Chapter 5 Calculating Rates Of Return 31220211999 SouthWestern

Chapter 5 Calculating Rates Of Return ® 3/12/20211999 South-Western College Publishing 1

Using Rates Of Return • Uses – Comparing investments in different assets – Measuring historical performance – Determining future investment – Estimating the cost of capital • Percentage Figures Standard Practice • Dollar Amount Meaningless ® 3/12/20211999 South-Western College Publishing 2

Measuring Historical Performance • Ex-Post Rates of Return – Realized rates of return • Ex-Ante Rates of Return – Expected rates of return • Requires Knowledge of Risk – Risk-return relationship ® 3/12/20211999 South-Western College Publishing 3

Determining Future Investment • Estimate – Future return – Future fluctuations of returns • Historical Averages – Give best estimate of future returns – Estimate future fluctuations of returns • Next Year’s Returns – May be dramatically different ® 3/12/20211999 South-Western College Publishing 4

Estimating Cost Of Capital • Rates of Return – Used to estimate the firm’s cost of capital – NPV calculations • Utilizing historical rates of return – Calculated in more than one way ® 3/12/20211999 South-Western College Publishing 5

Rate-Of-Return Calculations • Different Methods – Yield different results • Could Use Method Giving Best Result – Lack of standard would affect comparability • AIMR – Association of Investment Management and Research – Established strict guidelines ® 3/12/20211999 South-Western College Publishing 6

Simple Rates Of Return • HPR – Holding period return EMV - BMV + I R= BMV – Limitations (does not account for) • Timing of cash dividends • Accrued interest ® 3/12/20211999 South-Western College Publishing 7

Capital gain or loss Rate of return components Cash flow yield ® 3/12/20211999 South-Western College Publishing 8

Approaches To Computing The Rate Of Return • Linking Method – Calculate to each subperiod – Cash dividends date determines subperiod – Simple to calculate • Index Method superior calculation – Cash flows used to purchase additional units – Useful to understanding time weighted computations ® 3/12/20211999 South-Western College Publishing 9

Bond Returns • Cash Basis – Ignores accrued interest • Accrual Basis – Bond interest accrues daily – Price paid for bonds • Includes accrued interest – AIMR accepted ® 3/12/20211999 South-Western College Publishing 10

After-Tax Rates Of Return • Includes the Impact of Taxes – Ordinary income – Capital gains Rn = EMVn - BMVn - N 0(Pn - P 0)Tg+ In(I - T) ® 3/12/20211999 South-Western College Publishing BMVn 11

Inflation-Adjusted Rates Of Return • Reduction of Purchasing Power • Inflation Measured By CPI – Consumer Price Index • Real Rate of Return CPI 1 - CPI 0 h= CPI 0 ® 3/12/20211999 South-Western College Publishing 12

Exchange Rates • Falling Dollar – Good for U. S. investors in foreign countries – Bad foreign investors in U. S. – U. S. industry more competitive – Foreign securities become more valuable – Foreigners shy away from U. S. markets ® 3/12/20211999 South-Western College Publishing 13

Rate Of Return Adjusted Foreign Exchange Risk RD = fxn (DC / FC) fx 0 (DC / FC) (1 + RL) - 1 Alternative Method RD = (1 + Rfx) (1 + RL) - 1 ® 3/12/20211999 South-Western College Publishing 14

Average Rate Of Return • • Measuring Returns Across Years Arithmetic 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 Method – Compounds rates of return – Measures actual growth of assets ® 3/12/20211999 South-Western College Publishing 15

Adjusted Rate Of Return • Accounts for the Timing of Cash Dividends • Called Time-Weighted Rate of Return • Called Rate of Return in Rest of Textbook • AIMR Approved ® 3/12/20211999 South-Western College Publishing 16

Importance Of Indexes • Stock Indexes – Measure the general performance of an economy • Benchmark For Gauging Performance – Money manager – Bond fund manager • Serves as a Guide for Mutual Fund Performance • Assess Overall Direction of the Market • Estimates Statistical Parameters Beta • Used as Underlying Securities in Derivatives ® 3/12/20211999 South-Western College Publishing 17

Indexes Differ • By Which and How Many Securities • By How the Index is Adjusted for Change • By Method Used to Adjust Index ® 3/12/20211999 South-Western College Publishing 18

Types Of Indexes • Price-Weighted Index • Value-Weighted Index • Equally Weighted Index ® 3/12/20211999 South-Western College Publishing 19

Price-Weighted Index • Value – Found by adding the prices of each security and dividing by a divisor • Divisor – Adjusted for stock dividends and splits and other changes • Easy to Mimic ® 3/12/20211999 South-Western College Publishing 20

Value-Weighted Indexes • Value – Based on the total market value of a security • Market Capitalization – The greater the market capitalization the greater the securities influence • Not affected by stock dividends or splits ® 3/12/20211999 South-Western College Publishing 21

Equally Weighted Index • Value – Give each security the same weight • Arithmetic Method • Results in higher values than geometric • Multiplicative Method – Geometric ® 3/12/20211999 South-Western College Publishing 22

Stock Indexes • Most are Value-Weighted – Automatically adjusting for stock splits – Weight based on market capitalization • Easy to Develop and Maintain ® 3/12/20211999 South-Western College Publishing 23

Bond Indexes • • Track Different Segments of Bond Market Incorporate Total Returns (1970’s) Prior Indexes Ignored Coupon Payments Bonds Change Because – Of finite maturity change risk – Call features • Pricing Problems Due to Lack of Trading ® 3/12/20211999 South-Western College Publishing 24

Differences In Bond Indexes • Weighting Methods • Reinvest of Intramonth Cash Flows • Maturity Structure of Index ® 3/12/20211999 South-Western College Publishing 25

Tracking Rates Of Return Over Time • Common Stock is More Volatile than Bonds • Common Stock Offers Higher Return than Bonds • Positive Relationship Between Risk and Return ® 3/12/20211999 South-Western College Publishing 26