Introduction to Corporate Finance

PART 1: INTRODUCTION

A simple example illustrates the essence of the time value of money. Suppose you have $100 today,

and you can put that sum into an investment that pays 5% interest per year. If you invest $100 now, by

the end of one year you will earn $5 in interest (0.05 × $100 = $5). Your $100 initial investment will have

grown to $105 in one year ($5 in interest plus the original $100 investment). In a sense, then, receiving

$100 now is equivalent to receiving $105 in one year. Whether you receive $100 now and invest it at 5%,

or whether you have to wait a year to receive $105, you wind up with the same amount of cash. In this

case, we would say that $105 is the future value of $100 invested for one year at 5%. More generally, the

future value is the value of a cash receipt or payment as at some future date.

We can reframe the above example to illustrate another dimension of the time value of money. Suppose

you have no money today, but you expect to receive $105 in one year. Suppose also that a bank is willing

to lend you money, charging an interest rate of 5%. How much would they lend you today if you promise

to pay them the $105 that you will receive next year? From the calculations above, you can probably

guess that the answer is $100. The bank will give you $100 today in exchange for a payment next year of

$105. Here, $100 is the present value of $105 to be received in one year when the interest rate is 5%. More

generally, the present value is just the value of a future cash receipt or payment in terms of today’s dollars.

On an almost daily basis, managers use time value of money methods to compare the costs and benefits of

important business decisions. People buying houses with borrowings from banks can use the same techniques

to evaluate the terms of different mortgage products. Consumers do likewise when they compare offers to

purchase durable goods (like cars or furniture) that offer either an immediate cash discount or a low-interest

financing plan. The rest of this chapter shows you how to apply time value of money analytics to a wide

variety of problems that you may encounter either in your career or in your personal financial transactions.

LO3.1

LO3.2

present value
The value today of a cash flow
to be received at a specific
date in the future, accounting
for the opportunity to earn
interest at a specified rate

3-2 FUTURE VALUE OF A LUMP SUM

RECEIVED TODAY

Saving today allows investors to earn interest on their savings and enjoy higher future consumption. We

have already seen that a person who invests $100 today at 5% interest expects to receive $105 in one

year, representing $5 interest plus the original $100 investment. Now, let’s examine how much money

investors can earn when they set aside money for more than a single year.

3-2a THE CONCEPT OF FUTURE VALUE

We can calculate the future value of an investment made today by applying either simple interest or

compound interest over a specified period of time. Simple interest is interest paid only on the initial principal

simple interest

Interest paid only on the initial

principal of an investment, not

on the interest that accrues in

earlier periods

future value
The value of an investment
made today measured at a
specific future date accounting
for interest earned over the life
of the investment

CONCEPT REVIEW QUESTIONS 3-1

1 Why is it better to receive $1 today than at some point in the future?

2 During the global financial crisis, interest rates in Australia fell to low levels; but in the United

States, interest rates on relatively safe investments, such as bank deposits, were just barely above

zero. If the interest rate actually is zero, what is the relationship between the present value and the

future value of money?