LBO MODEL EXAMPLE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "182e46cc",
   "metadata": {},
   "source": [
    "## Paper LBO Model Example\n",
    "\n",
    "Case Study Source: <http://www.streetofwalls.com/finance-training-courses/private-equity-training/paper-lbo-model-example/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "id": "2cd14b5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "  Obtaining dependency information for scipy from https://files.pythonhosted.org/packages/e5/ee/c5bc0d4b66a9c38165adf86e8b57be6f76868edf5ea23b3bbee3680e7edf/scipy-1.11.3-cp312-cp312-macosx_10_9_x86_64.whl.metadata\n",
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      "  Building wheel for pyarrow (pyproject.toml) ... \u001b[?25lerror\n",
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      "  \u001b[31m   \u001b[0m writing requirements to pyarrow.egg-info/requires.txt\n",
      "  \u001b[31m   \u001b[0m writing top-level names to pyarrow.egg-info/top_level.txt\n",
      "  \u001b[31m   \u001b[0m ERROR setuptools_scm._file_finders.git listing git files failed - pretending there aren't any\n",
      "  \u001b[31m   \u001b[0m reading manifest file 'pyarrow.egg-info/SOURCES.txt'\n",
      "  \u001b[31m   \u001b[0m reading manifest template 'MANIFEST.in'\n",
      "  \u001b[31m   \u001b[0m warning: no files found matching '../LICENSE.txt'\n",
      "  \u001b[31m   \u001b[0m warning: no files found matching '../NOTICE.txt'\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '*.so' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '*.pyc' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '*~' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '#*' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '.git*' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m warning: no previously-included files matching '.DS_Store' found anywhere in distribution\n",
      "  \u001b[31m   \u001b[0m no previously-included directories found matching '.asv'\n",
      "  \u001b[31m   \u001b[0m writing manifest file 'pyarrow.egg-info/SOURCES.txt'\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/__init__.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_acero.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_acero.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_compute.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_compute.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_csv.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_csv.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_cuda.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_cuda.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_dataset.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_dataset.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_dataset_orc.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_dataset_parquet.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_feather.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_flight.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_fs.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_fs.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_gcsfs.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_hdfs.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_hdfsio.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_json.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_json.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_orc.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_orc.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_parquet.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_parquet.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_parquet_encryption.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_parquet_encryption.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_pyarrow_cpp_tests.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_pyarrow_cpp_tests.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_s3fs.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/_substrait.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/array.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/benchmark.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/builder.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/compat.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/config.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/error.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/gandiva.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/io.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/ipc.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/lib.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/lib.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/memory.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/pandas-shim.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/public-api.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/scalar.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/table.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tensor.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/types.pxi -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/common.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_feather.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_acero.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/__init__.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libgandiva.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_python.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_flight.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_dataset_parquet.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_dataset.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_substrait.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_cuda.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/includes/libarrow_fs.pxd -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/includes\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/bound_function_visit_strings.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/extensions.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/pyarrow_cython_example.pyx -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/feather\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/feather/v0.17.0.version.2-compression.lz4.feather -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/feather\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/README.md -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.emptyFile.jsn.gz -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.emptyFile.orc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.test1.jsn.gz -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.test1.orc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.testDate1900.jsn.gz -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/TestOrcFile.testDate1900.orc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/decimal.jsn.gz -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/orc/decimal.orc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/orc\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/parquet\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/parquet/v0.7.1.all-named-index.parquet -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/parquet\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/parquet/v0.7.1.column-metadata-handling.parquet -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/parquet\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/parquet/v0.7.1.parquet -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/parquet\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/tests/data/parquet/v0.7.1.some-named-index.parquet -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/tests/data/parquet\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow\n",
      "  \u001b[31m   \u001b[0m creating build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/CMakeLists.txt -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/api.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/arrow_to_pandas.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/arrow_to_pandas.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/arrow_to_python_internal.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/benchmark.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/benchmark.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/common.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/common.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/csv.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/csv.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/datetime.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/datetime.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/decimal.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/decimal.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/deserialize.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/deserialize.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/extension_type.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/extension_type.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/filesystem.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/filesystem.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/flight.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/flight.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/gdb.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/gdb.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/helpers.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/helpers.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/inference.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/inference.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/init.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/init.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/io.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/io.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/ipc.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/ipc.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/iterators.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_convert.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_convert.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_internal.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_interop.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_to_arrow.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/numpy_to_arrow.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/parquet_encryption.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/parquet_encryption.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/pch.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/platform.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/pyarrow.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/pyarrow.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/pyarrow_api.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/pyarrow_lib.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/python_test.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/python_test.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/python_to_arrow.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/python_to_arrow.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/serialize.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/serialize.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/type_traits.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/udf.cc -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/udf.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m copying pyarrow/src/arrow/python/visibility.h -> build/lib.macosx-10.9-universal2-cpython-312/pyarrow/src/arrow/python\n",
      "  \u001b[31m   \u001b[0m running build_ext\n",
      "  \u001b[31m   \u001b[0m creating /private/var/folders/g8/3_6lvv2s3875b9rfcncv8qyc0000gp/T/pip-install-crlgvzrm/pyarrow_174e976816f24a7fbb92d748df422418/build/temp.macosx-10.9-universal2-cpython-312\n",
      "  \u001b[31m   \u001b[0m -- Running cmake for PyArrow\n",
      "  \u001b[31m   \u001b[0m cmake -DCMAKE_INSTALL_PREFIX=/private/var/folders/g8/3_6lvv2s3875b9rfcncv8qyc0000gp/T/pip-install-crlgvzrm/pyarrow_174e976816f24a7fbb92d748df422418/build/lib.macosx-10.9-universal2-cpython-312/pyarrow -DPYTHON_EXECUTABLE=/Users/Larry/LBO-model-Python/env/bin/python -DPython3_EXECUTABLE=/Users/Larry/LBO-model-Python/env/bin/python -DPYARROW_CXXFLAGS= -DPYARROW_BUILD_CUDA=off -DPYARROW_BUILD_SUBSTRAIT=off -DPYARROW_BUILD_FLIGHT=off -DPYARROW_BUILD_GANDIVA=off -DPYARROW_BUILD_ACERO=off -DPYARROW_BUILD_DATASET=off -DPYARROW_BUILD_ORC=off -DPYARROW_BUILD_PARQUET=off -DPYARROW_BUILD_PARQUET_ENCRYPTION=off -DPYARROW_BUILD_GCS=off -DPYARROW_BUILD_S3=off -DPYARROW_BUILD_HDFS=off -DPYARROW_BUNDLE_ARROW_CPP=off -DPYARROW_BUNDLE_CYTHON_CPP=off -DPYARROW_GENERATE_COVERAGE=off -DCMAKE_BUILD_TYPE=release /private/var/folders/g8/3_6lvv2s3875b9rfcncv8qyc0000gp/T/pip-install-crlgvzrm/pyarrow_174e976816f24a7fbb92d748df422418\n",
      "  \u001b[31m   \u001b[0m error: command 'cmake' failed: No such file or directory\n",
      "  \u001b[31m   \u001b[0m \u001b[31m[end of output]\u001b[0m\n",
      "  \n",
      "  \u001b[1;35mnote\u001b[0m: This error originates from a subprocess, and is likely not a problem with pip.\n",
      "\u001b[?25h\u001b[31m  ERROR: Failed building wheel for pyarrow\u001b[0m\u001b[31m\n",
      "\u001b[0mFailed to build pyarrow\n",
      "\u001b[31mERROR: Could not build wheels for pyarrow, which is required to install pyproject.toml-based projects\u001b[0m\u001b[31m\n",
      "\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m23.2.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m23.3\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "# Install dependencies\n",
    "%pip install -r requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "id": "761c5c52",
   "metadata": {},
   "outputs": [],
   "source": [
    "import polars as pl\n",
    "import numpy_financial as npf\n",
    "import numpy as np\n",
    "from dataclasses import dataclass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e9a4e4c",
   "metadata": {},
   "source": [
    "### 1. Entry Assumptions\n",
    "\n",
    "Encapsulating assumptions as classes for maintainability.\n",
    "\n",
    "As a monthly statement I'll just assume year 1's monthly revenue is 1/12 of the annual revenue.\n",
    "\n",
    "Also the dataclasses are immutable to prevent accidental changes.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 576,
   "id": "949b713d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Entry price assumptions\n",
    "@dataclass(frozen=True)\n",
    "class Entry:\n",
    "    entry_multiple: float = 5.0\n",
    "    y1_rev: float = 100.0\n",
    "    ebitda_margin: float = 0.4\n",
    "    entry_cost = entry_multiple * y1_rev * ebitda_margin\n",
    "    y1_rev_monthly = y1_rev / 12\n",
    "\n",
    "\n",
    "# Debt & Equity Assumptions\n",
    "@dataclass(frozen=True)\n",
    "class Debt:\n",
    "    debt_ratio: float = 0.6\n",
    "    equity_ratio = 1 - debt_ratio\n",
    "    debt = debt_ratio * Entry.entry_cost\n",
    "    equity = equity_ratio * Entry.entry_cost\n",
    "\n",
    "\n",
    "# Income Statement Assumptions\n",
    "@dataclass(frozen=True)\n",
    "class Parameters:\n",
    "    rev_growth: float = 1.1\n",
    "    int_rate: float = 0.10\n",
    "    tax_rate: float = 0.4\n",
    "    capex_rate: float = 0.15\n",
    "    working_capital: float = 5 / 12\n",
    "    dep_n_amor: float = 20 / 12\n",
    "    project_years: int or float = 6\n",
    "    total_months = project_years * 12"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feb77c6c",
   "metadata": {},
   "source": [
    "Assumptions variable instances:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 577,
   "id": "4accb59a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr > th,\n",
       ".dataframe > tbody > tr > td {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>Entry Multiple</th><th>EBITDA (Year 1)</th><th>Cost of Acquisition</th><th>Interest Rate</th><th>Debt Ratio</th><th>Equity Ratio</th><th>Debt</th><th>Equity</th></tr><tr><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>5</td><td>40</td><td>200</td><td>0.1</td><td>0.6</td><td>0.4</td><td>120</td><td>80</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌──────────┬──────────┬───────────────┬───────────────┬────────────┬───────────────┬──────┬────────┐\n",
       "│ Entry    ┆ EBITDA   ┆ Cost of       ┆ Interest Rate ┆ Debt Ratio ┆ Equity Ratio  ┆ Debt ┆ Equity │\n",
       "│ Multiple ┆ (Year 1) ┆ Acquisition   ┆ ---           ┆ ---        ┆ ---           ┆ ---  ┆ ---    │\n",
       "│ ---      ┆ ---      ┆ ---           ┆ f64           ┆ f64        ┆ f64           ┆ f64  ┆ f64    │\n",
       "│ f64      ┆ f64      ┆ f64           ┆               ┆            ┆               ┆      ┆        │\n",
       "╞══════════╪══════════╪═══════════════╪═══════════════╪════════════╪═══════════════╪══════╪════════╡\n",
       "│ 5        ┆ 40       ┆ 200           ┆ 0.1           ┆ 0.6        ┆ 0.4           ┆ 120  ┆ 80     │\n",
       "└──────────┴──────────┴───────────────┴───────────────┴────────────┴───────────────┴──────┴────────┘"
      ]
     },
     "execution_count": 577,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entry = Entry()\n",
    "params = Parameters()\n",
    "\n",
    "debt = Debt().debt\n",
    "debt_ratio = Debt().debt_ratio\n",
    "equity = Debt().equity\n",
    "equity_ratio = Debt().equity_ratio\n",
    "y1_revenue = entry.y1_rev\n",
    "entry_multiple = entry.entry_multiple\n",
    "entry_cost = entry.entry_cost\n",
    "first_month_rev = entry.y1_rev_monthly\n",
    "rev_growth = params.rev_growth\n",
    "ebitda_margin = entry.ebitda_margin\n",
    "int_rate = params.int_rate\n",
    "tax_rate = params.tax_rate\n",
    "capex_rate = params.capex_rate\n",
    "working_capital = params.working_capital\n",
    "dep_n_amor = params.dep_n_amor\n",
    "total_months = params.total_months\n",
    "\n",
    "entry_assumptions = {\n",
    "    \"Entry Multiple\": [entry_multiple],\n",
    "    \"EBITDA (Year 1)\": [y1_revenue * ebitda_margin],\n",
    "    \"Cost of Acquisition\": [entry_cost],\n",
    "    \"Interest Rate\": [int_rate],\n",
    "    \"Debt Ratio\": [debt_ratio],\n",
    "    \"Equity Ratio\": [equity_ratio],\n",
    "    \"Debt\": [debt],\n",
    "    \"Equity\": [equity],\n",
    "}\n",
    "entry_assumptions = pl.DataFrame(data=entry_assumptions)\n",
    "entry_assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c4a0aab",
   "metadata": {},
   "source": [
    "### 2. Income Statement\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab8ff276",
   "metadata": {},
   "source": [
    "Build Income Statement Class:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 578,
   "id": "9185e5bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "class IncomeStatement:\n",
    "    def __init__(\n",
    "        self,\n",
    "        year1_rev_monthly: float,\n",
    "        rev_growth: float,\n",
    "        ebitda_margin: float,\n",
    "        int_rate: float,\n",
    "        tax_rate: float,\n",
    "        da: float,\n",
    "        debt: float,\n",
    "        total_months: int,\n",
    "    ) -> None:\n",
    "        self.year1_rev_monthly = year1_rev_monthly\n",
    "        self.rev_growth = rev_growth\n",
    "        self.ebitda_margin = ebitda_margin\n",
    "        self.int_rate = int_rate\n",
    "        self.tax_rate = tax_rate\n",
    "        self.da = da\n",
    "        self.debt = debt\n",
    "        self.total_months = total_months\n",
    "\n",
    "    def months(self) -> pl.DataFrame:\n",
    "        return pl.DataFrame(\n",
    "            data={\n",
    "                \"Month\": [f\"Month {month}\" for month in range(1, self.total_months + 1)]\n",
    "            }\n",
    "        )\n",
    "\n",
    "    def revenue(self) -> pl.DataFrame:\n",
    "        revenue = []\n",
    "        revenue_dict = {\"Revenue\": revenue}\n",
    "        month = 0\n",
    "        while month < self.total_months:\n",
    "            if len(revenue) == 0:\n",
    "                revenue.append(self.year1_rev_monthly)\n",
    "                month += 1\n",
    "            elif len(revenue) % 12 == 0:\n",
    "                revenue.append(revenue[-1] * 1.1)\n",
    "                month += 1\n",
    "            else:\n",
    "                revenue.append(revenue[-1])\n",
    "                month += 1\n",
    "\n",
    "        revenue = pl.DataFrame(data=revenue_dict)\n",
    "        return self.months().with_columns(revenue)\n",
    "\n",
    "    def ebitda(self) -> pl.DataFrame:\n",
    "        return self.revenue().with_columns(\n",
    "            (pl.col(\"Revenue\") * self.ebitda_margin).alias(\"EBITDA\")\n",
    "        )\n",
    "\n",
    "    # Assuming amortization is constant for now?\n",
    "    def ebit(self) -> pl.DataFrame:\n",
    "        statement = self.ebitda().with_columns(\n",
    "            pl.lit(self.da).alias(\"Depreciation & Amortization\")\n",
    "        )\n",
    "        return statement.with_columns(\n",
    "            (pl.col(\"EBITDA\") - pl.col(\"Depreciation & Amortization\")).alias(\"EBIT\")\n",
    "        )\n",
    "\n",
    "    def int_exp(self) -> pl.DataFrame:\n",
    "        int_exp = self.debt * (((1 + self.int_rate) ** (1 / 12)) - 1)\n",
    "        return self.ebit().with_columns(pl.lit(int_exp).alias(\"Less: Interest Expense\"))\n",
    "\n",
    "    def ebt(self) -> pl.DataFrame:\n",
    "        return self.int_exp().with_columns(\n",
    "            (pl.col(\"EBIT\") - pl.col(\"Less: Interest Expense\")).alias(\"EBT\")\n",
    "        )\n",
    "\n",
    "    def tax(self) -> pl.DataFrame:\n",
    "        return self.ebt().with_columns(\n",
    "            (pl.col(\"EBT\") * self.tax_rate).alias(\"Less: Tax Payable\")\n",
    "        )\n",
    "\n",
    "    def net_income(self) -> pl.DataFrame:\n",
    "        return self.tax().with_columns(\n",
    "            (pl.col(\"EBT\") - pl.col(\"Less: Tax Payable\")).alias(\"Net Income\")\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0af946a6",
   "metadata": {},
   "source": [
    "Create an income statement instance:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 579,
   "id": "5ec64304",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr > th,\n",
       ".dataframe > tbody > tr > td {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (72, 9)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>Month</th><th>Revenue</th><th>EBITDA</th><th>Depreciation &amp; Amortization</th><th>EBIT</th><th>Less: Interest Expense</th><th>EBT</th><th>Less: Tax Payable</th><th>Net Income</th></tr><tr><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;Month 1&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 2&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 3&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 4&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 5&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 6&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 7&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 8&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 9&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 10&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 11&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&quot;Month 12&quot;</td><td>8.33</td><td>3.33</td><td>1.67</td><td>1.66</td><td>0.96</td><td>0.71</td><td>0.28</td><td>0.42</td></tr><tr><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td><td>&hellip;</td></tr><tr><td>&quot;Month 61&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 62&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 63&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 64&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 65&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 66&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 67&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 68&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 69&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 70&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 71&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr><tr><td>&quot;Month 72&quot;</td><td>13.42</td><td>5.37</td><td>1.67</td><td>3.7</td><td>0.96</td><td>2.74</td><td>1.1</td><td>1.64</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (72, 9)\n",
       "┌──────────┬─────────┬────────┬────────────────┬───┬──────────┬──────┬───────────┬────────────┐\n",
       "│ Month    ┆ Revenue ┆ EBITDA ┆ Depreciation & ┆ … ┆ Less:    ┆ EBT  ┆ Less: Tax ┆ Net Income │\n",
       "│ ---      ┆ ---     ┆ ---    ┆ Amortization   ┆   ┆ Interest ┆ ---  ┆ Payable   ┆ ---        │\n",
       "│ str      ┆ f64     ┆ f64    ┆ ---            ┆   ┆ Expense  ┆ f64  ┆ ---       ┆ f64        │\n",
       "│          ┆         ┆        ┆ f64            ┆   ┆ ---      ┆      ┆ f64       ┆            │\n",
       "│          ┆         ┆        ┆                ┆   ┆ f64      ┆      ┆           ┆            │\n",
       "╞══════════╪═════════╪════════╪════════════════╪═══╪══════════╪══════╪═══════════╪════════════╡\n",
       "│ Month 1  ┆ 8.33    ┆ 3.33   ┆ 1.67           ┆ … ┆ 0.96     ┆ 0.71 ┆ 0.28      ┆ 0.42       │\n",
       "│ Month 2  ┆ 8.33    ┆ 3.33   ┆ 1.67           ┆ … ┆ 0.96     ┆ 0.71 ┆ 0.28      ┆ 0.42       │\n",
       "│ Month 3  ┆ 8.33    ┆ 3.33   ┆ 1.67           ┆ … ┆ 0.96     ┆ 0.71 ┆ 0.28      ┆ 0.42       │\n",
       "│ Month 4  ┆ 8.33    ┆ 3.33   ┆ 1.67           ┆ … ┆ 0.96     ┆ 0.71 ┆ 0.28      ┆ 0.42       │\n",
       "│ …        ┆ …       ┆ …      ┆ …              ┆ … ┆ …        ┆ …    ┆ …         ┆ …          │\n",
       "│ Month 69 ┆ 13.42   ┆ 5.37   ┆ 1.67           ┆ … ┆ 0.96     ┆ 2.74 ┆ 1.1       ┆ 1.64       │\n",
       "│ Month 70 ┆ 13.42   ┆ 5.37   ┆ 1.67           ┆ … ┆ 0.96     ┆ 2.74 ┆ 1.1       ┆ 1.64       │\n",
       "│ Month 71 ┆ 13.42   ┆ 5.37   ┆ 1.67           ┆ … ┆ 0.96     ┆ 2.74 ┆ 1.1       ┆ 1.64       │\n",
       "│ Month 72 ┆ 13.42   ┆ 5.37   ┆ 1.67           ┆ … ┆ 0.96     ┆ 2.74 ┆ 1.1       ┆ 1.64       │\n",
       "└──────────┴─────────┴────────┴────────────────┴───┴──────────┴──────┴───────────┴────────────┘"
      ]
     },
     "execution_count": 579,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income_statement = IncomeStatement(\n",
    "    first_month_rev,\n",
    "    rev_growth,\n",
    "    ebitda_margin,\n",
    "    int_rate,\n",
    "    tax_rate,\n",
    "    dep_n_amor,\n",
    "    debt,\n",
    "    total_months,\n",
    ")\n",
    "\n",
    "lbo_is = income_statement.net_income().with_columns(pl.exclude(\"Month\").round(2))\n",
    "\n",
    "# If you wish to go for the usual spreadsheet-like format:\n",
    "# lbo = lbo.with_columns(pl.exclude(\"Month\").round(2)).transpose(include_header=True, header_name=\"Month\", column_names=\"Month\")\n",
    "lbo_is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca585775",
   "metadata": {},
   "source": [
    "### 3. Calculate Cumulative Levered Free Cash Flow\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee026b8b",
   "metadata": {},
   "source": [
    "Build a class for Free Cash Flow:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 580,
   "id": "53fc30c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class FCF:\n",
    "    def __init__(\n",
    "        self,\n",
    "        capex_rate: float,\n",
    "        working_capital: float,\n",
    "        da: float,\n",
    "        income_statement: IncomeStatement,\n",
    "    ) -> None:\n",
    "        self.income_statement = income_statement\n",
    "        self.capex_rate = capex_rate\n",
    "        self.working_capital = working_capital\n",
    "        self.da = da\n",
    "\n",
    "    def capex(self) -> pl.DataFrame:\n",
    "        statement = self.income_statement.net_income()\n",
    "        return statement.with_columns(\n",
    "            (pl.col(\"Revenue\") * self.capex_rate).alias(\"Less: Capex\")\n",
    "        )\n",
    "\n",
    "    def work_cap(self) -> pl.DataFrame:\n",
    "        statement = self.capex()\n",
    "        return statement.with_columns(\n",
    "            (pl.lit(self.working_capital).alias(\"Less: Working Capital\"))\n",
    "        )\n",
    "\n",
    "    def da_addback(self) -> pl.DataFrame:\n",
    "        statement = self.work_cap()\n",
    "        return statement.with_columns(\n",
    "            (pl.lit(self.da).alias(\"Add: Depreciation & Amortization\"))\n",
    "        )\n",
    "\n",
    "    def fcf(self) -> pl.DataFrame:\n",
    "        statement = self.da_addback()\n",
    "        return statement.with_columns(\n",
    "            (\n",
    "                pl.col(\"Net Income\")\n",
    "                + pl.col(\"Add: Depreciation & Amortization\")\n",
    "                - pl.col(\"Less: Capex\")\n",
    "                - pl.col(\"Less: Working Capital\")\n",
    "            ).alias(\"Monthly FCF\")\n",
    "        )\n",
    "\n",
    "    def fcf_only(self) -> pl.DataFrame:\n",
    "        statement = self.fcf()\n",
    "        return statement.select(\n",
    "            pl.col(\"Month\"),\n",
    "            pl.col(\"Net Income\"),\n",
    "            pl.col(\"Less: Capex\"),\n",
    "            pl.col(\"Less: Working Capital\"),\n",
    "            pl.col(\"Add: Depreciation & Amortization\"),\n",
    "            pl.col(\"Monthly FCF\"),\n",
    "        )\n",
    "\n",
    "    def cfi(self) -> pl.DataFrame:\n",
    "        statement = self.fcf_only()\n",
    "        cfi = {\"CFI\": []}\n",
    "        for i in range(total_months):\n",
    "            if i == 0:\n",
    "                cfi[\"CFI\"].append(-equity)\n",
    "            else:\n",
    "                cfi[\"CFI\"].append(0)\n",
    "        cfi = pl.DataFrame(data=cfi)\n",
    "        return statement.with_columns(cfi)\n",
    "\n",
    "    def cum_fcf(self) -> pl.DataFrame:\n",
    "        statement = self.cfi()\n",
    "        return statement.with_columns(\n",
    "            pl.col(\"Monthly FCF\").cumsum().alias(\"Cumulative FCF\") + pl.col(\"CFI\")\n",
    "        )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc55eba8",
   "metadata": {},
   "source": [
    "### 4. Exit Value & Returns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 582,
   "id": "ea7d0c6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass\n",
    "class Exit:\n",
    "    def __init__(\n",
    "        self,\n",
    "        exit_multiple: float,\n",
    "        lbo_fcf: pl.DataFrame,\n",
    "        lbo_is: pl.DataFrame,\n",
    "        equity: float,\n",
    "        debt: float,\n",
    "    ) -> None:\n",
    "        self.exit_multiple = exit_multiple\n",
    "        self.lbo_fcf = lbo_fcf\n",
    "        self.lbo_is = lbo_is\n",
    "        self.equity = equity\n",
    "        self.debt = debt\n",
    "\n",
    "    def exit_table(self) -> pl.DataFrame:\n",
    "        table = (\n",
    "            self.lbo_is.select(pl.col(\"EBITDA\"))\n",
    "            .tail(12)\n",
    "            .sum()\n",
    "            .rename({\"EBITDA\": \"EBITDA (LTM)\"})\n",
    "        )\n",
    "        table = table.with_columns(pl.lit(self.exit_multiple).alias(\"Exit Multiple\"))\n",
    "        table = table.with_columns(pl.lit(self.debt).alias(\"Beginning Debt\"))\n",
    "\n",
    "        return table\n",
    "\n",
    "    def total_enterprise_val(self) -> pl.DataFrame:\n",
    "        df = self.exit_table().with_columns(\n",
    "            (pl.col(\"EBITDA (LTM)\") * self.exit_multiple).alias(\n",
    "                \"Total Enterprise Value\"\n",
    "            )\n",
    "        )\n",
    "        return df\n",
    "\n",
    "    def exit_debt(self) -> pl.DataFrame:\n",
    "        fcf = self.lbo_fcf.filter(pl.col(\"Month\") == \"Month 60\").select(\n",
    "            \"Cumulative FCF\"\n",
    "        )\n",
    "        fcf = fcf.with_columns(\n",
    "            (self.debt - pl.col(\"Cumulative FCF\")).alias(\"Remaining Debt\")\n",
    "        )\n",
    "        return self.total_enterprise_val().with_columns(fcf)\n",
    "\n",
    "    def equity_val(self) -> pl.DataFrame:\n",
    "        table = self.exit_debt()\n",
    "        table = table.with_columns(\n",
    "            (pl.col(\"Total Enterprise Value\") - pl.col(\"Remaining Debt\")).alias(\n",
    "                \"Equity Value\"\n",
    "            )\n",
    "        )\n",
    "        return table\n",
    "\n",
    "    def exit_no_irr(self) -> pl.DataFrame:\n",
    "        table = self.equity_val()\n",
    "        table = table.with_columns(\n",
    "            (pl.col(\"Equity Value\") / self.equity).alias(\"Exit Multiple\")\n",
    "        )\n",
    "        return table"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bcb4176",
   "metadata": {},
   "source": [
    "Create a FCF & exit table instance,\n",
    "alter the output of irr() to display either the FCF or exit values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 584,
   "id": "42ea3fa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr > th,\n",
       ".dataframe > tbody > tr > td {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (1, 8)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>EBITDA (LTM)</th><th>Exit Multiple</th><th>Beginning Debt</th><th>Total Enterprise Value</th><th>Cumulative FCF</th><th>Remaining Debt</th><th>Equity Value</th><th>IRR</th></tr><tr><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>64.43999999999998</td><td>2.9697201668391964</td><td>120</td><td>322.19999999999993</td><td>35.37761334713579</td><td>84.62238665286421</td><td>237.57761334713572</td><td>0.0831538038898052</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (1, 8)\n",
       "┌────────────┬────────────┬────────────┬───────────┬───────────┬───────────┬───────────┬───────────┐\n",
       "│ EBITDA     ┆ Exit       ┆ Beginning  ┆ Total Ent ┆ Cumulativ ┆ Remaining ┆ Equity    ┆ IRR       │\n",
       "│ (LTM)      ┆ Multiple   ┆ Debt       ┆ erprise   ┆ e FCF     ┆ Debt      ┆ Value     ┆ ---       │\n",
       "│ ---        ┆ ---        ┆ ---        ┆ Value     ┆ ---       ┆ ---       ┆ ---       ┆ f64       │\n",
       "│ f64        ┆ f64        ┆ f64        ┆ ---       ┆ f64       ┆ f64       ┆ f64       ┆           │\n",
       "│            ┆            ┆            ┆ f64       ┆           ┆           ┆           ┆           │\n",
       "╞════════════╪════════════╪════════════╪═══════════╪═══════════╪═══════════╪═══════════╪═══════════╡\n",
       "│ 64.4399999 ┆ 2.96972016 ┆ 120        ┆ 322.19999 ┆ 35.377613 ┆ 84.622386 ┆ 237.57761 ┆ 0.0831538 │\n",
       "│ 9999998    ┆ 68391964   ┆            ┆ 999999993 ┆ 34713579  ┆ 65286421  ┆ 334713572 ┆ 038898052 │\n",
       "└────────────┴────────────┴────────────┴───────────┴───────────┴───────────┴───────────┴───────────┘"
      ]
     },
     "execution_count": 584,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lbo_fcf = FCF(\n",
    "    capex_rate,\n",
    "    working_capital,\n",
    "    dep_n_amor,\n",
    "    income_statement=income_statement,\n",
    ").cum_fcf()\n",
    "\n",
    "exit_table = Exit(\n",
    "    exit_multiple=5,\n",
    "    lbo_fcf=lbo_fcf,\n",
    "    lbo_is=lbo_is,\n",
    "    equity=equity,\n",
    "    debt=debt,\n",
    ").exit_no_irr()\n",
    "\n",
    "\n",
    "def irr(exit_table: pl.DataFrame, lbo_fcf: pl.DataFrame, output: str) -> pl.DataFrame:\n",
    "    table = exit_table\n",
    "\n",
    "    exit_earning = {\"Exit Earnings\": []}\n",
    "\n",
    "    for i in range(total_months):\n",
    "        if len(exit_earning[\"Exit Earnings\"]) + 1 < total_months - 12:\n",
    "            exit_earning[\"Exit Earnings\"].append(0)\n",
    "        elif len(exit_earning[\"Exit Earnings\"]) + 1 == total_months - 12:\n",
    "            exit_earning[\"Exit Earnings\"].append(table[\"Equity Value\"][0])\n",
    "        elif len(exit_earning[\"Exit Earnings\"]) + 1 <= total_months:\n",
    "            exit_earning[\"Exit Earnings\"].append(0)\n",
    "\n",
    "    exit_earning = pl.DataFrame(data=exit_earning)\n",
    "    lbo_fcf = lbo_fcf.with_columns(exit_earning)\n",
    "    lbo_fcf = lbo_fcf.with_columns(\n",
    "        (pl.col(\"Cumulative FCF\") + pl.col(\"Exit Earnings\")).alias(\"Total CF\")\n",
    "    )\n",
    "\n",
    "    series = lbo_fcf.get_column(\"Total CF\")\n",
    "    irr = npf.irr(series)\n",
    "    exit_table = table.with_columns(pl.lit(irr).alias(\"IRR\"))\n",
    "\n",
    "    if output == \"exit\":\n",
    "        return exit_table\n",
    "    else:\n",
    "        return lbo_is\n",
    "\n",
    "\n",
    "# Change output to \"exit\" to get exit table, otherwise it will return the FCF.\n",
    "irr(exit_table, lbo_fcf, output=\"exit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb3a254e",
   "metadata": {},
   "source": [
    "Polars does not have a rounding function to dataframes yet,\n",
    "\n",
    "apologies for the excessive decimal points. lol\n",
    "\n",
    "Also the original case study's cashflow doesn't seem to incorporate the initial acquisition cost and the desposition value,\n",
    "therefore the IRR is different.\n"
   ]
  }
 ],
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