A thorough understanding of the material in this chapter is critical to understanding material in subsequent chapters. After studying this chapter you will be able to understand: How to determine the future value of an investment made today, how to determine the present value of cash to be received at a future date, how to fi nd the return on an investment, how long it takes for an investment to reach a desired value. | Chapter Outline Chapter 5 Introduction to Valuation: The Time Value of Money Chapter Organization Future Value and Compounding Present Value and Discounting More on Present and Future Values Summary and Conclusions CLICK MOUSE OR HIT SPACEBAR TO ADVANCE Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd. Consider the time line below: PV is the Present Value, that is, the value today. FV is the Future Value, or the value at a future date. The number of time periods between the Present Value and the Future Value is represented by “t”. The rate of interest is called “r”. All time value questions involve the four values above: PV, FV, r, and t. Given three of them, it is always possible to calculate the fourth. Time Value Terminology . . . 0 1 2 3 t PV FV Notice that 1. $110 = $100 (1 + .10) 2. $121 = $110 (1 + .10) = $100 = $100 3. $ = $121 (1 + .10) = $100 = $100 _ Future Value for a Lump Sum Notice that 1. $110 = $100 (1 + .10) 2. $121 = $110 (1 + .10) = $100 = $100 3. $ = $121 (1 + .10) = $100 = $100 ()3 In general, the future value, FVt, of $1 invested today at r% for t periods is FVt = $1 (1 + r)t The expression (1 + r)t is the future value interest factor. Future Value for a Lump Sum Chapter 5 Quick Quiz - Part 1 of 4 Q. Deposit $5,000 today in an account paying 12%. How much will you have in 6 years? How much is simple interest? How much is compound interest? A. Multiply the $5000 by the future value interest factor: $5000 (1 + r )t = $5000 _ = $5000 = $ At 12%, the simple interest is .12 $5000 = $_ per year. After 6 years, this is 6 $600 = $_ ; the difference between compound and simple interest is thus $_ - $3600 = $_ Chapter 5 Quick Quiz - Part 1 of 4 Q. Deposit $5,000 today in an account paying 12%. How much will you have in 6 | Chapter Outline Chapter 5 Introduction to Valuation: The Time Value of Money Chapter Organization Future Value and Compounding Present Value and Discounting More on Present and Future Values Summary and Conclusions CLICK MOUSE OR HIT SPACEBAR TO ADVANCE Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd. Consider the time line below: PV is the Present Value, that is, the value today. FV is the Future Value, or the value at a future date. The number of time periods between the Present Value and the Future Value is represented by “t”. The rate of interest is called “r”. All time value questions involve the four values above: PV, FV, r, and t. Given three of them, it is always possible to calculate the fourth. Time Value Terminology . . . 0 1 2 3 t PV FV Notice that 1. $110 = $100 (1 + .10) 2. $121 = $110 (1 + .10) = $100 = $100 3. $ = $121 (1 + .10) = $100 = $100 _ Future Value for a
