Chapter 1
The Role and
Environment
of Managerial
Finance
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
1.
2.
3.
4.
Learning Goals
Define finance, its major areas and opportunities
available in this field, and the legal forms of business
organization.
Describe the managerial finance function and its
relationship to economics and accounting.
Identify the primary activities of the financial
manager.
Explain the goal of the firm, corporate governance,
the role of ethics, and the agency issue.
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1-0
Learning Goals (cont.)
1.
Understand financial institutions and markets,
and the role they play in managerial finance.
2.
Discuss business taxes and their importance
in financial decisions.
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1-0
What is Finance?
£81
•
Finance can be defined as the art and science of
managing money.
•
Finance is concerned with the process,
institutions, markets, and instruments involved
in the transfer of money among individuals,
businesses, and governments.
d
Wings
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Major Areas & Opportunities in Finance:
Financial Services
•
1
owl
Financial Services is the area of finance
concerned with the design and delivery of
advice and financial products to individuals,
businesses, and government.
• Career opportunities include banking, personal
is
financial planning, investments, real estate, and
§ insurance.
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1-0
Major Areas & Opportunities in Finance:
Managerial Finance
•
•
•
USD18
'
>
£661
Managerial finance is concerned with the duties of the
financial manager in the business firm.
The financial manager actively manages the financial
affairs of any type of business, whether private or
public, large or small, profit-seeking or not-for-profit.
They are also more involved in developing corporate
strategy and improving the firm’s competitive position.
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Major Areas & Opportunities in Finance:
Managerial Finance (cont.)
•
•
Increasing globalization has complicated the
financial management function by requiring
them to be proficient in managing cash flows in
different currencies and protecting against the
risks inherent in international transactions.
Changing economic and regulatory conditions
also complicate the financial management
function.
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1-0
Table 1.1 Strengths and Weaknesses of the
Common Legal Forms of Business Organization
-
‫شركات فرادية‬
‫شركات االشخاص‬
‫شركات املساهمة العامة‬
-05
*
%
↳
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1-0
Figure 1.1 Corporate Organization
‫الهيكل التنظيمي للشركة املساهمة العامة‬
⑨
¥
31
← its
's
stockholders
2152,6311
HM
I.
a-
b
HI
.
¥1K
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→
I
1-0
Table 1.2 Other Limited Liability
Organizations
×
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1-0
Table 1.3 Career Opportunities in
Managerial Finance
X
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The Managerial Finance Function
Ea
•
The size and importance of the managerial finance
function depends on the size of the firm.
•
In small companies, the finance function may be
performed by the company president or accounting
department.
•
As the business expands, finance typically evolves into
a separate department linked to the president as was
previously described in Figure 1.1.
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1-0
The Managerial Finance Function:
Relationship to Economics
•
•
•
The field of finance is actually an outgrowth of
economics.
{
In fact, finance is sometimes referred to as
financial economics.
Financial managers must understand the
economic framework within which they operate
in order to react or anticipate to changes in
conditions.
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1-0
The Managerial Finance Function:
Relationship to Economics (cont.)
•
The primary economic principal used by
financial managers is marginal cost-benefit
analysis which says that financial decisions
should be implemented only when added
benefits exceed added costs.
e
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The Managerial Finance Function:
Relationship to Accounting
•
The firm’s finance (treasurer) and accounting
(controller) functions are closely-related and
overlapping.
•
In smaller firms, the financial manager generally
performs both functions.
F
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The Managerial Finance Function:
Relationship to Accounting (cont.)
•
•
One major difference in perspective and
emphasis between finance and accounting is that
accountants generally use the accrual method
while in finance, the focus is on cash flows.
The significance of this difference can be
illustrated using the following simple example.
e
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The Managerial Finance Function:
Relationship to Accounting (cont.)
•
The Nassau Corporation experienced the following
activity last year:
$100,000 (1 yacht sold, 100% still uncollected)
Sales
Costs
•
$ 80,000 (all paid in full under supplier terms)
Now contrast the differences in performance under the
accounting method versus the cash method.
e
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The Managerial Finance Function:
Relationship to Accounting (cont.)
e
INCOME STATEMENT SUMMARY
Sales
Less: Costs
Net Profit/(Loss)
ACCRUAL
$100,000
(80,000)
$ 20,000
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CASH
$
0
(80,000)
$(80,000)
1-0
The Managerial Finance Function:
Relationship to Accounting (cont.)
•
•
•
e
Finance and accounting also differ with respect to
decision-making.
While accounting is primarily concerned with the
presentation of financial data, the financial manager is
primarily concerned with analyzing and interpreting
this information for decision-making purposes.
The financial manager uses this data as a vital tool for
making decisions about the financial aspects of the
firm.
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1-0
Figure 1.2 Financial Activities
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d
1-0
•
I. II
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‫قرار التمويل‬
‫قرار االستثمار‬
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capital
Goal of the Firm: Maximize Profit???
•
Profit maximization fails to account for differences in the level of
cash flows (as opposed to profits), the timing of these cash
flows, and the risk of these cash flows.
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1-0
⇐
⑨
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$8000
③
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Goal of the Firm:
Maximize Shareholder Wealth!!!
•
•
•
Why?
Because maximizing shareholder wealth properly considers cash
flows, the timing of these cash flows, and the risk of these cash
flows.
This can be illustrated using the following simple stock valuation
equation: perf É
→ capital Assets Prisingmodie
B(rmerA )
'
+
16%6
Share Price = Future Dividends
Required Return
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
level & timing of
cash flows
risk of cash flows
1-0
Goal of the Firm:
Maximize Shareholder Wealth!!! (cont.)
•
The process of shareholder wealth maximization
can be described using the following flow chart:
Figure 1.3 Share Price Maximization
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1-0
Goal of the Firm:
What About Other Stakeholders?
•
Stakeholders include all groups of individuals who have
a direct economic link to the firm including employees,
customers, suppliers, creditors, owners, and others who
have a direct economic link to the firm.
•
The "Stakeholder View" prescribes that the firm make a
conscious effort to avoid actions that could be
detrimental to the wealth position of its stakeholders.
•
Such a view is considered to be "socially responsible."
← ↳ If
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s_ An
-
1-0
Corporate Governance
=
# two
•
Corporate Governance is the system used to direct and
control a corporation.
•
It defines the rights and responsibilities of key
corporate participants such as shareholders, the board
of directors, officers and managers, and other
stakeholders.
•
The structure of corporate governance was previously
described in Figure 1.1.
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Individual versus Institutional Investors
•
Individual investors are investors who purchase relatively small
quantities of shares in order to earn a return on idle funds, build a
source of retirement income, or provide financial security.
•
Institutional investors are investment professionals who are paid
to manage other people’s money.
•
They hold and trade large quantities of securities for individuals,
businesses, and governments and tend to have a much greater
impact on corporate governance.
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The Sarbanes-Oxley Act of 2002
•
The Sarbanes-Oxley Act of 2002 (commonly called SOX)
eliminated many disclosure and conflict of interest problems that
surfaced during the early 2000s.
•
SOX:
–
–
–
–
–
established an oversight board to monitor the accounting industry;
tightened audit regulations and controls;
toughened penalties against executives who commit corporate fraud;
strengthened accounting disclosure requirements;
established corporate board structure guidelines.
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The Role of Ethics: Ethics Defined
•
•
•
Ethics is the standards of conduct or moral
judgment—have become an overriding issue in
both our society and the financial community
Ethical violations attract widespread publicity
Negative publicity often leads to negative
impacts on a firm
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1-0
¥
The Role of Ethics: Considering Ethics
•
–
–
–
–
Robert A. Cooke, a noted ethicist, suggests that the
following questions be used to assess the ethical
viability of a proposed action:
Does the action unfairly single out an individual
or group?
Does the action affect the morals, or legal rights of any
individual or group?
Does the action conform to accepted moral standards?
Are there alternative courses of action that are less likely to
cause actual or potential harm?
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The Role of Ethics:
Considering Ethics (cont.)
•
–
–
–
–
–
x
Cooke suggests that the impact of a proposed decision should be
evaluated from a number of perspectives:
Are the rights of any stakeholder being violated?
Does the firm have any overriding duties to any stakeholder?
Will the decision benefit any stakeholder to the detriment of another
stakeholder?
If there is a detriment to any stakeholder, how should it be remedied, if at
all?
What is the relationship between stockholders and stakeholders?
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1-0
The Role of Ethics:
Ethics & Share Price
•
–
–
–
–
•
x
Ethics programs seek to:
reduce litigation and judgment costs
maintain a positive corporate image
build shareholder confidence
gain the loyalty and respect of all stakeholders
The expected result of such programs is to
positively affect the firm's share price.
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1-0
The Agency Issue:
The Agency Problem
•
Whenever a manager owns less than 100% of the firm’s equity, a
potential agency problem exists.
•
In theory, managers would agree with shareholder wealth
maximization.
•
However, managers are also concerned with their personal
wealth, job security, fringe benefits, and lifestyle.
•
This would cause managers to act in ways that do not always
benefit the firm shareholders.
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The Agency Issue:
Resolving the Problem
•
Market Forces such as major shareholders and
the threat of a hostile takeover act to keep
managers in check.
•
Agency Costs are the costs borne by
stockholders to maintain a corporate governance
structure that minimizes agency problems and
contributes to the maximization of shareholder
wealth.
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The Agency Issue:
Resolving the Problem (cont.)
•
Examples would include bonding or monitoring
management behavior, and structuring
management compensation to make
shareholders interests their own.
•
A stock option is an incentive allowing
managers to purchase stock at the market price
set at the time of the grant.
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The Agency Issue:
Resolving the Problem (cont.)
• Performance plans tie management
compensation to measures such as EPS growth;
performance shares and/or cash bonuses are
used as compensation under these plans.
• Recent studies have failed to find a strong
relationship between CEO compensation and
share price.
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1-35
Financial Institutions & Markets
• Firms that require funds from external sources
can obtain them in three ways:
– through a bank or other financial institution
– through financial markets
– through private placements
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1-36
Financial Institutions & Markets:
Financial Institutions
• Financial institutions are intermediaries that channel
the savings of individuals, businesses, and governments
into loans or investments.
• The key suppliers and demanders of funds are
individuals, businesses, and governments.
• In general, individuals are net suppliers of funds, while
businesses and governments are net demanders of
funds.
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1-37
Chapter 2
Financial
Statements
and Analysis
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1.
Learning Goals
Review the contents of the stockholders’ report and
the procedures for consolidating international
financial statements.
2.
Understand who uses financial ratios, and how.
3.
Use ratios to analyze a firm’s liquidity and activity.
4.
Discuss the relationship between debt and financial
leverage and the ratios used to analyze a firm’s debt.
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2-0
1.
2.
Learning Goals (cont.)
Use ratios to analyze a firm’s profitability and
market value.
Use a summary of financial ratios and the
DuPont system of analysis to perform a
complete ratio analysis.
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2-0
The Stockholders’ Report
•
The guidelines used to prepare and maintain financial records
and reports are known as generally accepted accounting
principles (GAAP).
•
GAAP is authorized by the Financial Accounting Standards
Board (FASB).
•
The Sarbanes-Oxley Act of 2002, passed to eliminate the many
disclosure and conflict of interest problems of corporations,
established the Public Company Accounting Oversight Board
(PCAOB), which is a not-for-profit corporation that overseas
auditors.
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2-0
The Stockholders’ Report (cont.)
•
The PCAOB is charged with protecting the interests of
investors and furthering the public interest in the
preparation of informative, fair, and independent audit
reports.
•
Public corporations with more than $5 million in assets
and more than 500 stockholders are required by the
SEC to provide their stockholders with an annual
stockholders report.
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2-0
The Four Key Financial Statements:
The Income Statement
•
The income statement provides a financial
summary of a company’s operating results
during a specified period.
•
Although they are prepared annually for
reporting purposes, they are generally computed
monthly by management and quarterly for tax
purposes.
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2-0
The Four Key Financial Statements
Table 2.1 Bartlett
Company Income
Statements ($000)
G.
↳21
¥+1
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2-0
The Four Key Financial Statements:
The Balance Sheet
•
The balance sheet presents a summary of a
firm’s financial position at a given point in time.
•
Assets indicate what the firm owns, equity
represents the owners’ investment, and liabilities
indicate what the firm has borrowed.
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2-0
The Four Key Financial Statements
Table 2.2a Bartlett
Company Balance Sheets
($000)
JIJI
Balance sheets
Assets
¥4!
B. s
Gab
equity
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2-0
The Four Key
Financial Statements (cont.)
Table 2.2b Bartlett
Company Balance
Sheets ($000)
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2-0
The Four Key Financial Statements:
Statement of Retained Earnings
•
✗
The statement of retained earnings reconciles the
net income earned and dividends paid during the
year, with the change in retained earnings.
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2-0
The Four Key Financial Statements
✗
Table 2.3 Bartlett Company Statement of Retained Earnings
($000) for the Year Ended December 31, 2009
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2-0
The Four Key Financial Statements:
Statement of Cash Flows
•
•
The statement of cash flows provides a
summary of the cash flows over the period of
concern, typically the year just ended.
This statement not only provides insight into a
company’s investment, financing and operating
activities, but also ties together the income
statement and previous and current balance
sheets.
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*2-0
The Four Key Financial Statements
Table 2.4 Bartlett
Company Statement of
Cash Flows ($000) for the
Year Ended December 31,
2009
%
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2-0
Chapter 4
Time Value of
Money
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
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start
1.
2.
3.
Learning Goals
Discuss the role of time value in finance, the use of
computational aids, and the basic patterns of cash
flow.
Understand the concept of future value and present
value, their calculation for single amounts, and the
relationship between them.
Find the future value and the present value of both an
ordinary annuity, and the present value of a perpetuity.
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4-0
1.
2.
3.
Learning Goals (cont.)
Calculate both the future value and the present value
of a mixed stream of cash flows.
Understand the effect that compounding interest
more frequently than annually has on future value and
the effective annual rate of interest.
Describe the procedures involved in (1) determining
deposits needed to accumulate to a future sum, (2)
loan amortization, (3) finding interest or growth rates,
and (4) finding an unknown number of periods.
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4-0
The Role of Time Value in Finance
•
•
•
–
–
•
Most financial decisions involve costs & benefits that
are spread out over time.
Time value of money allows comparison of cash
flows from different periods.
Question: Your father has offered to give you some
money and asks that you choose one of the following
two alternatives:
$1,000 today, or
$1,100 one year from now.
What do you do?
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4-0
The Role of Time Value in Finance (cont.)
•
•
•
The answer depends on what rate of interest
you could earn on any money you receive
today.
For example, if you could deposit the $1,000
today at 12% per year, you would prefer to be
paid today.
Alternatively, if you could only earn 5% on
deposited funds, you would be better off if you
chose the $1,100 in one year.
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4-0
Basic Concepts
•
Future Value: compounding or growth over
time
•
Present Value: discounting to today’s value
•
Single cash flows & series of cash flows can be
considered
•
Time lines are used to illustrate these
relationships
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4-0
Computational Aids
•
Use the Equations
•
Use the Financial Tables
•
Use Financial Calculators
•
Use Electronic Spreadsheets
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4-0
Computational Aids (cont.)
Figure 4.1 Time Line
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4-0
Computational Aids (cont.)
Figure 4.2 Compounding and
Discounting
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4-0
Computational Aids (cont.)
Figure 4.3 Calculator Keys
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4-0
Computational Aids (cont.)
Figure 4.4 Financial Tables
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Basic Patterns of Cash Flow
•
•
The cash inflows and outflows of a firm can be described by its general
pattern.
The three basic patterns include a single amount, an annuity, or a mixed
stream:
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4-0
Simple Interest
•
With simple interest, you don’t earn interest on interest.
•
Year 1: 5% of $100
=
$5 + $100 = $105
•
Year 2: 5% of $100
=
$5 + $105 = $110
•
Year 3: 5% of $100
=
$5 + $110 = $115
•
Year 4: 5% of $100
=
$5 + $115 = $120
•
Year 5: 5% of $100
=
$5 + $120 = $125
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
② Simple
$
Interest Rate
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Compound Interest
•
With compound interest, a depositor earns interest on interest!
•
Year 1: 5% of $100.00
= $5.00 + $100.00
= $105.00
•
Year 2: 5% of $105.00
= $5.25 + $105.00
= $110.25
•
Year 3: 5% of $110.25
= $5 .51+ $110.25
= $115.76
•
Year 4: 5% of $115.76
= $5.79 + $115.76
= $121.55
•
Year 5: 5% of $121.55
= $6.08 + $121.55
= $127.63
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Time Value Terms
•
PV0
=
present value or beginning amount
•
i = interest rate
•
FVn
=
•
n =
number of compounding periods
•
A = an annuity (series of equal payments
receipts)
future value at end of “n” periods
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
or
4-0
① future value
④ for
④
for
②
a
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•
FVn
=
PV0(1+i)n
•
PV0
=
FVn[1/(1+i)n]
•
FVAn
=
A (1+i)n - 1
=
PV x (FVIFi,n)
=
FV x (PVIFi,n)
= A x (FVIFAi,n)
i
•
PVA0
=
A 1 - [1/(1+i)n] =
Ax
(PVIFAi,n)
i
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount
•
Future Value techniques typically measure cash flows at the end
of a project’s life.
•
Future value is cash you will receive at a given future date.
•
The future value technique uses compounding to find the future
value of each cash flow at the end of an investment’s life and
then sums these values to find the investment’s future value.
•
We speak of compound interest to indicate that the amount of
interest earned on a given deposit has become part of the
principal at the end of the period.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount: Using
FVIF Tables
•
If Fred Moreno places $100 in a savings account
paying 8% interest compounded annually, how
much will he have in the account at the end of
one year?
$100 x (1.08)1 = $100 x FVIF8%,1
$100 x 1.08 = $108
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount: The
Equation for Future Value
•
Jane Farber places $800 in a savings account
paying 6% interest compounded annually. She
wants to know how much money will be in the
account at the end of five years.
FV5 = $800 X (1 + 0.06)5 = $800 X (1.338) = $1,070.40
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount:
Using a Financial Calculator
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount:
Using Spreadsheets
e@
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Single Amount:
A Graphical View of Future Value
Figure 4.5
Future Value
Relationship
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Single Amount
•
Present value is the current dollar value of a future amount of
money.
•
It is based on the idea that a dollar today is worth more than a
dollar tomorrow.
•
It is the amount today that must be invested at a given rate to
reach a future amount.
•
Calculating present value is also known as discounting.
•
The discount rate is often also referred to as the opportunity cost,
the discount rate, the required return, or the cost of capital.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
29
4-0
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Present Value of a Single Amount: Using
PVIF Tables
•
Paul Shorter has an opportunity to receive $300
one year from now. If he can earn 6% on his
investments, what is the most he should pay now
for this opportunity?
$300 x [1/(1.06)1]
$300 x 0.9434
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
=
=
$300 x PVIF6%,1
$283.02
4-0
Present Value of a Single Amount: The
Equation for Future Value
•
Pam Valenti wishes to find the present value of
$1,700 that will be received 8 years from now.
Pam’s opportunity cost is 8%.
PV = $1,700/(1 + 0.08)8 = $1,700/1.851 = $918.42
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Single Amount: Using
a Financial Calculator
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Single Amount: Using
Spreadsheets
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Single Amount: A
Graphical View of Present Value
Figure 4.6
Present
Value
Relationship
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Annuities
•
•
•
•
•
Annuities are equally-spaced cash flows of equal size.
Annuities can be either inflows or outflows.
An ordinary (deferred) annuity has cash flows that
occur at the end of each period.
An annuity due has cash flows that occur at the
beginning of each period.
An annuity due will always be greater than an
otherwise equivalent ordinary annuity because interest
will compound for an additional period.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Types of Annuities
•
Fran Abrams is choosing which of two annuities to
receive. Both are 5-year $1,000 annuities; annuity A is
an ordinary annuity, and annuity B is an annuity due.
Fran has listed the cash flows for both annuities as
shown in Table 4.1 on the following slide.
Note that the amount of both annuities total $5,000.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Table 4.1 Comparison of Ordinary
Annuity and Annuity Due Cash Flows
($1,000, 5 Years)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Finding the Future Value of an Ordinary
Annuity
•
Fran Abrams wishes to determine how much money she
will have at the end of 5 years if he chooses annuity A,
the ordinary annuity and it earns 7% annually. Annuity
a is depicted graphically below:
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of an Ordinary Annuity:
Using the FVIFA Tables
FVA = $1,000 (FVIFA,7%,5)
= $1,000 (5.751)
= $5,751
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of an Ordinary Annuity:
Using a Financial Calculator
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of an Ordinary Annuity:
Using Spreadsheets
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Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of an Ordinary Annuity
•
Braden Company, a small producer of plastic toys, wants to
determine the most it should pay to purchase a particular
annuity. The annuity consists of cash flows of $700 at the end
of each year for 5 years. The required return is 8%.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of an Ordinary Annuity:
The Long Method
Table 4.2 Long Method for Finding the Present
Value of an Ordinary Annuity
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of an Ordinary Annuity:
Using PVIFA Tables
PVA =
$700 (PVIFA,8%,5)
=
$700 (3.993)
=
$2,795.10
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of an Ordinary Annuity:
Using a Financial Calculator
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Perpetuity
•
•
A perpetuity is a special kind of annuity.
With a perpetuity, the periodic annuity or cash
flow stream continues forever.
PV = Annuity/Interest Rate
•
For example, how much would I have to deposit
today in order to withdraw $1,000 each year
forever if I can earn 8% on my deposit?
PV = $1,000/.08 = $12,500
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Mixed Stream
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Mixed Stream:
Using Excel
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Future Value of a Mixed Stream (cont.)
Table 4.3 Future Value of a Mixed Stream of
Cash Flows
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
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Present Value of a Mixed Stream
•
Frey Company, a shoe manufacturer, has been
offered an opportunity to receive the following
mixed stream of cash flows over the next 5
years.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Mixed Stream
•
•
If the firm must earn at least 9% on its investments,
what is the most it should pay for this opportunity?
This situation is depicted on the following time line.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Mixed Stream:
Using Excel
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Present Value of a Mixed Stream
Table 4.4 Present Value of a Mixed Stream of Cash
Flows
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually
•
Compounding more frequently than once a year results
in a higher effective interest rate because you are
earning on interest on interest more frequently.
•
As a result, the effective interest rate is greater than the
nominal (annual) interest rate.
•
Furthermore, the effective rate of interest will increase
the more frequently interest is compounded.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually (cont.)
•
Fred Moreno has found an institution that will pay him 8%
annual interest, compounded quarterly. If he leaves the money
in the account for 24 months (2 years), he will be paid 2%
interest compounded over eight periods.
Table 4.5 Future Value from Investing $100 at 8% Interest
Compounded Semiannually over 24 Months (2 Years)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually (cont.)
Table 4.6 Future Value from Investing $100 at 8%
Interest Compounded Quarterly over 24 Months (2 Years)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually (cont.)
Table 4.7 Future Value at the End of Years 1 and
2 from Investing $100 at 8% Interest, Given
Various Compounding Periods
{
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually (cont.)
•
A General Equation for Compounding More
Frequently than Annually
{
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently
Than Annually (cont.)
•
–
A General Equation for Compounding More Frequently
than Annually
Recalculate the example for the Fred Moreno example
assuming (1) semiannual compounding and (2) quarterly
compounding.
e
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently Than
Annually: Using a Financial Calculator
{
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Compounding Interest More Frequently Than
Annually: Using a Spreadsheet
&
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Continuous Compounding
•
With continuous compounding the number of
compounding periods per year approaches infinity.
•
Through the use of calculus, the equation thus becomes:
FVn (continuous compounding) = PV x
(eixn) where “e” has a value of 2.7183.
•
Continuing with the previous example, find the Future
value of the $100 deposit after 5 years if interest is
compounded continuously.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Continuous Compounding (cont.)
•
•
With continuous compounding the number of
compounding periods per year approaches infinity.
Through the use of calculus, the equation thus becomes:
FVn (continuous compounding) = PV x
(eixn) where “e” has a value of 2.7183.
FVn
= 100 x (2.7183).08x2 = $117.35
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Continuous Compounding:
Using a Financial Calculator
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Continuous Compounding:
Using a Spreadsheet
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Nominal & Effective Annual Rates of
Interest
•
•
•
The nominal interest rate is the stated or contractual
rate of interest charged by a lender or promised by a
borrower.
The effective interest rate is the rate actually paid or
earned.
In general, the effective rate > nominal rate whenever
compounding occurs more than once per year
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Nominal & Effective Annual Rates of
Interest (cont.)
•
Fred Moreno wishes to find the effective annual rate associated
with an 8% nominal annual rate (I = .08) when interest is
compounded (1) annually (m=1); (2) semiannually (m=2); and
(3) quarterly (m=4).
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Deposits Needed to Accumulate to a Future Sum
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value: Deposits
Needed to Accumulate to a Future Sum (cont.)
•
Suppose you want to buy a house 5 years from now and
you estimate that the down payment needed will be
$30,000. How much would you need to deposit at the
end of each year for the next 5 years to accumulate
$30,000 if you can earn 6% on your deposits?
PMT = $30,000/5.637 = $5,321.98
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value: Deposits
Needed to Accumulate to a Future Sum (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value: Deposits
Needed to Accumulate to a Future Sum (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Loan Amortization
Table 4.8 Loan Amortization Schedule
($6,000 Principal, 10% Interest, 4-Year Repayment Period)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Loan Amortization (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Interest or Growth Rates
•
At times, it may be desirable to determine the
compound interest rate or growth rate implied
by a series of cash flows.
Ray Noble wishes to find the rate of interest or growth
reflected in the stream of cash flows he received from a
real estate investment over the period from 2002 through
2006 as shown in the table on the following slide.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Interest or Growth Rates (cont.)
PVIFi,5yrs = PV/FV = ($1,250/$1,520) = 0.822
PVIFi,5yrs = approximately 5%
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Interest or Growth Rates (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Interest or Growth Rates (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Finding an Unknown Number of Periods
•
At times, it may be desirable to determine the number
of time periods needed to generate a given amount of
cash flow from an initial amount.
Ann Bates wishes to determine the number of years it
will take for her initial $1,000 deposit, earning 8% annual
interest, to grow to equal $2,500. Simply stated, at an
8% annual rate of interest, how many years, n, will it
take for Ann’s $1,000 (PVn) to grow to $2,500 (FVn)?
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Finding an Unknown Number of Periods (cont.)
PVIF8%,n = PV/FV = ($1,000/$2,500) = .400
PVIF8%,n = approximately 12 years
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Finding an Unknown Number of Periods (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Special Applications of Time Value:
Finding an Unknown Number of Periods (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Table 4.9 Summary of Key Definitions,
Formulas, and Equations for Time Value
of Money
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
Table 4.9 Summary of Key Definitions,
Formulas, and Equations for Time Value of
Money (cont.)
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
4-0
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