26a_tax_primer.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tax Primer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy_financial in d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages (1.0.0)\n",
      "Requirement already satisfied: numpy>=1.15 in d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages (from numpy_financial) (1.23.2)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "[notice] A new release of pip available: 22.2.1 -> 23.3.2\n",
      "[notice] To update, run: python.exe -m pip install --upgrade pip\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "!pip install numpy_financial\n",
    "import numpy_financial as npf\n",
    "import plotly.graph_objects as go\n",
    "import plotly.express as px\n",
    "pd.options.display.float_format = '{:,.2f}'.format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "      <th>rate</th>\n",
       "      <th>bin_income</th>\n",
       "      <th>bin_tax</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>10,275.00</td>\n",
       "      <td>0.10</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10275</td>\n",
       "      <td>41,775.00</td>\n",
       "      <td>0.12</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>41775</td>\n",
       "      <td>89,075.00</td>\n",
       "      <td>0.22</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>89075</td>\n",
       "      <td>170,050.00</td>\n",
       "      <td>0.24</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>170050</td>\n",
       "      <td>215,950.00</td>\n",
       "      <td>0.32</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>215950</td>\n",
       "      <td>539,900.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>539900</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.37</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    lower      upper  rate  bin_income  bin_tax\n",
       "1       0  10,275.00  0.10         NaN      NaN\n",
       "2   10275  41,775.00  0.12         NaN      NaN\n",
       "3   41775  89,075.00  0.22         NaN      NaN\n",
       "4   89075 170,050.00  0.24         NaN      NaN\n",
       "5  170050 215,950.00  0.32         NaN      NaN\n",
       "6  215950 539,900.00  0.35         NaN      NaN\n",
       "7  539900        inf  0.37         NaN      NaN"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LIMITS = [0, 10275, 41775, 89075, 170050, 215950, 539900]\n",
    "RATES  = [0.1, 0.12, 0.22, 0.24, 0.32, 0.35, 0.37]\n",
    "\n",
    "cols = ['lower','upper','rate','bin_income','bin_tax']\n",
    "df = pd.DataFrame(dtype=float, columns=cols, index=1+np.arange(len(LIMITS)))\n",
    "df['lower'] = LIMITS\n",
    "df['upper'] = LIMITS[1:] + [np.inf]\n",
    "df['rate']  = RATES\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "      <th>rate</th>\n",
       "      <th>bin_income</th>\n",
       "      <th>bin_tax</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>10,275.00</td>\n",
       "      <td>0.10</td>\n",
       "      <td>10,275.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10275</td>\n",
       "      <td>41,775.00</td>\n",
       "      <td>0.12</td>\n",
       "      <td>31,500.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>41775</td>\n",
       "      <td>89,075.00</td>\n",
       "      <td>0.22</td>\n",
       "      <td>47,300.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>89075</td>\n",
       "      <td>170,050.00</td>\n",
       "      <td>0.24</td>\n",
       "      <td>10,925.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>170050</td>\n",
       "      <td>215,950.00</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>215950</td>\n",
       "      <td>539,900.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>539900</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.37</td>\n",
       "      <td>0.00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    lower      upper  rate  bin_income  bin_tax\n",
       "1       0  10,275.00  0.10   10,275.00      NaN\n",
       "2   10275  41,775.00  0.12   31,500.00      NaN\n",
       "3   41775  89,075.00  0.22   47,300.00      NaN\n",
       "4   89075 170,050.00  0.24   10,925.00      NaN\n",
       "5  170050 215,950.00  0.32        0.00      NaN\n",
       "6  215950 539,900.00  0.35        0.00      NaN\n",
       "7  539900        inf  0.37        0.00      NaN"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "INCOME = 100000\n",
    "df['bin_income']= np.where(INCOME>df.lower, \n",
    "                    np.where(INCOME>df.upper, df.upper-df.lower, INCOME-df.lower),\n",
    "                    0)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check that sum of df.bin_income equals taxable income\n",
    "df.bin_income.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "      <th>rate</th>\n",
       "      <th>bin_income</th>\n",
       "      <th>bin_tax</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>10,275.00</td>\n",
       "      <td>0.10</td>\n",
       "      <td>10,275.00</td>\n",
       "      <td>1,027.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10275</td>\n",
       "      <td>41,775.00</td>\n",
       "      <td>0.12</td>\n",
       "      <td>31,500.00</td>\n",
       "      <td>3,780.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>41775</td>\n",
       "      <td>89,075.00</td>\n",
       "      <td>0.22</td>\n",
       "      <td>47,300.00</td>\n",
       "      <td>10,406.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>89075</td>\n",
       "      <td>170,050.00</td>\n",
       "      <td>0.24</td>\n",
       "      <td>10,925.00</td>\n",
       "      <td>2,622.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>170050</td>\n",
       "      <td>215,950.00</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>215950</td>\n",
       "      <td>539,900.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>539900</td>\n",
       "      <td>inf</td>\n",
       "      <td>0.37</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    lower      upper  rate  bin_income   bin_tax\n",
       "1       0  10,275.00  0.10   10,275.00  1,027.50\n",
       "2   10275  41,775.00  0.12   31,500.00  3,780.00\n",
       "3   41775  89,075.00  0.22   47,300.00 10,406.00\n",
       "4   89075 170,050.00  0.24   10,925.00  2,622.00\n",
       "5  170050 215,950.00  0.32        0.00      0.00\n",
       "6  215950 539,900.00  0.35        0.00      0.00\n",
       "7  539900        inf  0.37        0.00      0.00"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['bin_tax'] = df.bin_income*df.rate\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total tax: $17,835.50\n"
     ]
    }
   ],
   "source": [
    "# Total tax\n",
    "total_tax = df.bin_tax.sum()\n",
    "print(f'Total tax: ${total_tax:,.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tax_single_filer(income):\n",
    "    LIMITS = [0, 10275, 41775, 89075, 170050, 215950, 539900]\n",
    "    RATES  = [0.1, 0.12, 0.22, 0.24, 0.32, 0.35, 0.37]\n",
    "    cols = ['lower','upper','rate','bin_income','bin_tax']\n",
    "    df = pd.DataFrame(dtype=float, columns=cols, index=1+np.arange(len(LIMITS)))\n",
    "    df['lower'] = LIMITS\n",
    "    df['upper'] = LIMITS[1:] + [np.inf]\n",
    "    df['rate']  = RATES\n",
    "    df['bin_income']= np.where(income>df.lower, \n",
    "                    np.where(income>df.upper, df.upper-df.lower, income-df.lower),\n",
    "                    0)\n",
    "    df['bin_tax'] = df.bin_income*df.rate\n",
    "    return df.bin_tax.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "incomes = np.arange(1000,1001000,1000)\n",
    "taxes = [tax_single_filer(x) for x in incomes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "xaxis": {
         "tickformat": ",.2f",
         "title": {
          "text": "Income (after deductions)"
         }
        },
        "yaxis": {
         "tickformat": ",.2f",
         "title": {
          "text": "Tax"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of tax due\n",
    "fig = go.Figure()\n",
    "trace  = go.Scatter(x=incomes, y=taxes, mode=\"lines\")\n",
    "fig.add_trace(trace)\n",
    "\n",
    "# Formatting\n",
    "fig.update_xaxes(title='Income (after deductions)',tickformat=\",.2f\")\n",
    "fig.update_yaxes(title='Tax',tickformat=\",.2f\")\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
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          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "xaxis": {
         "tickformat": ",.0f",
         "title": {
          "text": "Income (after deductions)"
         }
        },
        "yaxis": {
         "tickformat": ",.2%",
         "title": {
          "text": "Average Tax Rate"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of average tax rate\n",
    "fig = go.Figure()\n",
    "trace  = go.Scatter(x=incomes, y=taxes/incomes, mode=\"lines\")\n",
    "fig.add_trace(trace)\n",
    "\n",
    "# Formatting\n",
    "fig.update_xaxes(title='Income (after deductions)',tickformat=\",.0f\")\n",
    "fig.update_yaxes(title='Average Tax Rate',tickformat=\",.2%\")\n",
    "fig.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "- Consider a single investor earning $65,000 per year.  \n",
    "- Assume they take the standard deduction of $12,590.\n",
    "- Under the 2022 tax rates & brackets, what is the investor's tax bill if do not have any other deductions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10447.2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GROSS_INCOME = 80000\n",
    "DEDUCTIBLE_SAVINGS = 0\n",
    "STANDARD_DEDUCTION = 12590\n",
    "tax1 = tax_single_filer(GROSS_INCOME - DEDUCTIBLE_SAVINGS - STANDARD_DEDUCTION)\n",
    "tax1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Under the 2022 tax rates & brackets, what is the investor's tax bill if they have contributed $6,000 to a traditional IRA?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9127.2"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GROSS_INCOME = 80000\n",
    "DEDUCTIBLE_SAVINGS = 6000\n",
    "STANDARD_DEDUCTION = 12590\n",
    "tax2 = tax_single_filer(GROSS_INCOME - DEDUCTIBLE_SAVINGS - STANDARD_DEDUCTION)\n",
    "tax2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1320.0\n",
      "1320.0\n"
     ]
    }
   ],
   "source": [
    "print(RATES[2]*DEDUCTIBLE_SAVINGS)\n",
    "print(tax1-tax2)"
   ]
  }
 ],
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