## The lnterest Rate

Which would you prefer - \$1,000 today or \$1,000 ten years from today? Common sense tells us to take the \$1,000 today because we recognize that there is a time value to money. The immediate receipt of \$1,000 provides us with the opportuniql to put our money to work and earn interest. In a world in which all cash flows are certain, the rate of interest can be used to express the time value of money. As we will soon discover, the rate of interest will allow us to adjust the vaiue of cash flows, whenever they occur, to a particular point in time. Given this ability, we will be able to answer more difficult questions, such as: which should you prefer - \$1,000 today or \$2,000 ten years from today? To answer this question, it will be necessary to position time-adjusted cash flows at a single point in time so that a fair comparison can be made.

If we allow for uncertainty surrounding cash flows to enter into our analysis, it will be necessary to add a risk premium to the interest rate as compensation for uncertainty. In later chapters we will study how to deal with uncertainty (risk). But for now, our focus is on the time value of money and the ways in which the rate of interest can be used to adjust the value of cash flows to a single point in time.

Most financial decisions, personal as well as business, involve time value of money considerations. In Chapter 1, we learned that the objective of management should be to maximize shareholder wealth, and that this depends, in part, on the timing of cash flows. Not surprisingly, one important application of the concepts stressed in this chapter will be to value a stream of cash flows. Indeed, much of the development of this book depends on your understanding of this chapter. You will never really understand finance until you understand the time value of money. Although the discussion that follows cannot avoid being mathematical in nature, we focus on only a handful of formulas so that you can more easily grasp the fundamentals. We start with a discussion of simple interesl and use this as a springboard to develop the concept of compound interest. Also, to obserye more easilythe effect of compound interest, most of the exarnples in this chapter assume an 8 percent annual interest rate.

Before we begin, it is important to sound a few notes of caution. The examples in the chapter frequently involve numbers that must be raised to the nth power - for example, (1.05) to the third power equals (1.05)3 equals [(1.05) x (1.05) x (1.05)]. However, this operation is easy to do with a calculator, and tables are provided in which this calculation has already been done for you. Although the tables provided are a useful aid, you cannot rely on them for solving every problem. Not every interest rate or time period can possibly be represented in each table. Therefore you wili need to become familiar with the operational formulas on which the tabies are based. (As a reminder, the appropriate formula is included at the top of every table.) Those of you possessing a business calculator may feel the urge to blpass both the tables and formulas and head straight for the various function keys designed to deal with time value of money problems. However, we urge you to master first the logic behind the procedures outlined in this chapter. Even the best of calculators cannot overcome a faulty sequence of steps programmed in by the user.