【正文】 ralia Pty Limited Slide: 1 60 Future Value annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3 1000 1000 1000 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 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 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 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: 1 100 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 90 chapter 9 Risk and rates of return 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 74 Other Cash Flow Patterns 0 1 2 3 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 58 Annuities –Annuity: a sequence of equal cash flows, occurring at the end of each period. 0 1 2 3 4 Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 51 ? In pounding we talked about the pound interest rate and initial investment。 2022 Pearson Education Australia Pty Limited Slide: 1 43 Future Value single sums If you deposit $100 in an account earning 6%, how much would you have in the account after 3 year? Mathematical Solution: FV3= FV2 (1+i) 1 =PV (1 + i)3 = 100 ()3 = $ 0 3 PV = 100 FV = ? Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 35 Chapter 4: Mathematics of Finance Copyright 169。 investment banking How do brokers / investment bankers help firms issue securities? Advising the firm Underwriting the issue Distributing the issue Enhancing Credibility Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 21 ? Partnership – The primary difference between a partnership and a sole proprietorship is that the partnership has more than one owner. – Each partner is jointly and severally responsible for the liabilities incurred by the partnership. Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 13 Agency problem The agency problem refers to the fact that a firm’s managers will not work to maximise benefits to the firm’s owners unless it is in the managers’ interest to do so. This problem is the result of a separation of the management and ownership of the firm. Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 5 ? After World War Ⅱ the emphasis of corporate finance switched from financial accounting and external reporting to cost accounting and reporting and financial analysis on behalf of the firm?s managers. ? That is, the perspective of finance changed from reporting only to outsiders to that of an insider charged with the management and control of the firm?s financial operations. Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 1 chapter 1 amp。 2022 Pearson Education Australia Pty Limited Slide: 1 8 ? Chief accountant is also called financial controller, whose responsibilities include financial reporting to outsiders as well as cost and managerial accounting and financial analysis on behalf of the firm?s managers. ? Corporate treasurer is in charge of raising funds, managing liquidity and banking relationships and controlling risks. Copyright 169。 2022 Pearson Education Australia Pty Limited Slide: 1 16 Financial Decisions and Riskreturn Relationships ? Almost all financial decisions involve some sort of riskreturn tradeoff. ? The more risk the firm is willing to assume, the higher the expected return from a given course of action. Copyright 169。 2022 Pearson