## Info

Notice that the answer has a negative sign; as we discussed above, that's because it represents an outflow today in exchange for the \$1,000 inflow later.

Recently, some businesses have been saying things like "Come try our product. If you do, we'll give you \$100 just for coming by!" If you read the fine print, what you find out is that they will give you a savings certificate that will pay you \$100 in 25 years or so. If the going interest rate on such certificates is 10 percent per year, how much are they really giving you today?

What you're actually getting is the present value of \$100 to be paid in 25 years. If the discount rate is 10 percent per year, then the discount factor is:

This tells you that a dollar in 25 years is worth a little more than nine cents today, assuming a 10 percent discount rate. Given this, the promotion is actually paying you about .0923 X \$100 = \$9.23. Maybe this is enough to draw customers, but it's not \$100.

As the length of time until payment grows, present values decline. As Example 5.7 illustrates, present values tend to become small as the time horizon grows. If you look out far enough, they will always get close to zero. Also, for a given length of time, the

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

5. Introduction to Valuation: The Time Value of Money

CHAPTER 5 Introduction to Valuation: The Time Value of Money

Interest Rate

Number of Periods

5%

10%

15%

20%

0 0