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(*NotebookOptionsPosition[     41993,       1184]*)
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Notebook[{
Cell[TextData[StyleBox["Deterministic Variables of Discounted Cash Flow \
Analysis",
  FontSize->16]], "Text"],

Cell["\<\
This notebook performs a number of functions

(a)\tIt lists all the relevant variables required to perform a multiperiod \
discounted 
\tcash flow analysis of a real estate investment
(b)\tIt performs that analysis, computing net present value and internal rate \
of return
(c)\tIt demonstrates the interdependencies between the variables
(d)\tIt sets up a series of scenarios for evaluating risk via sensitivity \
testing\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    StyleBox[\(\(Off[General::spell1];\)\n
      \(Off[General::spell];\)\),
      FontFamily->"Courier New"]], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(Null\^2\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "General inputs, rule of thumb measures and other investment performance \
variable definitions are:\n\ndp\t=\tdown payment, made at t=0 and assumed to \
be Jan 1 of the acquisition year. \n",
  Cell[BoxData[
      \(TraditionalForm\`cf\_0\)]],
  "\t=\tinitial cash flow to be received at the end of year 1 (atcf)\n",
  Cell[BoxData[
      \(TraditionalForm\`cf\_n\)]],
  "\t=\tsubsequent year cash flows, compounded annually based on growth rate, \
g\ncr",
  Cell[BoxData[
      \(TraditionalForm\`\_i\)]],
  "\t=\t\"going in\" capitalization rate\n",
  Cell[BoxData[
      \(TraditionalForm\`cr\_o\)]],
  "\t=\t\"going out\" capitalization rate\nr\t=\tdiscount rate (when pv = 0 \
this is the internal rate of return)\ng\t=\tgrowth rate for cash flow, as \
described above\nn\t=\tspecific year of the holding period (an iterator in ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " statements)\nk\t=\tlength of holding period (also year of sale, presumed \
to be at the end of the year)\ngrm\t=\tgross rent multiplier\nppu\t=\tprice \
per unit\nnpv \t=\tnet present value\n\nOperating variable definitions are:\n\
\ngsi\t=\tgross scheduled income\nvac\t=\tvacancy \nvacrt\t=\tvacancy factor \
(a rate multiplied times gsi)\negi\t=\teffective gross income\nexp\t=\t\
operating expenses\nexprt\t=\texpense factor (a rate multiplied times egi)\n\
noi\t=\tnet operating income (debt free cash flow)\t\nbtcf\t=\tbefore tax \
cash flow\n\nFinancing variable definitions are:\n\nltv\t=\tloan to value \
ratio\ndcr\t=\tdebt coverage ratio\nds\t=\tdebt service (usually paid monthly \
but annualized for the purpose of analysis)\ni\t=\tinterest rate (per payment \
period - if monthly, then i = annual interest/12) \ninitln\t=\tinitial loan \
balance\nt\t=\ttime period in payment periods over which the loan is fully \
amortized \n\t\t(if monthly, then t = years over which loan is amortized",
  Cell[BoxData[
      \(TraditionalForm\`*\)]],
  "12)\n",
  Cell[BoxData[
      \(TraditionalForm\`bal\_n\)]],
  "\t=\tbalance at end of period n\n",
  Cell[BoxData[
      \(TraditionalForm\`int\_n\)]],
  "\t=\tinterest paid over the 12 months prior to n\n\nIncome tax variable \
definitions are:\n\ntx\t=\tincome tax consequences \ntxrt\t=\tincome tax rate\
\ntxbl\t=\treal estate taxable income\nbasis\t=\tincome tax basis (dp + \
initln - accdepn)\nland\t=\tallocation of tax basis to land (as a percent of \
total value)\ndepn\t=\tannual depreciation\ndprt\t=\tdepreciation rate\n\n\
Equity reversion variable definitions are:\n\nsp\t=\tsales price calculated \
as ",
  Cell[BoxData[
      \(TraditionalForm\`noi\_\(k + 1\)\/cr\_o\)]],
  "\naccdp\t=\taccumulated depreciation\ncgtx\t=\tcapital gains tax (capital \
gain * capital gain rate)\ncg\t=\tcapital gain (sales price - basis - sales \
costs)\ncgrt\t=\tcapital gain tax rate\nsc\t=\tsales costs (sales cost rate * \
sales price)\nscrt\t=\tsales cost rate\nendbal\t=\tbalance of loan \
outstanding at the time of sale\nppmt\t=\tprepayment penalty on loan\ner\t=\t\
equity reversion (sales price - sales costs - endbal - ppmt - cgtx)\n\n\
Relationships between the variables ",
  StyleBox["for a single first year",
    FontSlant->"Italic"],
  " are as follows:"
}], "Text",
  PageWidth->PaperWidth,
  CellDingbat->None],

Cell[BoxData[{
    \(\(vac = gsi*vacrt;\)\), "\n", 
    \(\(egi = gsi - vac;\)\), "\n", 
    \(\(exp = egi*exprt;\)\), "\n", 
    \(\(noi = gsi - vac - exp;\)\), "\n", 
    \(\(ds = 12\ \((i\/\(1 - 1\/\((1 + i)\)\^t\))\)\ initln;\)\), "\n", 
    \(\(btcf = noi - ds;\)\), "\n", 
    \(\(grm = \((dp + initln)\)/gsi;\)\), "\n", 
    \(\(ppu = \((dp + initln)\)/units;\)\), "\n", 
    \(\(dcr = noi/ds;\)\), "\n", 
    \(\(ltv = initln/\((dp + initln)\);\)\), "\n", 
    \(\(basis = dp + initln;\)\), "\n", 
    \(\(depn = \((basis - \((basis*land)\))\)*dprt;\)\), "\n", 
    \(\(bal\_12 = ds\/12\ \(1 - 1\/\((1 + i)\)\^\(t - 12\)\)\/i;\)\), "\n", 
    \(\(int\_t = ds - \((initln - bal\_12)\);\)\), "\n", 
    \(\(txbl = noi - int\_t - depn;\)\), "\n", 
    \(\(tx = txbl*txrt;\)\), "\n", 
    \(\(cf0 = btcf - tx;\)\), "\n", 
    \(\(cri = noi/\((dp + initln)\);\)\n\)}], "Input",
  PageWidth->PaperWidth],

Cell["\<\
If we have a specific project in mind, the data for it is entered below in a \
list named \"data\"\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(data = {dp -> 375000, \n\t\tgsi -> 
            200000, \n\t\tvacrt ->  .1, \n\t\texprt ->  .35, \n\t\ttxrt ->  \
.35, \n\t\tdprt -> 
            1/31, \n\t\tland ->  .3, \n\t\tcro ->  .0936, \n\t\tg ->  .03, \n\
\t\ti ->  .11/12, \n\t\tinitln -> 875000, \n\t\tt -> 
            360, \n\t\tr ->  .14, \n\t\tk -> 5, \n\tscrt ->  .075, \n\t
          cgrt ->  .22, \n\tppmt -> 0, \nunits -> 22};\)\), "\n", 
    \(data // TableForm\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {\(dp \[Rule] 375000\)},
          {\(gsi \[Rule] 200000\)},
          {\(vacrt \[Rule] 0.1`\)},
          {\(exprt \[Rule] 0.35`\)},
          {\(txrt \[Rule] 0.35`\)},
          {\(dprt \[Rule] 1\/31\)},
          {\(land \[Rule] 0.3`\)},
          {\(cro \[Rule] 0.0936`\)},
          {\(g \[Rule] 0.03`\)},
          {\(i \[Rule] 0.009166666666666667`\)},
          {\(initln \[Rule] 875000\)},
          {\(t \[Rule] 360\)},
          {\(r \[Rule] 0.14`\)},
          {\(k \[Rule] 5\)},
          {\(scrt \[Rule] 0.075`\)},
          {\(cgrt \[Rule] 0.22`\)},
          {\(ppmt \[Rule] 0\)},
          {\(units \[Rule] 22\)}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {dp -> 375000, gsi -> 200000, vacrt -> .10000000000000001, 
        exprt -> .34999999999999998, txrt -> .34999999999999998, dprt -> 
        Rational[ 1, 31], land -> .29999999999999999, 
        cro -> .093600000000000003, g -> .029999999999999999, 
        i -> .0091666666666666667, initln -> 875000, t -> 360, 
        r -> .14000000000000001, k -> 5, scrt -> .074999999999999997, 
        cgrt -> .22, ppmt -> 0, units -> 22}]]], "Output"]
}, Open  ]],

Cell[TextData[{
  StyleBox["Important",
    FontWeight->"Bold",
    FontSlant->"Italic",
    FontVariations->{"Underline"->True}],
  StyleBox[":",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  " The ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " convention \"   /.  \" may be read as \"given that\" and is used to \
insert values from the data into any equation.\n\nThe relationships defined \
above handle the simple \"rule of thumb\" tests applied to first year \
performance.  Here are these in a list named \"rot\""
}], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(rot = 
      N[TableForm[{cri, grm, ppu, btcf, dcr} /. data, 
          TableHeadings -> {{"\<Cap Rate\>", "\<GRM\>", "\<PPU\>", \
"\<BTCF\>", "\<DCR\>"}}]]\)], "Input"],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {"\<\"Cap Rate\"\>", "0.0936`"},
          {"\<\"GRM\"\>", "6.25`"},
          {"\<\"PPU\"\>", "56818.181818181816`"},
          {"\<\"BTCF\"\>", "17006.043463113172`"},
          {"\<\"DCR\"\>", "1.1700707127919254`"}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {.093600000000000003, 6.25, 56818.181818181816, 
        17006.043463113172, 1.1700707127919254}, TableHeadings -> {{
        "Cap Rate", "GRM", "PPU", "BTCF", "DCR"}}]]], "Output"]
}, Open  ]],

Cell["\<\
We can also compute the monthly loan payment. Note that since ds is defined \
as an annual amount we must divide out the 12 to return to monthly.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ds/12 /. data\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(8332.829711407236`\)], "Output"]
}, Open  ]],

Cell[TextData[StyleBox[
"Likewise, here is the first year after tax cash flow"]], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(cf0 /. data\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(19554.44957613444`\)], "Output"]
}, Open  ]],

Cell["\<\
For multiyear projection we need several series of computations spanning the \
years of the holding period.  To begin, we need a method for determining the \
loan balance at the end of each year and a way of expressing each end-of-year \
loan balance in a table which we name \"amort\".\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(bal[n_] := 
        ds\/12\ \(1 - 1\/\((1 + i)\)\^\(t - n*12\)\)\/i;\)\), "\n", 
    \(amort = Table[bal[n] /. data, {n, 0, k /. data}]; 
    amort // TableForm\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {"875000"},
          {"871061.397334418`"},
          {"866667.0241521397`"},
          {"861764.1392194005`"},
          {"856293.8981482456`"},
          {"850190.6471466295`"}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {875000, 871061.39733441803, 866667.02415213967, 
        861764.13921940047, 856293.89814824564, 
        850190.64714662952}]]], "Output"]
}, Open  ]],

Cell[TextData[StyleBox[
"We define the ending balance of the loan (endbal) as the balance at the end \
of the holding period, k"]], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(endbal\  = bal[k] /. data\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(850190.6471466295`\)], "Output"]
}, Open  ]],

Cell["\<\
We also need information about how much interest is paid each year, which is \
a function of the debt service, the beginning of year balance and the end of \
year balance on the loan.  While we are at it, we also create a table showing \
each year's interest that we name \"intpd\"\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(int[n_] := \((ds /. data)\) - \((bal[n - 1] - bal[n])\)\), "\n", 
    \(\tintpd = Table[int[n] /. data, {n, 1, k /. data}]; 
    TableForm[intpd]\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {"96055.35387130489`"},
          {"95599.58335460839`"},
          {"95091.07160414767`"},
          {"94523.71546573204`"},
          {"93890.70553527074`"}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {96055.353871304891, 95599.583354608389, 95091.07160414767, 
        94523.715465732035, 93890.705535270739}]]], "Output"]
}, Open  ]],

Cell[TextData[StyleBox[
"We can \"pick out\" any specific year of interest paid, for instance here is \
year 3 interest"]], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(intpd[\([3]\)]\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(95091.07160414767`\)], "Output"]
}, Open  ]],

Cell["\<\
We need a way to determine the amount of depreciation deduction taken through \
any specific time period. The most common use of this is to determine cost \
basis at the time of sale so that the capital gain amount may be calculated.  \
Here is the accumulated depreciation for the project life, through the end \
year, k.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(accdp[n_] := depn*n\), "\n", 
    \(accdp[k] /. data\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(141129.03225806452`\)], "Output"]
}, Open  ]],

Cell["\<\
We often assume that income grows by some rate over the holding period.  \
Here, for simplicity, we assume the unlikely case of monotonic growth in a \
fixed unchanging amount each year,  Below we illustrate the NOI for the last \
year of the holding period.  Notice that since this is a function we cannot \
use the name \"noi\" which is already in use so we name this function \"netop\
\".\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(netop[n_] := noi\ \((1 + g)\)\^\(n - 1\)\), "\n", 
    \(netop[k] /. data\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(131684.53076999998`\)], "Output"]
}, Open  ]],

Cell[TextData[StyleBox[
"We need to be able to calculate the annual income tax consequence of owning \
the property.  Below we assume growing income, fixed interest on the loan and \
straight line depreciation.  The illustration is for Year #3 income tax \
due"]], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(yrtx[n_] := \((noi\ \((1 + g)\)\^\(n - 1\) - int[n] - depn)\)*
        txrt\), "\n", 
    \(yrtx[3] /. data\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(282.94768048379336`\)], "Output"]
}, Open  ]],

Cell[TextData[StyleBox[
"Relationships between the variables affecting the sale of the property at \
the end of the holding period are:"]], "Text",
  PageWidth->PaperWidth],

Cell[BoxData[{
    \(\(sp = \((noi\ \((1 + g)\)\^k)\)/cro;\)\), "\n", 
    \(\(cg = sp - sc - basis + accdp[k];\)\), "\n", 
    \(\(cgtx = cg*cgrt;\)\), "\n", 
    \(\(sc\  = \ scrt*sp;\)\), "\n", 
    \(\(er = sp - sc - cgtx - endbal - ppmt;\)\)}], "Input",
  PageWidth->PaperWidth],

Cell[TextData[StyleBox[
"With these in place we can calculate the after tax equity reversion, er, \
given the data above"]], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(er /. data\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(439281.27151590853`\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "A multiperiod projection involves compounding the change in the variables \
over the holding period. Compounding of cash flows is offset one year.  The \
idea is that an investor on January 1 makes a decision to purchase based on \
his expectation of the income to be received at the end of the year. Thus, ",
  Cell[BoxData[
      \(TraditionalForm\`cf\_\(0\ \)\)]],
  " is the initial cash flow to be received at the end of year one. The first \
year of compounding is 12 months later at the end of year two, hence only n-1 \
years of ",
  StyleBox["compounded",
    FontSlant->"Italic"],
  " cash flows are in a holding period.  This matter has repercussions when \
considering the equity reversion at the time of sale. ",
  StyleBox["Value",
    FontSlant->"Italic"],
  " still compounds for the full n periods.  The rationale is that at the \
time of sale, the next investor anticipates the end-of-year income (to be \
received 12 months after his acquistion) in making his acquisition decision.  \
So the first investor collects the first cash flow without any compounding \
and n-1 years of compounded cash flows but prices the property on the basis \
of n compounded cash flows.\n\nWe need a function that defines the after tax \
cash flow in any given year, with that we can compute any specific year's \
cash flow (here we calculate cash flow from year #3, given the data)"
}], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[{
    \(cf[n_] := noi\ \((1 + g)\)\^\(n - 1\) - ds - yrtx[n]\), "\n", 
    \(\tcf[3] /. data\)}], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(23848.39578262936`\)], "Output"]
}, Open  ]],

Cell["\<\
In order to determine net present value we need a function that iterates each \
annual cash flow, takes their  present value, sums these, adds the total to \
the present value of the after tax equity reversion and subtracts the initial \
investment (pd)\
\>", "Text",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(\(\n\)\(npv := 
      er\/\((1 + r)\)\^k + \((\[Sum]\+\(n = 1\)\%k Evaluate[
              cf[n]\/\((1 + r)\)\^n])\) - dp\)\)\)], "Input",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(npv /. data\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(-66766.2345509746`\)\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "We are interested in how the risk of financing a property such as this \
changes when the values of the variables change.  One way to assess this is \
to use a numerical analysis software such as Excel supplemented with a risk \
add-in package such as @Risk.  While this is fine for a project-by-project \
analysis, some changes are global in nature and affect all properties in the \
same way.\n\nA significant advantage of using ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " over a numerical method such as Excel is that one can see dependencies at \
the general level. For instance, in the simplest example, we look at what \
affects the gross rent multiplier.  We know this equation as:\n\n\t\t\t\tgrm \
= ",
  Cell[BoxData[
      \(TraditionalForm\`value\/\(gross\ income\)\)]],
  "\n\t\t\t\t\nHence is would seem that grm is simply dependent upon two \
variables, the value and the gross income.  ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " sees it differently.  Because value is itself a combination of \
deterministic variables, when evaluating the expression grm ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " considers and displays variables in the antecedent equation that makes up \
value."
}], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(grm\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(dp + initln\)\/gsi\)], "Output"]
}, Open  ]],

Cell["\<\
So we see that three things determine the grm, not the two we originally \
thought.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[TextData[{
  "Perhaps grm is too simple to illustrate the benefit of ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  ".   One can see by inspection on what grm depends. More difficult and \
complex examples are at the other end of the extreme. When we look at what \
affects after tax cash flow we see a really ugly equation"
}], "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(cf0 // FullSimplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(gsi - \(12\ i\ \((1 + i)\)\^t\ initln\)\/\(\(-1\) + \((1 + i)\)\^t\) - 
      txrt\ \((initln + \(\(1\/\(\(-1\) + \((1 + i)\)\^t\)\)\((initln\ \
\((\((1 + i)\)\^12 - \((1 + i)\)\^t\ \((1 + 12\ i)\) + 
                      dprt\ \((\(-1\) + \((1 + i)\)\^t)\)\ \((\(-1\) + 
                            land)\))\) + 
                dp\ dprt\ \((\(-1\) + \((1 + i)\)\^t)\)\ \((\(-1\) + 
                      land)\))\)\) + \((\(-1\) + exprt)\)\ gsi\ \((\(-1\) + 
                  vacrt)\))\) + exprt\ gsi\ \((\(-1\) + vacrt)\) - 
      gsi\ vacrt\)], "Output"]
}, Open  ]],

Cell["\<\
Sometimes we can gain insight by giving values to some of the variables. For \
instance, income tax rates, depreciation rates and land assessments are \
relatively fixed or at least handed down by government and out of the owner's \
ability to influence.  Taking part of the data from our list, below we \
reproduce the equation above, reducing the number of variables to cap rate, \
loan amount, interest rate, expense and vacancy rates and the gross scheduled \
income.  Do these affect cash flow?  They certainly do!\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(cf0 /. {txrt ->  .35, dprt -> 1/31, land ->  .3} // 
      FullSimplify\)], "Input"],

Cell[BoxData[
    \(gsi - \(12\ i\ \((1 + i)\)\^t\ initln\)\/\(\(-1\) + \((1 + i)\)\^t\) + 
      exprt\ gsi\ \((\(-1\) + vacrt)\) - gsi\ vacrt - 
      0.35`\ \((gsi + 
            initln - \(12\ i\ \((1 + i)\)\^t\ initln\)\/\(\(-1\) + \((1 + \
i)\)\^t\) - \(\((1 + i)\)\^t\ \((1 - \((1 + i)\)\^\(12 - t\))\)\ initln\)\/\(\
\(-1\) + \((1 + i)\)\^t\) - 0.02258064516129032`\ \((dp + initln)\) + 
            exprt\ gsi\ \((\(-1\) + vacrt)\) - gsi\ vacrt)\)\)], "Output"]
}, Open  ]],

Cell["\<\
Suppose we have already decided to purchase the property (or we already own \
it).  Under those conditions we know the income, loan details and expense and \
vacancy factors.  Inserting these show us that our cash flow is related to a \
bunch of constants and the interest rate. What does this tell us about the \
effect of variable interest rate loans? What does it tell us about so-called \
\"positive leverage\"?\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(cf0 /. {txrt ->  .35, dprt -> 1/31, land ->  .3, gsi -> 200000, 
          initln -> 875000, dp -> 375000, vacrt ->  .1, exprt ->  .35, 
          t -> 360} // FullSimplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(\(117000.`\)\(\[InvisibleSpace]\)\) + \(10500000\ i\)\/\(\(-1\) + 1\/\
\((1 + i)\)\^360\) - 
      0.35`\ \((\(\(963774.1935483871`\)\(\[InvisibleSpace]\)\) + \(10500000\ \
i\)\/\(\(-1\) + 1\/\((1 + i)\)\^360\) + \(875000\ \((1 - 1\/\((1 + i)\)\^348)\
\)\)\/\(\(-1\) + 1\/\((1 + i)\)\^360\))\)\)], "Output"]
}, Open  ]],

Cell["\<\
Below, we calculate the going in capitalization rate, cri.  Then, by varying \
the loan interest to a rate above and below the cap rate we show first \
negative leverage then positive leverage. Note the difference in cash flow.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(cri /. data\)], "Input"],

Cell[BoxData[
    \(0.0936`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    RowBox[{"cf0", "/.", 
      RowBox[{"{", 
        RowBox[{\(txrt ->  .35\), ",", \(dprt -> 1/31\), ",", \(land ->  .3\),
           ",", \(gsi -> 200000\), ",", \(initln -> 875000\), 
          ",", \(dp -> 375000\), ",", \(vacrt ->  .1\), 
          ",", \(exprt ->  .35\), ",", \(t -> 360\), ",", 
          StyleBox[\(i ->  .095/12\),
            CellFrame->True,
            Background->GrayLevel[0.849989]]}], "}"}]}]], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(26652.268274118735`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    RowBox[{"cf0", "/.", 
      RowBox[{"{", 
        RowBox[{\(txrt ->  .35\), ",", \(dprt -> 1/31\), ",", \(land ->  .3\),
           ",", \(gsi -> 200000\), ",", \(initln -> 875000\), 
          ",", \(dp -> 375000\), ",", \(vacrt ->  .1\), 
          ",", \(exprt ->  .35\), ",", \(t -> 360\), ",", 
          StyleBox[\(i ->  .09/12\),
            CellFrame->True,
            Background->GrayLevel[0.849989]]}], "}"}]}]], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(28921.247537626918`\)], "Output"]
}, Open  ]],

Cell["\<\
Another awful looking equation is what goes into the witches brew we call the \
equity reversion.  Note that since the loan is assumed to be paid off at the \
time of sale, the equation contains a constant, the final loan balance.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(er // FullSimplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(\(1\/cro\)\((cro\ \((\(-850190.6471466295`\) + 
              cgrt\ \((dp + initln)\)\ \((\(\(1.`\)\(\[InvisibleSpace]\)\) + 
                    dprt\ k\ \((\(-1.`\) + 1.`\ land)\))\) - 1.`\ ppmt)\) + 
        1.`\ \((1 + g)\)\^k\ gsi\ \((\(\(1.`\)\(\[InvisibleSpace]\)\) - 
              1.`\ scrt - 1.`\ vacrt + 1.`\ scrt\ vacrt + 
              exprt\ \((\(-1.`\) + 1.`\ scrt + 1.`\ vacrt - 
                    1.`\ scrt\ vacrt)\) + 
              cgrt\ \((\(-1.`\) + 1.`\ scrt + 1.`\ vacrt - 1.`\ scrt\ vacrt + 
                    exprt\ \((\(\(1.`\)\(\[InvisibleSpace]\)\) - 1.`\ scrt - 
                          1.`\ vacrt + 
                          1.`\ scrt\ vacrt)\))\))\))\)\)\)], "Output"]
}, Open  ]],

Cell["\<\
The capital gain is a little more more accessible.  Note below that it is, \
not surprisingly, quite dependent on the going out capitalization rate.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(cg // FullSimplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(-\(\(1\/cro\)\((cro\ \((dp + initln)\)\ \((1 + 
                dprt\ k\ \((\(-1\) + land)\))\) + \((\(-1\) + 
                exprt)\)\ \((1 + g)\)\^k\ gsi\ \((\(-1\) + 
                scrt)\)\ \((\(-1\) + vacrt)\))\)\)\)\)], "Output"]
}, Open  ]],

Cell["\<\
If we are interested in what drives before tax cash flow, we see that it is \
heavily dependent on the loan terms.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(btcf // FullSimplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\(-\(\(12\ i\ \((1 + i)\)\^t\ initln\)\/\(\(-1\) + \((1 + i)\)\^t\)\)\) \
+ \((\(-1\) + exprt)\)\ gsi\ \((\(-1\) + vacrt)\)\)], "Output"]
}, Open  ]],

Cell["\<\
Returning to an exceedingly simple term, the net operating income (or debt \
free before tax annual cash flow) is really only a function of the gross \
income and two rates, vacancy and expenses.\
\>", "Text",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(noi // Simplify\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    \(\((\(-1\) + exprt)\)\ gsi\ \((\(-1\) + vacrt)\)\)], "Output"]
}, Open  ]],

Cell["\<\
Of course the debt service, ds (the annualized monthly loan payment) is a \
function of the interest rate, the term and the amount borrowed.  Note the \
constant 12 multiplies out the monthly factor.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ds\)], "Input"],

Cell[BoxData[
    \(\(12\ i\ initln\)\/\(1 - \((1 + i)\)\^\(-t\)\)\)], "Output"]
}, Open  ]],

Cell["\<\
To recall Ellwood table #6 - the payment necessary to amortize a dollar, we \
divide out the 12 in our annual debt service equation and make the initial \
loan equal to 1.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(ds/12 /. initln -> 1\)], "Input"],

Cell[BoxData[
    \(i\/\(1 - \((1 + i)\)\^\(-t\)\)\)], "Output"]
}, Open  ]],

Cell["\<\
A useful exercise is to ask what happens to cash flow if interest rates rise. \
  Below, note the term with all the \" i \" variables in it. Of course it is \
debt service (all the other variables sum to NOI). Remembering what the \
negative exponent means in the denominator, we observe this function rising \
with rising interest rates. The entire term is negative so as it gets bigger, \
btcg grows smaller.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(btcf\)], "Input"],

Cell[BoxData[
    \(gsi - \(12\ i\ initln\)\/\(1 - \((1 + i)\)\^\(-t\)\) - gsi\ vacrt - 
      exprt\ \((gsi - gsi\ vacrt)\)\)], "Output"]
}, Open  ]],

Cell["\<\
Suppose the vacancy increases.  What does this do to after tax cash flow?  \
Notice below it affects only the last term in the equation for first year \
cash flow.  This is not too helpful as that last term also has the tax rate \
in it, something that has nothing to do with vacancy.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(cf0 // FullSimplify\)], "Input"],

Cell[BoxData[
    \(gsi - \(12\ i\ \((1 + i)\)\^t\ initln\)\/\(\(-1\) + \((1 + i)\)\^t\) - 
      txrt\ \((initln + \(\(1\/\(\(-1\) + \((1 + i)\)\^t\)\)\((initln\ \
\((\((1 + i)\)\^12 - \((1 + i)\)\^t\ \((1 + 12\ i)\) + 
                      dprt\ \((\(-1\) + \((1 + i)\)\^t)\)\ \((\(-1\) + 
                            land)\))\) + 
                dp\ dprt\ \((\(-1\) + \((1 + i)\)\^t)\)\ \((\(-1\) + 
                      land)\))\)\) + \((\(-1\) + exprt)\)\ gsi\ \((\(-1\) + 
                  vacrt)\))\) + exprt\ gsi\ \((\(-1\) + vacrt)\) - 
      gsi\ vacrt\)], "Output"]
}, Open  ]],

Cell["\<\
Most of the foregoing examples all have to do with isolating one \
deterministic variable.  Does the change in one variable affect another?  \
What about interest rates and capitalization rates? Vacancy and expenses?  \
Are these related? Yes, they are.  How about gross income and vacancy?  What \
happens when two of these change? Let's take a simple example.  When rents \
are increased vacancy should also increase. Below we see they both affect net \
operating income.  The key question is: how much of one will neutralize the \
other.  This is the sort of thing that sensitivity testing is doing. We are \
interested in knowing how sensitive tenants are to rent increases.  Will a \
small increase cause an exodus of tenants?\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(noi\)], "Input"],

Cell[BoxData[
    \(gsi - gsi\ vacrt - exprt\ \((gsi - gsi\ vacrt)\)\)], "Output"]
}, Open  ]],

Cell["\<\
Tenants may be assumed to stay if rent increases, relative to the old rent, \
are small and leave if they are large.  Our interest is in knowing how much \
of a rent increase is too much, causing turnover and vacancy.  One way to \
approach this is to assume a \"market equilibrium gross rent multiplier\".  \
This is the grm at which most buildings provide a \"market\" cash flow and \
\"market\" return using \"market\" financing terms.  We will assume our \
building is in a market where the average such grm is 6.  Since we know the \
grm for our building:  \
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(N[grm /. data]\)], "Input"],

Cell[BoxData[
    \(6.25`\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "We know we have to get the rents up to be at equilibrium.  It turns out \
that there is a formula for the necessary increase in rent to drive the grm \
down to equilibrium.  We define the required rent raise, rrr, as\n\n\t\t\t\t\
rrr = ",
  Cell[BoxData[
      \(TraditionalForm\`grm\/\(equilibrium\ grm\) - 1\)]]
}], "Text"],

Cell["\<\
So we ask for this number, below, and find that our required rent raise is \
just over 4%, which we conclude, after a careful rent survey in the \
neighborhood, the tenants will pay without excessive turnover or vacancy\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(rrr = N[\(grm /. data\)\/6 - 1]\)], "Input"],

Cell[BoxData[
    \(0.041666666666666664`\)], "Output"]
}, Open  ]],

Cell["\<\
We now must modify our data to consider the higher rents to see what happens \
to npv.  We define a new data set, data1, just like the first one with the \
only change being the gsi is increased by the rrr.\
\>", "Text"],

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    RowBox[{
      RowBox[{
        StyleBox["data1",
          CellFrame->True,
          Background->GrayLevel[0.849989]], "=", 
        RowBox[{"{", 
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            RowBox[{"gsi", "->", 
              StyleBox[\(200000*\((1 + rrr)\)\),
                CellFrame->True,
                Background->GrayLevel[0.849989]]}], ",", "\n", 
            "\t\t", \(vacrt ->  .1\), ",", "\n", "\t\t", \(exprt ->  .35\), 
            ",", "\n", "\t\t", \(txrt ->  .35\), ",", "\n", 
            "\t\t", \(dprt -> 1/31\), ",", "\n", "\t\t", \(land ->  .3\), ",",
             "\n", "\t\t", \(cro ->  .0936\), ",", "\n", 
            "\t\t", \(g ->  .03\), ",", "\n", "\t\t", \(i ->  .11/12\), ",", 
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            "\t\t", \(t -> 360\), ",", "\n", "\t\t", \(r ->  .14\), ",", "\n",
             "\t\t", \(k -> 5\), ",", "\n", "\t", \(scrt ->  .075\), ",", 
            "\n", "\t", \(cgrt ->  .22\), ",", "\n", "\t", \(ppmt -> 0\), ",",
             "\n", \(units -> 22\)}], "}"}]}], ";"}]], "Input",
  PageWidth->PaperWidth],

Cell["Then we ask what the npv is with this new information", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(npv /. data1\)], "Input"],

Cell[BoxData[
    \(\(-32678.294742158992`\)\)], "Output"]
}, Open  ]],

Cell["\<\
Even with this improvement we still do not have a positive after tax net \
present value. Something has to change.  We believe we have extracted the \
most out of the tenants in the form of increased rent. In the list below, \
data2, we assume a higher annual growth rate, 4%, on cash flow.\
\>", "Text"],

Cell[BoxData[
    RowBox[{
      RowBox[{"data2", "=", 
        RowBox[{"{", 
          
          RowBox[{\(dp -> 375000\), ",", "\n", 
            "\t\t", \(gsi -> 200000*\((1 + rrr)\)\), ",", "\n", 
            "\t\t", \(vacrt ->  .1\), ",", "\n", "\t\t", \(exprt ->  .35\), 
            ",", "\n", "\t\t", \(txrt ->  .35\), ",", "\n", 
            "\t\t", \(dprt -> 1/31\), ",", "\n", "\t\t", \(land ->  .3\), ",",
             "\n", "\t\t", \(cro ->  .0936\), ",", "\n", "\t\t", 
            StyleBox[\(g ->  .04\),
              CellFrame->True,
              Background->GrayLevel[0.849989]], ",", "\n", 
            "\t\t", \(i ->  .11/12\), ",", "\n", "\t\t", \(initln -> 875000\),
             ",", "\n", "\t\t", \(t -> 360\), ",", "\n", 
            "\t\t", \(r ->  .14\), ",", "\n", "\t\t", \(k -> 5\), ",", "\n", 
            "\t", \(scrt ->  .075\), ",", "\n", "\t", \(cgrt ->  .22\), ",", 
            "\n", "\t", \(ppmt -> 0\), ",", "\n", \(units -> 22\)}], "}"}]}], 
      ";"}]], "Input",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(npv /. data2\)], "Input"],

Cell[BoxData[
    \(366.5909463103744`\)], "Output"]
}, Open  ]],

Cell["\<\
As we can call this outcome close to zero, the project has an IRR of \
approximately 14%.  But these modifications have the buyer taking all the \
risk.  Why?  What is a way to transfer some of that risk to the seller?  Buy \
offering a lower price.  Why is that a risk transfer?  \"data3\" shows the \
reduction of down payment necessary to put the project in the positive NPV \
range.  Note the return to g = .03 in the next data list:\
\>", "Text"],

Cell[BoxData[
    RowBox[{
      RowBox[{"data3", "=", 
        RowBox[{"{", 
          RowBox[{
            StyleBox[\(dp -> 337000\),
              CellFrame->True,
              Background->GrayLevel[0.849989]], ",", "\n", 
            "\t\t", \(gsi -> 200000*\((1 + rrr)\)\), ",", "\n", 
            "\t\t", \(vacrt ->  .1\), ",", "\n", "\t\t", \(exprt ->  .35\), 
            ",", "\n", "\t\t", \(txrt ->  .35\), ",", "\n", 
            "\t\t", \(dprt -> 1/31\), ",", "\n", "\t\t", \(land ->  .3\), ",",
             "\n", "\t\t", \(cro ->  .0936\), ",", "\n", 
            StyleBox["\t\t",
              CellFrame->True,
              Background->None], 
            StyleBox[\(g ->  .03\),
              CellFrame->True,
              Background->GrayLevel[0.849989]], ",", "\n", 
            "\t\t", \(i ->  .11/12\), ",", "\n", "\t\t", \(initln -> 875000\),
             ",", "\n", "\t\t", \(t -> 360\), ",", "\n", 
            "\t\t", \(r ->  .14\), ",", "\n", "\t\t", \(k -> 5\), ",", "\n", 
            "\t", \(scrt ->  .075\), ",", "\n", "\t", \(cgrt ->  .22\), ",", 
            "\n", "\t", \(ppmt -> 0\), ",", "\n", \(units -> 22\)}], "}"}]}], 
      ";"}]], "Input",
  PageWidth->PaperWidth],

Cell[CellGroupData[{

Cell[BoxData[
    \(rot = 
      N[TableForm[{cri, grm, ppu, btcf, dcr} /. data, 
          TableHeadings -> {{"\<Cap Rate\>", "\<GRM\>", "\<PPU\>", \
"\<BTCF\>", "\<DCR\>"}}]]\)], "Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {"\<\"Cap Rate\"\>", "0.0936`"},
          {"\<\"GRM\"\>", "6.25`"},
          {"\<\"PPU\"\>", "56818.181818181816`"},
          {"\<\"BTCF\"\>", "17006.043463113172`"},
          {"\<\"DCR\"\>", "1.1700707127919254`"}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {.093600000000000003, 6.25, 56818.181818181816, 
        17006.043463113172, 1.1700707127919254}, TableHeadings -> {{
        "Cap Rate", "GRM", "PPU", "BTCF", "DCR"}}]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(N[TableForm[{npv, ltv, cri, cro} /. data3, 
        TableHeadings -> {{"\<npv\>", "\<ltv\>", "\<cri\>", "\<cro\>"}}]]\)], \
"Input",
  PageWidth->PaperWidth],

Cell[BoxData[
    InterpretationBox[GridBox[{
          {"\<\"npv\"\>", "438.9684915058315`"},
          {"\<\"ltv\"\>", "0.721947194719472`"},
          {"\<\"cri\"\>", "0.10055693069306931`"},
          {"\<\"cro\"\>", "0.0936`"}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      TableForm[ {
        438.96849150583148, .721947194719472, .10055693069306931, \
.093600000000000003}, TableHeadings -> {{"npv", "ltv", "cri", 
        "cro"}}]]], "Output"]
}, Open  ]],

Cell[TextData[{
  "Note the implicit assumption that capitalization rates will decline over \
the holding period. How valid is this?\n\nThis outcome, also nearly zero, \
says we have approximately a 14% IRR.  But is it the same 14%?  Is the risk \
of the project different under data3 even though the IRR is essentially the \
same?\n\nFinally, for those who want to know what the IRR is, ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " is as good at Excel in finding it.  First we create a list of after tax \
cash flows which we name \"cflist\". Note that we start with year #1 and we \
have to add the equity reversion to the last year, which takes some \
additional manipulation to get cflist in the right form. (The only output \
below is the data being used in the calculations, placed there to remind us \
what our parameters are)."
}], "Text"],

Cell[BoxData[
    \(<< LinearAlgebra`MatrixManipulation`\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(irrdata = data3\), "\[IndentingNewLine]", 
    \(\(partlist = {Table[
            cf[n] /. irrdata, {n, 1, 
              k - 1 /. irrdata}]};\)\), "\[IndentingNewLine]", 
    \(\(endcf = {{\((cf[k] /. irrdata)\) + \((er /. 
                  irrdata)\)}};\)\), "\[IndentingNewLine]", 
    \(\(cflist = \(AppendRows[partlist, endcf]\)[\([1]\)];\)\)}], "Input"],

Cell[BoxData[
    \({dp \[Rule] 337000, gsi \[Rule] 208333.33333333334`, 
      vacrt \[Rule] 0.1`, exprt \[Rule] 0.35`, txrt \[Rule] 0.35`, 
      dprt \[Rule] 1\/31, land \[Rule] 0.3`, cro \[Rule] 0.0936`, 
      g \[Rule] 0.03`, i \[Rule] 0.009166666666666667`, 
      initln \[Rule] 875000, t \[Rule] 360, r \[Rule] 0.14`, k \[Rule] 5, 
      scrt \[Rule] 0.075`, cgrt \[Rule] 0.22`, ppmt \[Rule] 0, 
      units \[Rule] 22}\)], "Output"]
}, Open  ]],

Cell[TextData[{
  "The internal rate of return is the number that solves the following \
equation for r\n\n\t",
  Cell[BoxData[
      \(TraditionalForm\`\[Sum]\+\(n = 1\)\%k ATCF\_n\/\((1 + r)\)\^n\)]],
  "+",
  Cell[BoxData[
      \(TraditionalForm\`ATER\_k\/\((1 + r)\)\^k\)]],
  "- initial investment = 0\n\t\n",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " considers this a problem of finding the \"root\" of the equation.  Thus \
we need a polynomial into which we insert the cflist.  We begin by  creating \
a table that will represent the power series necessary.  The variable v = ",
  Cell[BoxData[
      \(TraditionalForm\`1\/\((1 + r)\)\)]]
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(irrtbl = 
        Table[v\^i, {i, 1, Length[cflist]}];\)\), "\[IndentingNewLine]", 
    \(irrpoly = irrtbl . cflist\)}], "Input"],

Cell[BoxData[
    \(22422.876995489263`\ v + 24639.9198146455`\ v\^2 + 
      26909.800076984207`\ v\^3 + 29232.52058478873`\ v\^4 + 
      507036.38967702`\ v\^5\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(irrstep2 = 
        FindRoot[
          irrpoly == \((dp /. irrdata)\), {v, 1/1.1, 0, 
            1}];\)\), "\[IndentingNewLine]", 
    \(\(irr = \((v\^\(-1\) - 1)\) /. 
          irrstep2[\([1]\)];\)\), "\[IndentingNewLine]", 
    \(Print["\<The IRR for this data is: \>", irr]\)}], "Input"],

Cell[BoxData[
    InterpretationBox[\("The IRR for this data is: \
"\[InvisibleSpace]0.14033434230925268`\),
      SequenceForm[ "The IRR for this data is: ", .14033434230925268],
      Editable->False]], "Print"]
}, Open  ]]
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Modify the definitions below to change the default appearance of all cells in \
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    LineSpacing->{1, 0},
    FontSize->44],
  
  Cell[StyleData["Title", "Condensed"],
    CellMargins->{{8, 10}, {4, 8}},
    FontSize->20],
  
  Cell[StyleData["Title", "Printout"],
    CellMargins->{{2, 10}, {12, 30}},
    FontSize->24]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subtitle"],
    CellMargins->{{12, Inherited}, {20, 15}},
    CellGroupingRules->{"TitleGrouping", 10},
    PageBreakBelow->False,
    CounterIncrements->"Subtitle",
    CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, {
        "Subsubtitle", 0}},
    FontFamily->"Helvetica",
    FontSize->24],
  
  Cell[StyleData["Subtitle", "Presentation"],
    CellMargins->{{24, 10}, {20, 20}},
    LineSpacing->{1, 0},
    FontSize->36],
  
  Cell[StyleData["Subtitle", "Condensed"],
    CellMargins->{{8, 10}, {4, 4}},
    FontSize->14],
  
  Cell[StyleData["Subtitle", "Printout"],
    CellMargins->{{2, 10}, {12, 8}},
    FontSize->18]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubtitle"],
    CellMargins->{{12, Inherited}, {20, 15}},
    CellGroupingRules->{"TitleGrouping", 20},
    PageBreakBelow->False,
    CounterIncrements->"Subsubtitle",
    CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}},
    FontFamily->"Helvetica",
    FontSize->14,
    FontSlant->"Italic"],
  
  Cell[StyleData["Subsubtitle", "Presentation"],
    CellMargins->{{24, 10}, {20, 20}},
    LineSpacing->{1, 0},
    FontSize->24],
  
  Cell[StyleData["Subsubtitle", "Condensed"],
    CellMargins->{{8, 10}, {8, 8}},
    FontSize->12],
  
  Cell[StyleData["Subsubtitle", "Printout"],
    CellMargins->{{2, 10}, {12, 8}},
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Section"],
    CellDingbat->"\[FilledSquare]",
    CellMargins->{{25, Inherited}, {8, 24}},
    CellGroupingRules->{"SectionGrouping", 30},
    PageBreakBelow->False,
    CounterIncrements->"Section",
    CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}},
    FontFamily->"Helvetica",
    FontSize->16,
    FontWeight->"Bold"],
  
  Cell[StyleData["Section", "Presentation"],
    CellMargins->{{40, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontSize->24],
  
  Cell[StyleData["Section", "Condensed"],
    CellMargins->{{18, Inherited}, {6, 12}},
    FontSize->12],
  
  Cell[StyleData["Section", "Printout"],
    CellMargins->{{13, 0}, {7, 22}},
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsection"],
    CellDingbat->"\[FilledSmallSquare]",
    CellMargins->{{22, Inherited}, {8, 20}},
    CellGroupingRules->{"SectionGrouping", 40},
    PageBreakBelow->False,
    CounterIncrements->"Subsection",
    CounterAssignments->{{"Subsubsection", 0}},
    FontSize->14,
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsection", "Presentation"],
    CellMargins->{{36, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontSize->22],
  
  Cell[StyleData["Subsection", "Condensed"],
    CellMargins->{{16, Inherited}, {6, 12}},
    FontSize->12],
  
  Cell[StyleData["Subsection", "Printout"],
    CellMargins->{{9, 0}, {7, 22}},
    FontSize->12]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubsection"],
    CellDingbat->"\[FilledSmallSquare]",
    CellMargins->{{22, Inherited}, {8, 18}},
    CellGroupingRules->{"SectionGrouping", 50},
    PageBreakBelow->False,
    CounterIncrements->"Subsubsection",
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsubsection", "Presentation"],
    CellMargins->{{34, 10}, {11, 26}},
    LineSpacing->{1, 0},
    FontSize->18],
  
  Cell[StyleData["Subsubsection", "Condensed"],
    CellMargins->{{17, Inherited}, {6, 12}},
    FontSize->10],
  
  Cell[StyleData["Subsubsection", "Printout"],
    CellMargins->{{9, 0}, {7, 14}},
    FontSize->11]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Body Text", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Text"],
    PageWidth->PaperWidth,
    CellMargins->{{12, 10}, {7, 7}},
    LineSpacing->{1, 3},
    CounterIncrements->"Text"],
  
  Cell[StyleData["Text", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5}],
  
  Cell[StyleData["Text", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1}],
  
  Cell[StyleData["Text", "Printout"],
    CellMargins->{{2, 2}, {6, 6}}]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SmallText"],
    CellMargins->{{12, 10}, {6, 6}},
    LineSpacing->{1, 3},
    CounterIncrements->"SmallText",
    FontFamily->"Helvetica",
    FontSize->9],
  
  Cell[StyleData["SmallText", "Presentation"],
    CellMargins->{{24, 10}, {8, 8}},
    LineSpacing->{1, 5},
    FontSize->12],
  
  Cell[StyleData["SmallText", "Condensed"],
    CellMargins->{{8, 10}, {5, 5}},
    LineSpacing->{1, 2},
    FontSize->9],
  
  Cell[StyleData["SmallText", "Printout"],
    CellMargins->{{2, 2}, {5, 5}},
    FontSize->7]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Input/Output", "Section"],
  
  Cell["\<\
The cells in this section define styles used for input and output to the \
kernel.  Be careful when modifying, renaming, or removing these styles, \
because the front end associates special meanings with these style names. \
Some attributes for these styles are actually set in FormatType Styles (in \
the last section of this stylesheet). \
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Input"],
    CellMargins->{{45, 10}, {5, 7}},
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultInputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    CounterIncrements->"Input",
    FontWeight->"Bold"],
  
  Cell[StyleData["Input", "Presentation"],
    CellMargins->{{72, Inherited}, {8, 10}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["Input", "Condensed"],
    CellMargins->{{40, 10}, {2, 3}}],
  
  Cell[StyleData["Input", "Printout"],
    CellMargins->{{39, 0}, {4, 6}},
    FontSize->9]
  }, Closed]],
  
  Cell[StyleData["InputOnly"],
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    DefaultFormatType->DefaultInputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    CounterIncrements->"Input",
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Output"],
    PageWidth->PaperWidth,
    CellMargins->{{47, 10}, {7, 5}},
    CellEditDuplicate->True,
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Output",
    FontSize->12],
  
  Cell[StyleData["Output", "Presentation"],
    CellMargins->{{72, Inherited}, {10, 8}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["Output", "Condensed"],
    CellMargins->{{41, Inherited}, {3, 2}}],
  
  Cell[StyleData["Output", "Printout"],
    CellMargins->{{39, 0}, {6, 4}},
    FontSize->9]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Message"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Message",
    StyleMenuListing->None,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["Message", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["Message", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}}],
  
  Cell[StyleData["Message", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->8,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Print"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}},
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Print",
    StyleMenuListing->None],
  
  Cell[StyleData["Print", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0}],
  
  Cell[StyleData["Print", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}}],
  
  Cell[StyleData["Print", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Graphics"],
    CellMargins->{{4, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"GraphicsGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    FormatType->InputForm,
    CounterIncrements->"Graphics",
    ImageMargins->{{43, Inherited}, {Inherited, 0}},
    StyleMenuListing->None],
  
  Cell[StyleData["Graphics", "Presentation"],
    ImageMargins->{{62, Inherited}, {Inherited, 0}}],
  
  Cell[StyleData["Graphics", "Condensed"],
    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    Magnification->0.6],
  
  Cell[StyleData["Graphics", "Printout"],
    ImageMargins->{{30, Inherited}, {Inherited, 0}},
    FontSize->9,
    Magnification->0.8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["CellLabel"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->9,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["CellLabel", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["CellLabel", "Condensed"],
    FontSize->9],
  
  Cell[StyleData["CellLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->8,
    FontSlant->"Italic",
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell["Formulas and Programming", "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["InlineFormula"],
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5}],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1}],
  
  Cell[StyleData["InlineFormula", "Printout"],
    CellMargins->{{2, 0}, {6, 6}}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DisplayFormula"],
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5}],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1}],
  
  Cell[StyleData["DisplayFormula", "Printout"]]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell["Styles for Headers and Footers", "Section"],
  
  Cell[StyleData["Header"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontSize->10,
    FontSlant->"Italic"],
  
  Cell[StyleData["Footer"],
    CellMargins->{{0, 0}, {0, 4}},
    StyleMenuListing->None,
    FontSize->9,
    FontSlant->"Italic"],
  
  Cell[StyleData["PageNumber"],
    CellMargins->{{0, 0}, {4, 1}},
    StyleMenuListing->None,
    FontFamily->"Times",
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Palette Styles", "Section"],
  
  Cell["\<\
The cells below define styles that define standard ButtonFunctions, for use \
in palette buttons.\
\>", "Text"],
  
  Cell[StyleData["Paste"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, After]}]&)}],
  
  Cell[StyleData["Evaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["EvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionMove[ 
          FrontEnd`InputNotebook[ ], All, Cell, 1], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluate"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluate[ 
          FrontEnd`InputNotebook[ ], All]}]&)}],
  
  Cell[StyleData["CopyEvaluateCell"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`SelectionCreateCell[ 
          FrontEnd`InputNotebook[ ], All], 
        FrontEnd`NotebookApply[ 
          FrontEnd`InputNotebook[ ], #, All], 
        FrontEnd`SelectionEvaluateCreateCell[ 
          FrontEnd`InputNotebook[ ], All]}]&)}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Hyperlink Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making hypertext ButtonBoxes.  The \
\"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"]],
  
  Cell[StyleData["Hyperlink", "Condensed"]],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell["\<\
The following styles are for linking automatically to the on-line help \
system.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MainBookLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MainBookLink", "Presentation"]],
  
  Cell[StyleData["MainBookLink", "Condensed"]],
  
  Cell[StyleData["MainBookLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["AddOnsLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"]],
  
  Cell[StyleData["AddOnsLink", "Condensed"]],
  
  Cell[StyleData["AddOnLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"]],
  
  Cell[StyleData["RefGuideLink", "Condensed"]],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"]],
  
  Cell[StyleData["GettingStartedLink", "Condensed"]],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["OtherInformationLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["OtherInformationLink", "Presentation"]],
  
  Cell[StyleData["OtherInformationLink", "Condensed"]],
  
  Cell[StyleData["OtherInformationLink", "Printout"],
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["Placeholder Styles", "Section"],
  
  Cell["\<\
The cells below define styles useful for making placeholder objects in \
palette templates.\
\>", "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Placeholder"],
    Editable->False,
    Selectable->False,
    StyleBoxAutoDelete->True,
    Placeholder->True,
    StyleMenuListing->None],
  
  Cell[StyleData["Placeholder", "Presentation"]],
  
  Cell[StyleData["Placeholder", "Condensed"]],
  
  Cell[StyleData["Placeholder", "Printout"]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SelectionPlaceholder"],
    Editable->False,
    Selectable->False,
    StyleBoxAutoDelete->True,
    StyleMenuListing->None,
    DrawHighlighted->True],
  
  Cell[StyleData["SelectionPlaceholder", "Presentation"]],
  
  Cell[StyleData["SelectionPlaceholder", "Condensed"]],
  
  Cell[StyleData["SelectionPlaceholder", "Printout"]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell["FormatType Styles", "Section"],
  
  Cell["\<\
The cells below define styles that are mixed in with the styles of most \
cells.  If a cell's FormatType matches the name of one of the styles defined \
below, then that style is applied between the cell's style and its own \
options. This is particularly true of Input and Output.\
\>", "Text"],
  
  Cell[StyleData["CellExpression"],
    PageWidth->Infinity,
    CellMargins->{{6, Inherited}, {Inherited, Inherited}},
    ShowCellLabel->False,
    ShowSpecialCharacters->False,
    AllowInlineCells->False,
    AutoItalicWords->{},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->12,
    Background->GrayLevel[1]],
  
  Cell[StyleData["InputForm"],
    AllowInlineCells->False,
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["OutputForm"],
    PageWidth->Infinity,
    TextAlignment->Left,
    LineSpacing->{0.6, 1},
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["StandardForm"],
    LineSpacing->{1.25, 0},
    StyleMenuListing->None,
    FontFamily->"Courier"],
  
  Cell[StyleData["TraditionalForm"],
    LineSpacing->{1.25, 0},
    SingleLetterItalics->True,
    TraditionalFunctionNotation->True,
    DelimiterMatching->None,
    StyleMenuListing->None],
  
  Cell["\<\
The style defined below is mixed in to any cell that is in an inline cell \
within another.\
\>", "Text"],
  
  Cell[StyleData["InlineCell"],
    TextAlignment->Left,
    ScriptLevel->1,
    StyleMenuListing->None],
  
  Cell[StyleData["InlineCellEditing"],
    StyleMenuListing->None,
    Background->RGBColor[1, 0.749996, 0.8]]
  }, Open  ]]
  }, Open  ]]
  }]
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of 
the file.  The cache data will then be recreated when you save this file 
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
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*)

(*CellTagsIndex
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Cell[CellGroupData[{
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Cell[CellGroupData[{
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Cell[CellGroupData[{
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*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)