2. ®1999 South-Western College Publishing 1 Chapter 5 Calculating Rates Of Return

3. ®1999 South-Western College Publishing 2 Using Rates Of Return UsesUses –Comparing investments in different assets –Measuring historical performance –Determining future investment –Estimating the cost of capital Percentage Figures Standard PracticePercentage Figures Standard Practice Dollar Amount MeaninglessDollar Amount Meaningless

4. ®1999 South-Western College Publishing 3 Measuring Historical Performance Ex-Post Rates of ReturnEx-Post Rates of Return –Realized rates of return Ex-Ante Rates of ReturnEx-Ante Rates of Return –Expected rates of return Requires Knowledge of RiskRequires Knowledge of Risk –Risk-return relationship

5. ®1999 South-Western College Publishing 4 Determining Future Investment EstimateEstimate –Future return –Future fluctuations of returns Historical AveragesHistorical Averages –Give best estimate of future returns –Estimate future fluctuations of returns Next Year’s ReturnsNext Year’s Returns –May be dramatically different

6. ®1999 South-Western College Publishing 5 Estimating Cost Of Capital Rates of ReturnRates of Return –Used to estimate the firm’s cost of capital –NPV calculations Utilizing historical rates of returnUtilizing historical rates of return –Calculated in more than one way

7. ®1999 South-Western College Publishing 6 Rate-Of-Return Calculations Different MethodsDifferent Methods –Yield different results Could Use Method Giving Best ResultCould Use Method Giving Best Result –Lack of standard would affect comparability AIMRAIMR –Association of Investment Management and Research –Established strict guidelines

8. ®1999 South-Western College Publishing 7 Simple Rates Of Return HPRHPR –Holding period return EMV - BMV + I EMV - BMV + I R = R = BMV BMV –Limitations (does not account for) Timing of cash dividendsTiming of cash dividends Accrued interestAccrued interest

9. ®1999 South-Western College Publishing 8 Capital gain or loss Capital gain or loss Rate of return components Rate of return components Cash flow yield Cash flow yield

10. ®1999 South-Western College Publishing 9 Approaches To Computing The Rate Of Return Linking MethodLinking Method –Calculate to each subperiod –Cash dividends date determines subperiod –Simple to calculate Index Method superior calculationIndex Method superior calculation –Cash flows used to purchase additional units –Useful to understanding time weighted computations

11. ®1999 South-Western College Publishing 10 Bond Returns Cash BasisCash Basis –Ignores accrued interest Accrual BasisAccrual Basis –Bond interest accrues daily –Price paid for bonds Includes accrued interestIncludes accrued interest –AIMR accepted

12. ®1999 South-Western College Publishing 11 After-Tax Rates Of Return Includes the Impact of TaxesIncludes the Impact of Taxes –Ordinary income –Capital gains EMV n - BMV n - N 0 (P n - P 0 )T g + I n (I - T) EMV n - BMV n - N 0 (P n - P 0 )T g + I n (I - T) Rn = Rn = Rn = Rn = BMV n BMV n

13. ®1999 South-Western College Publishing 12 Inflation-Adjusted Rates Of Return Reduction of Purchasing PowerReduction of Purchasing Power Inflation Measured By CPIInflation Measured By CPI –Consumer Price Index Real Rate of ReturnReal Rate of Return CPI 1 - CPI 0 CPI 1 - CPI 0 h = h = CPI 0 CPI 0

14. ®1999 South-Western College Publishing 13 Exchange Rates Falling DollarFalling Dollar –Good for U. S. investors in foreign countries –Bad for foreign investors in U. S. –U. S. industry more competitive –Foreign securities become more valuable –Foreigners shy away from U. S. markets

15. ®1999 South-Western College Publishing 14 Rate Of Return Adjusted For Foreign Exchange Risk fx n (DC / FC) fx n (DC / FC) R D = (1 + R L ) - 1 R D = (1 + R L ) - 1 fx 0 (DC / FC) fx 0 (DC / FC) Alternative Method R D = (1 + R fx ) (1 + R L ) - 1 R D = (1 + R fx ) (1 + R L ) - 1

16. ®1999 South-Western College Publishing 15 Average Rate Of Return Measuring Returns Across YearsMeasuring Returns Across Years Arithmetic AverageArithmetic Average –Adds the realized rate of return over different periods –Correct for one period of time –Unbiased estimate of future expected rates of return Geometric MethodGeometric Method –Compounds rates of return –Measures actual growth of assets

17. ®1999 South-Western College Publishing 16 Adjusted Rate Of Return Accounts for the Timing of Cash DividendsAccounts for the Timing of Cash Dividends Called Time-Weighted Rate of ReturnCalled Time-Weighted Rate of Return Called Rate of Return in Rest of TextbookCalled Rate of Return in Rest of Textbook AIRM ApprovedAIRM Approved

18. ®1999 South-Western College Publishing 17 Importance Of Indexes Stock IndexesStock Indexes –Measure the general performance of an economy Benchmark For Gauging PerformanceBenchmark For Gauging Performance –Money manager –Bond fund manager Serves as a Guide for Mutual Fund PerformanceServes as a Guide for Mutual Fund Performance Assess Overall Direction of the MarketAssess Overall Direction of the Market Estimates Statistical Parameters BetaEstimates Statistical Parameters Beta Used as Underlying Securities in DerivativesUsed as Underlying Securities in Derivatives

19. ®1999 South-Western College Publishing 18 Indexes Differ By Which and How Many SecuritiesBy Which and How Many Securities By How the Index is Adjusted for ChangeBy How the Index is Adjusted for Change By Method Used to Adjust IndexBy Method Used to Adjust Index

20. ®1999 South-Western College Publishing 19 Types Of Indexes Price-Weighted IndexPrice-Weighted Index Value-Weighted IndexValue-Weighted Index Equally Weighted IndexEqually Weighted Index

21. ®1999 South-Western College Publishing 20 Price-Weighted Index ValueValue –Found by adding the prices of each security and dividing by a divisor DivisorDivisor –Adjusted for stock dividends and splits and other changes Easy to MimicEasy to Mimic

22. ®1999 South-Western College Publishing 21 Value-Weighted Indexes ValueValue –Based on the total market value of a security Market CapitalizationMarket Capitalization –The greater the market capitalization the greater the securities influence Not affected by stock dividends or splitsNot affected by stock dividends or splits

23. ®1999 South-Western College Publishing 22 Equally Weighted Index ValueValue –Give each security the same weight Arithmetic MethodArithmetic Method Results in higher values than geometricResults in higher values than geometric Multiplicative MethodMultiplicative Method –Geometric

24. ®1999 South-Western College Publishing 23 Bond Indexes Track Different Segments of Bond MarketTrack Different Segments of Bond Market Incorporate Total Returns (1970’s)Incorporate Total Returns (1970’s) Prior Indexes Ignored Coupon PaymentsPrior Indexes Ignored Coupon Payments Bonds Change BecauseBonds Change Because –Of finite maturity change risk –Call features Pricing Problems Due to Lack of TradingPricing Problems Due to Lack of Trading

25. ®1999 South-Western College Publishing 24 Differences In Bond Indexes Weighting MethodsWeighting Methods Reinvest of Intramonth Cash FlowsReinvest of Intramonth Cash Flows Maturity Structure of IndexMaturity Structure of Index

26. ®1999 South-Western College Publishing 25 Stock Indexes Most are Value-WeightedMost are Value-Weighted –Automatically adjusting for stock splits –Weight based on market capitalization Easy to Develop and MaintainEasy to Develop and Maintain

27. ®1999 South-Western College Publishing 26 Tracking Rates Of Return Over Time Common Stock is More Volatile than BondsCommon Stock is More Volatile than Bonds Common Stock Offers Higher Return than BondsCommon Stock Offers Higher Return than Bonds Positive Relationship Between Risk and ReturnPositive Relationship Between Risk and Return