Introduction to Corporate Finance

PART 1: INTRODUCTION

3-3 PRESENT VALUE OF A LUMP SUM

RECEIVED IN THE FUTURE

So far we have examined how to project the amount of cash that builds over time as an initial investment

earns interest. Now we reverse that focus, asking what an investor would pay today in exchange for

receiving a lump-sum payment at some point in the future. In other words, we want to know the present

value of the future cash flow.

FIGURE 3.2 THE POWER OF COMPOUND INTEREST: FUTURE VALUE OF $1 INVESTED TODAY AT DIFFERENT

ANNUAL INTEREST RATES

This figure shows that the future value of $1 invested today increases over time as long as the interest rate is greater

than 0%. Notice that each line gets steeper the longer the money remains invested, because the future value grows at

an increasing rate. This is the power of compound interest. For the same reason, the future value grows faster at higher

interest rates. (Observe how the lines get steeper as the interest rates increase.)

$30

$25

$20

$15

$10

$5

$1

0 2 4 6 8 10 12 14 16 18 20

Periods

Future value of one dollar ($)

0%

5%

10%

15%

20%

$35

$40

CONCEPT REVIEW QUESTIONS 3-2

3 If compounding occurs once per year, will a deposit made in an account paying compound interest

yield a higher future value after one period than an equal-size deposit in an account paying simple

interest? What about future values for investments held longer than one period?

4 How would the future value of a deposit be affected by: (a) a decrease in the interest rate; or (b) an

increase in the holding period? Why?