Time Value of Money参考.ppt

* * * * * * * * * * * * * * * * * * * * * * * * * Why is it important to consider effective rates of return? See how the effective return varies between investments with the same nominal rate, but different compounding intervals. EARANNUAL 10.00% EARSEMIANNUALLY 10.25% EARQUARTERLY 10.38% EARMONTHLY 10.47% EARDAILY (365) 10.52% 5-* When is each rate used? INOM: Written into contracts, quoted by banks and brokers. Not used in calculations or shown on time lines. IPER: Used in calculations and shown on time lines. If M = 1, INOM = IPER = EAR. EAR: Used to compare returns on investments with different payments per year. Used in calculations when annuity payments don’t match compounding periods. 5-* What is the FV of $100 after 3 years under 10% semiannual compounding? Quarterly compounding? 5-* Can the effective rate ever be equal to the nominal rate? Yes, but only if annual compounding is used, i.e., if M = 1. If M 1, EFF% will always be greater than the nominal rate. 5-* What’s the FV of a 3-year $100 annuity, if the quoted interest rate is 10%, compounded semiannually? Payments occur annually, but compounding occurs every 6 months. Cannot use normal annuity valuation techniques. 5-* 0 1 100 2 3 5% 4 5 100 100 6 Method 1:Compound Each Cash Flow 5-* FV3 = $100(1.05)4 + $100(1.05)2 + $100 FV3 = $331.80 110.25 121.55 331.80 0 1 100 2 3 5% 4 5 100 6 100 Method 2:Financial Calculator or Excel Find the EAR and treat as an annuity. EAR = (1 + 0.10/2)2 – 1 = 10.25%. Excel: =FV(.1025,3,-100,0,0) 5-* INPUTS OUTPUT N I/YR PMT PV FV 3 -100 10.25 0 331.80 Find the PV of This 3-Year Ordinary Annuity Could solve by discounting each cash flow, or… Use the EAR and treat as an annuity to solve for PV. Excel: =PV(.1025,3,100,0,0) 5-* INPUTS OUTPUT N I/YR PMT PV FV 3 100 10.25 -247.59 0 Loan Amortization Amortization tables are widely used for home mortgages, auto loans, business loans, retirement plans, etc. Financial calculators and spreadsheets are grea