Introduction to Corporate Finance

3: The Time Value of Money

3-3a THE CONCEPT OF PRESENT VALUE

In finance, we use the term discounting to describe the process of calculating present values. The technique

of discounting helps us to answer this question: If I can earn r% on my money, then what is the most I

would be willing to pay now for the opportunity to receive FV dollars n periods from today? This process

is actually the inverse of compounding interest:

■ Compounding tells us the future value of present dollars invested at a given interest rate

■ Discounting helps us determine the present value of a future amount, assuming an opportunity to

earn a given return (r) on the money.^2

To see how this works, suppose an investment will pay you $300 one year from now. How much

would you be willing to spend today to acquire this investment if you can earn 6% on an alternative

investment of equal risk? To answer this question, you must determine how many dollars you would have

to invest at 6% today in order to have $300 one year from now. Let PV equal this unknown amount, and

use the same notation as in our discussion of future value:

PV × (1 + 0.06) = $300

Solving this equation for PV gives us

=

+

PV =

$300

(1 0.06)

$283.02

The present value of $300 one year from today is $283.02 in today’s dollars. That is, $283.02 invested

today at a 6% interest rate would grow to $300 at the end of one year. Therefore, today, you would be

willing to pay no more than $283.02 for an investment that pays you $300 in one year.

3-3b THE EQUATION FOR PRESENT VALUE

We can find the present value of a lump sum mathematically by solving Equation 3.1 for P V. In other

words, the present value (PV) of some future amount (FV) to be received n periods from now, assuming

an opportunity cost of r, is given by Equation 3.2:

Eq. 3.2

() ()

PV

FV

1

FV

1

rrnn 1

= =

+

×

+

Investors use Equation 3.2 to determine the value today of an investment that pays off in the future.

There are many applications of this formula. One application helps companies determine how much

money they need to charge a customer today to cover a liability looming in the future.

2 This interest rate, r, is variously referred to as the discount rate, the required return, the cost of capital, the hurdle rate or the opportunity cost

of capital.

discounting

The process of calculating

present values

LO3.2