【正文】 After graduation, you plan to invest $400 per month in the stock market. If you earn 12% per year on your stocks, how much will you have accumulated when you retire in 30 years? 0 1 2 3 . . . 360 400 400 400 400 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 86 Mathematical Solution: FV = PMT (FVIFA i, n ) FV = 400 (FVIFA .01, 360 ) (can’t use FVIFA table) FV = PMT (1 + i)n 1 i FV = 400 ()360 1 = $1,397, .01 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 87 House Payment Example If you borrow $100,000 at 7% fixed interest for 30 years in order to buy a house, what will be your monthly house payment? Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 88 Mathematical Solution: PV = PMT (PVIFA i, n ) 100,000 = PMT (PVIFA .005833, 360 ) (can’t use PVIFA table) 1 PV = PMT 1 (1 + i)n i 1 100,000 = PMT 1 ( )360 PMT=$ Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 89 ? Calculating Present and Future Values – for single cash flows – for an uneven stream of cash flows – for annuities and perpetuities ? For each problem identify: i, n, PMT, PV and FV Summary Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 90 chapter 9 Risk and rates of return Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 91 ? In financial markets, firms seek financing for their investments and shareholders of a pany achieve much of their wealth through share price movements. ? Involvement with financial markets is risky. ? The degree of risk varies from one financial security to another. Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 92 Important principle Return Risk Almost always true: The greater the expected return, the greater the risk Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 93 19261999： the annual rates of return in American financial market 6 0 4 0 2 0020406026 30 35 40 45 50 55 60 65 70 75 80 85 90 95C o m m o n S t o cksL o n g T B o n d sT B i l l sCopyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 94 Rates of return ? Historical return The return that an asset has already produced over a specified period of time ? Expected return The return that an asset is expected to produce over some future period of time ? Required return The return that an investor requires an asset to produce if he/she is to be a future investor in that asset Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 95 Rates of return ? Nominal The actual rate of return paid or earned without making any allowance for inflation ? Real The nominal rate of return adjusted for the effect of inflation ? Effective The nominal rate of return adjusted for more frequent calculation (or pounding) than once per annum Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 96 ? When an interest rate is quoted in financial markets it is generally expressed as a nominal rate. ? For example, if a bank advertises that it will pay interest of 5% per annum on deposits, this interest rate is most likely to be the nominal rate. ? When inflation is deducted from this nominal rate, the real rate of interest is obtained. (But this is not exactly correct!) ?To be more precise, … … Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 97 Interest rate determinants Interest Rates Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 98 Adjusting for inflation Conceptually: Nominal interest rate i = Real interest rate R + Anticipated inflation rate r Mathematically: ( 1 + i ) = ( 1 + R ) ( 1 + r ) ? i = R + r + r R Usually small and ignored Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 99 Calculating expected returns State of economy Recession Normal Boom Probability P Return A B 4% 10% 14% 10% 14% 30% Expected return is just a weighted average R* = P(R1) x R1 + P(R2) x R2 + … + P(R n) x Rn Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 100 Case study State of economy Recession Normal Boom Probability P Return A B 4% 10% 14% 10% 14% 30% Company A R* = P(R1) x R1 + P(R2) x R2 + … + P(R n) x Rn RA* = x 4% + x 10% + x 14% = 10% Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 101 Case study State of economy Recession Normal Boom Probability P Return A B 4% 10% 14% 10% 14% 30% Company B R* = P(R1) x R1 + P(R2) x R2 + … + P(R n) x Rn RB* = x 10% + x 14% + x 30% = 14% Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 102 Based only on your expected return calculations, which pany share would you prefer? Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 103 The above example illustrates that, ? Although it is extremely difficult to predict with accuracy what the return will be on an investment, what we can do is make predictions about the range of returns, the probability with which a certain return will eventuate and hence the return that we could expect to get. ? So, the expected rate of return may be defined as the weighted average of all possible outes ! C