem of circularity that results in a near matching with the Adjusted Present Value APV, proposed by Myers, 1974. They use as the basic principle the fact that there is a near constant relation between Ke the cost of equity and Kd the cost of debt. They consider as well that the cost of debt Kd is not constant and changes proportionately with the leverage D%.

We propose a very simple and precise approach to solve the above mentioned circularity problem.

Adjusted Present Value, APV, weighted average cost of capital, circularity problem, discounted cash flow, DCF equity value, cost of equity

Abstract:
Using illustrative examples, this paper shows that the Net Present Value for project evaluation should be based on estimates of free cash flows at nominal prices. It is a widespread practice to evaluate projects at constant or real prices. These days, the use of constant or real prices is an unnecessary oversimplification. In particular, we present an example where the results from the constant and real price methodologies are biased upwards and there is a risk that in practice, bad projects will be accepted as good projects.

Project evaluation, engineering economy, NPV, Net Present Value, inflation, constant price methodology, current price methodology, nominal price methodology, free cash flows, pro-forma financial statements, relative prices

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this second chapter we deal with the Basic concept in Finance: the time value of Money. A dollar today is worth more than a dollar tomorrow. This concept allows us to find equivalent amounts of Money in different period of time. This will enable us to compare different cash flow profiles. In the last part f the chapter we study the Net Present Value NPV and the Internal Rate of Return, IRR. We use intensively the spreadsheet.

Time value of money, interest, discount process, annuities, real interest rate, discount rate, Net Present Value, NPV, Internal Rate of Return, IRR

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this fourth chapter we deal with the forecasting methods. We use a very simple example to explain the decomposition method. In this method we separate diiferent components in order to make the forecast. We identify using an actual series the trend, the seasonality, cycle and error. Finally, we compare the forecasting with this method with simple regression and moving average. We also include the Delphi Method as a tool to convey consensus for better decisions.

Forecasting, decomposition method, seasonality, trend, cycle, error

Abstract:
In this teaching note, we present an integrated, consistent market-based framework for valuing finite cash flows. We derive the relevant cash flows from integrated financial statements, and based on Modigliani and Miller's (M & M) theories, we estimate the appropriate cost of capital and value the cash flows in seven different ways. The first five methods are variations of the Discounted Cash Flow (DCF) method.

The last two methods, the RIM and EVA, are interesting because they differ from the DCF methods. In particular, they apply a charge for equity (based on the book value of equity) to the net income or a charge for invested capital (based on the book value of invested capital) to the Net Operating Profit after tax (NOPLAT), roughly speaking. Happily, the results from the DCF methods are fully consistent with the RIM and EVA.

Since the results from the seven methods must always match, calculating the (present) values with the seven methods is a powerful check on the consistency of the valuation exercise. With the availability of computing resources, it is easy to implement the seven methods on a routine basis.

In Principles of Cash Flow Valuation, 2004, Academic Press we present and explain the valuation methods in detail.

Multiperiod WACC, firm valuation, levered equity, valuation with EVA, cost of equity

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

This Chapter 1 deals with the decision process including some psycohological aspects. In the chapter we study the decision problem, including the sequential approach to decision making.

Decision making, psychological basis of decision making

Abstract:
In a forthcoming paper, Fernandez (2002) claims to derive a formula for the valuation of debt tax shields for firms with cash flows that grow perpetually at a constant rate. We show that his formula is incorrect and provide an example where his valuation would admit arbitrage.

Present value of tax shield, perpetuities

Abstract:
Fernandez (2004) claims to derive a formula for the valuation of debt tax shields for firms with cash flows that grow perpetually at a constant rate. We show that his formula is incorrect.

Present value of tax shield, perpetuities

Abstract:
In a recent paper, Pablo Fernandez (2002) makes the unusual and paradoxical sounding claim that for cash flows in perpetuity with a constant growth rate g, the value of the tax shields VTS is NOT equal to the present value of the tax shields. To be specific, Fernandez purportedly shows that the formula for the present value of the tax shields is as follows.

VTS = TDKu/(Ku - g)

Where Ku is the return to unlevered equity, g is the constant growth rate, T is the tax rate and D is the market value of debt.

Fernandez (2002) asserts that the value of the tax shield, as given in equation, should be properly interpreted as the difference in the taxes paid by the unlevered and levered firms, where the taxes have different risk profiles. Let VTxU be the present value of the taxes paid by the unlevered firm, discounted by KTxU, which is the appropriate risk-adjusted discount, and let VTxL be the present value of the taxes paid by the levered firm, discounted by KTxL, which is the appropriate risk-adjusted discount.

In this note, we assess the validity of the proposed expression for the value of the tax shield. The note is organized is as follows. In Section One, we review and discuss the assumptions underlying the model that Fernandez uses to derive equation 1. In Section Two, we examine critically the derivation of equation 1 and its general relevance and applicability.

Present value of tax shield

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this fifth chapter we deal with the attitudes toward risk. We present the classical cardinal utility theory and illustrate the three well know cases of attitudes toward risk: averse toward risk, indifferent toward risk and propense toward risk. We also present the concept of certainty equivalent. We mention the limitations of the cardinal utility theory. We include a short reference to the prospect theory by Kahneman and Tversky. We illustrate the concept of risk aversion with a real life lottery example.

Risk, risk attitudes, cardinal utility theory, risk aversion, risk propension, risk indifference

Abstract:
It is widely known that if the leverage is constant over time, then the after-tax Weighted Average Cost of Capital (WACC) is constant over time. In other words, it is inappropriate to use a constant after-tax WACC to discount the free cash flow (FCF) if the leverage changes over time. However, it is common to find analysts who inconsistently use a constant after-tax WACC even if the leverage is not constant.

In this teaching note, we use a simple numerical example to illustrate how to model cash flows that are consistent with constant leverage. We verify the consistency of the example with two basic principles: conservation of cash flows and conservation of values.

WACC, constant leverage, cash flows

Abstract:
We show that project evaluation should be based on free cash flows at nominal prices. We present a case where the results from the constant price method are biased upwards and there is a risk to accept bad projects. It is a widespread practice to evaluate projects at constant prices. With an example presented in the training on economic regulation of public utilities developed by the World Bank Institute we asses that methodology. We show an overvaluation of 21% when compared with the current prices methodology and using a correct Weighted Average Cost of Capital, WACC.

World Bank, regulatory policy for infrastructure, developing countries, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
This is a course material for an introductory course in Probability and Statistics for Engineering and Management. It is part of some course notes for my courses in Spanish on that subject. The draft of the book is Apuntes de Probabilidad y Estadística para Ingeniería y Administración (Notes for Probability and Statistic for Engineering and Management) and this part is Conceptos básicos de probabilidad (Basic Concepts in Probability). When we make decisions and we are confronted with future and known events the only reason a decision maker makes a mistake is when she has made mistake in her analysis. This is known as decision making under certainty. Unfortunately this is not the most common situation.

Reality is unpredictable and we make decisions under risk and uncertainty and the decision maker has to assume risks. For these typical and common situations we need to study the probability associated to each event and we need to know how to measure and apply it in the decision process.

In this chapter we study the basic concepts of events and probability, including the idea of inductive and deductive processes. We study the notion of statistical independence and Bayes' Theorem. All these methods are studied using intensively the spreadsheet.

Probability ruels, induction, deduction, random variable, independence

Abstract:
Frequently analysts and teachers use the capitalized rate of interest for the cost of debt when forecasting and discounting cash flows. On the other hand, some authors (and analysts) estimate the interest payments when forecasting annual financial statements or cash flows based on the average of debt calculated with the beginning balance and the end of year balance. This makes some sense because usually firms repay debt in a monthly or quarterly basis and calculating interest payments might not reflect reality. Others use the end of year convention that calculates the yearly interest multiplying the beginning balance times the contractual cost of debt.

In this teaching note we show the differences when we use those different approaches and make a simple proposal to solve the problem.

Cost of debt, forecasting financial statements, seasonality

Abstract:
In the standard Weighted Average Cost of Capital (WACC) applied to the free cash flow (FCF), we assume that the cost of debt is the market, unsubsidized rate. With debt at the market rate and perfect capital markets, debt only creates value in the presence of taxes through the tax shield. In some cases, the firm may be able to obtain a loan at a rate that is below the market rate. In a previous work, we showed how to adjust the WACC in the presence of a subsidy and no taxes. There, we showed that plugging the lower (subsidized) cost of debt into the WACC formula is not the correct approach to measuring the value creation due to the subsidy. With subsidized debt and taxes, there would be a benefit to debt financing, and the unleveraged and leveraged values of the cash flows would be unequal. The benefit of lower tax savings are offset by the benefit of the subsidy. These two benefits have to be introduced explicitly. How would we adjust the WACC to take account of the subsidized debt? And how would we adjust the expression for the required return to leveraged equity?

In this paper, using a multiple period example we present the adjustments to the WACC with subsidized debt and taxes. We demonstrate the analysis for both the WACC applied to the FCF and the WACC applied to the capital cash flow (CCF). We use the calculation of the Adjusted Present Value, APV, to consider both, the tax savings and the subsidy. We show how all the methods match.

Adjusted Present Value, APV, weighted average cost of capital, discounted cash flow, DCF equity value, cost of equity, WACC, subsidized debt with taxes, valuation of cash flows, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
For cash flows in perpetuity without growth, analysts typically use the following formula for the return to levered equity Ke.

Ke = Ku + (Ku ­ Kd)(1 ­ T)D/E (1)

where Ku is the return to unlevered equity, Kd is the cost of debt, T is the tax rate, D is the market value of debt and E is the market value of equity.

What is the corresponding formula for finite cash flows? Is it the same as equation 1? In other words, is equation 1 appropriate for both finite and infinite cash flows? One may be tempted to believe that equation 1 is the general formulation for the return to levered equity and applies to both cash flows in perpetuity and finite cash flows. However, this conclusion is misleading.

In this short note, using simple algebra, we derive the general formulation for the return to levered equity for finite cash flows, and show that equation 1 is not the general formulation for finite cash flows.

Present value of the tax shield, formulation for Ke, cost of levered equity, cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity, tax savings, growth rate for the free cash flow

Abstract:
In the standard Weighted Average Cost of Capital (WACC) applied to the free cash flow (FCF), we assume that the cost of debt is the market, unsubsidized rate. With debt at the market rate and perfect capital markets, debt only creates value in the presence of taxes through the tax shield. In some cases, the firm may be able to obtain a loan at a rate that is below the market rate. With subsidized debt and no taxes, there would be a benefit to debt financing, and the unlevered and levered values of the cash flows would be unequal. How would we adjust the WACC to take account of the subsidized debt? And how would we adjust the expression for the required return to levered equity?

In this paper, using a single period example we present the adjustments to the WACC with subsidized debt. We demonstrate the analysis for both the WACC applied to the FCF and the WACC applied to the capital cash flow (CCF). For simplicity, we assume that there are no taxes. The analysis can be extended easily to multiple periods in the presence of taxes.

WACC, cost of capital, subsidized debt, valuation of cash flows, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
In cash flow valuation, on grounds of simplicity, it is common to assume that the leverage is constant over time. With constant leverage, the return to levered equity is constant and consequently, the Weighted Average Cost of Capital (WACC) applied to the Free Cash Flow is constant. However, typically the constant leverage is not reflected in the financial statements. Specifically, the values of the annual debt (as listed in the balance sheet) as percentages of the annual levered values are not constant. The Hershey case study in the popular book on valuation by Copeland et al. (2nd edition, 1995) is a good illustration of this common and widespread inconsistency. Distressingly, readers may not realize or recognize the inconsistency between the cost of capital and the financial statements and authors of textbooks make no attempt to mention it. The consistency between the leverage assumption in the WACC applied to the FCF and the values for the debt in the balance sheet can be resolved if the debt is rebalanced each year to maintain the constant leverage. In this paper, we demonstrate the inconsistency. First, we calculate the annual leverage and show that it is not constant. Second, we calculate the annual equity by subtracting the annual debt values from the annual levered values and demonstrate the discrepancies with the present value of the CFE. This paper is aimed to those who have learnt valuation with that edition (1995).

Cash flows, Copeland, Hershey, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity, tax savings

Abstract:
In Consistency in Chocolate: A Fresh Look at Copeland's Hershey Foods & Co Case we showed the inconsistencies regarding the assumption of constant leverage and the inconsistency in the values for equity calculated with different approaches. In this second part we show the differences in the calculated values using an approach consistent with the assumptions implicit in the calculation of Copeland et al. (1995)'s Hershey example. In particular, we show the calculation of the levered value for the firm using the proper calculations for WACC and cost of levered equity assuming that the discount rate for the tax savings is Kd, the cost of debt and using finite cash flows. In this paper, we use the terminal value calculated in the original example. We also calculate the levered values assuming that the discount rate for the tax savings is Ku, the cost of the unlevered equity and using finite cash flows. We calculate the differences in values and show the consistency of our approach regarding the calculated values for equity. This paper is aimed to those who have learnt valuation with that edition (1995).

Cash flows, free cash flow, cash flow to equity, valuation, levered value, levered equity value, terminal value, cost of levered equity, cost of unlevered equity, tax savings, cash flows, Copeland, Hershey

Abstract:
This is a course material from the book Managerial Decision Making Under Risk and Uncertainty. The book is originally in Spanish and is untitled as Decisiones empresariales bajo riesgo e incertidumbre. The level of the book is basic. We use very few mathematics and it is expected to be used by managers.

In this tenth and last chapter we present a brief and simple introduction to financial options and the Black-Scholes model. Using the basic concept of options we introduce the reader to the idea of real options to profit from flexibility and variability and volatility.

Options, real options, Black-Scholes model, NPV, Net Present Value

Abstract:
In this note we correct the findings reported by Vélez-Pareja and Tham (2005).

Although perpetuities are somewhat artificial in the sense that in practice they do not exist, they are relevant because no matter how detailed and complex a forecasted financial plan for a firm or project could be, terminal value usually is calculated as a perpetuity. This terminal value might be a growing or a non growing perpetuity. On the other hand, usually terminal value is a substantial part of the firm value.

In this note we examine in detail the proper discount rate for cash flows in perpetuity, the present value of tax savings and the calculation of terminal value, which is the value of the perpetuity.

We compare the typical textbook proposals for calculating the value of a perpetuity and we found that there are significant deviations. We compare with the Miller and Modigliani (1961) plowback proposal adopted by Copeland et al. (2000).

The findings contradict what is generally accepted in the literature.

WACC, perpetuities, terminal value, tax savings

Abstract:
We show that project evaluation should be based on free cash flows at nominal prices. We present a case where the results from the constant price method are biased upwards and there is a risk to accept bad projects. It is a widespread practice to evaluate projects at constant prices. With an example presented in the training on economic regulation of public utilities developed by the World Bank Institute we asses that methodology. We show an overvaluation of 21% when compared with the current prices methodology and using a correct Weighted Average Cost of Capital, WACC.

World Bank, regulatory policy for infrastructure, developing countries, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
World Bank (WB) has played a crucial role in the development of the economies of the world, especially in the emerging countries. We recognize the leadership it has shown and the intellectual authority the WB has on planning offices, practitioners and consultants. For this reason it is very sensitive whatever improvements made in the methodologies it uses in assessing the feasibility of infrastructure projects. This influence affects private practice in valuation and project appraisal as well.

Velez-Pareja in 1999 warned: constant price methodology implies some assumptions and a mixture of items, some deflated, and some others not deflated. Velez-Pareja and Tham 2002 warned again: financial statements at constant prices will be useless when the project is implemented because what occurs in reality (that is what we are interested in) is very different from what is written in the final report of a project evaluation. Some of the items are deflated while others (say depreciation charges and interest payments) are in nominal prices. Hence, for managerial purposes, it is of no use to have this mixed information in the financial statements. In general, both papers warn about the overvaluation of a project when appraised at constant prices. Some reactions to these assertions were that it was the construction of a straw man to destroy it. We have a beautiful case where the constant prices methodology is fully at work: the Financial Modeling of Regulatory Policy by the World Bank.

On the other hand Tham and Velez-Pareja 2004 mentioned the most frequent (and avoidable) mistakes when valuing cash flows.

In this paper we show how in that case they present several conceptual mistakes such as valuation at constant prices, mixing deflated and non-deflated items in financial statements, using constant leverage when in the forecasted financial statements it is not constant, inconsistency in the cash flow and value calculations and some other irregularities that will be described in the body of the paper. This analysis shows an overvaluation of more than 21% when the constant prices methodology is compared with the current prices methodology and using market values to calculate the WACC.

The last two appendixes show the correspondence between the author and officials and consultants from the World Bank.

World Bank, regulatory policy for infrastructure, developing countries, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
When forecasting financial statements care has to be taken to construct a consistent and correct model. This is not an easy task. Even the most experienced expert in modeling makes mistakes. This is especially relevant when we construct a financial model without plugs and without circularity.

In this work we list some common mistakes made while constructing financial models. This list comes from our experience teaching and coaching students in the process of constructing the model and from the professional practice and consulting in finance, especially in firm valuation.

The purpose of this work is to help future students and practitioners when doing the job of forecasting financial statements. After the mistakes have been detected and corrected, they might look like silly mistakes, however, everybody knows that it is easy to be very smart after things have happened. When the mismatching appeared they were real huge problems. After many headaches and lots of work they were found and corrected. Today even after we have worked hard in finding out where the mistakes were, we might consider them as ridiculous or even silly mistakes.

An additional thought is to consider that the exercise to forecast the financial statements of a firm from the outside is a futile one. A fruitful forecasting work is done when the analyst is an insider or is a consultant with full access to the relevant information.

We expect that these thoughts be useful to our students and colleagues and that they avoid mistakes in their academic and professional work.

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem

Abstract:
Although we know there exists a simple approach to solve the circularity between value and the discount rate, known as the Adjusted Present Value proposed by Myers, 1974, it seems that practitioners still rely on the traditional Weighted Average Cost of Capital, WACC approach of weighting the cost of debt, Kd and the cost of equity, Ke and discounting the Free Cash Flow, FCF. We show how to solve circularity when calculating value with the free cash flow, FCF and the WACC. As a result of the solution we arrive at a known solution when we assume the discount rate of the tax savings as Ke, the cost of unlevered equity: the capital cash flow, CCF discounted at Ku. When assuming Kd as the discount rate for the tax savings, we find an expression for calculating value that does not implies circularity. We do this for a single period and for N periods.

Firm valuation, cost of capital, cash flows, free cash flow, capital cash flow, WACC, circularity

Abstract:
It is widely known that if the leverage is constant over time, then the cost of equity and the Weighted Average Cost of Capital (WACC) for the free cash flow, FCF, is constant over time. In other words, it is inappropriate to use a constant WACCFCF to discount the free cash flow (FCF) if the leverage changes over time and some conditions are not satisfied. However, it is common to find analysts who inconsistently use a constant WACCFCF even if the leverage is not constant and the proper conditions are not satisfied.

In this teaching note, we use a simple numerical example to illustrate how to model cash flows that are consistent with constant leverage. We verify the consistency of the example with two basic principles: conservation of cash flows and conservation of values.

The note is based on a previous one and includes the procedure to value with constant leverage when some restrictive conditions are not satisfied.

WACC, constant leverage, cash flows

Abstract:
In this note, we show that with respect to the Miles and Ezzell (M&E) Weighted Average Cost of Capital (WACC), the return to levered equity for finite cash flows is constant if the debt-equity ratio is constant. We assume that the reader is familiar with the M&E WACC. The expression that we derive is not new. We hope that our straightforward derivation with simple algebra makes the M&E WACC more widely known.

M&E WACC, tax shields

Abstract:
This is a teaching material for a module of Financial analysis at Universidad Tecnologica de Bolivar. The educational material was developed with Professor Ricardo Davila from Universidad Javeriana, Bogota, Colombia. The written material has been modified several times, but the basic content is the one we developed many years ago.

This chapter is a broad presentation of accounting concepts in particular of financial statements including the Income Statement, the Balance Sheet and the Cash Budget (the listing of all the inflows and outflows the firm has).

We adopted a graphical approach to explain the relationship between the financial statements.

Accounting, financial management, financial statements, balance sheet, Income Statement

Abstract:
In this work we show a simplified financial planning model. In reality, financial planning models are huge and cumbersome. This is a very simplified model compared with what is found in practice. We present some basic principles for constructing the financial statements needed for valuation. We show in detail all the items of the financial model and show the formulas to be used for constructing the financial planning model. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from input data and policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements. The contribution of this work is double: one is to show that we can construct financial statements without the use of plugs and circularity and the second is that we can use a very simple approach to construct cash flows and to value them. The model shown has two parts. One is the proper financial statements forecast. The second one is a simple cash flow calculation and valuation exercise using the Capital Cash Flow and assuming the risk of the tax savings equal to Ku, the cost of unlevered equity.

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem, cash flows, firm valuation, cost of unlevered equity

Abstract:
In this teaching note we show that using the findings of Tham and Velez-Pareja 2002, for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and general formulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF.

In Tham and Velez-Pareja 2002, they derive a general expression for Ke, the cost of levered equity and for the Weighted Average Cost of Capital (WACC) applied to the Free Cash Flow (FCF) and Capital Cash Flow (CCF). For finite cash flows and perpetuities, the derivation presents the analysis for different levels of risk with respect to discounting the tax shields (TS). Taggart 1991 presents a revision of the set of formulations for the cost of levered Ke and WACC. He introduces the formulation with and without personal taxes and for different level of risk for discounting the TS, including the proposal by Miles and Ezzel 1980. However, Taggart does not include the case of Kd, the cost of debt as the level of risk for the TS and finite cash flows.

A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the Ke and WACC are also assumed to be constant. For cash flows in perpetuity, and with Kd as the discount rate for the tax shield, it is indeed the case that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows. Though it might be convenient to perform calculations under such assumption, it is not in fact always true that Ke and WACC are constant under the constant leverage financing policy. As could be seen from the findings and example of Inselbag and Kaufold (1997), and as a general expression for Ke and WACC derived by Tham and Velez-Pareja (2002) shows, both the cost of levered equity and the Weighted Average Cost of Capital depend on the value of the interest tax shield (VTS), and in the case of finite cash flows valuation they could be changing from period to period if certain choice is made for the rate to discount for the expected tax shields.

The teaching note is organized as follows: An Introduction to state the problem; in Section Two we present the generalized formulation for the cost of capital for the finite cash flow valuation, and in particular formulae under the assumption that the discount rate for the tax shield (TS) is Kd. In Section Three we show a simple example. In Section Four we conclude.

WACC, constant cost of capital, constant leverage, cash flows

Abstract:
In the latest edition of Principles of Corporate Finance (Brealey, Myers and Allen, 2006) the authors use a finite cash flow example to illustrate the valuation procedure for using the Discounted Cash Flow (DCF) method with the free cash flow (FCL) and the Adjusted Present Value (APV). The two firm values obtained are different. They say that the "... difference [...] is not a big deal considering all the lurking risks and pitfalls in forecasting [...] cash flows".

In this teaching note we show that the two methods give identical values when the proper discount rates are used.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, Adjusted Present Value, APV, Discounted Cash Flow, DCF, weighted average cost of capital, WACC, cost of unlevered equity, tax savings

Abstract:
This is a teaching material (slides) accompanying the book in Spanish Decisiones Empresariales bajo Riesgo e Incertidumbre (Managerial Decision Making under Risk and Uncertainty). It shows the general content of the book. In this material we show the basics of risk analysis with Monte Carlo Simulation and how to perform it. We illustrate it with SimulAr a software available in the web. SimulAr is not a freeware program but rather it is software considered emailware, what means that you have to send the author an email with your comments about the program and the model developed in Excel in order to share it with the rest of users through the SimulAr Website.

Simulation, Monte Carlo Smulation, Risk analysis

Abstract:
In a forthcoming paper, Fernandez (2002) claims to derive a formula for the valuation of debt tax shields for firms with cash flows that grow perpetually at a constant rate. We show that his formula is incorrect.

Present value of tax shield, perpetuities

Abstract:
When valuating cash flows they should be based on estimates of free cash flows at nominal prices. In particular, we show that results from the valuation of cash flows with the constant and real price methods are biased upwards and there is a risk that in practice, bad projects will be accepted as good projects or that the valuation of free cash flows for valuing firms is overstated. Generally speaking, inflation has a negative impact on the Net Present Value of a project. When expected inflation rates over the cash flow horizon are high, which is a typically case in emerging and transitional markets, the use of the real and constant prices methodology could lead to serious mistakes in valuation.

Financial statements at constant or real prices will be of no use when the project is implemented because what occurs in reality (that is what we are interested in) is very different from what is written in the final report of a project evaluation. Some items are deflated while others (say depreciation charges and interest payments) are in nominal prices. For managerial purposes, it is useless to have this mixed information in the financial statements.

We present some examples where we show that the value of a cash flow should be based on estimates of free cash flows at nominal prices. It is an accepted practice to evaluate projects at constant or real prices. In particular, we present an example where the results from the constant and real price methodologies are biased upwards and there is a risk that in practice, bad projects will be accepted as good projects. It is a third party and near real life example (an example presented in the training material on economic regulation of public utilities developed by the World Bank Institute) we compare the results of the constant prices methodology with results of the nominal prices methodology. World Bank has played a crucial role in the development of the economies of the world, especially in the emerging countries. We recognize the leadership it has shown and the intellectual authority it has on planning offices, practitioners and consultants. For this reason it is critical whatever improvements made in the methodologies it uses in assessing the feasibility of infrastructure projects. This influence affects private practice in valuation and project appraisal as well.

We show how in the case based on the example from WB where they use some current practices several improvements to some areas of the model can be made, such as valuation at constant prices, mixing deflated and non-deflated items in a financial statements, using constant leverage when in the forecasted financial statements it is not constant, inconsistency in the cash flow and value calculations and some other irregularities that will be described in the body of the chapter. This analysis shows an overvaluation of more than 21% when the constant prices methodology is compared with the current prices methodology and using market values to calculate the WACC. This is a dramatic number.

World Bank, regulatory policy for infrastructure, developing countries, project evaluation, project appraisal, firm valuation, cost of capital, cash flows, free cash flow, capital cash flow

Abstract:
Typical textbooks on corporate finance and forecasting and budgeting recommend closing and matching the financial statements what is known as a plug. A plug is a formula to match the Balance Sheet using the differences in some items listed in it in such a way that the accounting equation holds. This is a very easy way to do it but it encompasses some risks. The risks are that certain numbers in the financial statements could be in error and still the plug would indicate that everything is correct because the Balance Sheet matches.

In this work the reader finds a simplified financial model. In reality, financial models are huge and cumbersome. This is a very simplified model compared with what is found in practice.

We present some basic principles for constructing consistent financial statements. The reader is encouraged to construct the financial statements for herself on a spreadsheet. The relevant financial statements are: the Balance Sheet (BS), the Income statement (IS) and the Cash Budget (CB). The construction of the financial statements starts from policies and/or targets (i.e. accounts receivable policy or target). With these targets or policies we can construct the financial statements.

The contribution of this work is to show that we can construct financial statements without the use of plugs and circularity.

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem

Abstract:
When forecasting financial statements care has to be taken to construct a consistent and correct model. This is not an easy task. Even the most experienced expert in modeling make mistakes. This is especially relevant when we construct a financial model without plugs and without circularity.

In this teaching note we list some common mistakes made while constructing financial models. This list comes from our experience teaching and coaching students in the process of constructing the model and from the professional practice and consulting in finance, especially in firm valuation.

The purpose of this work is to help future students and practitioners when doing the job of forecasting financial statements. After the mistakes have been detected and corrected, they might look like silly mistakes, however, everybody knows that it is easy to be very smart after things have happened. When the mismatching appeared they were real huge problems. After many headaches and lots of work they were found and corrected. Today even after we have worked hard in finding out where the mistakes were, we might consider them as ridiculous or even silly mistakes.

An additional thought is to consider that the exercise to forecast the financial statements of a firm from the outside is a futile one. A fruitful forecasting work is done when the analyst is an insider or is a consultant with full access to the relevant information.

We expect that these thoughts be useful to our students and colleagues and that they avoid mistakes in their academic and professional work

Accounting, Forecasting Financial Statements, Decision Making, plugs, Planning and control, double entry principle, unbalancing problem

Abstract:
In theory, different valuation methods, with consistent assumptions, must give identical results. Numerical examples that purport to illustrate the theory should demonstrate the identical results. Unfortunately, in popular textbooks it is all too easy to find numerical examples that are at odds with the theory. There are several possible explanations for the discrepancies. First, there might be some conceptual confusion about the underlying assumptions. Second, it could simply be "rounding errors." It is intellectual laziness to ascribe the discrepancies to the tyranny of rounding errors when in fact it is easy to show that rounding errors are not the reasons for the discrepancies.

It is common to read that different valuation methods give different results. For instance, Brealey and Myers (2000, 2003) say: "If the company's debt ratio is constant over time, the flow-to-equity method should give the same answer as discounting company cash flows at the WACC and subtracting debt." On the other hand, they say, "If financial leverage will change significantly discounting flows to equity at today's cost of equity will not give the right answer."

Inselbag and Kaufold, 1997, conclude that the APV is better than the DCF when the debt schedule is given. This is misleading in two senses: one, they mix methods because they disregard the possibility to solve the circularity posed by the relationship between value and discount rates and second, as a consequence, they say that "one must already have calculated the firm's value" in order to know the WACC.

In the latest edition of Principles of Corporate Finance (Brealey, Myers and Allen, 2006) the authors use a finite cash flow example to illustrate the valuation procedure for using the Discounted Cash Flow (DCF) method with the free cash flow (FCF) and the Adjusted Present Value (APV). The two firm values obtained are different. They say that the "... difference [...] is not a big deal considering all the lurking risks and pitfalls in forecasting [...] cash flows".

Once more, in this teaching note we show that the two methods give identical values when the proper discount rates are used.

Cash flows, free cash flow, cash flow to equity, valuation, levered value, Adjusted Present Value, APV, Discounted Cash Flow, DCF, weighted average cost of capital, WACC, cost of unlevered equity, tax savings