Chapter 4 - Topics CoveredFuture ValuesSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Future Values with CompoundingManhattan Island SalePresent ValuesSlide 12Slide 13Slide 14Time Value of Money (applications)Present Values with CompoundingSlide 17PV of Multiple Cash FlowsSlide 19Slide 20Perpetuities & AnnuitiesSlide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29InflationSlide 31Slide 32Effective Interest RatesSlide 34Slide 35Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 1Chapter 4 - Topics CoveredFuture Values and Compound InterestPresent ValuesMultiple Cash FlowsLevel Cash Flows Perpetuities and AnnuitiesInflation & Time ValueEffective Annual Interest RateCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 2Future ValuesFuture Value - Amount to which an investment will grow after earning interest.Compound Interest - Interest earned on interest.Simple Interest - Interest earned only on the original investment.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 3Future ValuesExample - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.Interest Earned Per Year = 100 x .06 = $ 6Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 4Example - Simple InterestInterest earned at a rate of 6% for five years on a principal balance of $100.Today Future Years 1 2 3 4 5Interest EarnedValue 100Future Values61066112611861246130Value at the end of Year 5 = $130Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 5Future ValuesExample - Compound InterestInterest earned at a rate of 6% for five years on the previous year’s balance.Interest Earned Per Year =Prior Year Balance x .06Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 6Example - Compound InterestInterest earned at a rate of 6% for five years on the previous year’s balance.Today Future Years 1 2 3 4 5Interest EarnedValue 100Future Values61066.36112.366.74119.107.15126.257.57133.82Value at the end of Year 5 = $133.82Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 7Future ValuesFuture Value of $100 = FVFV rt $100 ( )1Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 8Future ValuesFV rt $100 ( )1Example - FVWhat is the future value of $100 if interest is compounded annually at a rate of 6% for five years?82.133$)06.1(100$5FVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 9Future Values with CompoundingInterest RatesCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 10Manhattan Island SalePeter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? trillionFV 57.120$)08.1(24$380To answer, determine $24 is worth in the year 2006, compounded at 8%. FYI - The value of Manhattan Island land is FYI - The value of Manhattan Island land is well below this figure.well below this figure.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 11Present ValuesPresent ValueValue today of a future cash flow.Discount RateInterest rate used to compute present values of future cash flows.Discount FactorPresent value of a $1 future payment.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 12Present ValuesPresent Value = PVPV =Future Value after t periods (1+r)tCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 13Present ValuesExampleYou just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?572,2$2)08.1(3000PVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 14Present ValuesDiscount Factor = DF = PV of $1Discount Factors can be used to compute the present value of any cash flow.DFrt11( )Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 15The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable. PV FVrt 11( )Time Value of Money(applications)Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 16Present Values with CompoundingInterest RatesCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 17Value of Free CreditImplied Interest RatesInternal Rate of ReturnTime necessary to accumulate fundsTime Value of Money(applications)Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 18PV of Multiple Cash FlowsExampleYour auto dealer gives you the choice to pay $15,500 cash now, or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money is 8%, which do you prefer?$15,133.06 PVTotal36.429,370.703,38,000.0021)08.1(000,42)08.1(000,41payment ImmediatePVPVCopyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 19PV of Multiple Cash FlowsFinding the present value of multiple cash flows by using a spreadsheetTime until CFCash flowPresent value Formula in Column C0 8000 $8,000.00 =PV($B$11,A4,0,-B4)1 4000 $3,703.70 =PV($B$11,A5,0,-B5)2 4000 $3,429.36 =PV($B$11,A6,0,-B6)SUM: $15,133.06 =SUM(C4:C6)Discount rate: 0.08Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 20PV of Multiple Cash FlowsPVs can be added together to evaluate multiple cash flows.PVCrCr 11221 1( ) ( )....Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 21Perpetuities & AnnuitiesPerpetuity A stream of level cash payments that never ends.Annuity Equally spaced level stream of cash flows for a limited period of time.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin4- 22Perpetuities & AnnuitiesPV of Perpetuity FormulaC = cash payment r = interest rate PVCrCopyright © 2007 by The
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