Principles of Cash Flow Valuation

Principles of Cash Flow Valuation

An Integrated Market-Based Approach

1st Edition - February 2, 2004

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  • Authors: Joseph Tham, Ignacio Velez-Pareja
  • eBook ISBN: 9780080514802

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Description

Principles of Cash Flow Valuation is the only book available that focuses exclusively on cash flow valuation. This text provides a comprehensive and practical, market-based framework for the valuation of finite cash flows derived from a set of integrated financial statements, namely, the income statement, balance sheet, and cash budget. The authors have distilled the essence of years of gathering academic wisdom in the study of cash flow analysis and the cost of capital. Their work should go a long way toward bridging the gap between the application of cost benefit analysis and the theory of capital budgeting. This book covers the basic concepts in market-based cash flow valuation. Topics include the tme value of money (TVM) and an introduction to cost of capital; basic review of financial statements and accounting concepts; construction of integrated pro-forma financial statements; derivation of free cash flows; use of the WACC in theory and in practice; estimating the WACC for non traded firms; calculating the terminal value beyond the planning period. It also revisits the theory for cost of capital and explains how cash flows are valued in reality. The ideas are illustrated using examples and a case study. The presentation is appropriate for a range of technical backgrounds. This text will be of interest to finance professionals as well as MBA and other graduate students in finance.

Key Features

* Provides the only exclusive treatment of cash flow valuation
* Authors use examples and a case study to illustrate ideas
* Presentation appropriate for a range of technical backgrounds: ideas are presented clearly, full exposition is also provided
* Named among the Top 10 financial engineering titles by Financial Engineering News

Readership

Finance professionals; MBA and other graduate students in finance

Table of Contents

  • Chapter One Basic concepts in market-based cash flow valuation
    1.1 Introduction
    1.1.1 Finite streams of cash flows
    1.1.2 Content and organization of the chapters
    1.2 Market-based procedure for valuation
    1.2.1 Integrated valuation framework with complete financial statements
    1.3 Steps in cash flow valuation
    1.3.1 Why invest?
    1.3.2 The role of information and expectations
    1.4 Present value (PV)
    1.4.1 Perfect capital markets and arbitrage opportunities
    1.4.2 Valuation in an imperfect but real world
    1.4.3 Perfect capital markets
    1.4.4 Replicating portfolio strategy
    1.4.5 Traded firms in the U.S. stock market
    1.4.6 Traded firms in an emerging market
    1.5 The standard after-tax Weighted Average Cost of Capital (WACC)
    1.6 Types of cash flows
    1.6.1 What is FCF?
    1.6.2 What is cash flow to (existing) debt?
    1.6.3 What is cash flow to equity (CFE)?
    1.7 The WACC in a Modigliani and Miller (M & M) world
    1.7.1 WACC in an M & M world without taxes
    1.7.2 An unlevered company versus a levered company
    1.7.3 The no-arbitrage argument
    1.7.4 Slicing the cake
    1.7.5 Debt and equity financing
    1.7.6 Formula for the WACC without taxes
    1.7.7 Equality of the unlevered and levered returns
    1.8 WACC in an M & M world with taxes
    1.8.1 The expanding cake
    1.8.2 Why firms do not have 100% debt?
    1.9 The fundamental FCF relationship
    1.10 The main valuation methods and formulas for cost of capital
    1.10.1 The tax shield (TS)
    1.10.2 After-tax WACC applied to the FCF
    1.10.3 Alternative expression for the WACC applied to the FCF
    1.10.4 The WACC with the CCF method
    1.10.5 Losses carried forward (LCF)
    1.10.6 The FCF WACC versus the CCF WACC
    1.11 The CFE approach
    1.12 Estimating the cost of capital
    1.13 The Adjusted Present Value (APV) approach
    1.14 Various formulations for the cost of capital 1.15 Summary and concluding remarks
    KEY CONCEPTS AND IDEAS

    Chapter Two
    Time Value of Money (TVM) and introduction to cost of capital
    2.1 Introduction
    Section One
    2.1.1 The expected inflation rate
    2.1.2 Relationship between the real rate of return and the nominal rate of return
    2.1.3 Expression for the cost of capital
    2.2 Nominal prices, constant prices and real prices
    2.2.1 Expected real increase is 2% and expected inflation rate is 3%
    2.2.2 Expected real increase is 2% and expected inflation rate is 0%
    2.2.3 Expected real increase is 0% and expected inflation rate is 3%
    2.2.4 Real increase is 0% and expected inflation rate is 0%
    2.2.5 The use of nominal prices versus real prices
    2.2.6 Multi-period example with nominal and real prices
    2.3 Risk premium with CAPM
    2.4 Calculating (present) value with a finite stream of cash flows
    2.4.1 Future value with the nominal risk-free rate: single period case
    2.4.2 Time value of money (TVM)
    2.4.3 Variable rates of return
    2.4.4 The discounting process
    2.4.5 Variable discount rates
    2.4.6 Single and multi-period cash flows
    2.4.7 Assessing an investment opportunity with the PV concept
    Section Two
    2.5 Valuation with a finite stream of cash flows
    2.5.1 Unlevered values
    2.5.2 Debt financing with constant leverage
    2.5.3 (Present) Value of TS
    2.5.4 The corrected return to levered equity and WACC
    2.5.4 Alternative formulation for the WACC with circularity
    2.5.5 After-tax WACC applied to the FCF
    2.6 Summary and concluding remarks
    KEY CONCEPTS AND IDEAS
    APPENDIX A for Chapter Two
    A2.1 Calculating the present value (PV) with cash flow in perpetuity (without growth)
    A2.1.1 WACC in an M & M world without taxes
    A2.1.2 Unlevered value
    A2.1.3 Value of the cash flow to debt (CFD)
    A2.1.4 Value of the cash flow to equity (CFE)
    A2.1.5 Formula for the return to levered equity e
    A2.1.6 Deriving the Weighted Average Cost of Capital (WACC) without taxes
    A2.1.7 Numerical example
    A2.2 WACC in an M & M world with taxes
    A2.2.1 Annual tax shield
    A2.2.2 Capital cash flow
    A2.2.3 (Present) value of the annual tax shield
    A2.2.4 The levered value VL in the presence of corporate tax
    A2.3.1 Value of levered equity
    A2.3.2 Cash flow to equity
    A2.3.3 Return to levered equity with taxes
    A2.3.4 Formula for the return to levered equity
    A2.4.1 Traditional after-tax WACC with the FCF
    A2.4.2 Alternative expression for the WACC with the FCF
    A2.4.3 WACC with the Capital Cash Flow (CCF)
    A2.4.4 Another WACC formulation with the Capital Cash Flow (CCF)
    A2.5 FCF in perpetuity with growth
    A2.5.1 Unlevered value
    A2.5.2 Value of the debt
    A2.5.3 The annual tax shield
    A2.5.4 (Present) Value of the tax shield
    A2.6 Cash flow to equity
    A2.6.1 Value of levered equity
    A2.6.2 Return to levered equity
    APPENDIX B
    B2 Using CAPM to find the cost of capital
    B2.1 Discount rate for the tax shield is the cost of debt d
    B2.2 Discount rate for the tax shield is the return to unlevered equity r
    Basic Review of Financial Statements and Accounting Concepts
    3.1 Financial statements and accounting concepts
    SECTION ONE
    3.1.1 Pro-forma financial statements
    3.1.2 Integrated framework
    3.2 Balance sheet
    3.2.1 Assets
    3.2.2 Current assets
    3.2.3 Liabilities
    3.2.4 Current liabilities
    3.3 Working capital
    3.4 (Book) Value of equity
    3.5 Income statement
    3.5.1 Line items in the income statement
    3.5.2 Gross profit
    3.5.3 Earnings before Interest and Taxes (EBIT)
    3.5.4 EBT
    3.5.5 Taxes
    3.5.6 Net income
    3.5.7 Dividends
    3.5.8 Retained and accumulated retained earnings
    3.6 Cash flow statement
    3.6.1 Cash flow from operating activities
    3.6.2 Cash flow from investing activities
    3.6.3 Cash flow from financing activities
    3.7 Cash budget statement
    3.7.1 Annual cash budget statement
    3.7.2 NCB before financing and reinvestment
    3.7.3 NCB after debt financing
    3.7.4 NCB after equity financing
    3.7.5 Reinvestment of surplus funds
    3.7.6 Final NCB after reinvestment
    3.7.7 Cumulative Cash balance
    3.8 Differences between the CFS according to GAAP and the CB statement
    3.9 Integration of the financial statements
    SECTION TWO
    3.10 Preliminary tables
    3.10.1 Depreciation schedule
    3.10.2 Loan schedule
    3.10.3 Quantity sold, inventories and purchases
    3.10.4 Cost of Goods Sold (COGS)
    3.10.5 Adjustments for credit sales and purchases
    3.10.6 Accounts Receivable (A.R.)
    3.10.7 Accounts Payable (A.P.)
    3.11 Summary and concluding remarks
    Appendix A
    APPENDIX B
    Sample Balance Sheet
    Sample Income Statement
    Chapter Four
    Constructing Integrated Pro-forma Financial Statements, Part One
    4.1 Basic financial statements
    4.2 Simple numerical example
    4.2.1 Basic data for the simple example
    4.2.2 Cash Required for Operations (CRO)
    4.2.3 Reinvestment of surplus funds
    4.2.4 Terminal value calculation
    4.3 Goals and policies for selected variables
    4.4 Depreciation schedule
    4.5 Estimated target variables
    4.5.1 Annual sales volume
    4.5.2 Annual sales revenues
    4.5.3 Selling and administrative expenses
    4.6 Preliminary tables for the simple example
    4.6.1 Initial cash budget statement for year 0
    4.6.2 Loan schedule
    4.6.3 Inventory and purchases
    4.6.4 Final inventory in year 1
    4.6.5 Purchases (units)
    4.6.6 Cost of goods sold (COGS)
    4.6.7 Receivables and payables
    4.6.8 Accounts receivable
    4.6.9 Accounts payable
    4.6.10 Cash receipts and cash expenditures
    4.7 Constructing the financial statements for the simple example
    4.7.1 Cash budget statement in year 0 revisited
    4.7.2 Cash budget statement for year 1
    4.7.3 Income statement for year 2
    4.7.4 Iterations between the income statement and cash budget statement
    4.7.5 Cash budget statement for year 2
    4.7.6 Completed income statement for all years
    4.7.7 Complete budget statement for all years
    4.7.8 Calculation of the new loan in year 4
    4.8 Detailed cash budget statement in year 5
    4.8.1 NCB before financing and reinvestment in year 5
    4.8.2 NCB after debt financing in year 5
    4.8.3 NCB after debt and equity financing in year 5
    4.8.4 Reinvestment of surplus funds in year 5
    4.8.5 Final NCB after reinvestment in year 5
    4.8.6 Cumulative cash balance in year 5
    4.8.7 Adjustments in the cash budget statement
    4.9 Balance sheet
    4.10 Cash Flow Statement according to GAAP
    4.11 Summary and concluding remarks
    Key Concepts and Ideas
    Appendix A:
    A4.12 Detailed income statement for year 1
    A4.12.1 Gross profits in year 1
    A4.12.2 EBIT in year 1
    A4.12.3 EBT in year 1
    A4.12.4 Net income in year 1
    A4.12.5 Dividends declared in year 1
    A4.12.6 Retained earnings in year 1
    A4.13 Detailed cash budget statement for year 1
    A4.13.1 NCB before financing and reinvestment
    A4.13.2 NCB after debt financing
    A4.13.3 NCB after equity financing
    A4.13.4 Reinvestment of surplus funds in year 1
    A4.13.5 Final NCB after reinvestment
    A4.13.6 Cash balance after reinvestment in year 1
    A4.14 Detailed cash budget statement for year 2
    A4.14.1 NCB before financing and reinvestment
    A4.14.2 NCB after debt financing
    A4.14.3 NCB after equity financing
    A4.14.4 Reinvestment of surplus funds
    A4.14.5 Final NCB after reinvestment
    A4.14.6 Cumulative cash balance in year 1
    Chapter Five
    5.1 Constructing Financial Statements (continued), Part Two
    5.1.1 The construction of the financial statements
    5.1.2 A complex example
    5.1.3 Model assumptions
    5.1.4 Goals and policies for selected variables
    5.1.5 Relationship between the quantity purchased and the purchase price
    5.1.6 Simulation of market demand
    5.2 Impact on demand of changes in price and of expenditures on advertising and promotion
    5.2.1 Annual Sales
    5.2.2 Impact on demand of change in price
    5.2.3 Impact on demand of expenditures on advertising and promotion
    5.2.4 Preliminary tables for the complex example
    5.2.5 Annual increase in the volume of sales
    5.2.6 Annual expenditures on advertising and promotion
    5.2.7 Cash Requirements for Operations (CRO)
    5.2.8 Expected domestic inflation rate
    5.2.9 Annual sales volume
    5.2.10 Annual sales revenue
    5.3 Real rate of interest, the risk-premium for debt and the reinvestment return: Interest rates estimation
    5.4 Depreciation Schedule
    5.4 Initial cash budget for year 0
    5.5 Loan schedule
    5.6 Inventory and quantity purchased
    5.7 Relationship between the quantity purchased and the purchase price
    5.8 Cost of goods sold (COGS)
    5.9 Selling and administrative expenses
    5.10 Receivables and payables
    5.11 The logic of the model
    5.12 Constructing the financial statements for the complex example
    5.12.1 Income Statement
    5.12.2 Cash budget statement
    5.12.3 Balance Sheet
    5.12.4 The Cash flow statement
    5.13 Summary and concluding remarks
    Key concepts and ideas
    Appendix A
    A Brief Introduction to Price-Demand Elasticity
    A1.1 Own Price.
    A1.2 Consumption.
    A1.3 Income.
    A1.4 Substitutability.
    A1.5 Kind of goods.
    A1.6 Habits and time.
    A1.7 Taste.
    A1.8 Determinants of quantity sold
    A1.9 An expression for the Quantity demanded
    APPENDIX B
    A Detailed Spreadsheet Example
    6.1 Derivation of the free cash flows
    6.2 The fundamental free cash flow (FCF) relationship
    6.2.1 CB statement versus free cash flow
    6.2.2 Operational cash flow
    6.2.3 Inflation adjustments for financial statements
    6.2.4 Treatment of tax savings
    6.3 Deriving the FCF from the CB statement
    6.3.1 Cash flow to equity (CFE)
    6.3.2 Cash Flow to Debt
    6.3.3 Tax shields
    6.3.4 Deferred taxes
    6.3.5 Total Free Cash Flow
    6.3.6 Capital cash flow
    6.4 Total CCF versus operational CCF
    6.4.1 Total capital cash flow
    6.4.2 Operational CCF
    6.4.3 Non-operational CCF
    6.4.4 Other relationships for operational cash flows
    6.5 Deriving the FCF from the CF statement according to GAAP
    6.6 Deriving the FCF from the EBIT in the income statement
    6.6.1 Adjustments to the income statement
    6.6.2 Depreciation charges and amortization
    6.6.3 Working capital adjustment
    6.6.4 Deriving the FCF from the EBIT
    6.7 Deriving the CFE from the Net Income, NI
    6.8 Advantages of using the CB Approach
    6.9 Summary and concluding remarks
    APPENDIX A
    A1: Calculating the excess cash from the Income Statement and the Balance Sheet
    APPENDIX B
    B1: Deriving the FCF from NI
    B2: Deriving the CCF from NI
    Chapter Seven
    Using the WACC in theory and in practice
    Section One: Introduction
    7.1 Approaches to the cost of capital
    7.2 Review of basic ideas
    7.2.1 Impact of taxes
    7.2.2 Cash flow relationships
    7.2.3 Relationships between values and cash flows
    7.2.4 Two period example
    7.2.5 Discount rate for the tax shield
    7.2.6 Return to levered equity ei
    7.3 Three simple expressions for the cost of capital
    7.3.1 Standard after-tax WACC applied to the FCF
    7.3.2 Adjusted WACC applied to the FCF
    7.3.3 WACC applied to the CCF
    7.4 General framework
    7.4.1 First dimension
    7.4.2 Second dimension
    7.4.3 Third dimension
    7.4.4 Matrix for the WACC applied to the FCF
    7.4.5 Matrix for the WACC applied to the CCF
    7.4.6 How do we estimate the cost of capital? Practical issues.
    7.5 Numerical examples with the complex example
    7.5.1 Standard WACC applied to the FCF
    7.5.2 Adjusted WACC applied to the FCF
    7.5.3 WACC applied to the CCF
    7.5.4 Cash flow to equity (CFE) approach
    7.6 Summary and concluding remarks
    APPENDIX A
    A.1 Algebraic approach
    A.1.1 General expression for the return to levered equity ei
    A.1.2 Standard WACC applied to the FCF
    A.1.3 Adjusted WACC applied to the FCF
    A.1.4 Standard WACC applied to the CCF
    A.1.5 Adjusted WACC applied to the CCF
    APPENDIX B:
    Using the Capital Asset Pricing Model (CAPM) to find the cost of capital
    Appendix C
    The Calculation of Levered Values with Operational Cash Flows
    Operating CFD, CFE, TS, FCF and CCF
    7.5.1 Standard WACC applied to the FCF
    7.5.2 Adjusted WACC applied to the FCF
    7.5.3 WACC applied to the CCF
    7.5.4 Cash flow to equity (CFE) approach
    Chapter Eight
    Estimating the WACC for Non Traded firms
    Introduction
    8.1 Practical Approaches to the Cost of Capital for Traded and Non Traded Firms
    8.2 Finding the Relationship between Levered and Unlevered b’s
    8.3 Valuation for Traded Firms
    8.3.1 Estimating the Return to Levered Equity e for a Traded Firm
    8.3.2 Using CAPM to find the Cost of Capital
    8.3.3 Adjusted WACC applied to the FCF
    8.3.4 WACC applied to the CCF
    8.4 Valuation for Non-Traded Firms
    8.4.1 Valuing Firms, both Traded and Non-traded, in Emerging Markets
    8.4.2 Systematic Risk and Total Risk
    8.4.3 The Estimation of the Cost of Levered Equity with Systematic Risk
    8.4.3.1 Using a Proxy Traded Firm
    8.4.3.2 Accounting Betas
    8.4.4 The Estimation of the Unlevered Return to Equity, r with Systematic Risk
    8.5 Summary and Concluding Remarks
    APPENDIX A
    A.1 The Estimation with Total Risk
    A.1.1 The Estimation of the Levered Cost of Equity, e with Total Risk
    A.1.2 The Estimation of the Unlevered Return to Equity, r with Total Risk
    APPENDIX B
    Appendix C
    Chapter Nine
    Beyond the planning period: calculating the terminal value
    9.1 Introduction
    9.2 Operation versus liquidation
    9.3 Calculating the salvage (or liquidation) value
    9.4 Terminal value versus salvage value
    9.5 The standard approach for estimating the terminal value
    9.5.1 Assumptions in the model
    9.5.2 Simple numerical example
    9.5.3 Estimating the key parameters
    9.5.4 Growth in the steady state
    9.5.5 Estimating the growth rate of the NOPLAT, g
    9.6 Terminal Value is Calculated for Discounted Cash Flow (DCF) Method Using NOPLAT and Using Constant Leverage
    9.7 Amount of reinvestment for the growth in the Free Cash Flow
    9.8 Calculating the Return on the Market Value of the Invested Capital (ROMVIC)
    9.9 A Comment on constant leverage
    9.9.1 The Tax Savings with Terminal Value
    9.9.2 CFE with terminal value
    9.9.3 CFD with terminal value
    9.9.4 CCF with terminal value
    9.10 Calculating the terminal value with the CCF and APV approaches
    9.11 Summary and concluding remarks
    Appendix A: Terminal value and amount of reinvestment
    A.1 Return on the Market Value of the Invested Capital
    A.2 Additional reinvestment for higher growth of NOPLAT
    Appendix B: Independent Calculation of the TV Levered Value
    B.1 Value of debt in the terminal period N
    B.2 Value of tax shield in the terminal year N
    B.3 Levered value in terminal year N
    B.4 The Terminal Value with CCF and APV
    Appendix C
    Pure Free Cash Flow and non pure Free Cash Flow
    Matching the RIM (Residual Income Model), EVA® and DCF (Discounted Cash Flow)
    D9.1 What is value added?
    D9.2 Assumptions and financial statements for the complex example
    D9.2.1 RIM for the complex example
    D9.2.2 EVA for the complex example
    D9.3 Conclusion
    Chapter Ten
    Theory for cost of capital revisited
    10.1 Cost of capital with a finite stream of cash flows
    10.1.1 WACC in an M & M world without taxes
    10.1.2 Value relationships
    10.1.3 Cash flow relationships
    10.1.4 Unlevered value in year 1
    10.1.5 Unlevered value in year 0
    10.2 Numerical example
    10.2.1 Unlevered equity schedule
    10.2.2 Loan Schedule for the debt financing
    10.2.3 Value of debt in year 1
    10.2.4 Value of debt in year 0
    10.2.5 Annual cash flow to (levered) equity
    10.2.6 Debt-Equity Ratios
    10.2.7 Returns to levered equity in year 1 and year 2
    10.2.8 Value of (levered) equity in year 1
    10.2.9 Value of (levered) equity in year 0
    10.2.10 Levered equity schedule
    10.2.11 Calculation of the multi-period WACC
    10.3 Loan schedule with constant leverage
    10.3.1 Calculation of the multi-period WACC
    10.4 Policy on debt financing and the WACC in the presence of taxes
    10.4.1 Risk-free tax shields
    10.4.2 Fixed loan schedule
    10.4.3 Constant leverage
    10.5 The M & E WACC
    10.5.1 The M & E argument in the limit
    10.5.2 Relaxation of the M & E assumptions (Optional)
    10.6 WACC for a finite stream of cash flows in an M & M world with taxes
    10.6.1 Fixed loan schedule
    10.6.2 Option 1: WACC applied to finite FCF (fixed amount of debt) with y = r
    10.6.3 Option 2: WACC applied to the finite CCF (fixed amount of debt) with y = r
    10.7 Fixed percentage of debt
    10.7.1 M & E specification for the WACC applied to the FCF
    10.7.2 Harris & Pringle (H & P) specification
    10.7.2.1 Option 1: WACC applied to FCF (fixed percentage of debt and y = r)
    10.7.2.2 Option 2: WACC applied to the CCF (fixed percentage of debt and y = r)
    10.7.3. Standard (inaccurate) specification
    10.7.3.1 Option 1: WACC applied to FCF (fixed percentage of debt and y = d)
    10.8 Theory on the cost of capital applied to finite cash flows
    10.8.1 Value relationships
    10.8.2 Cash flow relationships
    10.8.3 Tax shield in year 1 and year 2
    10.8.5 (Present) value of the tax shield in year 0
    10.9 Standard WACC applied to the CCF
    10.10 Standard after-tax WACC applied to the FCF
    10.11 Return to (levered) equity
    10.11.1 Case 1
    10.11.2 Case 2
    10.11.3 Case 3
    10.12 Alternative adjusted WACC applied to the FCF (Optional)
    10.12.1 Alternative adjusted WACC in year 1 applied to the FCF
    10.12.2 Assuming the discount rate for the tax shield is r
    10.13 Alternative WACC applied to the CCF (Optional)
    10.14 Numerical example
    10.14.1 Amount of the Tax Shields
    10.14.2 Summary of the cash flows
    10.14.3 (Present) Value of the tax shields
    10.15 Adjusted Present Value (APV) approach
    10.15.1 Percent debt and percent equity in year 1
    10.15.2 Percent debt and percent equity in year 2
    10.15.3 Returns to levered equity in year 1 and year 2
    10.15.4 WACC applied to the CCF
    10.15.5 Standard after-tax WACC applied to the FCF
    10.15.6 Alternative WACC applied to the FCF
    10.16 Summary and concluding remarks
    KEY CONCEPTS AND IDEAS
    Appendix A
    A10.1 Derivation of the M & E WACC
    A10.1.1 Levered value in Year 2
    A10.1.2 Levered value in Year 1
    A10.1.3 Levered value in Year 0
    APPENDIX B
    B10.1 Numerical example with constant leverage
    B10.1.1 Leverages in year 1 and year 2
    B10.1.2 Relationship between the levered and unlevered value in year 1
    B10.1.3 Relationship between the levered and unlevered value in year 0
    B10.2 Basic information
    B10.2.1 Levered values in year 0 and year 1
    B10.2.2 Values of debt in year 0 and year 1
    B10.2.3 Tax shields in year 1 and year 2
    B10.2.4 CCF in year 1 and year 2
    B10.2.5 Return to levered equity
    B10.3 WACC applied to the CCF
    B10.4 Standard after-tax WACC applied to the FCF
    B10.5 Alternative adjusted WACC for the FCF

Product details

  • No. of pages: 350
  • Language: English
  • Copyright: © Academic Press 2004
  • Published: February 2, 2004
  • Imprint: Academic Press
  • eBook ISBN: 9780080514802

About the Authors

Joseph Tham

Affiliations and Expertise

Visiting Assistant Professor, Duke Center for International Development(DCID), Sanford Institute of Public Policy, Duke University

Ignacio Velez-Pareja

Affiliations and Expertise

Politécnico Grancolombiano, Bogotá, Colombia

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