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1、Chapter 5 Formulas Introduction to Valuation: The Time Value of Money,McGraw-Hill/Irwin,Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.,Key Concepts and Skills,Be able to compute the future value of an investment made today Be able to compute the present value of cash to be re
2、ceived at some future date Be able to compute the return on an investment Be able to compute the number of periods that equates a present value and a future value given an interest rate Be able to use a financial calculator and/or a spreadsheet to solve time value of money problems,5F-2,Chapter Outl
3、ine,Future Value and Compounding Present Value and Discounting More about Present and Future Values,5F-3,什么是货币的时间价值,货币时间价值：是指货币随着时间的推移而发生的增值，也称为资金时间价值。 是不是货币在任何状态下都可以产生时间价值呢？ 是不是货币作为资本投入到经营活动中所获得的增值额都是时间价值呢？,利率的构成,利率=时间价值+风险报酬+通货膨胀贴水 利率在经济生活中的表现形式 银行存款利息率 银行贷款利率 债券利息率 股息率 时间价值是扣除风险报酬和通货膨胀贴水后的真实收益率（社
4、会平均资金收益率）。,Basic Definitions,Present Value 现值（PV），是指未来某一时点上的一定量现金折合到现在的价值，又称本金。 Future Value 终值（FV），是现在一定量现金在未来某一时点上的价值，即本利和，又称将来值。 Interest rate “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return,5F-6,Future Values,Suppose
5、 you invest $1,000 for one year at 5% per year. What is the future value in one year? Interest = 1,000(.05) = 50 Value in one year = principal + interest = 1,000 + 50 = 1,050 Future Value (FV) = 1,000(1 + .05) = 1,050 Suppose you leave the money in for another year. How much will you have two years
6、from now? FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50,5F-7,Future Values: 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 复利终值系数，可查表，中文教材表现为（F/P，i, n),5F-8,Effects
7、 of Compounding,Simple interest Compound interest Consider the previous example FV with simple interest = 1,000 + 50 + 50 = 1,100 两年期单利 FV with compound interest = 1,102.50 两年期复利 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment,5F-9,Calculator Keys 计算器,Te
8、xas Instruments BA-II Plus FV = future value PV = present value I/Y = period interest rate P/Y must equal 1 for the I/Y to be the period rate Interest is entered as a percent, not a decimal N = number of periods Remember to clear the registers (CLR TVM) after each problem Other calculators are simil
9、ar in format 了解即可,5F-10,Future Values Example 2,Suppose you invest the $1,000 from the previous example for 5 years. How much would you have? FV = 1,000(1.05)5 = 1,276.28 The effect of compounding is small for a small number of periods, but increases as the number of periods increases. (Simple inter
10、est would have a future value of $1,250, for a difference of $26.28.),5F-11,Future Values Example 3,Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? FV = 10(1.055)200 = 447,189.84 What is the effect of compounding? Simple interest =
11、 10 + 200(10)(.055) = 120.00 Compounding added $447,069.84 to the value of the investment,5F-12,Future Value as a General Growth Formula,Suppose your company expects to increase unit sales of widgets（小部件） by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how
12、many widgets do you expect to sell in 5 years? FV = 3,000,000(1.15)5 = 6,034,072,5F-13,Quick Quiz Part I,What is the difference between simple interest and compound interest? Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years. How much would you have
13、 at the end of 15 years using compound interest? How much would you have using simple interest?,5F-14,Present Values 现值,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
14、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.,5F-15,Present Value One Period Example,Suppose you need $10,000 in one year for the down payment on a new car. If yo
15、u can earn 7% annually, how much do you need to invest today? PV = 10,000 / (1.07)1 = 9,345.79 Calculator 1 N 7 I/Y 10,000 FV CPT PV = -9,345.79,5F-16,Present Values Example 2,You want to begin saving for your daughters college education and you estimate that she will need $150,000 in 17 years. If y
16、ou feel confident that you can earn 8% per year, how much do you need to invest today? PV = 150,000 / (1.08)17 = 40,540.34,5F-17,Present Values Example 3,Your parents set up a trust fund （托管基金）for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest? PV = 19,671.51 / (1.07)10 = 10,000,5F-18,Present Value Important Relationship I,For a given interest rate the longer the time period, the lower the present value What
