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1、 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Time Value of MoneyFuture Value Present Value Annuities Rates of Return AmortizationChapter 55-1 2013 Cengage Learning. All Rights Reserved. May not
2、 be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Time LinesShow the timing of cash flows. Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.5-2
3、CF0CF1CF3CF20123 I% 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Drawing Time Lines5-31001001000123I%3-year $100 ordinary annuity100012I%$100 lump sum due in 2 years 2013 Cengage Learning. All R
4、ights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Drawing Time Lines5-4100 50 750123 I%-50Uneven cash flow stream 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly ac
5、cessible website, in whole or in part.What is the future value (FV) of an initial $100 after 3 years, if I/YR = 10%?Finding the FV of a cash flow or series of cash flows is called compounding. FV can be solved by using the step-by-step, financial calculator, and spreadsheet methods.5-5FV = ?0123 10%
6、100 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for FV: The Step-by-Step and Formula MethodsAfter 1 year: FV1= PV(1 + I) = $100(1.10) = $110.00 After 2 years: FV2= PV(1 + I)2 = $100(1.1
7、0)2 = $121.00 After 3 years: FV3= PV(1 + I)3 = $100(1.10)3 = $133.10 After N years (general case): FVN= PV(1 + I)N5-6 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for FV: Calculator and
8、Excel MethodsSolves the general FV equation. Requires 4 inputs into calculator, and will solve for the fifth. (Set to P/YR = 1 and END mode.)Excel: =FV(rate,nper,pmt,pv,type)5-7INPUTSOUTPUTNI/YRPMTPVFV3010-100133.10 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicate
9、d, or posted to a publicly accessible website, in whole or in part.What is the present value (PV) of $100 due in 3 years, if I/YR = 10%?Finding the PV of a cash flow or series of cash flows is called discounting (the reverse of compounding). The PV shows the value of cash flows in terms of todays pu
10、rchasing power.5-8PV = ?1000123 10% 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for PV: The Formula MethodSolve the general FV equation for PV:PV= FVN /(1 + I)NPV= FV3 /(1 + I)3= $100/(
11、1.10)3= $75.135-9 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for PV: Calculator and Excel MethodsSolves the general FV equation for PV. Exactly like solving for FV, except we have diff
12、erent input information and are solving for a different variable.Excel: =PV(rate,nper,pmt,fv,type)5-10100INPUTSOUTPUTNI/YRPMTPVFV3010-75.13100 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solvin
13、g for I: What annual interest rate would cause $100 to grow to $125.97 in 3 years?Solves the general FV equation for I/YR. Hard to solve without a financial calculator or spreadsheet.Excel: =RATE(nper,pmt,pv,fv,type,guess)5-11INPUTSOUTPUTNI/YRPMTPVFV308-100125.97 2013 Cengage Learning. All Rights Re
14、served. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for N: If sales grow at 20% per year, how long before sales double?Solves the general FV equation for N. Hard to solve without a financial calculator or spreadsheet.EXCEL: =NPER
15、(rate,pmt,pv,fv,type)5-12INPUTSOUTPUTNI/YRPMTPVFV3.8020-12 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.What is the difference between an ordinary annuity and an annuity due?5-13Ordinary Annuity
16、PMTPMTPMT0123I%PMTPMT0123I%PMTAnnuity Due 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.Solving for FV: 3-Year Ordinary Annuity of $100 at 10%$100 payments occur at the end of each period, but there is no PV.Excel: =FV(rate,nper,pmt,pv,type)Here type = 0.5-14INPUTSOUTPUTNI/YRPMTPVFV3-100100331 2013 Cengage Learning. All Rights Reserv
