2 NPV vs. IRR.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "359.41043083900206\n"
     ]
    }
   ],
   "source": [
    "class Cashflow:\n",
    "    def __init__(self, val,t,r):\n",
    "        self.val = val\n",
    "        self.t = t\n",
    "        self.r = r\n",
    "        self.PV = self.valAt(0)\n",
    "    def valAt(self,time):\n",
    "        return self.val*(1+self.r)**(time-self.t)\n",
    "def NPV(arr):\n",
    "    return sum([x.PV for x in arr])\n",
    "print(NPV([Cashflow(-1500,0,.05),Cashflow(1000,1,.05),Cashflow(1000,2,.05)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Cashflow:\n",
    "    def __init__(self, val,t,r):\n",
    "        self.val = val\n",
    "        self.t = t\n",
    "        self.r = r\n",
    "        self.PV = self.valAt(0)\n",
    "    def valAt(self,time):\n",
    "        return self.val*(1+self.r)**(time-self.t)\n",
    "    def tryR(self,r):\n",
    "        return self.val*(1+r)**(0-self.t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def NPV2(r,arr):\n",
    "    return sum([x.tryR(r) for x in arr])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import fsolve\n",
    "def findIRR(arr):\n",
    "    return fsolve(NPV2, 0,(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.21525044]\n",
      "-8.417373464908451e-10\n"
     ]
    }
   ],
   "source": [
    "print(findIRR([Cashflow(-1500.0,0.0,.05),Cashflow(1000.0,1.0,.05),Cashflow(1000.0,2.0,.05)]))\n",
    "print(NPV2(.215250437022,[Cashflow(-1500.0,0,.05),Cashflow(1000.0,1,.05),Cashflow(1000.0,2,.05)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "500.0 Yes Yes\n",
      "470.39505930791086 Yes Yes\n",
      "441.56093810073037 Yes Yes\n",
      "413.46969554152145 Yes Yes\n",
      "386.0946745562128 Yes Yes\n",
      "359.41043083900206 Yes Yes\n",
      "333.3926664293341 Yes Yes\n",
      "308.01816752554805 Yes Yes\n",
      "283.264746227709 Yes Yes\n",
      "259.11118592711034 Yes Yes\n",
      "235.53719008264443 Yes Yes\n",
      "212.52333414495604 Yes Yes\n",
      "190.05102040816348 Yes Yes\n",
      "168.10243558618538 Yes Yes\n",
      "146.66051092643897 Yes Yes\n",
      "125.70888468809096 Yes Yes\n",
      "105.23186682520816 Yes Yes\n",
      "85.21440572722634 Yes Yes\n",
      "65.64205688020695 Yes Yes\n",
      "46.50095332250555 Yes Yes\n",
      "27.777777777777942 Yes Yes\n",
      "9.459736356806275 Yes Yes\n",
      "-8.465466272507342 No No\n",
      "-26.009650340405756 No No\n",
      "-43.184183142559846 No No\n",
      "-60.0 No No\n",
      "-76.46762408667178 No No\n",
      "-92.59718519437047 No No\n",
      "-108.3984375 No No\n",
      "-123.88077639564938 No No\n",
      "-139.05325443787 No No\n",
      "-153.92459646873726 No No\n",
      "-168.50321395775939 No No\n",
      "-182.79721861043595 No No\n",
      "-196.8144352862555 No No\n",
      "-210.56241426611814 No No\n",
      "-224.04844290657456 No No\n",
      "-237.2795567158613 No No\n",
      "-250.2625498844783 No No\n",
      "-263.003985300968 No No\n",
      "-275.5102040816328 No No\n",
      "-287.7873346411148 No No\n",
      "-299.84130132910155 No No\n",
      "-311.67783265685375 No No\n",
      "-323.3024691358027 No No\n",
      "-334.7205707491084 No No\n",
      "-345.9373240758117 No No\n",
      "-356.95774908602925 No No\n",
      "-367.7867056245438 No No\n",
      "-378.4288995991174 No No\n"
     ]
    }
   ],
   "source": [
    "flows = [Cashflow(-1500,0.0,.05),Cashflow(1000,1.0,.05),Cashflow(1000,2.0,.05)]\n",
    "cutoff = findIRR(flows)[0]\n",
    "r=0\n",
    "decision1 =\"Yes\"\n",
    "decision2 =\"Yes\"\n",
    "for _ in range(50):\n",
    "    value = NPV2(r,flows)\n",
    "    if value>0:\n",
    "        decision1 =\"Yes\"\n",
    "    else:\n",
    "        decision1 =\"No\"\n",
    "    if r<cutoff:\n",
    "        decision2 =\"Yes\"\n",
    "    else:\n",
    "        decision2 =\"No\"\n",
    "    r+=.01\n",
    "    print(value,decision1,decision2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-500.0 No Yes\n",
      "-470.39505930791086 No Yes\n",
      "-441.56093810073037 No Yes\n",
      "-413.46969554152145 No Yes\n",
      "-386.0946745562128 No Yes\n",
      "-359.41043083900206 No Yes\n",
      "-333.3926664293341 No Yes\n",
      "-308.01816752554805 No Yes\n",
      "-283.264746227709 No Yes\n",
      "-259.11118592711034 No Yes\n",
      "-235.53719008264443 No Yes\n",
      "-212.52333414495604 No Yes\n",
      "-190.05102040816348 No Yes\n",
      "-168.10243558618538 No Yes\n",
      "-146.66051092643897 No Yes\n",
      "-125.70888468809096 No Yes\n",
      "-105.23186682520816 No Yes\n",
      "-85.21440572722634 No Yes\n",
      "-65.64205688020695 No Yes\n",
      "-46.50095332250555 No Yes\n",
      "-27.777777777777942 No Yes\n",
      "-9.459736356806275 No Yes\n",
      "8.465466272507342 Yes No\n",
      "26.009650340405756 Yes No\n",
      "43.184183142559846 Yes No\n",
      "60.0 Yes No\n",
      "76.46762408667178 Yes No\n",
      "92.59718519437047 Yes No\n",
      "108.3984375 Yes No\n",
      "123.88077639564938 Yes No\n",
      "139.05325443787 Yes No\n",
      "153.92459646873726 Yes No\n",
      "168.50321395775939 Yes No\n",
      "182.79721861043595 Yes No\n",
      "196.8144352862555 Yes No\n",
      "210.56241426611814 Yes No\n",
      "224.04844290657456 Yes No\n",
      "237.2795567158613 Yes No\n",
      "250.2625498844783 Yes No\n",
      "263.003985300968 Yes No\n",
      "275.5102040816328 Yes No\n",
      "287.7873346411148 Yes No\n",
      "299.84130132910155 Yes No\n",
      "311.67783265685375 Yes No\n",
      "323.3024691358027 Yes No\n",
      "334.7205707491084 Yes No\n",
      "345.9373240758117 Yes No\n",
      "356.95774908602925 Yes No\n",
      "367.7867056245438 Yes No\n",
      "378.4288995991174 Yes No\n"
     ]
    }
   ],
   "source": [
    "flows = [Cashflow(1500,0.0,.05),Cashflow(-1000,1.0,.05),Cashflow(-1000,2.0,.05)]\n",
    "cutoff = findIRR(flows)[0]\n",
    "r=0\n",
    "decision1 =\"Yes\"\n",
    "decision2 =\"Yes\"\n",
    "for _ in range(50):\n",
    "    value = NPV2(r,flows)\n",
    "    if value>0:\n",
    "        decision1 =\"Yes\"\n",
    "    else:\n",
    "        decision1 =\"No\"\n",
    "    if r<cutoff:\n",
    "        decision2 =\"Yes\"\n",
    "    else:\n",
    "        decision2 =\"No\"\n",
    "    r+=.01\n",
    "    print(value,decision1,decision2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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fnH/PjGX4nJ2s2n+WD7qGyn7u+d35g7BpnLHxU1oSVGgJdV+E8k1kYmAeZWbHusLo87ik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\ncMJj1oQXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1093982e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "flows = [Cashflow(-1500,0,.05),Cashflow(1000,1,.05),Cashflow(1000,2,.05)]\n",
    "\n",
    "r = 0\n",
    "rates=[]\n",
    "values=[]\n",
    "for _ in range(50):\n",
    "    rates+=[r]\n",
    "    values+=[NPV2(r,flows)]\n",
    "    r+=.01\n",
    "plt.plot(rates,values)\n",
    "\n",
    "flows = [Cashflow(1500,0,.05),Cashflow(-1000,1,.05),Cashflow(-1000,2,.05)]\n",
    "\n",
    "r = 0\n",
    "rates=[]\n",
    "values=[]\n",
    "for _ in range(50):\n",
    "    rates+=[r]\n",
    "    values+=[NPV2(r,flows)]\n",
    "    r+=.01\n",
    "plt.plot(rates,values)\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"NPV\")\n",
    "plt.legend([\"Cash Flows 1\",\"Negative Cash Flows 1\"])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PMmzKUrKyrZCYknfWb0ARqRWoIKFkX2YWKWlH7dReE/T6dKzLi/06sGDzAYZP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\nN38pAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10939bf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flows = [Cashflow(-1200,0,.05),Cashflow(2000,3,.05),Cashflow(2000,6,.05),Cashflow(-3000,10,.05)]\n",
    "\n",
    "r = 0\n",
    "rates=[]\n",
    "values=[]\n",
    "for _ in range(50):\n",
    "    rates+=[r]\n",
    "    values+=[NPV2(r,flows)]\n",
    "    r+=.01\n",
    "plt.axhline(0, color='black')\n",
    "plt.plot(rates,values)\n",
    "plt.xlabel(\"r\")\n",
    "plt.ylabel(\"NPV\")\n",
    "plt.title(\"Cash Flows with Mixed Signs\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}