CHAPTER 4 Time Value of Money 159present value
The current dollar value of a
future amount—the amount of
money that would have to be
invested today at a given interest
rate over a specified period to
equal the future amount.
discounting cash flows
The process of finding present
values; the inverse of compound-
ing interest.
- The theoretical underpinning of this “required return” is introduced in Chapter 5 and further refined in subse-
quent chapters.
higher the interest rate, the higher the future value, and (2) the longer the period
of time, the higher the future value. Note that for an interest rate of 0 percent, the
future value always equals the present value ($1.00). But for any interest rate
greater than zero, the future value is greater than the present value of $1.00.Present Value of a Single Amount
It is often useful to determine the value today of a future amount of money. For
example, how much would I have to deposit today into an account paying 7 per-
cent annual interest in order to accumulate $3,000 at the end of 5 years? Present
valueis the current dollar value of a future amount—the amount of money that
would have to be invested today at a given interest rate over a specified period to
equal the future amount. Present value depends largely on the investment oppor-
tunities and the point in time at which the amount is to be received. This section
explores the present value of a single amount.The Concept of Present Value
The process of finding present values is often referred to as discounting cash
flows.It is concerned with answering the following question: “If I can earn i
percent on my money, what is the most I would be willing to pay now for an
opportunity to receive FVndollars nperiods from today?”
This process is actually the inverse of compounding interest. Instead of find-
ing the future value of present dollars invested at a given rate, discounting deter-
mines the present value of a future amount, assuming an opportunity to earn a
certain return on the money. This annual rate of return is variously referred to as
the discount rate, required return, cost of capital, andopportunity cost.^7 These
terms will be used interchangeably in this text.EXAMPLE Paul Shorter has an opportunity to receive $300 one year from now. If he can
earn 6% on his investments in the normal course of events, what is the most he
should pay now for this opportunity? To answer this question, Paul must deter-
mine how many dollars he would have to invest at 6% today to have $300 one
year from now. Letting PVequal this unknown amount and using the same nota-
tion as in the future value discussion, we have
PV(10.06)$300 (4.7)
Solving Equation 4.7 for PVgives us Equation 4.8:PV (4.8)$283.02
The value today (“present value”) of $300 received one year from today,
given an opportunity cost of 6%, is $283.02. That is, investing $283.02 today at
the 6% opportunity cost would result in $300 at the end of one year.$300
(10.06)