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

(^166) © The McGraw−Hill
Companies, 2002
CHAPTER 5 Introduction to Valuation: The Time Value of Money 135
Well, $72 quadrillion is a lot of money. How much? If you had it, you could buy the United
States. All of it. Cash. With money left over to buy Canada, Mexico, and the rest of the world,
for that matter.
This example is something of an exaggeration, of course. In 1626, it would not have been
easy to locate an investment that would pay 10 percent every year without fail for the next
375 years.
(^1) The reason financial calculators use N and %i is that the most common use for these calculators is
determining loan payments. In this context, N is the number of payments and %i is the interest rate on
the loan. But, as we will see, there are many other uses of financial calculators that don’t involve loan
payments and interest rates.

CALCULATOR HINTS

Using a Financial Calculator

Although there are the various ways of calculating future values we have de-

scribed so far, many of you will decide that a financial calculator is the way to go. If you

are planning on using one, you should read this extended hint; otherwise, skip it.

A financial calculator is simply an ordinary calculator with a few extra features. In par-

ticular, it knows some of the most commonly used financial formulas, so it can directly

compute things like future values.

Financial calculators have the advantage that they handle a lot of the computation, but

that is really all. In other words, you still have to understand the problem; the calculator just

does some of the arithmetic. In fact, there is an old joke (somewhat modified) that goes like

this: Anyone can make a mistake on a time value of money problem, but to really screw

one up takes a financial calculator! We therefore have two goals for this section. First, we’ll

discuss how to compute future values. After that, we’ll show you how to avoid the most

common mistakes people make when they start using financial calculators.

How to Calculate Future Values with a Financial Calculator Examining a typi-

cal financial calculator, you will find five keys of particular interest. They usually look like this:

For now, we need to focus on four of these. The keys labeled and are just

what you would guess, present value and future value. The key labeled refers to the

number of periods, which is what we have been calling t.Finally, stands for the inter-

est rate, which we have called r.^1

If we have the financial calculator set up right (see our next section), then calculating a

future value is very simple. Take a look back at our question involving the future value of

$100 at 10 percent for five years. We have seen that the answer is $161.05. The exact

keystrokes will differ depending on what type of calculator you use, but here is basically

all you do:

1. Enter
   100. Press the key. (The negative sign is explained below.)


2. Enter 10. Press the key. (Notice that we entered 10, not .10; see below.)


3. Enter 5. Press the Nkey.

%i

PV

%i

N

PV FV

N %i PMT PV FV