(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 12194, 383]*) (*NotebookOutlinePosition[ 18035, 551]*) (* CellTagsIndexPosition[ 17378, 526]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["DCF", "Title", FontSlant->"Italic", FontColor->RGBColor[1, 0, 0]], StyleBox[" Example (infinite case, firm income tax) by Kruschwitz/L\ \[ODoubleDot]ffler", "Title", FontColor->RGBColor[1, 0, 0]] }], "Section", CellFrame->True, CellDingbat->None, ShowCellBracket->False, TextAlignment->Center, Background->GrayLevel[0.811765], CellTags->{"b:8", "c:1"}], Cell["\<\ In this notebook we only consider examples where the stochastic structure of \ the cash flows is not used. This excludes exotic financing schedule (chapter \ 2.6).\ \>", "Text", ShowCellBracket->False, CellTags->"b:8"] }, Open ]], Cell[CellGroupData[{ Cell["Parameters of the Model", "Section", Editable->False, CellFrame->True, CellDingbat->"\[FilledSquare]", ShowCellBracket->False, Background->GrayLevel[0.811765], CellTags->{"b:9", "c:2"}], Cell["\<\ We are dealing here with an (unlevered) company,which will bear infinitely \ many years of payments to its owners.They,however,cannot be predicted with \ certainty. We know that the firm will live infinitevily and the free cash \ flow after tax will have constant expectation. \ \>", "Text", CellFrame->True, ShowCellBracket->False, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}, CellTags->"b:9"], Cell[BoxData[ \(C\_1 = 100; \ \[Tau] = 0.5; \ r\_f = 0.1;\)], "Input", CellFrame->False, CellGroupingRules->"InputGrouping", AutoIndent->Automatic, StyleBoxAutoDelete->True, TextAlignment->Left, ParagraphIndent->0, FontWeight->"Bold", CellTags->{"parameter of the model", "b:9"}] }, Open ]], Cell[CellGroupData[{ Cell["Valuation concept: the unlevered company", "Section", CellFrame->True, CellDingbat->"\[FilledSquare]", ShowCellBracket->False, Background->GrayLevel[0.811765], CellTags->{"b:10", "c:3"}], Cell[TextData[{ "To value the firm we need to know the cost of capitel of the (unlevered) \ firm. These cost of capital are expected returns of holding the firm's share \ for one period. This allows us to value the unlevered company.\n\nNotice that \ we will use a slightly different notation for the cost of capital than in the \ ", StyleBox["DCF", FontSlant->"Italic"], "-book. For more details see ", StyleBox["DCF", FontSlant->"Italic"], ", chapter 2.1. " }], "Text", CellFrame->True, ShowCellBracket->False, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}, CellTags->"b:10"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(k\_u = 0.2;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(V\_u = Sum[C\_1\/\((1 + k\_u)\)\^t, \ {t, \ 1, \[Infinity]}]\)}], "Input", CellFrame->False, CellGroupingRules->"InputGrouping", AutoIndent->Automatic, StyleBoxAutoDelete->True, TextAlignment->Left, ParagraphIndent->0, CellTags->{"the unlevered company", "b:10"}], Cell[BoxData[ \(500\)], "Output", CellTags->"b:10"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Autonomous financing or APV-formula", "Section", Editable->False, CellFrame->True, CellDingbat->"\[FilledSquare]", ShowCellBracket->False, Background->GrayLevel[0.811765], CellTags->{"b:11", "c:4"}], Cell[TextData[{ "When all future amounts of debt are already determined at valuation time \ t=0, we are speaking of\nautonomous financing. In this case, the firm is \ following a completely fixed redemption plan.\n\nNotice that due to some \ limitations of ", StyleBox["Mathematica", FontSlant->"Italic"], " we will use a slightly different time index for debt than in the ", StyleBox["DCF", FontSlant->"Italic"], "-book. For more details see ", StyleBox["DCF", FontSlant->"Italic"], ", chapter 2.3." }], "Text", Editable->False, CellFrame->True, ShowCellBracket->False, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}, CellTags->"b:11"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Dbt = 100;\)\ \[IndentingNewLine]\), "\[IndentingNewLine]", \(V\_l = \(\(V\_u\)\(+\)\(Sum[\(\[Tau]\ r\_f\ Dbt\)\/\((1 + r\_f)\)\^\(t \ + 1\), \ {t, \ 0, \ \[Infinity]}]\)\(\ \)\)\)}], "Input", CellFrame->False, CellGroupingRules->"InputGrouping", AutoIndent->Automatic, StyleBoxAutoDelete->True, TextAlignment->Left, ParagraphIndent->0, ButtonBoxOptions->{Active->True, ButtonStyle->"MainBookLink"}, CellTags->{"autonomous financing", "b:11"}], Cell[BoxData[ \(550.`\)], "Output", CellTags->"b:11"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Financing based on market values or WACC-formula", "Section", Editable->False, CellFrame->True, CellDingbat->"\[FilledSquare]", ShowCellBracket->False, Background->GrayLevel[0.811765], CellTags->{"b:12", "c:5"}], Cell[TextData[{ "If a firm's debt ratios and not its amount of debt are available, then \ autonomous financing is no\nlonger the case. In the case of such a leverage \ policy, there are three different calculation procedures, which all\nlead to \ the same firm value. Which of the three calculations should be used by the \ valuator depends upon, among other things, the state of information that she \ has on hand. \n\nNotice that due to some limitations of ", StyleBox["Mathematica", FontSlant->"Italic"], " we will use a slightly different time index for WACC than in the ", StyleBox["DCF", FontSlant->"Italic"], "-book. We will use the WACC approach. 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In this case they follow a \ different financing policy. In order to get any further, we have to \ characterize the investment policy of the firm more in detail. We will an investment policy based on cash flows, and we assume that there \ are no changes in subscribed capital. For more details see DCF, chapter 2.5, \ in particular section 2.5.4.\ \>", "Text", CellFrame->True, ShowCellBracket->False, FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}, CellTags->"b:13"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{\(Y\_0 = 100; \[Alpha] = 0.5; \ n = 2; \ lev\_b = 0.5; \[CapitalPhi] = 0;\), " ", "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{\(Array[Inv, \ n - 1, \ 1 - n];\), " ", StyleBox[\( (*\ index\ starts\ at\ 1 - n\ *) \), FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}]}], "\[IndentingNewLine]", RowBox[{\(For[t = 1 - n, \ t \[LessEqual] 0, \ Inv[t] = 0; \ \(t++\)];\), "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]"}], "\[IndentingNewLine]", \(V\_l = V\_u + \[Tau]\ r\_f\ Sum[ lev\_b\ \((\(Y\_0 + \[CapitalPhi] - Sum[\(Min[n - s, t]\/n\) \ Inv[s], \ {s, \ 1 - n, \ 0}]\)\/\((1 + r\_f)\)\^\(t + 1\))\), \ {t, \ 0, \ \[Infinity]}] + \[Tau]\ r\_f\ Sum[\(\(\[Alpha]\ \ C\_1\)\/\((1 + k\_u)\)\^t\) \((Sum[\(\(n - s\)\/n\ lev\_b\)\/\((1 + r\_f)\)\^\ \(s + 1\), \ {s, \ 0, \ n - 1}])\), \ {t, \ 1, \ \[Infinity]}]\), "\[IndentingNewLine]", "Null"}], "Input", CellFrame->False, CellGroupingRules->"InputGrouping", AutoIndent->Automatic, StyleBoxAutoDelete->True, TextAlignment->Left, ParagraphIndent->0, CellTags->{"financing based on book values", "b:13"}], Cell[BoxData[ \(533.2644628099174`\)], "Output", CellTags->"b:13"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Financing based on cash flow-debt ratio", "Section", CellFrame->True, CellDingbat->"\[FilledSquare]", Background->GrayLevel[0.811765], CellTags->{"b:14", "c:7"}], Cell["\<\ Der dynamische Verschuldungsgrad ist eine Kennzahl, bei der der Cash flow ins \ Verh\[ADoubleDot]ltnis zu den Schulden des Unternehmens gesetzt wird. Diese \ Kennzahl dient als (vereinfachter) Ma\[SZ]stab f\[UDoubleDot]r die Zeitdauer, \ in der das Unternehmen bei ausschlie\[SZ]licher Verwendung des Cashflows zur \ Schuldentilgung v\[ODoubleDot]llig eigenfinanziert werden w\[UDoubleDot]rde. \ Wir wollen diese Kennzahl verwenden, um eine sechste Finanzierungspolitik zu \ untersuchen. 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