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determined, and why is it important to the financial manager?
12. Goals of the Firm. You may have heard big business criticized for focusing on short-term
performance at the expense of long-term results. Explain why a firm that strives to maxi-
mize stock price should be less subject to an overemphasis on short-term results than one
that maximizes profits.
13. Goals of the Firm. We claim that the goal of the firm is to maximize stock price. Are the
following actions necessarily consistent with that goal?

a. The firm donates $3 million to the local art museum.
b. The firm reduces its dividend payment, choosing to reinvest more of earnings in the
c. The firm buys a corporate jet for its executives.
14. Goals of the Firm. Explain why each of the following may not be appropriate corporate
a. Increase market share
b. Minimize costs
c. Underprice any competitors
d. Expand profits
15. Agency Issues. Sometimes lawyers work on a contingency basis. They collect a percentage
of their client™s settlement instead of receiving a fixed fee. Why might clients prefer this
arrangement? Would this sort of arrangement be more appropriate for clients that use
lawyers regularly or infrequently?
16. Reputation. As you drive down a deserted highway you are overcome with a sudden desire
for a hamburger. Fortunately, just ahead are two hamburger outlets; one is owned by a na-
tional brand, the other appears to be owned by “Joe.” Which outlet has the greater incentive
to serve you catmeat? Why?
17. Agency Problems. If agency problems can be mitigated by tying the manager™s compensa-
tion to the fortunes of the firm, why don™t firms compensate managers exclusively with
shares in the firm?

18. Agency Problems. Many firms have devised defenses that make it much more costly or dif-
ficult for other firms to take them over. How might such takeover defenses affect the firm™s
agency problems? Are managers of firms with formidable takeover defenses more or less
likely to act in the firm™s interests rather than their own?
19. Agency Issues. One of the “Finance through the Ages” episodes that we cite on page 27 is
the 1993 collapse of Barings Bank, when one of its traders lost $1.3 billion. Traders are com-
pensated in large part according to their trading profits. How might this practice have con-
tributed to an agency problem?
20. Agency Issues. Discuss which of the following forms of compensation is most likely to
align the interests of managers and shareholders:
a. A fixed salary
b. A salary linked to company profits
c. A salary that is paid partly in the form of the company™s shares
d. An option to buy the company™s shares at an attractive price
21. Agency Issues. When a company™s stock is widely held, it may not pay an individual share-
holder to spend time monitoring the manager™s performance and trying to replace poor man-
agement. Explain why. Do you think that a bank that has made a large loan to the company
is in a different position?
22. Ethics. In some countries, such as Japan and Germany, corporations develop close long-
term relationships with one bank and rely on that bank for a large part of their financing
needs. In the United States companies are more likely to shop around for the best deal. Do
you think that this practice is more or less likely to encourage ethical behavior on the part
of the corporation?
23. Ethics. Is there a conflict between “doing well” and “doing good”? In other words, are poli-
cies that increase the value of the firm (doing well) necessarily at odds with socially re-
sponsible policies (doing good)? When there are conflicts, how might government regula-
tions or laws tilt the firm toward doing good? For example, how do taxes or fees charged on
pollutants affect the firm™s decision to pollute? Can you cite other examples of “incentives”
used by governments to align private interests with public ones?
24. Ethics. The following report appeared in the Financial Times (October 28,1999, p. 1):
“Coca-Cola is testing a vending machine that automatically raises the price of the world™s
favorite soft drink when the temperature increases . . . [T]he new machine, believed to have
been tested in Japan, may well create controversy by using hot weather to charge extra. One
rival said the idea of charging more when temperatures rose was ˜incredible.™” Discuss.

Solutions to 1 a. The consulting firm is most suited to a partnership. Each senior consultant might be a
partner, with partial responsibility for managing the firm and its clients.
Self-Test b. The college student would set up the business as a sole proprietorship. He or she is the
only manager, and has little need for partners to contribute capital.
Questions c. The large firm would be set up as a corporation. It requires great amounts of capital and
with the budgetary, payroll, and management issues that arise with such a large number
of employees, it probably needs a professional management team.
2 a. The development of a microprocessor is a capital budgeting decision. The investment of
$500 million will purchase a real asset, the microprocessor.
b. The bank loan is a financing decision. This is how Volkswagen will raise money for its
c. Capital budgeting.
d. Financing.
The Firm and the Financial Manager 31

e. Capital budgeting. Though intangible, the license is a real asset that is expected to pro-
duce future sales and profits.
f. Financing.
3 a. Real assets support the operations of the business. They are necessary to produce future
profits and cash inflows. Financial assets or securities are claims on the profits and cash
inflows generated by the firm™s real assets and operations.
b. A company invests in real assets to support its operations. It finances the investment by
raising money from banks, shareholders, or other investors.
c. Capital budgeting deals with investment decisions. Capital structure is the composition of
the company™s sources of financing.
d. When a company raises money from investors, it sells financial assets or securities in the
primary market. Later trades among investors occur in the secondary market.
e. A company can raise money by selling securities directly to investors in financial mar-
kets, or it can deal with a financial intermediary. The intermediary raises money from in-
vestors and reinvests it in the company™s securities. The intermediary invests primarily in
financial assets.
4 Sal would more likely be the treasurer and Sally the controller. The treasurer raises money
from the credit and financial markets and requires background in financial institutions. The
controller is more of an overseer who requires background in accounting.
5 Harry™s has a far bigger stake in the reputation of the business than Victor™s. The store has
been in business for a long time. The owners have spent years establishing customer loyalty.
In contrast, Victor™s has just been established. The owner has little of his own money tied up
in the firm, and so has little to lose if the business fails. In addition, the nature of the busi-
ness results in little customer loyalty. Harry™s is probably more reliable.
6 An investor would like top management to be compensated according to the fortunes of the
firm. If management is willing to bet its own compensation on the success of the firm, that
is good news, first because it shows management has confidence in the firm, and second be-
cause it gives managers greater incentives to work hard to make the firm succeed.
Future Values and Compound Interest
Present Values
Finding the Interest Rate

Multiple Cash Flows
Future Value of Multiple Cash Flows
Present Value of Multiple Cash Flows

Level Cash Flows: Perpetuities and Annuities
How to Value Perpetuities
How to Value Annuities
Annuities Due
Future Value of an Annuity

Inflation and the Time Value of Money
Real versus Nominal Cash Flows
Inflation and Interest Rates
Valuing Real Cash Payments
Real or Nominal?

Effective Annual Interest Rates

Kangaroo Auto™s view of the time value of money.
Do you truly understand what these percentages mean? Do you realize that the dealership is
not quoting effective annual interest rates? If the dealership quotes a monthly payment on a
four-year, $10,000 car loan, would you be able to double-check the dealership™s calculations?
Cameramann International, LTD.
ompanies invest in lots of things. Some are tangible assets”that is, as-

C sets you can kick, like factories, machinery, and offices. Others are in-
tangible assets, such as patents or trademarks. In each case the company
lays out some money now in the hope of receiving even more money later.
Individuals also make investments. For example, your college education may cost
you $20,000 per year. That is an investment you hope will pay off in the form of a higher
salary later in life. You are sowing now and expecting to reap later.
Companies pay for their investments by raising money and in the process assuming
liabilities. For example, they may borrow money from a bank and promise to repay it
with interest later. You also may have financed your investment in a college education
by borrowing money which you plan to pay back out of that fat salary.
All these financial decisions require comparisons of cash payments at different dates.
Will your future salary be sufficient to justify the current expenditure on college tuition?
How much will you have to repay the bank if you borrow to finance your education?
In this material we take the first steps toward understanding the relationship between
the value of dollars today and that of dollars in the future. We start by looking at how
funds invested at a specific interest rate will grow over time. We next ask how much you
would need to invest today to produce a specified future sum of money, and we describe
some shortcuts for working out the value of a series of cash payments. Then we con-
sider how inflation affects these financial calculations.
After studying this material you should be able to
Calculate the future value to which money invested at a given interest rate will grow.
Calculate the present value of a future payment.
Calculate present and future values of streams of cash payments.
Find the interest rate implied by the present or future value.
Understand the difference between real and nominal cash flows and between real and
nominal interest rates.
Compare interest rates quoted over different time intervals”for example, monthly
versus annual rates.
There is nothing complicated about these calculations, but if they are to become sec-
ond nature, you should read the material thoroughly, work carefully through the exam-
ples (we have provided plenty), and make sure you tackle the self-test questions. We are
asking you to make an investment now in return for a payoff later.

Future Values and Compound Interest
You have $100 invested in a bank account. Suppose banks are currently paying an in-
terest rate of 6 percent per year on deposits. So after a year, your account will earn in-
terest of $6:

The Time Value of Money 35

Interest = interest rate — initial investment
= .06 — $100 = $6
You start the year with $100 and you earn interest of $6, so the value of your investment
will grow to $106 by the end of the year:
Value of investment after 1 year = $100 + $6 = $106
Notice that the $100 invested grows by the factor (1 + .06) = 1.06. In general, for any
interest rate r, the value of the investment at the end of 1 year is (1 + r) times the initial
Value after 1 year = initial investment — (1 + r)
= $100 — (1.06) = $106
What if you leave this money in the bank for a second year? Your balance, now $106,
will continue to earn interest of 6 percent. So
Interest in Year 2 = .06 — $106 = $6.36
You start the second year with $106 on which you earn interest of $6.36. So by the end
of the year the value of your account will grow to $106 + $6.36 = $112.36.
In the first year your investment of $100 increases by a factor of 1.06 to $106; in the
second year the $106 again increases by a factor of 1.06 to $112.36. Thus the initial
$100 investment grows twice by a factor 1.06:
Value of account after 2 years = $100 — 1.06 — 1.06
= $100 — (1.06)2 = $112.36
If you keep your money invested for a third year, your investment multiplies by 1.06
each year for 3 years. By the end of the third year it will total $100 — (1.06)3 = $119.10,
scarcely enough to put you in the millionaire class, but even millionaires have to start
Clearly for an investment horizon of t years, the original $100 investment will grow
to $100 — (1.06)t. For an interest rate of r and a horizon of t years, the future value of
your investment will be
Amount to which an
investment will grow after
(1 + r)t
Future value of $100 = $100
earning interest.
Notice in our example that your interest income in the first year is $6 (6 percent of
$100), and in the second year it is $6.36 (6 percent of $106). Your income in the second
year is higher because you now earn interest on both the original $100 investment and
the $6 of interest earned in the previous year. Earning interest on interest is called com-
pounding or compound interest. In contrast, if the bank calculated the interest only on
your original investment, you would be paid simple interest.
Interest earned on interest.
Table 1.5 and Figure 1.3 illustrate the mechanics of compound interest. Table 1.5
shows that in each year, you start with a greater balance in your account”your savings
have been increased by the previous year™s interest. As a result, your interest income
Interest earned only on the
also is higher.
original investment; no
Obviously, the higher the rate of interest, the faster your savings will grow. Figure
interest is earned on interest.
1.4 shows that a few percentage points added to the (compound) interest rate can dra-
matically affect the future balance of your savings account. For example, after 10 years
$1,000 invested at 10 percent will grow to $1,000 — (1.10)10 = $2,594. If invested at 5
percent, it will grow to only $1,000 — (1.05)10 = $1,629.

Balance at Interest Earned Balance at
Compound interest
Year Start of Year during Year End of Year
— $100.00 = $6.00
1 $100.00 .06 $106.00
— $106.00 = $6.36
2 $106.00 .06 $112.36
— $112.36 = $6.74
3 $112.36 .06 $119.10
— $119.10 = $7.15
4 $119.10 .06 $126.25
— $126.25 = $7.57
5 $126.25 .06 $133.82

Calculating future values is easy using almost any calculator. If you have the pa-
tience, you can multiply your initial investment by 1 + r (1.06 in our example) once for
each year of your investment. A simpler procedure is to use the power key (the yx key)


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