The Time Value of Money

Chapter 7The Time Value of MoneyCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedChapter OverviewTime Value of Money ConceptMarket Value ConceptTime Value of Money CalculationsFuture ValuePresent ValueTime Period and CompoundingLoan AmortizationCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedTime Value of Money ConceptTime Value of Money (TVM)Based on face value and interest that can be earnedPresent Value (PV)Current value of an asset based on the amount and timing of projected cash flowsFuture ValueValue of an asset some time in the future assuming a compounded rate of interestCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedMarket Value ConceptPresent value of an asset based onProjected future cash flowsFactoring in theTiming of the cash flowRisk of the cash flow being generatedMix of capital used to finance the dealCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedCalculating TVMCalculations can be done utilizingComplicated mathematical formulasShorter formulas using interest tablesBusiness calculatorComputer spreadsheetsCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedIntroduction to theBusiness CalculatorFive basic function keysN = number of yearsI/Y = interest or discount ratePV = present valuePMT = annuity paymentFV = future valueCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedIntroduction to theBusiness CalculatorSet the calculator to four decimal places.Steps to follow:Press the “2nd” key and the “.” keyThe calculator will display DEC = 2.00Now enter “4” and press “ENTER”Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedIntroduction to theBusiness CalculatorSet the calculator to annual compounding.Steps to follow:Press 2nd and I/Y.For new calculators, the factory setting will display P/Y = 12. Press the “1” key and the ENTER key which is on the top row of the calculator.The display will show P/Y = 1.00 To exit, press 2nd and CPT (QUIT)Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedSingle SumOnly a single sum of money is involved in the calculation Future Value of a Single Sum |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years $1,000 at 12% interest FV =?Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedSingle Sum Present Value of a Single Sum |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years PV =? $1,762.34 at 12% interestCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedSingle SumThe following items must be known in order to calculate:Future ValuePVNI/YCPT FVPresent ValueFVNI/YCPT PVCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedAnnuityAmount of money received or paid during each compounding period for a set timeRegular AnnuityMoney is received or paid at the end of each compounding periodAnnuity DueMoney is received or paid at the beginning of each compounding periodCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedRegular Annuity Calculations |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 600 600 600 600 600 at 12% interest PMT = $600 N = 5 I/Y = 12% CPT FV = $3,811.71 CPT PV = $2,162.88Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedAnnuity Due Calculations |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 600 600 600 600 600 at 12% interest PMT = $600N = 5I/Y = 12%CPT FV = $4,269.11CPT PV = $2,422.41Change calculator to Annuity Due modeSteps to follow: [2nd][PMT] If display shows the word END, enter: [2nd][ENTER] [2nd][CPT]Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedPerpetuitySpecial type of annuity that pays or receives cash with no time limit PV perpetuity = PMT / r, where PMT = annuity payment r = interest rateCopyright © 2007 by John Wiley & Sons, Inc. All rights reservedUneven Stream of Cash FlowWhere payments are not the same in all compounding periods Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedUneven Stream of Cash Flow |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 50 100 300 305 320 at 10% interestUtilize [CF] button and enter:CF0 = 0CF1 = 50CF2 = 100CF3 = 300CF4 = 305CF5 = 320Now enter [CPT][NPV]I/Y = 10CPT NPV = $760.5075Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedCompounding PeriodMonthly compounding favors the lenderInterest expense is being accrued or paid monthly Annual CompoundingFV = $1,762.34N = 5I/Y = 12%CPT PV = $1,000.00Monthly CompoundingFV = $1,762.34N = 5 X 12 = 60I/Y = 12% / 12 = 1%CPT PV = $970.08Copyright © 2007 by John Wiley & Sons, Inc. All rights reservedLoan Amortization ScheduleYear Payment Principal Interest Balance 1 40,211.48 30,211.48 10,000.00 69,788.52 2 40,211.48 33,232.63 6,978.85 36,555.89 3 40,211.48 36,555.89 3,655.59 0.00 Total 120,634.44 100,000.00 20,634.44Steps in developing a Loan Amortization ScheduleStep 1 - Calculate debt serviceStep 2 - Calculate the interest amountStep 3 - Calculate principal paidStep 4 - Calculate the balanceCopyright © 2007 by John Wiley & Sons, Inc. All rights reserved