Discounted Cash Flow A Theory of the Valuation of Firms Lutz Kruschwitz and Andreas Löffler Discounted Cash Flow For other titles in the Wiley Finance Series please see www.wiley.com/finance Discounted Cash Flow A Theory of the Valuation of Firms Lutz Kruschwitz and Andreas Löffler Copyright©2006 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester, WestSussexPO198SQ,England Telephone (+44)1243779777 Email(forordersandcustomerserviceenquiries):[email protected] VisitourHomePageonwww.wiley.com AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemor transmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningor otherwise,exceptunderthetermsoftheCopyright,DesignsandPatentsAct1988orunderthetermsofa licenceissuedbytheCopyrightLicensingAgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK, withoutthepermissioninwritingofthePublisher.RequeststothePublishershouldbeaddressedtothe PermissionsDepartment,JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex PO198SQ,England,[email protected],orfaxedto(+44)1243770620. 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Contents List of Figures ix List of Symbols xi List of Definitions, Theorems, etc. xiii Acknowledgments xv Introduction xvii 1 Basic Elements 1 1.1 Fundamental terms 1 1.1.1 Cash flows 2 1.1.2 Taxes 3 1.1.3 Cost of capital 4 1.1.4 Time 6 Problems 9 1.2 Conditional expectation 9 1.2.1 Uncertainty and information 9 1.2.2 Rules 12 1.2.3 Example 13 Problems 17 1.3 A first glance at business values 19 1.3.1 Valuation concept 19 1.3.2 Cost of capital as conditional expected returns 22 1.3.3 A first valuation equation 25 1.3.4 Fundamental theorem of asset pricing 26 Problems 29 1.4 Further literature 29 References 30 vi Contents 2 Corporate Income Tax 31 2.1 Unlevered firms 31 2.1.1 Valuation equation 32 2.1.2 Weak autoregressive cash flows 33 2.1.3 Example (continued) 40 Problems 43 2.2 Basics about levered firms 46 2.2.1 Equity and debt 46 2.2.2 Earnings and taxes 47 2.2.3 Financing policies 49 2.2.4 Default 52 2.2.5 Example (finite case continued) 56 Problems 60 2.3 Autonomous financing 61 2.3.1 Adjusted present value (APV) 61 2.3.2 Example (continued) 63 Problems 64 2.4 Financing based on market values 65 2.4.1 Flow to equity (FTE) 66 2.4.2 Total cash flow (TCF) 67 2.4.3 Weighted average cost of capital (WACC) 69 2.4.4 Miles–Ezzell and Modigliani–Miller adjustments 71 2.4.5 Example (continued) 75 Problems 78 2.5 Financing based on book values 79 2.5.1 Assumptions 79 2.5.2 Full distribution policy 82 2.5.3 Replacement investments 84 2.5.4 Investment policy based on cash flows 85 2.5.5 Example (continued) 88 Problems 89 2.6 Other financing policies 90 2.6.1 Financing based on cash flows 90 2.6.2 Financing based on dividends 92 2.6.3 Financing based on debt–cash flow ratio 95 2.7 Comparing alternative forms of financing 97 Problems 98 2.8 Further literature 99 References 100 3 Personal Income Tax 103 3.1 Unlevered and levered firms 103 3.1.1 ‘Leverage’ interpreted anew 104 3.1.2 The unlevered firm 105 3.1.3 Income and taxes 106 3.1.4 Fundamental theorem 110 Contents vii 3.1.5 Tax shield and distribution policy 112 3.1.6 Example (continued) 113 Problems 114 3.2 Excursus: Cost of equity and tax rate 115 Problems 118 3.3 Retention policies 119 3.3.1 Autonomous retention 119 3.3.2 Retention based on cash flow 121 3.3.3 Retention based on dividends 122 3.3.4 Retention based on market value 124 Problems 127 3.4 Further literature 127 References 128 4 Corporate and Personal Income Tax 129 4.1 Assumptions 129 4.2 Identification and evaluation of tax advantages 130 4.3 Epilogue 133 Problem 134 References 134 Appendix: Proofs 135 A.1 Proofs of theorems 2.2 and 2.3 135 A.2 Proof of theorem 2.17 136 A.3 Proof of theorem 2.18 141 A.4 Proofs of theorems 2.19 and 2.20 142 A.5 Proof of theorem 2.21 144 A.6 Proofs of theorems 2.22 and 2.23 147 A.7 Proof of theorem 3.2 148 A.8 Proof of theorem 3.9 152 References 153 Index 155