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10066CalculatorsDiscounted Cash Flow ValuationDiscounted Cash Flow Valuation11Key Concepts and SkillsKey Concepts and Skills¾¾Be able to compute the future value of multiple Be able to compute the future value of multiple cash flowscash flows¾¾Be able to compute the present value of multiple Be able to compute the present value of multiple cash flowscash flows¾¾Be able to compute loan paymentsBe able to compute loan payments¾¾Be able to find the interest rate on a loanBe able to find the interest rate on a loan¾¾Understand how interest rates are quotedUnderstand how interest rates are quoted¾¾Understand how loans are amortized or paid offUnderstand how loans are amortized or paid off22Chapter OutlineChapter Outline¾¾Future and Present Values of Multiple Future and Present Values of Multiple Cash FlowsCash Flows¾¾Valuing Level Cash Flows: Annuities and Valuing Level Cash Flows: Annuities and PerpetuitiesPerpetuities¾¾Comparing Rates: The Effect of Comparing Rates: The Effect of CompoundingCompounding¾¾Loan Types and Loan AmortizationLoan Types and Loan Amortization33Annuities and Perpetuities Annuities and Perpetuities DefinedDefined¾¾Annuity Annuity ––finite series of equal payments that finite series of equal payments that occur at regular intervalsoccur at regular intervalszzIf the first payment occurs at the end of the period, it If the first payment occurs at the end of the period, it is called an ordinary annuityis called an ordinary annuityzzIf the first payment occurs at the beginning of the If the first payment occurs at the beginning of the period, it is called an annuity dueperiod, it is called an annuity due¾¾Perpetuity Perpetuity ––infinite series of equal paymentsinfinite series of equal payments44Annuities and Perpetuities Annuities and Perpetuities ––Basic FormulasBasic Formulas¾¾Perpetuity: PV = C / rPerpetuity: PV = C / r¾¾Annuities:Annuities:⎥⎦⎤⎢⎣⎡−+=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡+−=rrCFVrrCPVtt1)1()1(1155Annuity DueAnnuity Due¾¾You are saving for a new house and you put $10,000 You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 made today. How much will you have at the end of 3 years?years?zz22ndndBGN 2BGN 2ndndSet (you should see BGN in the display)Set (you should see BGN in the display)zz3 N3 Nzz--10,000 PMT10,000 PMTzz8 I/Y8 I/YzzCPT FV = 35,061.12CPT FV = 35,061.12zz22ndndBGN 2BGN 2ndndSet (be sure to change it back to an ordinary Set (be sure to change it back to an ordinary annuity)annuity)266Table 6.2Table 6.277Effective Annual Rate (EAR)Effective Annual Rate (EAR)¾¾This is the actual rate paid (or received) after This is the actual rate paid (or received) after accounting for compounding that occurs during accounting for compounding that occurs during the yearthe year¾¾If you want to compare two alternative If you want to compare two alternative investments with different compounding periods investments with different compounding periods you need to compute the EAR and use that for you need to compute the EAR and use that for comparison.comparison.88Annual Percentage RateAnnual Percentage Rate¾¾This is the annual rate that is quoted by lawThis is the annual rate that is quoted by law¾¾By definition APR = period rate times the By definition APR = period rate times the number of periods per yearnumber of periods per year¾¾Consequently, to get the period rate we Consequently, to get the period rate we rearrange the APR equation:rearrange the APR equation:zzPeriod rate = APR / number of periods per yearPeriod rate = APR / number of periods per year¾¾You should NEVER divide the effective rate by You should NEVER divide the effective rate by the number of periods per year the number of periods per year ––it will NOT it will NOT give you the period rategive you the period rate99Computing APRsComputing APRs¾¾What is the APR if the monthly rate is .5%?What is the APR if the monthly rate is .5%?zz.5(12) = 6%.5(12) = 6%¾¾What is the APR if the semiannual rate is .5%?What is the APR if the semiannual rate is .5%?zz.5(2) = 1%.5(2) = 1%¾¾What is the monthly rate if the APR is 12% with What is the monthly rate if the APR is 12% with monthly compounding?monthly compounding?zz12 / 12 = 1%12 / 12 = 1%1010Things to RememberThings to Remember¾¾You ALWAYS need to make sure that the interest rate You ALWAYS need to make sure that the interest rate and the time period match.and the time period match.zzIf you are looking at annual periods, you need an annual If you are looking at annual periods, you need an annual rate.rate.zzIf you are looking at monthly periods, you need a monthly If you are looking at monthly periods, you need a monthly rate.rate.¾¾If you have an APR based on monthly compounding, If you have an APR based on monthly compounding, you have to use monthly periods for lump sums, or you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have adjust the interest rate appropriately if you have payments other than monthlypayments other than monthly1111¾¾Draw a Time LineDraw a Time Line¾¾Begin with the End in MindBegin with the End in Mind¾¾Watch the Signs of the Cash FlowsWatch the Signs of the Cash Flows¾¾The Number of Periods (N) usually equals the greater of the The Number of Periods (N) usually equals the greater of the number of Cash Flows or the Number of Yearsnumber of Cash Flows or the Number of Years¾¾Always use either the Effective Annual or the Periodic Interest Always use either the Effective Annual or the Periodic Interest RateRate¾¾Recognize hidden Perpetuities, Annuities, and Annuities Due.Recognize hidden Perpetuities, Annuities, and Annuities Due.¾¾Set up the Calculator correctly and always Clear the Set up the Calculator correctly and always Clear the Calculator before starting a problem.Calculator before starting a problem.¾¾Use the course webpageUse the course webpage¾¾PracticePracticeHints on Solving Time Value of Money Problems31212Contact InformationContact Information¾¾Our course website (e.g. WEBCT or Our course website (e.g. WEBCT or Ulearn, or Blackboard)Ulearn, or Blackboard)¾¾Instant Messenger: Instant Messenger: [email protected]@hotmail.com¾¾Cell Phone: 770Cell Phone: 770--301301--86488648¾¾Office Phone:


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