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BU FIN 311 - Calculating Annuities and Cash Flows
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FIN 311 1st Edition Lecture 9Outline of Last Lecture I. Compute (Implied) Discount Rate ContinuedII. Time Value of Money ContinuedIII. Future Value of an Annuity, FVAIV. Annuity DueOutline of Current LectureI. Ordinary AnnuityII. Deferred AnnuityIII. PerpetuitiesIV. Uneven Cash FlowsV. Computing PeriodsCurrent LectureI. Ordinary Annuity- First cash flow occurs at the end of period 1. - Finite cash flows- PVA valuing the cash flow stream exactly 1 period prior to the cash flow- PV Annuity Due = PV Ordinary Annuity (1 + r)1- FV Annuity Due = FV Ordinary Annuity (1 + r)11. Use BGN mode on calculator2. Set type = 1 in ExcelAlternatively:10 10 10 10 10 00 1 2 3 4 5Value 4 year ordinary annuity + $10 todayPMT = 10N =4R = 5%FV = 0PV = ?? PV = 35.46These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.II. Deferred Annuity- First cash flow occurs later than t=1- Remember how the TVM formulas are derived- PVA: Finds values of annuity exactly one period prior to the first cash flow- FVA: Finds value of annuity exactly at the time the last cash flow occursExample:0 0 0 5000 5000 5000 50001 2 3 4 5 6 7R = 12%PMT = 5000 End of period 4, beginning of period 5FV = 0N = 4PV = ?? PV = 15,186.75Then…FV = 15,186.75R = 12PMT= 0N = 4PV = ?? PV = 10,809.63Example:0 0 0 0 [12000 12000 12000 12000 12000 12000 12000] 01 2 3 4 5 6 7 8 9 10 11 121. N = 7PMT = 12000 For 7 periods I get $12,000 R = 8%FV = 0PV ?? PV = 62,476.44 @ t = 42. FV = 62,476.44N = 4 PMT = 0R = 8%PV =?? PV = 45,922.05 @ t = 0III. Perpetuities- Infinite cash flows, some cash flows each period, forever- Example: UK issued consol bonds, Common stock is assumed to have infinite title -CF /(1+r)t(¿)PVA=∑t =1n¿ let n →∞- PV Perpetuity = CF/r- Compute PV of this perpetuity estimating Vo, intrinsic value what we believe the asset is worth, using a valuation model- Example: Vo= CF/r = 175/.063 = $2,777.78 Decision compare Vo and Po  If V0 is greater than P0, buy or invest Yes, buy this consul bond it cost less than it is worth IV. Uneven Cash FlowsExample:50 0 10 150 1 2 3 4Compute PV of each separately and add upPV = 50/(1.08)1 + 0/(1.08)2 + 10/(1.08)3 + 15/(1.08)4 = 46.296 + 0 + 7.938 + 11.025 = 65.26Financial Calculator hit CF button, enter Frequencies (50, 0, 10, 15), press I/Y, enternumber then hit = NPV(.08, 50, 0, 10, 15) Example: 6350 7280 84701 2 3PMT = 0N =3R = 8%FV= ?? PV=18,844.82FV= 23,739.05V. Computing Periods- The more frequent an interest is compounded, the more money you can make.- Cash flows occurred annually - Interest was compounded annually - Savers prefer more frequent


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BU FIN 311 - Calculating Annuities and Cash Flows

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