专业英语3.ppt

The Time Value of Money Chapter 3 Chapter Outline Future Value and Compounding Present Value and Discounting More on Present and Future Values Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows: Annuities and Perpetuities Loan Types and Loan Amortization Basic Definitions Present Value – earlier money on a time line Future Value – later money on a time line Interest rate – “exchange rate” between earlier money and later money Discount rate Cost of capital Opportunity cost of capital Required return 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(1.05)(1.05) = 1000(1.05)2 = 1102.50 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 Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment Figure 3.1 Figure 3.2 Future Values – Example 2 Suppose you invest the $1000 from the previous example for 5 years. How much would you have? FV = 1000(1.05)5 = 1276.28 The effect of compounding is small for a small number of periods, but increases as the number of periods increases. (Simple interest would have a future value of $1250, for a difference of $26.28.) 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 = 10 + 200(10)(.055) = 210.55 Compounding added