【正文】 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: 1 100 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 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 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 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 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 90 chapter 9 Risk and rates of return 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 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 84 period CF PV (CF) 0 10,000 10, 1 2,000 1, 2 4,000 3, 3 6,000 4, 4 7,000 4, PV of Cash Flow Stream: $ 4, 0 1 2 3 4 10,000 2,000 4,000 6,000 7,000 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 82 ?Is this an annuity? ?How do we find the PV of a cash flow stream when all of the cash flows are different? (Use a 10% discount rate). Uneven Cash Flows 0 1 2 3 4 10,000 2,000 4,000 6,000 7,000 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 80 0 1 2 3 1000 1000 1000 Present Value annuity due What is the PV of $1,000 at the beginning of each of the next 3 years, if your opportunity cost is 8%? Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 78 0 1 2 3 1000 1000 1000 Future Value annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? ? Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 76 Earlier, we examined this “ordinary” annuity: Using an interest rate of 8%, we find that: ?The Future Value (at 3) is $3,. ?The Present Value (at 0) is $2,. 0 1 2 3 1000 1000 1000 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 74 Other Cash Flow Patterns 0 1 2 3 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 72 What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment? PMT i PV = = $10,000 = $125,000 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 70 1 1 (1 + i) n i When n gets very large, 1 we’re left with PVIFA = i Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 68 Present Value of a Perpetuity ?When we find the PV of an annuity, we think of the following relationship: PV = PMT (PVIFA i, n ) Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 66 Interpolation within financial tables: finding missing table values ? Example 1: – PV=1000(%,6) ? Example 2: – 1000=100(PVIFA?%,12 months) Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 64 Mathematical Solution: PV = PMT (PVIFA i, n ) PV = 1,000 (PVIFA .08, 3 ) (use PVIFA table, or) 1 PV = PMT 1 (1 + i)n i 1 PV = 1000 1 ( )3 = $2, .08 Copyright 169