Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

6. Discounted Cash Flow
   Valuation

© The McGraw−Hill^195

Companies, 2002

A Note on Cash Flow Timing

In working present and future value problems, cash flow timing is critically important.
In almost all such calculations, it is implicitly assumed that the cash flows occur at the
endof each period. In fact, all the formulas we have discussed, all the numbers in a stan-
dard present value or future value table, and, very importantly, all the preset (or default)
settings on a financial calculator assume that cash flows occur at the end of each period.
Unless you are very explicitly told otherwise, you should always assume that this is
what is meant.
As a quick illustration of this point, suppose you are told that a three-year investment
has a first-year cash flow of $100, a second-year cash flow of $200, and a third-year
cash flow of $300. You are asked to draw a time line. Without further information, you
should always assume that the time line looks like this:

0123

$100 $200 $300

On our time line, notice how the first cash flow occurs at the end of the first period, the
second at the end of the second period, and the third at the end of the third period.
We will close out this section by answering the question we posed concerning Mike
Piazza’s MLB contract at the beginning of the chapter. Recall that the contract called for
a signing bonus of $7.5 million ($4 million payable in 1999, $3.5 million in 2002) plus
a salary of $83.5 million, to be distributed as $6 million in 1999, $11 million in 2000,
$12.5 million in 2001, $9.5 million in 2002, $14.5 million in 2003, and $15 million in
both 2004 and 2005. If 12 percent is the appropriate discount rate, what kind of deal did
Piazza catch?
To answer, we can calculate the present value by discounting each year’s salary back
to the present as follows (notice that we combine salary and signing bonus in 1999 and
2002):

Year 1: $10.0 million 1/1.12^1 $8,928,571.43

Year 2: $11.0 million 1/1.12^2 $8,769,132.65

Year 3: $12.5 million 1/1.12^3 $8,897,253.10







Year 7: $15.0 million 1/1.12^7 $6,785,238.23

If you fill in the missing rows and then add (do it for practice), you will see that Piazza’s
contract had a present value of about $57.5 million, less than 2/3 of the $91 million
reported.

CONCEPT QUESTIONS

6.1a Describe how to calculate the future value of a series of cash flows.

6.1bDescribe how to calculate the present value of a series of cash flows.

6.1c Unless we are explicitly told otherwise, what do we always assume about the

timing of cash flows in present and future value problems?

CHAPTER 6 Discounted Cash Flow Valuation 165