internatinalfinancemanagement【國際財(cái)務(wù)管理】lecture4timevalueofmoney(已修改)
2025-10-23 16:13 本頁面
【正文】 Lecture 4 Time Value of Money Learning Objectives ? Understand the concept of present value (NPV) ? Calculate the present and future values of any set of expected future cash flows, including annuities, perpetuity. ? Prepare loan amortization schedule ? Chapters covered: Chapter 5, 6, 7, 8 Timevalueofmoney ? The relation between one dollar today and one dollar in the future is called timevalueofmoney ? The timevalueofmoney can be viewed as the opportunity to earn interest on a bank savings account. Future values ? Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? – Interest = 1000(.05) = 50 – Value in one year = principal + interest = 1000 + 50 = 1050 – Future Value (FV) = 1000(1 + .05) = 1050 ? Suppose you leave the money in for another year. How much will you have two years from now? – FV = 1000()() = 1000()2 = General formula ? FV = PV(1 + r)t – FV = future value – PV = present value – r = period interest rate, expressed as a decimal – t = number of periods ? Future value interest factor = (1 + r)t Compounding period ? If the stated interest rate is r, but pounding m times each period, then ? Distinction between stated annual interest rate and effective annual interest rate ? Continuous time pounding ( 1 ) mrF V P V m??e f f e c it v e a n n u a l in te r e s t r a te = ( 1 ) 1mr rm? ? ?* rtF V P V e?The power of pounding ? Look at this example: according to Ibboston, the average rate of return in . stock market is %, if you invest one dollar at the beginning of 1926, that one dollar would worth $2845 at the end of 1999. However, if you don’t reinvest and withdraw cents at the end of each year, the one dollar would only worth $ at the end of 1999. That’s why reinvestment can generate huge wealth in the long term Present value ? How much do I have to invest today to have some amount in the future? – FV = PV(1 + r)t – Rearrange to solve for PV = FV / (1 + r)t ? When we talk about discounting, we mean finding the present value of some future amount. ? When we talk about the “value” of something, we are talking about the present value unless we specifically indicate that we want the future value. Present valueexample ? You want to begin saving for your daughter’s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today? ? Formula: 150,000 / ()17 = 150,000(.270268951) = 40, Discount rate ? Often we will want to know what the implied interest rate is on an investment ? Rearrange the basic PV equation and solve for r
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