Xem mẫu
www.downloadslide.com
PA R T
two
SPECIFIC
APPLICATIONS
6
Investments
7
Retirement Plans
8
Mathematics of Pricing
9
Taxes
International Business
12
Financial Statements
13
Insurance and Risk Management
14
Evaluating Projected Cash Flows
15
bie24825_ch06.indd 249
Consumer Mathematics
11
Copyright © 2008, The McGraw-Hill Companies, Inc.
10
Payroll and Inventory
16
Business Statistics
5/23/07 3:10:00 PM
C H A P T E R
6
www.downloadslide.com
Investments
“October: This is one of the peculiarly
dangerous months to speculate in stocks.
The others are July, January, September,
April, November, May, March, June,
December, August and February.”
—Mark Twain, “Pudd’nhead Wilson’s Calendar for 1894”
Learning Objectives
Chapter Outline
LO 1
6.1
Stocks
6.2
Bonds
6.3
Commodities, Options, and Futures Contracts
6.4
Mutual Funds and Investment Portfolios
Identify the key characteristics of different types
of investments, including stocks, bonds, futures
and options, and mutual funds.
LO 2 Correctly use technical terminology related to
various types of investments.
LO 3
Calculate values used to measure the financial
results, including dividend rates, dividend yields,
compound annual growth rates, and total rates
of return.
LO 4 Recognize how investment concepts such as
risk, volatility, diversification, and leverage
can affect investment choice and investment
performance.
LO 5 Assess a reasonable rate of return expectation
for an investment portfolio based on the types
of investments it contains.
6.1
Stocks
In our work so far, we have put a great deal of effort into the mathematics of money
invested growing over time. When money is put to work as a loan, this growth is due to
the payment of interest. We have also recognized, though, that there are other ways that
money can be put to work aside from simple notes and bank deposits. We have seen that
present and future values can be calculated in the same way regardless of whether the
250
bie24825_ch06.indd 250
5/23/07 3:10:04 PM
www.downloadslide.com
Copyright © 2008, The McGraw-Hill Companies, Inc.
6.1 Stocks
251
growth really comes from interest or from other types of investment gain, and so we have
not spent much time discussing the details of these other sorts of possible investments. In
this chapter we will.
Money can be put to work by loaning it to someone else, but it can also be put to work by
buying something that we hope will provide a good return on the money invested. We could
buy a piece of real estate or gold coins in the hope that they will increase in value. One of the
main ways to put money to work, though, is by using it to start or buy part of a business. We
will begin this section by looking at money invested in the ownership of a business.
Businesses can legally be set up in a range of different ways. In a sole proprietorship
the business is owned entirely by one individual, the person who runs it. Many small businesses are set up in this way. For example, if Tom owns a snow plow and runs a business
plowing driveways in the winter, his business may well be a set up as a sole proprietorship.
A partnership is a business owned by two or more people, again typically the people who
actually run the business. If Lisa and Sunita work together preparing tax returns, their
business may be set up as a partnership.
There are other ways that a business can be structured though. You may be familiar with
such terms as limited partnership, limited liability company (LLC), and corporation. Each
type of structure has its advantages and disadvantages, and the choice of how to structure
a business requires weighing considerations such as taxes, exposure to risk and liability,
paperwork requirements, and other concerns.
One of the most commonly used structures for a business is a corporation. A corporation is a legal entity that can be thought of in many ways as an artificial legal person, able
to own property, enter into contracts, borrow money, and conduct business and financial
affairs just as an actual person could. To most people the word corporation suggests big
business, like Home Depot, Exxon Mobil, or General Electric. Those businesses are all corporations, but small businesses like Tom’s snowplowing business, or Lisa and Sunita’s tax
service, could equally well be set up as corporations. Setting up a business as a corporation
is generally more complicated than a sole proprietorship or simple partnership, but it can
offer significant advantages to its owners. One of the biggest advantages of a corporation
is that it exists as a separate legal entity from its owners; if things go badly and business
is sued or suffers severe financial losses, generally its owners can not be held personally
responsible for those liabilities.
A sole proprietorship is owned by its sole proprietor, and a partnership is owned by its
partners, but who owns a corporation? The ownership of a corporation is divided up among
its stockholders. Each individual piece of this ownership is called a share of the company’s
stock. How much of the business each share of stock represents depends on how many
shares of stock the company has issued. A corporation can have any number of shares, so
it is impossible to know how large a percent of the ownership one share represents unless
you know the total. If you own one share of stock in a company with just 10 shares, then
you own 1/10 (or 10%) of the company. If the company has issued one billion shares, then
one share equates to owning 1/1,000,000,000 (or 0.0000001%) of the company.
When stock is first issued by a corporation, it may be issued with a par value. Loosely
speaking, a stock’s par value is a reflection of a portion of the money paid by the original
shareholders into the corporation. Par value used to be considered more important than it
usually is today, and in fact it is not unusual today for a stock to have no par value, or to
have a par value which is absurdly low compared to the realistic value of the stock.
Some companies also issue several different types of stock. As its name suggests,
common stock is the most common type, though preferred stock is another. While both
types of stock represent ownership of a piece of a corporation, the two types differ in
how their owners share in the company’s profits, who has first claim to the corporation’s
remaining assets in the event it goes into bankruptcy, and in their voting rights in the election
of the board of directors (the group of people who direct the corporation’s activities).
Except as noted, we will be discussing only common stocks in this text. Small businesses
seldom issue preferred stock, and even among very large corporations it is not unusual to
see little, it any, preferred stock issued.
bie24825_ch06.indd 251
5/23/07 3:10:12 PM
www.downloadslide.com
252
Chapter 6 Investments
Dividends
The profits earned by a corporation properly belong to its shareholders, the people who
own the corporation. However, since the corporation is a separate legal entity, a shareholder
does not have the right to access the corporation’s funds directly. Each shareholder receives
a portion of the corporation’s profits when they are paid out in the form of dividends. A
corporation’s board of directors will periodically evaluate the business’s performance and
decide how much money should be paid out to its shareholders (this is known as declaring
a dividend.) Corporations normally hold on to at least some of their profits to use in growing the business for the future, and some corporations don’t pay out any dividends at all.
On the other hand, sometimes a corporation will pay more in dividends than it earns if it
has a significant amount of unused cash on hand. In either case, the dividends paid out by
a corporation are seldom exactly equal to the corporation’s profits.
Dividends are divided up among the shareholders according to the number of shares
each owns.
Example 6.1.1 Zarofire Systems earned $743,000 in the last quarter, and the
company’s management has declared a dividend of $450,000. The company has
1,000,000 shares of stock issued. If you own 200 shares of the company’s stock, how
much will you receive as a dividend?
The $450,000 total dividend must be distributed among the shareholders based on the
number of shares each one owns; $450,000/1,000,000 shares works out to $0.45 per
share. Since you own 200 shares, you will receive (200 shares)($0.45 per share) ϭ $90.00.
Rounding can be an issue with dividend rate calculations. In Example 6.1.1 the dividend
rate came out evenly, but this will not always happen. Since the dividend rate per share
often comes out to be a fairly small amount of money, it is not uncommon to see dividend
rates carried out to a tenth of a cent. For example, a company might pay a dividend of
12.5 cents per share, or $0.125 per share.
Dividend calculations work out the same way with small businesses as with large ones.
Example 6.1.2 Jason and Dave’s dry cleaning business is set up as a corporation.
There are 100 shares of stock; Jason owns 51 shares and Dave owns 49. In the last
quarter the business earned $39,750 in profits, and the company declared a dividend
of $35,000. How much will Jason and Dave each get?
The $35,000 profit will be distributed based on the number of shares each person owns;
$35,000/100 shares ϭ $350 per share. Since Jason owns 51 shares, he will receive (51 shares)
($350 per share) ϭ $17,850.
Dave will receive (49 shares)($350 per share) ϭ $17,150.
In this example, Jason and Dave both own nearly the same number of shares, and so they
receive nearly the same amounts in dividends. Financially speaking, they are close to being
equal owners of the business. However, in another important respect they are not equal at
all. Since Jason owns 51% of the shares of the business, whenever any decisions need to
be made his vote will always beat out Dave’s. With respect to control of the business, they
are not equal at all. While Dave is entitled to his nearly equal share of the dividends, the
decision of how much to pay out in dividends is entirely Jason’s.1
If you compare Example 6.1.1 with 6.1.2, the difference in the dividend payable per share
is striking. Jason and Dave’s dry cleaning business pays a much larger dividend per share than
Zarofire Systems. Directly comparing these numbers can be very misleading though, among
other reasons because the number of shares is largely arbitrary. The dry cleaning business
has only 100 shares. If they wanted to, Jason and Dave could have structured the company
to have 100,000 shares instead, with Jason owning 51,000 and Dave owning 49,000. The
1
This assumes that the corporation’s bylaws require that votes will be decided by a majority vote. Corporation
bylaws can be set up so that votes require a larger majority (such as a two-thirds majority). Also some corporations
have different classes of shares, where some shares carry more votes than others.
bie24825_ch06.indd 252
5/23/07 3:10:12 PM
www.downloadslide.com
6.1 Stocks
253
dividend rate would then be $0.35 per share. Yet Jason would still own 51%, Dave would
still own 49%, and each man would still receive the same overall dividend. The dividend per
share can be a misleading measure of how desirable a stock investment is.
Distributing Profits of a Partnership
If a business is not set up as a corporation, how are the profits to be distributed among its
owners? The technical and legal details of how other businesses are structured fall outside
the scope of this book, but however the details are set up, there must be some agreement as
to how much each owner is entitled to receive.
If a business is set up as a partnership, the partners may agree to distribute all profits
equally. In that case, dividing them up is just a matter of dividing the profits to be distributed by the number of equal partners. This would not be unusual if all the partners of a
business contribute essentially the same effort, skills, and capital to the business. However,
it is also not unusual for the partners in a business to agree that some should receive a larger
share than others. One partner might work more hours or contribute more valuable expertise or more financial capital than another. In those cases, there is no formula that must be
used to determine how the profits would be split up; it is a matter of whatever distribution
the partners can agree is fair.
The partners may agree on a split of the profits based on the percent each will receive.
In that case, finding each individual’s take is simple a matter of applying her percent to the
total profit. Sometimes, rather than use percents, the partners may decide to split the profits
based on “parts” each is to receive. Mathematically, we treat each part as though it were a
share of stock. The following example will illustrate.
Example 6.1.3 Suppose that TJ, Rudy, Eric, and Kevin have a band, which they
have set up as a business partnership. They agree to distribute their profits in unequal
shares, because Rudy owns most of the band’s equipment and Eric wrote most of the
songs. They agree to distribute the profits as follows: TJ gets 3 parts, Rudy 5 parts,
Eric 4 parts, and Kevin gets 3 parts. (This sort of distribution can be abbreviated as
3:5:4:3 split, as long as it is clear which number goes with which person.)
The band earned $7,250 last month, and all four partners agree to distribute this
entire amount among them. How much does each person receive?
Even though this is not a corporation, we can pretend that each part is a share of stock for
the purposes of distributing the profits. So there are a total of 3 ϩ 5 ϩ 4 ϩ 3 ϭ 15 “shares,”
and so each share should receive $7,250/15 ϭ $483.33.
Copyright © 2008, The McGraw-Hill Companies, Inc.
Thus, TJ would receive 3($483.33) ϭ $1,449.49, as would Kevin. Similarly, Eric gets
4($483.33) ϭ $1,933.32, and Rudy gets 5($483.33) ϭ $2,416.65.
This could also be done with percents. Since he gets 3 parts out of 15, we could instead say that
TJ gets 3/15 ϭ 20%. Applying this 20% to the total profit, we get (20%)($7,250) ϭ $1,450.
(The penny difference is due to rounding.) Likewise, the other three bandmates would
receive 33.3%, 26.7%, and 20%, respectively, and their shares could be calculated with
percents in the same way.
Dividend Yields
It is often desirable to express a company’s dividend rate as a percent, to make comparisons
more meaningful. This rate is called the stock’s dividend yield.
The difficulty here is what that percent should be of. The most common way to do this
is to express the dividend as a percent of the current fair market value of a share of the
company’s stock. It is also common practice to express this as a rate per year, making it
more comparable to an interest rate.
The shares of many large corporations can be bought and sold through any stock broker.
Large companies, with many shares of stock outstanding, typically have their shares listed
on a major stock exchange such as the New York Stock Exchange or NASDAQ. There are
bie24825_ch06.indd 253
5/23/07 3:10:13 PM
nguon tai.lieu . vn
PA R T
two
SPECIFIC
APPLICATIONS
6
Investments
7
Retirement Plans
8
Mathematics of Pricing
9
Taxes
International Business
12
Financial Statements
13
Insurance and Risk Management
14
Evaluating Projected Cash Flows
15
bie24825_ch06.indd 249
Consumer Mathematics
11
Copyright © 2008, The McGraw-Hill Companies, Inc.
10
Payroll and Inventory
16
Business Statistics
5/23/07 3:10:00 PM
C H A P T E R
6
www.downloadslide.com
Investments
“October: This is one of the peculiarly
dangerous months to speculate in stocks.
The others are July, January, September,
April, November, May, March, June,
December, August and February.”
—Mark Twain, “Pudd’nhead Wilson’s Calendar for 1894”
Learning Objectives
Chapter Outline
LO 1
6.1
Stocks
6.2
Bonds
6.3
Commodities, Options, and Futures Contracts
6.4
Mutual Funds and Investment Portfolios
Identify the key characteristics of different types
of investments, including stocks, bonds, futures
and options, and mutual funds.
LO 2 Correctly use technical terminology related to
various types of investments.
LO 3
Calculate values used to measure the financial
results, including dividend rates, dividend yields,
compound annual growth rates, and total rates
of return.
LO 4 Recognize how investment concepts such as
risk, volatility, diversification, and leverage
can affect investment choice and investment
performance.
LO 5 Assess a reasonable rate of return expectation
for an investment portfolio based on the types
of investments it contains.
6.1
Stocks
In our work so far, we have put a great deal of effort into the mathematics of money
invested growing over time. When money is put to work as a loan, this growth is due to
the payment of interest. We have also recognized, though, that there are other ways that
money can be put to work aside from simple notes and bank deposits. We have seen that
present and future values can be calculated in the same way regardless of whether the
250
bie24825_ch06.indd 250
5/23/07 3:10:04 PM
www.downloadslide.com
Copyright © 2008, The McGraw-Hill Companies, Inc.
6.1 Stocks
251
growth really comes from interest or from other types of investment gain, and so we have
not spent much time discussing the details of these other sorts of possible investments. In
this chapter we will.
Money can be put to work by loaning it to someone else, but it can also be put to work by
buying something that we hope will provide a good return on the money invested. We could
buy a piece of real estate or gold coins in the hope that they will increase in value. One of the
main ways to put money to work, though, is by using it to start or buy part of a business. We
will begin this section by looking at money invested in the ownership of a business.
Businesses can legally be set up in a range of different ways. In a sole proprietorship
the business is owned entirely by one individual, the person who runs it. Many small businesses are set up in this way. For example, if Tom owns a snow plow and runs a business
plowing driveways in the winter, his business may well be a set up as a sole proprietorship.
A partnership is a business owned by two or more people, again typically the people who
actually run the business. If Lisa and Sunita work together preparing tax returns, their
business may be set up as a partnership.
There are other ways that a business can be structured though. You may be familiar with
such terms as limited partnership, limited liability company (LLC), and corporation. Each
type of structure has its advantages and disadvantages, and the choice of how to structure
a business requires weighing considerations such as taxes, exposure to risk and liability,
paperwork requirements, and other concerns.
One of the most commonly used structures for a business is a corporation. A corporation is a legal entity that can be thought of in many ways as an artificial legal person, able
to own property, enter into contracts, borrow money, and conduct business and financial
affairs just as an actual person could. To most people the word corporation suggests big
business, like Home Depot, Exxon Mobil, or General Electric. Those businesses are all corporations, but small businesses like Tom’s snowplowing business, or Lisa and Sunita’s tax
service, could equally well be set up as corporations. Setting up a business as a corporation
is generally more complicated than a sole proprietorship or simple partnership, but it can
offer significant advantages to its owners. One of the biggest advantages of a corporation
is that it exists as a separate legal entity from its owners; if things go badly and business
is sued or suffers severe financial losses, generally its owners can not be held personally
responsible for those liabilities.
A sole proprietorship is owned by its sole proprietor, and a partnership is owned by its
partners, but who owns a corporation? The ownership of a corporation is divided up among
its stockholders. Each individual piece of this ownership is called a share of the company’s
stock. How much of the business each share of stock represents depends on how many
shares of stock the company has issued. A corporation can have any number of shares, so
it is impossible to know how large a percent of the ownership one share represents unless
you know the total. If you own one share of stock in a company with just 10 shares, then
you own 1/10 (or 10%) of the company. If the company has issued one billion shares, then
one share equates to owning 1/1,000,000,000 (or 0.0000001%) of the company.
When stock is first issued by a corporation, it may be issued with a par value. Loosely
speaking, a stock’s par value is a reflection of a portion of the money paid by the original
shareholders into the corporation. Par value used to be considered more important than it
usually is today, and in fact it is not unusual today for a stock to have no par value, or to
have a par value which is absurdly low compared to the realistic value of the stock.
Some companies also issue several different types of stock. As its name suggests,
common stock is the most common type, though preferred stock is another. While both
types of stock represent ownership of a piece of a corporation, the two types differ in
how their owners share in the company’s profits, who has first claim to the corporation’s
remaining assets in the event it goes into bankruptcy, and in their voting rights in the election
of the board of directors (the group of people who direct the corporation’s activities).
Except as noted, we will be discussing only common stocks in this text. Small businesses
seldom issue preferred stock, and even among very large corporations it is not unusual to
see little, it any, preferred stock issued.
bie24825_ch06.indd 251
5/23/07 3:10:12 PM
www.downloadslide.com
252
Chapter 6 Investments
Dividends
The profits earned by a corporation properly belong to its shareholders, the people who
own the corporation. However, since the corporation is a separate legal entity, a shareholder
does not have the right to access the corporation’s funds directly. Each shareholder receives
a portion of the corporation’s profits when they are paid out in the form of dividends. A
corporation’s board of directors will periodically evaluate the business’s performance and
decide how much money should be paid out to its shareholders (this is known as declaring
a dividend.) Corporations normally hold on to at least some of their profits to use in growing the business for the future, and some corporations don’t pay out any dividends at all.
On the other hand, sometimes a corporation will pay more in dividends than it earns if it
has a significant amount of unused cash on hand. In either case, the dividends paid out by
a corporation are seldom exactly equal to the corporation’s profits.
Dividends are divided up among the shareholders according to the number of shares
each owns.
Example 6.1.1 Zarofire Systems earned $743,000 in the last quarter, and the
company’s management has declared a dividend of $450,000. The company has
1,000,000 shares of stock issued. If you own 200 shares of the company’s stock, how
much will you receive as a dividend?
The $450,000 total dividend must be distributed among the shareholders based on the
number of shares each one owns; $450,000/1,000,000 shares works out to $0.45 per
share. Since you own 200 shares, you will receive (200 shares)($0.45 per share) ϭ $90.00.
Rounding can be an issue with dividend rate calculations. In Example 6.1.1 the dividend
rate came out evenly, but this will not always happen. Since the dividend rate per share
often comes out to be a fairly small amount of money, it is not uncommon to see dividend
rates carried out to a tenth of a cent. For example, a company might pay a dividend of
12.5 cents per share, or $0.125 per share.
Dividend calculations work out the same way with small businesses as with large ones.
Example 6.1.2 Jason and Dave’s dry cleaning business is set up as a corporation.
There are 100 shares of stock; Jason owns 51 shares and Dave owns 49. In the last
quarter the business earned $39,750 in profits, and the company declared a dividend
of $35,000. How much will Jason and Dave each get?
The $35,000 profit will be distributed based on the number of shares each person owns;
$35,000/100 shares ϭ $350 per share. Since Jason owns 51 shares, he will receive (51 shares)
($350 per share) ϭ $17,850.
Dave will receive (49 shares)($350 per share) ϭ $17,150.
In this example, Jason and Dave both own nearly the same number of shares, and so they
receive nearly the same amounts in dividends. Financially speaking, they are close to being
equal owners of the business. However, in another important respect they are not equal at
all. Since Jason owns 51% of the shares of the business, whenever any decisions need to
be made his vote will always beat out Dave’s. With respect to control of the business, they
are not equal at all. While Dave is entitled to his nearly equal share of the dividends, the
decision of how much to pay out in dividends is entirely Jason’s.1
If you compare Example 6.1.1 with 6.1.2, the difference in the dividend payable per share
is striking. Jason and Dave’s dry cleaning business pays a much larger dividend per share than
Zarofire Systems. Directly comparing these numbers can be very misleading though, among
other reasons because the number of shares is largely arbitrary. The dry cleaning business
has only 100 shares. If they wanted to, Jason and Dave could have structured the company
to have 100,000 shares instead, with Jason owning 51,000 and Dave owning 49,000. The
1
This assumes that the corporation’s bylaws require that votes will be decided by a majority vote. Corporation
bylaws can be set up so that votes require a larger majority (such as a two-thirds majority). Also some corporations
have different classes of shares, where some shares carry more votes than others.
bie24825_ch06.indd 252
5/23/07 3:10:12 PM
www.downloadslide.com
6.1 Stocks
253
dividend rate would then be $0.35 per share. Yet Jason would still own 51%, Dave would
still own 49%, and each man would still receive the same overall dividend. The dividend per
share can be a misleading measure of how desirable a stock investment is.
Distributing Profits of a Partnership
If a business is not set up as a corporation, how are the profits to be distributed among its
owners? The technical and legal details of how other businesses are structured fall outside
the scope of this book, but however the details are set up, there must be some agreement as
to how much each owner is entitled to receive.
If a business is set up as a partnership, the partners may agree to distribute all profits
equally. In that case, dividing them up is just a matter of dividing the profits to be distributed by the number of equal partners. This would not be unusual if all the partners of a
business contribute essentially the same effort, skills, and capital to the business. However,
it is also not unusual for the partners in a business to agree that some should receive a larger
share than others. One partner might work more hours or contribute more valuable expertise or more financial capital than another. In those cases, there is no formula that must be
used to determine how the profits would be split up; it is a matter of whatever distribution
the partners can agree is fair.
The partners may agree on a split of the profits based on the percent each will receive.
In that case, finding each individual’s take is simple a matter of applying her percent to the
total profit. Sometimes, rather than use percents, the partners may decide to split the profits
based on “parts” each is to receive. Mathematically, we treat each part as though it were a
share of stock. The following example will illustrate.
Example 6.1.3 Suppose that TJ, Rudy, Eric, and Kevin have a band, which they
have set up as a business partnership. They agree to distribute their profits in unequal
shares, because Rudy owns most of the band’s equipment and Eric wrote most of the
songs. They agree to distribute the profits as follows: TJ gets 3 parts, Rudy 5 parts,
Eric 4 parts, and Kevin gets 3 parts. (This sort of distribution can be abbreviated as
3:5:4:3 split, as long as it is clear which number goes with which person.)
The band earned $7,250 last month, and all four partners agree to distribute this
entire amount among them. How much does each person receive?
Even though this is not a corporation, we can pretend that each part is a share of stock for
the purposes of distributing the profits. So there are a total of 3 ϩ 5 ϩ 4 ϩ 3 ϭ 15 “shares,”
and so each share should receive $7,250/15 ϭ $483.33.
Copyright © 2008, The McGraw-Hill Companies, Inc.
Thus, TJ would receive 3($483.33) ϭ $1,449.49, as would Kevin. Similarly, Eric gets
4($483.33) ϭ $1,933.32, and Rudy gets 5($483.33) ϭ $2,416.65.
This could also be done with percents. Since he gets 3 parts out of 15, we could instead say that
TJ gets 3/15 ϭ 20%. Applying this 20% to the total profit, we get (20%)($7,250) ϭ $1,450.
(The penny difference is due to rounding.) Likewise, the other three bandmates would
receive 33.3%, 26.7%, and 20%, respectively, and their shares could be calculated with
percents in the same way.
Dividend Yields
It is often desirable to express a company’s dividend rate as a percent, to make comparisons
more meaningful. This rate is called the stock’s dividend yield.
The difficulty here is what that percent should be of. The most common way to do this
is to express the dividend as a percent of the current fair market value of a share of the
company’s stock. It is also common practice to express this as a rate per year, making it
more comparable to an interest rate.
The shares of many large corporations can be bought and sold through any stock broker.
Large companies, with many shares of stock outstanding, typically have their shares listed
on a major stock exchange such as the New York Stock Exchange or NASDAQ. There are
bie24825_ch06.indd 253
5/23/07 3:10:13 PM