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

(^176) © The McGraw−Hill
Companies, 2002
A slightly more extreme example involves money bequeathed by Benjamin Franklin,
who died on April 17, 1790. In his will, he gave 1,000 pounds sterling to Massachusetts
and the city of Boston. He gave a like amount to Pennsylvania and the city of Philadel-
phia. The money had been paid to Franklin when he held political office, but he believed
that politicians should not be paid for their service (it appears that this view is not
widely shared by modern-day politicians).
Franklin originally specified that the money should be paid out 100 years after his
death and used to train young people. Later, however, after some legal wrangling, it was
agreed that the money would be paid out in 1990, 200 years after Franklin’s death. By
that time, the Pennsylvania bequest had grown to about $2 million; the Massachusetts
bequest had grown to $4.5 million. The money was used to fund the Franklin Institutes
in Boston and Philadelphia. Assuming that 1,000 pounds sterling was equivalent to
$1,000, what rate of return did the two states earn (the dollar did not become the official
U.S. currency until 1792)?
For Pennsylvania, the future value is $2 million and the present value is $1,000.
There are 200 years involved, so we need to solve for rin the following:
$1,000 $2 million/(1 r)^200
(1 r)^200 2,000
Solving for r, we see that the Pennsylvania money grew at about 3.87 percent per year.
The Massachusetts money did better; verify that the rate of return in this case was 4.3
percent. Small differences in returns can add up!
CHAPTER 5 Introduction to Valuation: The Time Value of Money 145
Saving for College
You estimate that you will need about $80,000 to send your child to college in eight years. You
have about $35,000 now. If you can earn 20 percent per year, will you make it? At what rate
will you just reach your goal?
If you can earn 20 percent, the future value of your $35,000 in eight years will be:
FV $35,000 1.20^8 $35,000 4.2998 $150,493.59
So, you will make it easily. The minimum rate is the unknown rin the following:
FV $35,000 (1 r)^8 $80,000
(1 r)^8 $80,000/35,000 2.2857
EXAMPLE 5.11

CALCULATOR HINTS

We can illustrate how to calculate unknown rates using a financial calculator

using these numbers. For Pennsylvania, you would do the following:

As in our previous examples, notice the minus sign on the present value, representing

Franklin’s outlay made many years ago. What do you change to work the problem for

Massachusetts?

N %i PMT PV FV

Enter 200 
1,000 2,000,000

Solve for 3.87