34:["$","title",null,{"children":"Evaluating Corporate Car Lease Policy | Rithwik Anand | Observable"}] 3c:T47c,# Evaluating Corporate Car Lease Policy To assess the corporate car lease policy using Net Present Value (NPV), let's examine the cash flows in two scenarios: ## Scenario A: Car Lease with EMI **Negative Cash Flows:** 1. **EMI Payments:** Monthly lease payments. 2. **Residual Value Payment:** Final payment to purchase the car. **Positive Cash Flows:** 1. **Tax Savings on EMI:** Reduced taxable income due to EMI deduction. 2. **Driver Allowance (Taxed):** Taxed monthly allowance for a driver. ## Scenario B: Purchase the Car Outright **Negative Cash Flow:** 1. **Initial Purchase Price:** Full on-road price paid upfront. ## NPV Calculation for Scenario A To determine if Scenario A is superior to Scenario B, calculate the NPV of Scenario A's cash flows and compare it to the initial purchase price in Scenario B: 1. **Identify Cash Flows:** - EMI payments, tax savings, driver allowance, and the residual value payment. 2. **Choose a Discount Rate:** Represents the opportunity cost of money (e.g., expected ROI, inflation). 3. **Calculate NPV:** - Use the NPV formula to discount future cash flows to their present value:3d:T1dbe,f = { //Finance.js //For more information, visit http://financejs.org //Copyright 2014 - 2015 Essam Al Joubori, MIT license // Instantiate a Finance class var Finance = function() {}; // Present Value (PV) Finance.prototype.PV = function (rate, cf1, numOfPeriod) { numOfPeriod = typeof numOfPeriod !== 'undefined' ? numOfPeriod : 1; var rate = rate/100, pv; pv = cf1 / Math.pow((1 + rate),numOfPeriod); return Math.round(pv * 100) / 100; }; // Future Value (FV) Finance.prototype.FV = function (rate, cf0, numOfPeriod) { var rate = rate/100, fv; fv = cf0 * Math.pow((1 + rate), numOfPeriod); return Math.round(fv * 100) / 100; }; // Net Present Value (NPV) Finance.prototype.NPV = function (rate) { var rate = rate/100, npv = arguments[1]; for (var i = 2; i < arguments.length; i++) { npv +=(arguments[i] / Math.pow((1 + rate), i - 1)); } return Math.round(npv * 100) / 100; }; // seekZero seeks the zero point of the function fn(x), accurate to within x \pm 0.01. fn(x) must be decreasing with x. function seekZero(fn) { var x = 1; while (fn(x) > 0) { x += 1; } while (fn(x) < 0) { x -= 0.01 } return x + 0.01; } // Internal Rate of Return (IRR) Finance.prototype.IRR = function(cfs) { var args = arguments; var numberOfTries = 1; // Cash flow values must contain at least one positive value and one negative value var positive, negative; Array.prototype.slice.call(args).forEach(function (value) { if (value > 0) positive = true; if (value < 0) negative = true; }) if (!positive || !negative) throw new Error('IRR requires at least one positive value and one negative value'); function npv(rate) { numberOfTries++; if (numberOfTries > 1000) { throw new Error('IRR can\'t find a result'); } var rrate = (1 + rate/100); var npv = args[0]; for (var i = 1; i < args.length; i++) { npv += (args[i] / Math.pow(rrate, i)); } return npv; } return Math.round(seekZero(npv) * 100) / 100; }; // Payback Period (PP) Finance.prototype.PP = function(numOfPeriods, cfs) { // for even cash flows if (numOfPeriods === 0) { return Math.abs(arguments[1]) / arguments[2]; } // for uneven cash flows var cumulativeCashFlow = arguments[1]; var yearsCounter = 1; for (let i = 2; i < arguments.length; i++) { cumulativeCashFlow += arguments[i]; if (cumulativeCashFlow > 0) { yearsCounter += (cumulativeCashFlow - arguments[i]) / arguments[i]; return yearsCounter; } else { yearsCounter++; } } }; // Return on Investment (ROI) Finance.prototype.ROI = function(cf0, earnings) { var roi = (earnings - Math.abs(cf0)) / Math.abs(cf0) * 100; return Math.round(roi * 100) / 100; }; // Amortization Finance.prototype.AM = function (principal, rate, period, yearOrMonth, payAtBeginning) { var numerator, denominator, am; var ratePerPeriod = rate / 12 / 100; // for inputs in years if (!yearOrMonth) { numerator = buildNumerator(period * 12); denominator = Math.pow((1 + ratePerPeriod), period * 12) - 1; // for inputs in months } else if (yearOrMonth === 1) { numerator = buildNumerator(period) denominator = Math.pow((1 + ratePerPeriod), period) - 1; } else { console.log('not defined'); } am = principal * (numerator / denominator); return Math.round(am * 100) / 100; function buildNumerator(numInterestAccruals){ if( payAtBeginning ){ //if payments are made in the beginning of the period, then interest shouldn't be calculated for first period numInterestAccruals -= 1; } return ratePerPeriod * Math.pow((1 + ratePerPeriod), numInterestAccruals); } }; // Profitability Index (PI) Finance.prototype.PI = function(rate, cfs){ var totalOfPVs = 0, PI; for (var i = 2; i < arguments.length; i++) { var discountFactor; // calculate discount factor discountFactor = 1 / Math.pow((1 + rate/100), (i - 1)); totalOfPVs += arguments[i] * discountFactor; } PI = totalOfPVs/Math.abs(arguments[1]); return Math.round(PI * 100) / 100; }; // Discount Factor (DF) Finance.prototype.DF = function(rate, numOfPeriods) { var dfs = [], discountFactor; for (var i = 1; i < numOfPeriods; i++) { discountFactor = 1 / Math.pow((1 + rate/100), (i - 1)); let roundedDiscountFactor = Math.ceil(discountFactor * 1000)/1000; dfs.push(roundedDiscountFactor); } return dfs; }; // Compound Interest (CI) Finance.prototype.CI = function(rate, numOfCompoundings, principal, numOfPeriods) { var CI = principal * Math.pow((1 + ((rate/100)/ numOfCompoundings)), numOfCompoundings * numOfPeriods); return Math.round(CI * 100) / 100; }; // Compound Annual Growth Rate (CAGR) Finance.prototype.CAGR = function(beginningValue, endingValue, numOfPeriods) { var CAGR = Math.pow((endingValue / beginningValue), 1 / numOfPeriods) - 1; return Math.round(CAGR * 10000) / 100; }; // Leverage Ratio (LR) Finance.prototype.LR = function(totalLiabilities, totalDebts, totalIncome) { return (totalLiabilities + totalDebts) / totalIncome; }; // Rule of 72 Finance.prototype.R72 = function(rate) { return 72 / rate; }; // Weighted Average Cost of Capital (WACC) Finance.prototype.WACC = function(marketValueOfEquity, marketValueOfDebt, costOfEquity, costOfDebt, taxRate) { let E = marketValueOfEquity; let D = marketValueOfDebt; let V = marketValueOfEquity + marketValueOfDebt; let Re = costOfEquity; let Rd = costOfDebt; let T = taxRate; var WACC = ((E / V) * Re/100) + (((D / V) * Rd/100) * (1 - T/100)); return Math.round(WACC * 1000) / 10; }; // PMT calculates the payment for a loan based on constant payments and a constant interest rate Finance.prototype.PMT = function(fractionalRate, numOfPayments, principal) { return -principal * fractionalRate/(1-Math.pow(1+fractionalRate,-numOfPayments)) }; // IAR calculates the Inflation-adjusted return Finance.prototype.IAR = function(investmentReturn, inflationRate){ return 100 * (((1 + investmentReturn) / (1 + inflationRate)) - 1); } // XIRR - IRR for irregular intervals Finance.prototype.XIRR = function(cfs, dts, guess) { if (cfs.length != dts.length) throw new Error('Number of cash flows and dates should match'); var positive, negative; Array.prototype.slice.call(cfs).forEach(function (value) { if (value > 0) positive = true; if (value < 0) negative = true; }); if (!positive || !negative) throw new Error('XIRR requires at least one positive value and one negative value'); guess = !!guess ? guess : 0; var limit = 100; //loop limit var guess_last; var durs = []; durs.push(0); //Create Array of durations from First date for(var i = 1; i < dts.length; i++) { durs.push(durYear(dts[0], dts[i])); } do { guess_last = guess; guess = guess_last - sumEq(cfs, durs, guess_last); limit--; }while(guess_last.toFixed(5) != guess.toFixed(5) && limit > 0); var xirr = guess_last.toFixed(5) != guess.toFixed(5) ? null : guess*100; return Math.round(xirr * 100) / 100; }; //Returns Sum of f(x)/f'(x) function sumEq(cfs, durs, guess) { var sum_fx = 0; var sum_fdx = 0; for (var i = 0; i < cfs.length; i++) { sum_fx = sum_fx + (cfs[i] / Math.pow(1 + guess, durs[i])); } for ( i = 0; i < cfs.length; i++) { sum_fdx = sum_fdx + (-cfs[i] * durs[i] * Math.pow(1 + guess, -1 - durs[i])); } return sum_fx / sum_fdx; } //Returns duration in years between two dates function durYear(first, last) { return (Math.abs(last.getTime() - first.getTime()) / (1000 * 3600 * 24 * 365)); } return new Finance() }3e:[] 38:{"id":"5b696f37abfa4a3e","slug":"evaluating-corporate-car-lease-policy-old","title":"Evaluating Corporate Car Lease Policy","thumbnail":"df45faeb14bdab3b013a659f71059313cb11bbce8e25c944970731e0f4223dc7","access_level":"public","create_time":"$D2024-08-13T11:37:59.705Z","update_time":"$D2024-08-16T03:49:34.270Z","view_time":null,"first_public_time":"$D2024-08-13T16:42:06.190Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"77b49d5139b68ed8","login":"rithwikanand","name":"Rithwik Anand","avatar_url":"https://avatars-next.observableusercontent.com/2d11b8fc94986ebb4c9233d528cbb27cc8b80f1263a7ad00b479736ba2da942f","tier":"starter_2024","bio":"","followed_by_you":false,"follows_you":false},"version":399,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"2e0717d814773a4a","login":"rithwikanand","name":"Rithwik Anand","avatar_url":"https://avatars-next.observableusercontent.com/2d11b8fc94986ebb4c9233d528cbb27cc8b80f1263a7ad00b479736ba2da942f","tier":null,"bio":"","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"2e0717d814773a4a","login":"rithwikanand","name":"Rithwik Anand","avatar_url":"https://avatars-next.observableusercontent.com/2d11b8fc94986ebb4c9233d528cbb27cc8b80f1263a7ad00b479736ba2da942f","tier":null,"role":"editor"},{"type":"team","id":"77b49d5139b68ed8","login":"rithwikanand","name":"Rithwik Anand","avatar_url":"https://avatars-next.observableusercontent.com/2d11b8fc94986ebb4c9233d528cbb27cc8b80f1263a7ad00b479736ba2da942f","tier":"starter_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Evaluating Corporate Car Lease Policy","cells":[{"id":148,"value":"$3c","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":181,"value":"\\text{NPV} = \\sum_{t=1}^{n} \\left(\\frac{\\text{Cash Flow}_t}{(1 + r)^t}\\right)","pinned":false,"hidden":false,"mode":"tex","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":184,"value":"## Comparison\n\n1. **NPV of Scenario A:** Sum the present values of all cash flows, including the residual payment.\n2. **Compare NPV to Scenario B:** If Scenario A's NPV is lower than Scenario B's purchase price, leasing is financially superior.\n\n## Conclusion\n\n- If Scenario A's NPV is lower than Scenario B's purchase price, leasing is more cost-effective.\n- Consider other factors like ownership preferences and maintenance when making your decision.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":193,"value":"## Worksheet for SAP Kia Sonet Car lease","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":325,"value":"md`\n| Name | Value |\n| ------ | -------- |\n${Object.entries(info).map(([key, value]) => {\n return `| ${labelise(key)} | ${['Tax_slab', 'Inflation', 'Employee_effective_interest_rate', 'Fleet_Mgmt_interest_rate'].includes(key) ? d3.format('.1%')(value) : ['Tenure'].includes(key) ? `${value} months` : format(value)} |\\n`\n})}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":200,"value":"The NPV for the car lease scenario, based on the above calculations, is **${format(-npv)}**.\n\nThe On-Road Price for the same car is **${format(info.On_road_price)}**.\n\n${-npv < info.On_road_price ? `Leasing is more cost-effective than buying.` : `Buying is more cost-effective than leasing.`}\n\nYou can save **${format(Math.abs(-npv - info.On_road_price))}** (${d3.format('.0%')(Math.abs(-npv - info.On_road_price) / info.On_road_price)}) by choosing to ${-npv < info.On_road_price ? 'lease' : 'buy'}.\n\nIf you can sell the car for **${format(f.FV(info.Inflation / 12, -npv, info.Tenure))}**, you’ve essentially driven it for free! 😉","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":240,"value":"---\n\n---\n\n---\n\n---\n\n---\n\n---\n\n---\n\n---\n\n_Data_","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":30,"value":"info = {\n const raw = {\n Tenure: 44,\n Ex_showroom: 12_99_000,\n Road_tax_registration: 2_47_688,\n Insurance: 72_502,\n TCS: 9_743,\n Monthly_lease_rental: 31_022,\n Employer_rental: 6_746,\n RV_amount: 2_72_790,\n RV_gst: 84_565,\n RV_total: 3_57_355,\n Petrol_monthly_allowance: 6_000,\n Inflation: 0.05,\n Tax_slab: 0.3\n }\n return {\n ...raw,\n On_road_price: raw.Ex_showroom + raw.Road_tax_registration + raw.TCS + raw.Insurance,\n //Employee_effective_interest_rate: f.IRR(-raw.Ex_showroom, ...d3.range(raw.Tenure).fill(raw.Monthly_lease_rental)) * 12 / 100,\n //Fleet_Mgmt_interest_rate: f.IRR(-raw.Ex_showroom, ...d3.range(raw.Tenure).fill(raw.Monthly_lease_rental + raw.Employer_rental)) * 12 / 100,\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":116,"value":"npv = {\n const monthly_cashflow =\n -info.Monthly_lease_rental // EMI\n + (info.Tax_slab) * info.Monthly_lease_rental // Tax saving on EMI\n + (1 - info.Tax_slab) * info.Petrol_monthly_allowance // Petrol allowance post tax\n \n return f.NPV(\n info.Inflation * 100/12, // Discount rate\n ...d3.range(info.Tenure - 1).map(() => monthly_cashflow), // From month 1 to n - 1\n monthly_cashflow - info.RV_total) // Last month includes residual value\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"function labelise(str) {\n return str.replace(/_/g, ' ')\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"format = {\n const { format } = Intl.NumberFormat('en-in', { style: 'currency', currency: 'INR', maximumFractionDigits: 0 });\n return format\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"$3d","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3e","stdlib":"1"}} 33:null