【文章內(nèi)容簡介】 n relative inflation will lead to changes in exchange rates.? An increase in country risk will also cause that country’s currency to fall.? Future value? Present value? Rates of return? AmortizationChapter 2Time Value of MoneyTime lines show timing of cash flows.CF0 CF1 CF3CF20 1 2 3i%Tick marks at ends of periods, so Time 0 is today。 Time 1 is the end of Period 1。 or the beginning of Period 2.Time line for a $100 lump sum due at the end of Year 2.1000 1 2 Yeari%Time line for an ordinary annuity of $100 for 3 years.100 1001000 1 2 3i%Time line for uneven CFs: $50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3.100 50 750 1 2 3i%50What’s the FV of an initial $100 after 3 years if i = 10%?FV = ?0 1 2 310%Finding FVs (moving to the righton a time line) is called pounding.100After 1 year:FV1 = PV + INT1 = PV + PV (i)= PV(1 + i)= $100() = $.After 2 years:FV2 = FV1(1+i) = PV(1 + i)(1+i)= PV(1+i)2= $100()2= $.After 3 years:FV3 = FV2(1+i)=PV(1 + i)2(1+i)= PV(1+i)3= $100()3= $.In general,FVn = PV(1 + i)n.Three Ways to Find FVs? Solve the equation with a regular calculator.? Use a financial calculator.? Use a spreadsheet.Financial calculator: HP17BII? Adjust display contrast: hold down CLR and push + or .? Choose algebra mode: Hold down orange key (., the shift key), hit MODES (the shifted DSP key), and select ALG.? Set number of decimal places to display: Hit DSP key, select FIX, then input desired decimal places (., 3).HP17BII (Continued)? Set decimal mode: Hit DSP key, select the “.” instead of the “,”. Note: many nonUS countries reverse the US use of decimals and mas when writing a number.HP17BII: Set Time Value Parameters? Hit EXIT until you get the menu starting with FIN. Select FIN.? Select TVM.? Select OTHER.? Select P/YR. Input 1 (for 1 payment per year).? Select END (for cash flows occuring at the end of the year.) Financial calculators solve this equation:There are 4 variables. If 3 are known, the calculator will solve for the 4th.Financial Calculator Solution3 10 100 0N I/YR PV PMT FV Here’s the setup to find FV:Clearing automatically sets everything to 0, but for safety enter PMT = 0.Set:P/YR = 1, END.INPUTSOUTPUTSpreadsheet Solution? Use the FV function: see spreadsheet in Ch 02 Mini .– = FV(Rate, Nper, Pmt, PV)– = FV(, 3, 0, 100) = 10%What’s the PV of $100 due in 3 years if i = 10%?Finding PVs is discounting, and it’s the reverse of pounding.1000 1 2 3PV = ?Solve FVn = PV(1 + i )n for PV:? ?PV = $100 = $ = $.??????3Financial Calculator Solution3 10 0 100N I/YR PV PMT FV Either PV or FV must be negative. HerePV = . Put in $ today, take out $100 after 3 years.INPUTSOUTPUTSpreadsheet Solution? Use the PV function: see spreadsheet.– = PV(Rate, Nper, Pmt, FV)– = PV(, 3, 0, 100) = Finding the Time to Double20%20 1 2 ?1 FV= PV(1 + i)n $2= $1(1 + )n ()n = $2/$1 = 2nLN()= LN(2) n= LN(2)/LN() n= 20 1 0 2N I/YR PV PMT FV INPUTSOUTPUTFinancial CalculatorSpreadsheet Solution? Use the NPER function: see spreadsheet. – = NPER(Rate, Pmt, PV, FV)– = NPER(, 0, 1, 2) = Finding the Interest Rate?%20 1 2 31 FV= PV(1 + i)n $2= $1(1 + i)3 (2)(1/3)= (1 + i) = (1 + i) i = = %.3 1 0 2N I/YR PV PMT FVINPUTSOUTPUTFinancial CalculatorSpreadsheet Solution? Use the RATE function: – = RATE(Nper, Pmt, PV, FV)– = RATE(3, 0, 1, 2) = Ordinary AnnuityPMT PMTPMT0 1 2 3i%PMT PMT0 1 2 3i%PMTAnnuity DueWhat’s the difference between an ordinary annuity and an annuity due?PV FVWhat’s the FV of a 3year ordinary annuity of $100 at 10%?100 1001000 1 2 310% 110 121FV = 331FV Annuity Formula? The future value of an annuity with n periods and an interest rate of i can be found with the following formula:Financial calculators solve this equation:There are 5 variables. If 4 are known, the calculator will solve for the 5th.Financial Calculator Formula for Annuities3 10 0 100 N I/YR PV PMT FVFinancial Calculator SolutionHave payments but no lump sum PV, so enter 0 for present value.INPUTSOUTPUTSpreadsheet Solution? Use the FV function: see spreadsheet.– = FV(Rate, Nper, Pmt, Pv)– = FV(, 3, 100, 0) = What’s the PV of this ordinary annuity?100 1001000 1 2 310% = PVPV Annuity Formula? The present value of an annuity with n periods and an interest rate of i can be found with the following formula:Have payments but no lump sum FV, so enter 0 for future value.3 10 100 0N I/YR PV PMT FVINPUTSOUTPUTFinancial Calculator SolutionSpreadsheet Solution? Use the PV function: see spreadsheet.– = PV(Rate, Nper, Pmt, Fv)– = PV(, 3, 100, 0) = Find the FV and PV if theannuity were an annuity due.100 1000 1 2 310%100PV and FV of Annuity Due vs. Ordinary Annuity? PV of annuity due:– = (PV of ordinary annuity) (1+i) – = () (1+ ) = ? FV of annuity due:– = (FV of ordinary annuity) (1+i)– = () (1+ ) = 3 10 100 0 N I/YR PV PMT FVSwitch from “End” to “Begin”.Then enter variables to find PVA3 = $.Then enter PV = 0 and press FV to findFV = $.INPUTSOUTPUTExcel Function for Annuities DueChange the formula to:=PV(10%,3,100,0,1)The fourth term, 0, tells the function there are no other cash flows. The fifth term tells the function that it is an annuity due. A similar function gives the future value of an annui