Introduction to Corporate Finance

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

(^172) © The McGraw−Hill
Companies, 2002
higher the discount rate is, the lower is the present value. Put another way, present
values and discount rates are inversely related. Increasing the discount rate decreases the
PV and vice versa.
The relationship between time, discount rates, and present values is illustrated in Fig-
ure 5.3. Notice that by the time we get to 10 years, the present values are all substan-
tially smaller than the future amounts.
CHAPTER 5 Introduction to Valuation: The Time Value of Money 141

TABLE 5.3

Present Value Interest

Factors

Interest Rate

Number of Periods 5% 10% 15% 20%

1 .9524 .9091 .8696 .8333

2 .9070 .8264 .7561 .6944

3 .8638 .7513 .6575 .5787

4 .8227 .6830 .5718 .4823

5 .7835 .6209 .4972 .4019

FIGURE 5.3

Present

value

of $1 ($)

1.00

.90

.80

.70

.60

.50

.40

.30

.20

.10

Time

12345678910 (years)

r = 0%

r = 5%

r = 10%

r = 15%

r = 20%

Present Value of $1 for Different Periods and Rates