المملكة العربية السعودية
وزارة التعليم
الجامعة السعودية اإللكترونية
Kingdom of Saudi Arabia
Ministry of Education
Saudi Electronic University
College of Administrative and Financial Sciences
Assignment 2
Principles of Finance (FIN 101)
Due Date: 08/08/2022 @ 23:59
Course Name: Principles of Finance
Student’s Name:
Course Code: FIN 101
Student’s ID Number:
Semester: Summer
CRN:
Academic Year:2021-22-Summer Semester
For Instructor’s Use only
Instructor’s Name:
Students’ Grade: /15
Level of Marks: High/Middle/Low
General Instructions – PLEASE READ THEM CAREFULLY
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The Assignment must be submitted on Blackboard (WORD format only) via
allocated folder.
Assignments submitted through email will not be accepted.
Students are advised to make their work clear and well presented, marks may be
reduced for poor presentation. This includes filling your information on the cover
page.
Students must mention question number clearly in their answer.
Late submission will NOT be accepted.
Avoid plagiarism, the work should be in your own words, copying from students
or other resources without proper referencing will result in ZERO marks. No
exceptions.
All answered must be typed using Times New Roman (size 12, double-spaced)
font. No pictures containing text will be accepted and will be considered
plagiarism).
Submissions without this cover page will NOT be accepted.
Learning Outcomes:
1. Explain the relationship between risk and return. (2.1)
2. Evaluate the cost of capital for decisions related to financing the operations of a
corporation. (2.3)
3. Measure financial corporate performance. (2.4)
Assignment Question(s): (6 x 2.5 = 15 Marks)
1. You are currently thinking about investing in a stock valued at $25.00 per share.
The stock recently paid a dividend of $2.25 and its dividend is expected to grow at
a rate of 5 percent for the foreseeable future. You normally require a return of 14
percent on stocks of similar risk. Is the stock overpriced, underpriced, or correctly
priced?
2. Critical Thinking Question: What does it mean when a company has a very high
P/E ratio? Give examples of industries in which you believe high P/E ratios are
justified.
3. Nonconstant growth: Diaz Corp. is expected to grow rapidly at a rate of 35 percent
for the next seven years. The company’s first dividend, to be paid three years from
now, will be $5. After seven years, the company (and the dividends it pays) will
grow at a rate of 8.5 percent. What is the value of Diaz stock with a required rate
of return of 14 percent?
4. Calculate and interpret net present value (NPV), internal rate of return (IRR),
payback period, discounted payback period, and profitability index (PI) of a single
capital project.
5. Critical Thinking Question: Your manager just finished calculating your
company’s weighted average cost of capital. He is relieved because he says that he
can now use that cost of capital to evaluate all projects that the company is
considering for the next 4 years. Evaluate that statement.
6. WACC for a company: Contemporary Products Ltd currently has $200 million of
market value debt outstanding. The 9 percent coupon bonds (semiannual pay) have
a maturity of 15 years, a face value of $1000 and are currently priced at $1,024.87
per bond. The company also has an issue of 2 million preference shares outstanding
with a market price of $20. The preference shares offer an annual dividend of
$1.20. Contemporary Products also has 14 million ordinary shares outstanding
with a price of $20.00 per share. The company is expected to pay a $2.20 ordinary
dividend 1 year from today, and that dividend is expected to increase by 7 percent
per year forever. If the corporate tax rate is 40 percent, then what is the company’s
weighted average cost of capital?
Answers:
Chapter 1: The Financial Manager and
the Firm
Learning Objectives
1. IDENTIFY THE KEY FINANCIAL DECISIONS
FACING THE FINANCIAL MANAGER OF ANY
BUSINESS FIRM.
2. IDENTIFY THE BASIC FORMS OF BUSINESS
ORGANIZATION IN THE UNITED STATES AND
THEIR RESPECTIVE STRENGTHS AND
WEAKNESSES.
Learning Objectives
3. DESCRIBE THE TYPICAL ORGANIZATION OF
THE FINANCIAL FUNCTION IN A LARGE
CORPORATION.
4. EXPLAIN WHY MAXIMIZING THE CURRENT
VALUE OF THE FIRM’S STOCK IS THE
APPROPRIATE GOAL FOR MANAGEMENT.
5. DISCUSS HOW AGENCY CONFLICTS AFFECT
THE GOAL OF MAXIMIZING SHAREHOLDER
VALUE.
Learning Objectives
6. EXPLAIN WHY ETHICS IS AN APPROPRIATE
TOPIC IN THE STUDY OF CORPORATE
FINANCE.
The Role of the Financial Manager
o THREE KEY FINANCIAL DECISIONS
• Capital Budgeting: decide which long-term
assets to acquire
• Financing: decide how to pay for short-term and
long-term assets
• Working Capital: decide how to manage shortterm resources and obligations
The Role of the Financial Manager
o THREE KEY FINANCIAL DECISIONS
• Capital Budgeting
Choose the long-term assets that will yield the greatest
net benefits for the firm.
The Role of the Financial Manager
o THREE KEY FINANCIAL DECISIONS
• Financing
Finance assets with the optimal combination of shortterm debt, long-term debt, and equity.
The Role of the Financial Manager
o THREE KEY FINANCIAL DECISIONS
• Working Capital Management
Adjust current assets and current liabilities as needed
to promote growth in cash flow.
Cash Flows Between the Firm and Its
Stakeholders and Owners
How the Financial Manager’s Decisions
Affect the Balance Sheet
The Role of the Financial Manager
o THREE KEY FINANCIAL DECISIONS
• Poor decisions about capital budgeting,
financing, or working capital may lead to
bankruptcy or business failure
Basic Forms of Business Organization
o BUSINESS STRUCTURE
• Sole Proprietorship
• Partnership
• Corporation
Basic Forms of Business Organization
o SOLE PROPRIETORSHIP
• Owned by a single person who is financially
responsible for the actions and obligations of
the business
Basic Forms of Business Organization
o SOLE PROPRIETORSHIP
• Advantages
easiest to create
easiest to control
easiest to dissolve
right to all profit
Basic Forms of Business Organization
o SOLE PROPRIETORSHIP
• Disadvantages
owner’s personal assets at risk
owner’s unlimited liability for firm obligations
equity only from owner or business profit
business income taxed as personal income
difficult to transfer ownership
Basic Forms of Business Organization
o PARTNERSHIP
• A business owned by more than one person; one
or more of them financially responsible for the
actions and obligations of the business
Basic Forms of Business Organization
o PARTNERSHIP
• Advantages vs. sole proprietorship
limited protection of owners’ personal assets
owners’ limited liability for firm obligations
more sources of equity
more sources of expertise
Basic Forms of Business Organization
o PARTNERSHIP
• Disadvantages vs. proprietorship
shared control
shared profit
harder to dissolve
Basic Forms of Business Organization
o CORPORATION
• A business owned by more than one person;
none of them financially responsible for the
actions and obligations of the business. The
corporation is responsible for its obligations and
actions.
Basic Forms of Business Organization
o CORPORATION
• Advantages
protects personal assets
no shareholder liability for business
easiest to change ownership
greatest access to sources of funds
Basic Forms of Business Organization
o CORPORATION
• Disadvantages
most difficult and expensive to establish
dilutes individual control over the firm
overall higher taxes on income for shareholders
Basic Forms of Business Organization
o HYBRID FORMS OF BUSINESS ORGANIZATION
• Limited Liability Partnerships (LLPs)
• Limited Liability Companies (LLCs)
• Professional Companies (PCs)
All have the limited liability of a corporation and tax
advantage of a partnership.
Organization of the Financial Function
o CHIEF EXECUTIVE OFFICER (CEO)
• Chief manager in the firm
• Ultimate power to make decisions and ultimate
responsibility for decisions
• Reports directly to the board-of-directors who
protect shareholder’s interests
Simplified Corporate Organization
Chart
Organization of the Financial Function
o CHIEF FINANCIAL OFFICER (CFO)
• The V.P. of Finance/CFO is responsible for the
quality of the financial reports received by the
CEO
Organization of the Financial Function
o KEY FINANCIAL REPORTS
• The Treasurer manages and reports on the
collection and disbursement of cash
• The Risk Manager manages and reports on
activities to limit the firm’s risks in financial and
commodity markets
Organization of the Financial Function
o KEY FINANCIAL REPORTS
• The Controller is the firm’s accountant and
prepares its financial reports
• The Internal Auditor controls and reports on
activities to limit the firm’s exposure to internal
threats such as fraud and inefficient use of
resources
Organization of the Financial Function
o EXTERNAL AUDITOR
• Conducts an independent audit of a firm’s
financial activities
• Provides an opinion about whether the financial
reports the firm prepared are reasonably
accurate and conform to generally accepted
accounting principles
The Goal of the Firm
o DO NOT MAXIMIZE MARKET SHARE
• Giving away goods or services for free will
maximize a firm’s market share for a while, but
the firm will not be able to pay its bills and stay
in business
The Goal of the Firm
o DO NOT MAXIMIZE PROFIT
• Accounting profit differs from economic profit
• Profit earned may not equal cash received
Cash not received can’t be used to pay bills
• The strategy ignores the timing of future cash
flows
• The strategy ignores the risks associated with
having to wait for cash flows
The Goal of the Firm
o MAXIMIZE SHAREHOLDERS’ WEALTH!
• Future cash flows are considered
• The timing of future cash flows is considered
• The risks associated with having to wait to for
cash flows are considered
The Goal of the Firm
o MAXIMIZE SHAREHOLDERS’ WEALTH!
• Maximizing the price of a firm’s stock will
maximize the value of a firm and the wealth of
its shareholders (owners)
The Goal of the Firm
o ITS ALL ABOUT CASH FLOW!
• Positive residual cash flow may be paid to firm
owners as dividends or invested in the firm
• The larger the positive residual cash flow, the
greater the value of a firm
• Negative residual cash flow – over the long run leads to bankruptcy or closing a business
Agency Conflicts
o AGENCY RELATIONSHIP
• An agency relationship is created when the
owner (a principal) of a business hires an
employee (an agent)
• The owner surrenders some control over the
enterprise and its resources to the employee
• Separating ownership from control creates the
potential for agency conflicts
Agency Conflicts
o AGENCY RELATIONSHIP
• An agency relationship exists between
stockholders (principals) and the firm’s hired
management (agents)
• In large corporations, shared ownership among
many shareholders may result in relatively little
control over management
Agency Conflicts
o OWNERSHIP AND CONTROL
• Shareholders own the corporation, but
managers control the firm’s assets and may use
them for their own benefit
Major Factors Affecting Stock Prices
Agency Conflicts
o AGENCY COSTS
• Arise from (incurring and preventing) conflictsof-interests between a firm’s owners and its
managers
• May reduce positive residual cash flow, stock
price, and shareholder wealth
Agency Conflicts
o GIVING AGENTS THE RIGHT INCENTIVE
• Managers tend to focus on wealth maximization
when their compensation depends on stock
price
Agency Conflicts
o GIVING AGENTS THE RIGHT INCENTIVE
• Today, the firm’s stock trades at $0.95 per share.
The CEO has an option to buy 2.5 million
shares from the firm for $1.15 per share at any
time, beginning one year from today. If the
stock price rises to $3.15, the option will be
worth $5 million.
Agency Conflicts
o GIVING AGENTS THE RIGHT INCENTIVE
• Want to keep their jobs
• Oversight by the board of directors
• Oversight by large blockholders
• Potential takeover of the firm
• The legal and regulatory environment.
Agency Conflicts
o SARBANES-OXLEY AND REGULATORY REFORM
• Better corporate governance reduces agency
costs by requiring
more effective monitoring of managers’ activities
programs that promote appropriate behavior by
managers
penalties for executives who do not fulfill their fiduciary
responsibilities
Corporate Governance Regulations
Designed to Reduce Agency Costs
Ethics in Corporate Finance
o WHAT ARE ETHICS?
• Ethics
society’s standards for judging whether an action is
right or wrong
• Business Ethics
society’s standards for acceptable behavior applied to
business and financial markets
Ethics in Corporate Finance
o EXAMPLES OF ETHICAL CONFLICT IN BUSINESS
• Agency Cost
employee’s unacceptable use of employer’s computer
• Conflict of Interest
mortgage contract which a home-buyer is unlikely to
fulfill but earns a mortgage broker more money
• Information Asymmetry
seller knows about prior damage to the vehicle but the
potential buyer does not
Ethics in Corporate Finance
o BUSINESS BEHAVIOR
• Regulation and market forces are not enough to
maintain integrity in the marketplace
• Business norms must be based on ethical
beliefs, customs, and practices
Ethics in Corporate Finance
o CONSEQUENCES OF UNETHICAL BEHAVIOR
• Inefficiency in the economy and costs to society
• High legal and social costs
• Problems such as the recent financial crisis in
the U.S.
Ethics in Corporate Finance
o ETHICAL BEHAVIOR
• Sometimes, it is difficult to judge whether
behavior is ethical or not
Was the manager too careful?
Did the manager take too much risk?
Was it an honest mistake?
Was it against policy, but well-intentioned?
A Framework for the Analysis of Ethical
Conflicts
Chapter 2: The Financial System and
the Level of Interest Rates
Learning Objectives
1. DESCRIBE THE ROLE OF THE FINANCIAL
SYSTEM IN THE ECONOMY AND THE TWO
BASIC WAYS IN WHICH MONEY FLOWS
THROUGH THE SYSTEM.
2. DISCUSS DIRECT FINANCING AND THE
IMPORTANT ROLE THAT INVESTMENT BANKS
PLAY IN THIS PROCESS.
Learning Objectives
3. DESCRIBE THE PRIMARY, SECONDARY, AND
MONEY MARKETS, EXPLAINING THE SPECIAL
IMPORTANCE OF SECONDARY AND MONEY
MARKETS TO BUSINESS ORGANIZATIONS.
4. EXPLAIN WHAT AN EFFICIENT MARKET IS
AND WHY MARKET EFFICIENCY IS
IMPORTANT TO FINANCIAL MANAGERS.
Learning Objectives
5. EXPLAIN HOW FINANCIAL INSTITUTIONS
SERVE THE NEEDS OF CONSUMERS, SMALL
BUSINESSES, AND CORPORATIONS.
6. COMPUTE THE NOMINAL AND THE REAL
RATES OF INTEREST, DIFFERENTIATING
BETWEEN THEM.
The Financial System
o FINANCIAL MARKETS AND INSTITUTIONS
• Financial markets include markets for trading
financial assets such as stocks and bonds
• Financial institutions include banks, credit
unions, insurance companies, and finance
companies
The Financial System
o THE FINANCIAL SYSTEM AT WORK
• The financial system is competitive
• Money is borrowed in small amounts and
loaned in large amounts
• The system directs money to the best
investment opportunities in the economy
• Lenders earn profit from the spread between
lending and borrowing rates
The Financial System
o MOVE FUNDS FROM LENDER TO BORROWER
• The primary function of a financial system is to
efficiently transfer funds from lender-savers to
borrower-spenders
• Basic mechanisms by which funds are
transferred in the financial system
Direct Financing
Indirect Financing
The Flow of Funds Through the
Financial System
Direct Financing
o DIRECT TRANSFER OF FUNDS
• lender-saver contracts with a borrower-spender
• minimum transaction $1 million
• investment banks and money center banks help
with origination, underwriting and distribution
of new debt and equity
Direct Financing
o DIRECT TRANSFER OF FUNDS
• Underwriting is a service to assist firms in
selling their debt or equity securities in a direct
financing market
Types of Financial Markets
o WHOLESALE AND RETAIL MARKETS
• Primary Market
wholesale market where firms’ new securities are
issued and sold for the first time
• Secondary Market
retail market where previously issued securities are
resold (traded)
Types of Financial Markets
o MARKETABILITY AND LIQUIDITY
• Marketability
ease with which a seller or buyer for an asset can be
found
• Liquidity
ease with which an asset can be converted into cash
without loss of value
Types of Financial Markets
o MARKETABILITY AND LIQUIDITY
• Financial markets increase marketability and
liquidity of securities
• Financial markets lower the costs of making
transactions and make participants more willing
and able to pay higher prices
Types of Financial Markets
o BROKERS AND DEALERS
• A broker brings a seller and a buyer together but
does not buy or sell in the transaction
broker does not take on risk
• A dealer participates in trades as a buyer or
seller using her own inventory of securities
dealer takes on risk
Types of Financial Markets
o EXCHANGES & OVER-THE-COUNTER MARKETS
• Exchange
location where sellers and buyers meet to conduct
transactions
– New York Stock Exchange (NYSE)
– Chicago Board Options Exchange (CBOE)
– Saudi Stock Exchange (TADAWUL)
Types of Financial Markets
o EXCHANGES & OVER-THE-COUNTER MARKETS
• Over-the-Counter Market
dealers conduct transactions over the phone or via
computer.
– National Association of Securities Dealers Automated
Quotations (NASDAQ)
Types of Financial Markets
o MONEY AND CAPITAL MARKETS
• Money Market
market for low-risk securities with maturities of less than one year.
-Treasury Bills (T-bills): are short-term debt instruments issued
by the U.S Treasury. T-bills are issued for a term of one year of
less. T-bills are considered the world’s safest debt as they are
backed by the full faith and credit of the United States
government.
-Commercial Paper: Commercial paper is an unsecured, shortterm debt instrument issued by a corporation, typically for the
financing of accounts receivable, inventories and meeting shortterm liabilities. Maturities on commercial paper rarely range any
longer than 270 days. Commercial paper is usually issued at a
discount from face value and reflects prevailing market interest
rates.
o
Types of Financial Markets
o MONEY AND CAPITAL MARKETS
• Capital Market
market for securities with maturities longer than one
year
– bonds
– common stock
Selected Money Market and Capital
Market Instruments June 2010
Market Efficiency
o EFFICIENT MARKET
• Current prices of securities incorporate the
knowledge and expectations of all participants
• Security prices are correct: securities are not
over-valued or under-valued.
• Participants are confident they pay or receive
the intrinsic (fair) value of a security
Market Efficiency
o MARKET EFFICIENCY
• Operational Efficiency
extent to which transaction costs are minimized
• Informational Efficiency
extent to which security prices reflect all relevant
information
Market Efficiency
o EFFICIENT MARKET HYPOTHESIS
• A theory about how efficiently the stock market
processes and incorporates information
available from
private sources of information
public sources of information
historical stock prices
Market Efficiency
o EFFICIENT MARKET HYPOTHESIS
• Strong-Form Efficiency
Security prices always reflect all information, from
every source. Even inside, or confidential information,
is reflected.
Market Efficiency
o EFFICIENT MARKET HYPOTHESIS
• Semi-strong-Form Efficiency
Security prices always reflect all public information.
Inside, or confidential information, is not reflected.
Market Efficiency
o EFFICIENT MARKET HYPOTHESIS
• Weak-Form Efficiency
Security prices always reflect the information in past
prices. No other information is reflected.
Market Efficiency
o EFFICIENT MARKET HYPOTHESIS
• Public markets, such as the NYSE are more
efficient than private markets due to the
information provided by a large number of
participants and effective regulation
Financial Institutions and Indirect
Financing
o INDIRECT FINANCING
• An institution is both a borrower and lender
borrows money from a saver
lends money to a borrower
must repay funds to the saver – whether or not it is
repaid by the borrower
– Examples: banks & insurance companies
Financial Institutions and Indirect
Financing
o FINANCIAL INSTITUTIONS
• Provide lending and borrowing opportunities at
the retail level for small customers and
wholesale level for large customers
• Efficiently collect funds in small amounts and
lend them in larger amounts
• Tailor loan amounts and contract terms to fit the
needs of consumers, corporations, and small
businesses
Cash Flows Between the Firm and the
Financial System
The Determinants of Interest Rate
Levels
o INTEREST RATE
• The fee for borrowing money expressed as a
percentage of a loan
real rate of interest
– interest rate that would exist in the absence of inflation
(deflation)
nominal rate of interest
– interest rate adjusted for inflation (deflation)
The Determinants of Interest Rate
Levels
o REAL RATE OF INTEREST
• Determinants of the real rate of interest
expected return on productive assets
time preference for consumption
The Determinants of Interest Rate
Levels
o EQUILIBRIUM RATE OF INTEREST
• Is a function of supply and demand
savers supply more funds at higher rates
spenders borrow (demand) less at higher rates
• Is the interest rate at which the quantity of
funds supplied equals the quantity of funds
demanded
The Determinants of the Equilibrium
Rate of Interest
The Determinants of Interest Rate
Levels
o INFLATION AND LOAN CONTRACTS
• Lenders want the interest rates in loan contracts
to include compensation for the inflation
predicted to occur over the life of the contract
• Compensation for expected inflation adjusts
loan rates to offset the higher prices for goods
and services expected to exist when a loan is
repaid and a lender spends the money
The Determinants of Interest Rate
Levels
o FISHER EQUATION & NOMINAL INTEREST RATE
• The Fisher Equation
o
i r P rP
e
e
(2.1)
Where:
i = nominal interest rate
r = real rate of interest
∆Pe = expected annualized price-level change
r∆Pe = adjustment for expected price-level
change
The Determinants of Interest Rate
Levels
o FISHER EQUATION & NOMINAL INTEREST RATE
• Simplified Fisher Equation
i r P
e
(2.2)
The Determinants of Interest Rate
Levels
o FISHER EQUATION EXAMPLE
r 0.04
P 0.10
e
i?
i r P rP
e
e
0.04 0.10 (0.04 x 0.10)
0.1440 or 14.40%
The Determinants of Interest Rate
Levels
o SIMPLIFIED FISHER EQUATION EXAMPLE
r 0.04
Pe 0.10
i r Pe
0.04 0.10
0.14 or 14%
i?
The Determinants of Interest Rate
Levels
o REAL RATE OF INTEREST EXAMPLE
i 0.14
P 0.10
e
i r P
e
0.14 r 0.10
0.14 – 0.10 r
0.04 r
r ?
The Determinants of Interest Rate
Levels
o CYCLICAL & LONG-TERM INTEREST RATES
• Interest rates tend to rise and fall with changes
in the rate of inflation
• Rates tend to rise when the growth rate of the
economy increases and tend to fall when the
growth rate of the economy slows
The Determinants of Interest Rate
Levels
o INTEREST RATE, BUSINESS CYCLE & INFLATION
• Interest rates tend to follow the business cycle
• Interest rates tend to increase during an
economic expansion
• Interest rates tend to decrease during an
economic contraction
Relation Between Annual Inflation
Rate and Long-Term Interest Rate
Chapter 3: Financial Statements, Cash
Flows, and Taxes
Learning Objectives
1. DISCUSS GENERALLY ACCEPTED
ACCOUNTING PRINCIPLES (GAAP) AND THEIR
IMPORTANCE TO THE ECONOMY.
2. EXPLAIN THE BALANCE SHEET IDENTITY AND
WHY A BALANCE SHEET MUST BALANCE.
3. DESCRIBE HOW MARKET-VALUE BALANCE
SHEETS DIFFER FROM BOOK-VALUE BALANCE
SHEETS.
Learning Objectives
4. IDENTIFY THE BASIC EQUATION FOR THE
INCOME STATEMENT AND THE INFORMATION IT
PROVIDES.
5. UNDERSTAND THE CALCULATION OF CASH
FLOWS FROM OPERATING, INVESTING, AND
FINANCING ACTIVITIES REQUIRED IN THE
STATEMENT OF CASH FLOWS.
6. EXPLAIN HOW THE FOUR MAJOR FINANCIAL
STATEMENTS DISCUSSED IN THIS CHAPTER ARE
RELATED.
Learning Objectives
7. IDENTIFY THE CASH FLOW TO A FIRM’S
INVESTORS USING ITS FINANCIAL
STATEMENTS.
8. DISCUSS THE DIFFERENCE BETWEEN
AVERAGE AND MARGINAL TAX RATES.
Financial Statements
o PURPOSE OF FINANCIAL STATEMENTS
• Provide stakeholders a foundation for evaluating
the financial health of a firm
creditors
employees
management
stockholders
Financial Statements
o PURPOSE OF FINANCIAL STATEMENTS
• Provide stakeholders a foundation for evaluating
the financial health of a firm.
customers
general Public
regulators
suppliers
Financial Statements
o PURPOSE OF FINANCIAL STATEMENTS
• Evaluate a firm’s internal environment
efficiency
effectiveness
risk level
Financial Statements
o PURPOSE OF FINANCIAL STATEMENTS
• Evaluate a firm’s interaction with the external
environment
corporate citizenship
social responsibility
assessment of the external environment
response to the external environment
Financial Statements
o PURPOSE OF FINANCIAL STATEMENTS
• Provide information about the performance of
the firm
stakeholders want to compare actual vs. potential
performance
Financial Statements and Accounting
Principles
o GAAP
• Generally Accepted Accounting Principles
(GAAP)
accounting rules and standards that public companies
must adhere to when they prepare financial statements
and reports
established by the Financial Accounting Standards
Board (FASB) and authorized by the Securities and
Exchange Commission (SEC)
Financial Statements and Accounting
Principles
o INTERNATIONAL GAAP
• Uniform accounting rules and procedures
promoted by the International Accounting
Standards Board
• Firms in the European Union are moving
toward a “European GAAP”
• Economic and political pressure is building in
the United States and Europe to develop a
unified accounting system
Financial Statements and Accounting
Principles
o GAAP
• Guidelines, not rules
Firms have discretion about how their financial
information is presented.
No two firms are required to have identical statements.
Financial Statements and Accounting
Principles
o GAAP
• Guidelines, not rules.
Alternative terms on financial statements
– balance sheet, statement of financial condition
– income statement, statement of operations, profit and loss
statement
– cost-of-goods-sold, cost-of -sales, cost-of-revenue, cost-ofservices-sold
Financial Statements and Accounting
Principles
o FIVE IMPORTANT ACCOUNTING PRINCIPLES
1. Assumption of Arm’s Length Transaction
Parties involved in an economic transaction arrive at a
decision independently and rationally.
2. Cost Principle
Asset values are recorded at the cost for which they
were acquired.
Financial Statements and Accounting
Principles
o FIVE IMPORTANT ACCOUNTING PRINCIPLES
3. Realization Principle
Revenue is recognized when a transaction is
completed, although cash may be received earlier or
later.
4. Matching Principle
Revenue is matched with the expense incurred to
generate it.
Financial Statements and Accounting
Principles
o FIVE IMPORTANT ACCOUNTING PRINCIPLES
5. Going Concern Assumption
Assume a company will continue to operate for the
predictable future.
Financial Statements and Accounting
Principles
o ANNUAL REPORT
• Summarizes the overall performance of a firm
for the most recent fiscal year
• Information
the company, its products, its activities, and its future
summary of financial performance for the most recent
year
audited financial statements, five-year summary of
financial data
The Balance Sheet
o FIRM ASSETS & FUNDING AT A POINT IN TIME
• Left side of a balance shows assets a firm owns
and uses to generate revenue
• Right side of the balance sheet shows sources
of the funds used to acquire assets
Total Assets
Total Liabilities Total Stockholde rs'Equity
(3.1)
Diaz Manufacturing Balance Sheets as
of December 31
The Balance Sheet
o ITEM ORDER
• Assets listed in order of liquidity
• Liabilities listed in order in which they are due
to be paid
• Stockholders’ equity listed last
Common stockholders are entitled to assets remaining
after all other providers of funds are paid.
The Balance Sheet
o CURRENT ASSETS
• Assets likely to be converted to cash within a
year (or one operating cycle)
marketable securities
accounts receivable
inventory
The Balance Sheet
o CURRENT LIABILITIES
• Liabilities scheduled to be paid within a year (or
one operating cycle)
accounts payable
accrued wages
debt with less than a year’s maturity
taxes
The Balance Sheet
o NET WORKING CAPITAL
Net Working Capital Total Current Assets
- Total Current Liabilitie s
(3.2)
The Balance Sheet
o NET WORKING CAPITAL EXAMPLE
• Diaz Manufacturing
Total current assets = $1,039.8 million
Total current liabilities = $377.8 million
Net working capital = Total current assets
- Total current liabilities
= $1,039.8 million - $377.8 million
= $662.0 million
The Balance Sheet
o INVENTORY ACCOUNTING
• Inventory (least liquid current asset) reported
using one of two methods
FIFO (first-in-first-out) assumes merchandise is sold in
the order it was acquired by a firm.
LIFO (last-in-first-out) assumes merchandise is sold in
the reverse of the order it was acquired by a firm.
The Balance Sheet
o INVENTORY ACCOUNTING
• When the cost of inventory is increasing
FIFO reporting says a firm sold the less expensive
inventory and leads to
– higher balance in inventory
– lower cost-of-goods-sold
– higher taxable income
– higher income taxes
– higher net income
The Balance Sheet
o INVENTORY ACCOUNTING
• When the cost of inventory is increasing
LIFO reporting says a firm sold the more expensive
inventory and leads to
– lower balance in inventory
– higher cost-of-goods-sold
– lower taxable income
– lower income taxes
– lower net income
The Balance Sheet
o INVENTORY ACCOUNTING
• When the cost of inventory is decreasing
FIFO reporting says a firm sold the more expensive
inventory and leads to
– lower balance in inventory
– higher cost-of-goods-sold
– lower taxable income
– lower income taxes
– lower net income
The Balance Sheet
o INVENTORY ACCOUNTING
• When the cost of inventory is decreasing
LIFO reporting says a firm sold the less expensive
inventory and leads to
– higher balance in inventory
– lower cost-of-goods-sold
– higher taxable income
– higher income taxes
– higher net income
The Balance Sheet
o INVENTORY ACCOUNTING
• Firms may switch from one inventory
accounting method to the other under
extraordinary circumstances but not frequently
The Balance Sheet
o LONG-TERM ASSETS
• Real Assets
land
buildings
equipment
• Intangible Assets
goodwill
patents
copyrights
The Balance Sheet
o LONG-TERM ASSETS
• Real assets decline with use and are depreciated
Depreciation expense reduces taxable income and
income taxes.
Assets are depreciated using either the straight line or
accelerated depreciation method.
• Intangible assets lose value over time and are
amortized (equivalent to depreciated)
The Balance Sheet
o LONG-TERM LIABILITIES
• Long-term debt
bank loans
mortgages
bonds with a maturity longer than one year
The Balance Sheet
o EQUITY
• Common Stock
ownership with control in a firm
• Preferred Stock
ownership without control in a firm
features make it an equity security that resembles debt
The Balance Sheet
o OTHER BALANCE SHEET ACCOUNTS
• Retained earnings
Profit kept and used to acquire assets.
• Treasury stock
Shares of its own stock a firm holds rather than sell
them to the public.
Market Value vs. Book Value
o RECORDING ASSET VALUE
• Assets are traditionally reported at historical
cost on a balance sheet
• Balance sheet amount does not reflect current
market value – only the acquisition cost
Market Value vs. Book Value
o ASSET VALUATION
• Better information is provided to management
and investors by marking-to-market —
reporting balance sheet items at current market
values
difficult to determine market values of assets
• The difference between the market values of
assets and liabilities is a realistic estimate of the
market value of shareholders’ equity
The Income Statement
o INCOME STATEMENT: OVERVIEW
• Measures the profitability of a firm for a
reporting period
• Revenue is income from selling products and
services – for cash or credit
• Expenses include costs of providing products
and services, and asset utilization (depreciation
and amortization)
Net income Revenues – Expenses
(3.3)
Diaz Manufacturing Income
Statements
The Income Statement
o NET INCOME EXAMPLE
• Diaz Manufacturing
Revenues = $1,563.7 million
Expenses = $1,445.2 million
Net Income = Revenues – Expenses
= $1,563.7 million - $1,445.2 million
= $ 118.5 million
The Income Statement
o DEPRECIATION
• The cost of a physical asset, such as plant or
machinery, is written off over its lifetime. This
is called depreciation, a non-cash expense
• Firms use one of these depreciation methods
straight-line depreciation
accelerated depreciation
– Firms may choose to use one for internal purposes and
another for tax purposes or for statements released to the
public.
The Income Statement
o AMORTIZATION
• Amortization expense is related to using
intangible assets
goodwill
patents
licenses
– Like depreciation, it is a non-cash expense.
The Income Statement
o EXTRAORDINARY ITEM
• Income or expense associated with events that
are infrequent and abnormal
separated from the results of ordinary income
shown separately on the income statement
The Income Statement
o EBITDA AND EBIT
• Earnings-before-interest-taxes-depreciationand-amortization (EBITDA)
income from selling goods and services minus the cost
of providing them
• Earnings-before-interest-and-taxes (EBIT)
EBITDA minus depreciation and amortization
The Income Statement
o EBT AND NI
• Earnings-before-taxes (EBT)
EBIT minus interest expense
taxable income
• Net income (NI)
EBT minus taxes
Statement of Retained Earnings
o RETAINED EARNINGS
• Shows cumulative effect of adjustments to
shareholders’ equity resulting from profit,
losses, and paying dividends
• Shows changes in the account for a period
based on profit, loss, or dividend paid
Diaz Manufacturing Statement of
Retained Earnings
Cash Flows
o NET CASH FLOWS VERSUS NET INCOME
• Accountants focus on net income and
shareholders focus on net cash flows. These are
not the same because of delays in inflows and
outflows, and non-cash revenues and expenses
Cash Flows
o CASH FLOWS TO INVESTORS
• Cash flows available to investors from operating
activities (CFOA)
CFOA EBIT – Current Taxes
Noncash expenses
(3.4)
Cash Flows
o CFOA EXAMPLE
• Diaz Manufacturing
EBIT = $168.4 million
Current Taxes = $44.3 million
Non-cash expenses = $83.1 million
CFOA EBIT – Current Taxes Non - Cash Expenses
$168.4m - $44.3m $83.1m
$207.2 million
Cash Flows
o CASH FLOWS TO WORKING CAPITAL
• To compute the net cash flows into or out of
working capital
CFNWC NWCCurrent Period - NWCPrevious Period
(3.5)
Cash Flows
o CFNWC EXAMPLE
• Diaz Manufacturing
NWC 2011 = $662.0 million
NWC 2010 = $342.0 million
CFNWC NWC
2011
2011
– NWC
2010
$662.0m - $342.0
$320.0 million
Cash Flows
o STATEMENT OF CASH FLOWS
• Summarizes cash outflows and cash inflows
during a period
• Cash flows result from operating activities,
investing activities, and financing activities
• Net cash flows equals cash inflows minus cash
outflows
Diaz Manufacturing Statement of Cash
Flows
Cash Flows
o STATEMENT OF CASH FLOWS ORGANIZATION
• Operating Activities
cash inflows
– sell goods and services
cash outflows
– raw materials
– inventory
– salaries and wages
– utilities
– rent
Cash Flows
o STATEMENT OF CASH FLOWS ORGANIZATION
• Investing Activities
cash outflows and inflows due to
– buying and selling long-term assets such as plant and
equipment
– buying and selling bonds and stocks issued by other firms
Cash Flows
o STATEMENT OF CASH FLOWS ORGANIZATION
• Financing Activities
cash inflow
– issue debt
– issue equity
– borrow money
cash outflow
– pay interest or dividends
– repay loan principal
– purchase treasury stock
Interrelations Among the Financial
Statements
Federal Income Tax
o CORPORATE INCOME TAX
• U.S. has a progressive tax with rates ranging
from 15 percent to 39 percent
higher taxable income = higher the tax liability
Corporate Tax Rates for 2010
Federal Income Tax
o AVERAGE VERSUS MARGINAL TAX RATE
• Average tax rate
total taxes paid divided by taxable income for the
period
• Marginal tax rate
rate paid on the last dollar earned or the next dollar
that will be earned
Federal Income Tax
o DIVIDENDS AND INTEREST ARE NOT EQUAL
• U.S. tax code
allows interest payments on debt to reduce firms’
taxable income
does not allow dividend payments to equity to reduce
firms’ taxable income
– debt financing has a lower cost relative to equity financing
Chapter 4: Analyzing Financial
Statements
Learning Objectives
1. EXPLAIN THE THREE PERSPECTIVES FROM
WHICH FINANCIAL STATEMENTS CAN BE
VIEWED.
2. DESCRIBE COMMON-SIZE FINANCIAL
STATEMENTS, EXPLAIN WHY THEY ARE USED,
AND BE ABLE TO PREPARE AND USE THEM TO
ANALYZE THE HISTORICAL PERFORMANCE
OF A FIRM.
Learning Objectives
3. DISCUSS HOW FINANCIAL RATIOS FACILITATE
FINANCIAL ANALYSIS, AND BE ABLE TO
COMPUTE AND USE THEM TO ANALYZE A
FIRM’S PERFORMANCE.
4. DESCRIBE THE DUPONT SYSTEM OF ANALYSIS
AND BE ABLE TO USE IT TO EVALUATE A
FIRM’S PERFORMANCE AND IDENTIFY
CORRECTIVE ACTIONS THAT MAY BE
NECESSARY.
Learning Objectives
5. EXPLAIN WHAT BENCHMARKS ARE, DESCRIBE
HOW THEY ARE PREPARED, AND DISCUSS
WHY THEY ARE IMPORTANT IN FINANCIAL
STATEMENT ANALYSIS.
6. IDENTIFY THE MAJOR LIMITATIONS IN USING
FINANCIAL STATEMENT ANALYSIS.
Background for Financial Statement
Analysis
o PERSPECTIVES FOR ANALYSIS
• Stockholder
• Manager
• Creditor
Background for Financial Statement
Analysis
o STOCKHOLDER’S PERSPECTIVE
• Focus on
net cash flows
risk
rate of return
market value of firm’s stock
Background for Financial Statement
Analysis
o MANAGER’S PERSPECTIVE
• Focus on
rate of return
efficient use of assets
controlling costs
increasing net cash flows
increasing market value of firm’s stock
job security
Background for Financial Statement
Analysis
o CREDITOR’S PERSPECTIVE
• Focus on
predictability of revenues and expenses
ability to meet short-term obligations
ability to make loan payments as scheduled
no unanticipated change in risk
Common-Size Financial Statements
.
o COMMON-SIZE
FINANCIAL STATEMENTS
• Show the dollar amount of each item as a
percentage of a reference value
Common-size balance sheet may use total assets as the
reference value; each item is expressed as a percentage
of total assets.
Common-size income statement may use net sales as
the reference value; each item is expressed as a
percentage of net sales.
Common-Size Financial Statements
o COMMON-SIZE BALANCE SHEET
• Standardizes the amount in a balance sheet
account by converting the dollar value of each
item to its percentage of total assets
Dollar values on a regular balance sheet provide
information on the number of dollars associated with a
balance sheet account.
Percentage values on a common-size balance sheet
provide information on the relative size or importance
of the dollars associated with a balance sheet account.
Exhibit 4.1: Common-Size Balance
Sheets for Diaz Manufacturing
Exhibit 4.2: Common-Size Income
Statements for Diaz Manufacturing
Financial Ratios and Firm Performance
o RATIOS IN FINANCIAL ANALYSIS.
• Ratios establish a common reference point
across firms - even though the numerical value
of the reference point will differ from firm-tofirm
Ratios make it easier to compare the performance of
large firms to that of small firms.
Ratios make it easier to compare the current and
historical performance of a single firm as the firm
changes over time.
Financial Ratios and Firm Performance
o RATIOS USED VARY ACROSS FIRMS
• occupancy ratios (hotel)
• sales-per-square foot (retailing)
• loans-to-assets (banking)
• medical cost ratio (health insurance)
Financial Ratios and Firm Performance
o RATIO VALUES VARY WITHIN AN INDUSTRY
• 2010 Gross Margin
Big Lots
40.6%
Target
30.5%
Walmart
24.9%
Financial Ratios and Firm Performance
o CATEGORIES OF COMMON FINANCIAL RATIOS
• Liquidity ratios
• Efficiency ratios
• Leverage ratios
• Profitability ratios
• Market Value ratios
Financial Ratios and Firm Performance
o LIQUIDITY RATIOS
• Indicate a firm’s ability to pay short-term
obligations with short-term assets without
endangering the firm. In general, higher ratios
are a favorable indicator.
Current Ratio
Current assets
Current liabilites
Current assets - Inventory
Quick Ratio
Current liabilites
(4.1)
(4.2)
Financial Ratios and Firm Performance
o EFFICIENCY RATIOS
• Indicate a firm’s ability to use assets to produce
sales. These are also called turnover ratios. In
general, higher numbers are a favorable
indicator.
Cost of Goods Sold
Inventory Turnover
Inventory
Net Sales
Total Asset Turnover
Total Assets
(4.3)
(4.7)
Financial Ratios and Firm Performance
o EFFICIENCY RATIOS
• For the efficiency ratio below, a lower number is
generally a positive signal
365 Days
Days Sales in Inventory
Inventory Turnover
(4.4)
Financial Ratios and Firm Performance
o LEVERAGE (DEBT) RATIOS
• Indicate whether a firm is using the appropriate
amount of debt financing. In general, higher
ratios indicate greater potential return and
greater bankruptcy risk.
Total Debt
Total Debt Ratio
Total Assets
(4.9)
Total Debt
Debt - to - Equity
Total Equity
(4.10)
Financial Ratios and Firm Performance
o LEVERAGE (DEBT) RATIOS
• For the ratio below, a higher number generally
indicates less bankruptcy risk and (possibly)
lower potential return
Times Interest Earned
Earnings Before Interest & Taxes
Interest Expense
(4.12)
Financial Ratios and Firm Performance
o PROFITABILITY RATIOS
• Indicate whether a firm is generating adequate
profit from its assets. In general, higher ratios
indicate better performance.
Net Profit Margin
Net Income
Net Sales
Return on Assets
Net Income
(4.18)
Total Assets
Return on Equity
Net Income
Total Equity
(4.16)
(4.19)
Financial Ratios and Firm Performance
o MARKET VALUE RATIOS
• Indicate how the market is valuing the firm’s
equity. Higher ratios indicate greater
shareholder wealth.
Price - Earnings Ratio
Market - to - Book
Price Per Share
Earnings Per Share
(4.21)
Price Per Share
Book Value of Equity Per Share
(4.22)
Exhibit 4.3: Ratios for Time-Trend
Analysis for Diaz Manufacturing
The DuPont System
o THE DUPONT SYSTEM
• Diagnostic tool for evaluating a firm’s financial
health
• Uses related ratios that link the balance sheet
and income statement
• Based on two equations that connect a firm’s
ROA and ROE
• Used by management and shareholders to
understand factors that drive ROE
The DuPont System
o THE DUPONT EQUATION
• In ratio form (Equation 4.26)
Net Income
Net Sales
Total Assets
ROE
Net Sales
Total Assets Total Equity
• Shows that return-on-equity is driven by
profitability, operating efficiency, and amount of
leverage (debt)
Exhibit 4.4: Two Basic Strategies to
Earn a Higher ROA
Exhibit 4.5: Relations in the
DuPont System of Analysis
Selecting a Benchmark
o BENCHMARK RELEVANCE
• A ratio or ratio analysis is relevant only when
compared to an appropriate benchmark
Trend Analysis – comparison to the firm’s historical
performance
Peer Group Analysis – comparison to a select group of
firms in the same industry
Industry Analysis – comparison to the aggregate of
firms in the same industry
Selecting a Benchmark
o BENCHMARK RELEVANCE
• A ratio or a ratio analysis is relevant only when
compared to the appropriate benchmark(s).
Benchmarks may be used in combination.
Level and trend should be considered when evaluating
a firm’s performance and its future.
Exhibit 4.6: Peer Group Ratios for
Diaz Manufacturing
Exhibit 4.7: Peer Group Analysis
for Diaz Manufacturing
Limitations of Financial Statement
Analysis
o FINANCIAL STATEMENT ANALYSIS
• Weaknesses
not an exact science
relies on accounting data and historical costs
few guidelines or principles for determining whether a
ratio is “high” or “low”, or is a reason for confidence or
for concern
Chapter 5: The Time Value of Money
Learning Objectives
1. EXPLAIN WHAT THE TIME VALUE OF MONEY
IS AND WHY IT IS SO IMPORTANT IN THE
FIELD OF FINANCE.
2. EXPLAIN THE CONCEPT OF FUTURE VALUE,
INCLUDING THE MEANING OF THE TERMS
PRINCIPAL, SIMPLE INTEREST AND
COMPOUND INTEREST, AND USE THE
FUTURE VALUE FORMULA TO MAKE
BUSINESS DECISIONS.
Learning Objectives
3. EXPLAIN THE CONCEPT OF PRESENT VALUE,
HOW IT RELATES TO FUTURE VALUE, AND
USE THE PRESENT VALUE FORMULA TO MAKE
BUSINESS DECISIONS.
4. DISCUSS WHY THE CONCEPT OF
COMPOUNDING IS NOT RESTRICTED TO
MONEY, AND USE THE FUTURE VALUE
FORMULA TO CALCULATE GROWTH RATES.
The Time Value of Money
o EXCHANGING CONSUMPTION
OPPORTUNITIES
• How does a manager determine the value of a
future cash-flow, whether the cash-flow is a
payment to be made or income to be received?
• How much is a series of future cash-flows
worth today?
• The price/value today of cash-flows that occur
in the future is determined by the time-value-ofmoney (TVM).
The Time Value of Money
o CONSUME TODAY OR TOMORROW?
• TVM is based on the belief that people prefer to
consume goods today rather than wait to
consume the same goods tomorrow
An apple we can have today is more valuable to us
than an apple we can have in one year.
Money has a time value because buying an apple
today is more important than buying an apple in one
year.
The Time Value of Money
o CONSUME TODAY OR TOMORROW?
• A dollar someone has today can be spent for
consumption or loaned to earn interest
• A dollar loaned earns interest that increases
wealth and the ability to consume
• The rate of interest determines the trade-off
between consumption today and saving
(investing)
The Time Value of Money
o TIMELINES AID PROBLEM SOLVING
• Timelines are an effective way to visualize cash
flows
• Present cash outflows as negative values
• Present cash inflows as positive values
Five-year Timeline for a $10,000
Investment
The Time Value of Money
o FUTURE VALUE VERSUS PRESENT VALUE
• Cash-flows are evaluated based on future value
or present value
• Future value measures what cash-flows are
worth after a certain amount of time has passed
• Present value measures what future cash-flows
are worth before a certain amount of time has
passed
The Time Value of Money
o FUTURE VALUE VERSUS PRESENT VALUE
• Compounding is the process of increasing cashflows to a future value
• Discounting is the process of reducing future
cash-flows to a present value
Future Value of $100 at 10 Percent
Future Value and Compounding
o SINGLE PERIOD LOAN
• We can determine the balance in an account at
the end of a period if we know the interest rate
earned on the principal
• If principal of $X is loaned for one period at the
interest rate i, the account balance will increase
to $X(1 + i)1
• The term (1+ i)n is the future value interest factor
or future value factor
Future Value and Compounding
o TWO-PERIOD LOAN
• A two-period loan is two consecutive singleperiod loans
• Interest earned is added to the account at the
end of the first period and the new account
balance is the amount that earns the interest
rate i during the second period
• The account balance is $X(1 + i)1 at the end of
the first period and $X(1 + i)2 at the end of the
second period.
Future Value and Compounding
o TWO-PERIOD LOAN
• The principal is the initial deposit or loan
amount
• Simple interest is paid on the original principal
amount only
• Compound interest consists of both simple
interest and interest-on-interest
Example 1
15
o SUPPOSE WE PLACE $100 IN A SAVINGS
ACCOUNT
THAT
PAYS
6%
INTEREST
COMPOUNDED ANNUALLY. HOW WILL OUR
SAVINGS GROW?
VALUE AT THE END OF YEAR 1 = PRESENT VALUE X (1+ I)
I = INTEREST RATE
o
= $100 𝟏 + 𝟎. 𝟎𝟔 𝟏
o = $100 (1.06)
o = $106
16
VALUE AT THE END OF YEAR 2= VALUE AT THE END OF YEAR 1 X 𝟏 + 𝒓 𝟐
= PRESENT VALUE X (𝟏 + 𝒊) X (𝟏 + 𝒊)
= $106 ( 1.06) X (1.06)
= $119.10
VALUE AT THE END OF YEAR 3 = VALUE AT THE END OF YEAR 2 X
(𝟏. 𝟎𝟔)𝟑
= $119.10 (𝟏. 𝟎𝟔)𝟑
= $ 141.85
How Compound Interest Grows on
$100 at 10 Percent
Future Value and Compounding
o FUTURE VALUE EQUATION
• The general equation to find a future value
FVn PV x (1 i) n
(5.1)
where:
FVn = future value of investment at end of period n
PV = original principle (P0) or present value
i = the rate of interest per period
n = the number of periods, often in years
Future Value and Compounding
FUTURE VALUE EXAMPLE
You deposit $100 in a savings account earning 10%
compounded annually for five years. How much is
in the account at the end of that time?
FV5 $100 (1 0.10)5
= $100 (1.10)5
= $100 1.6105
= $161.05
Future Value Factors
Future Value: Example 2
21
o IF WE PLACE $1,000 IN A SAVINGS ACCOUNT
PAYING 5% INTEREST COMPOUNDED ANNUALLY,
HOW MUCH WILL OUR ACCOUNT ACCRUE TO IN 10
YEARS?
o FUTURE VALUE = PRESENT VALUE X (𝟏 + 𝒊)𝒏
o 𝑭𝑽𝒏 = $1,000 (𝟏 + 𝟎. 𝟎𝟓)𝟏𝟎
o = $1,000 (1.62889)
o = $1,628.89
Refer Table A-1
Future Value: Example 3
22
IF WE PLACE $500 IN A SAVINGS ACCOUNT
PAYING 8% INTEREST COMPOUNDED ANNUALLY,
HOW MUCH WILL OUR ACCOUNT ACCRUE TO IN
7 YEARS?
FUTURE VALUE = PRESENT VALUE X (𝟏 + 𝒊)𝒏
𝑭𝑽𝒏 = $500 (𝟏 + 𝟎. 𝟎𝟖)𝟕
= $500 (1.714)
= $857
Example 4
o
FUTURE VALUE: YOU ARE INTERESTED IN INVESTING $10,000, A GIFT FROM YOUR
GRANDPARENTS, FOR THE NEXT FOUR YEARS IN A MUTUAL FUND THAT WILL EARN AN
ANNUAL RETURN OF 8 PERCENT. WHAT WILL YOUR INVESTMENT BE WORTH AT THE END OF
FOUR YEARS? (ROUND TO THE NEAREST DOLLAR.)
Present value of the investment = PV = $10,000
Return on mutual fund = i = 8%
No. of years = n = 4.
0 1 2 3
4
├───┼───┼───┼────┤
-$10,000
FV=?
FV4 PV (1 i )n $10,000 (1.08)4
$13,604.89
Example 5
o
FUTURE VALUE: NING GAO IS PLANNING TO BUY A HOUSE IN FIVE YEARS. SHE IS LOOKING TO
INVEST $25,000 TODAY IN AN INDEX MUTUAL FUND THAT WILL PROVIDE HER A RETURN OF 12
PERCENT ANNUALLY. HOW MUCH WILL SHE HAVE AT THE END OF FIVE YEARS? (ROUND TO THE
NEAREST DOLLAR.)
Present value of the investment = PV = $25,000
Return on mutual fund = i = 12%
No. of years = n = 5.
0 1 2 3
4 5
├───┼───┼───┼────┼───┤
-$25,000
FV = ?
FV5 PV (1 i )n $25,000 (1.12)5
$44,058.54
Future Value of $1 for Different
Periods and Interest Rates
Future Value and Compounding
o COMPOUNDING MORE THAN ONCE A YEAR
• The more frequently interest is compounded,
the larger the future value of $1 at the end of a
given time period
• If compounding occurs m times within a
period, the future value equation becomes
𝑭𝑽𝒏 = 𝑷𝑽 𝑿 𝟏 + 𝒊/𝒎 𝒎𝒏
Future Value and Compounding
o COMPOUNDING WITHIN A PERIOD EXAMPLE
• You deposit $100 in an account that pays 5%
annually with semi-annual compounding for
two years. What is the ending account balance?
FV2 $100 (1+0.05 / 2)22
= $100 (1+0.025)4
= $100 (11038)
= $110.38
Future values with Non-Annual Periods:
o IF WE PLACE $100 IN A SAVINGS ACCOUNT THAT
YIELDS 12% COMPOUNDED QUARTERLY, WHAT
WILL OUR INVESTMENT GROW TO AT THE END OF 5
YEARS?
𝒎∗𝒏
𝒊
𝑭𝑽𝒏 = 𝑷𝑽 𝟏 +
𝒎
𝟎. 𝟏𝟐 𝟒∗𝟓
𝑭𝑽𝒏 = $𝟏𝟎𝟎 𝟏 +
𝟒
= $100 (1.8061)
= $180.61
REFER TABLE A-1
Future Value and Compounding
o CONTINUOUS COMPOUNDING
• When compounding occurs on a continuous
basis, the future value equation becomes
FV PV e
n
i n
(5.3)
e = 2.71828, the base of the natural logarithm
Future Value and Compounding
o CONTINUOUS COMPOUNDING EXAMPLE
• Your grandmother wants to put $10,000 in a
savings account. How much money will she
have at the end of five years if the bank pays 5%
annual interest compounded continuously?
FV PV e
n
FV $10,000 e
0.055
n
$10,000 (2.71828)
$10,000 1.284025
$12,840.25
0.055
i n
(5.3)
Using Excel – Future Value and
Compounding
Future Value and Compounding
o CALCULATOR EXAMPLE
• Future Value
Suppose we lend $5,000 at 15% for 10 years. How
much money will we have at the end of that time?
Enter
Answer
10
15
-5,000
0
N
i
PV
PMT
FV
20,227.79
Present Value and Discounting
o PRESENT VALUE EQUATION
• General equation to find present value
o
FV
PV
(1 i)
n
n
(5.4)
• This equation has the same elements as
Equation 5.1, the future value equation. They
differ only in the arrangement of the elements.
Here, (1 + i)n is used for division and is called
the present value factor or discount factor.
Present Value and Discounting
Comparing Future Value & Present
Value Calculations
Present Value and Discounting
o PRESENT VALUE EQUATION
• A present value calculation takes end-of-theperiod cash flows and reverses the effect of
compounding to determine the equivalent
beginning-of-the-period cash flows
This is discounting and the interest rate i is called the
discount rate.
Present value (PV) is often referred to as the
discounted value of future cash-flows.
Present Value and Discounting
o PRESENT VALUE CALCULATION EXAMPLE
• You intend to buy a BMW 330 Sports Coupe one
year from today. You predict the car will cost
$40,000. If your bank pays 5% interest on
savings, compounded annually, how much will
you need to deposit today to have $40,000 after
one year?
$10,000
PV
$38, 095.24
1 0.05
Present Value and Discounting
o PRESENT VALUE CONCEPTS
• Time and the discount rate affect present value
The greater the amount of time before a cash flow is
to occur, the smaller the present value of the cashflow.
The higher the discount rate, the smaller the present
value of a future cash-flow.
Example 5
39
WHAT IS THE VALUE OF $500 TO BE RECEIVED 10
YEARS FROM TODAY IF OUR DISCOUNT RATE IS 6%.
P𝒓𝒆𝒔𝒆𝒏𝒕 𝑽𝒂𝒍𝒖𝒆 = 𝑭𝑽𝒏 [
𝟏
(𝟏+𝒊)𝒏
]
FV = $500, N = 10, I = 6% OR 0.06
= $500 [
𝟏
(𝟏+𝟎.𝟎𝟔)𝟏𝟎
= $500 (0.558)
= $279.20
Refer Table A -3
]
Example 6
WHAT IS THE PRESENT VALUE OF AN INVESTMENT
THAT YIELDS $1,000 TO BE RECEIVED IN 7 YEARS AND
$1,000 TO BE RECEIVED IN 10 YEARS IF THE
DISCOUNT RATE IS 6 PERCENT?
𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 = 𝑭𝑽𝒏 [
PV= $𝟏, 𝟎𝟎𝟎 [
o
o
o
𝟏
(𝟏+𝟎.𝟎𝟔)𝟕
𝟏
(𝟏+𝒊)𝒏
] + 𝑭𝑽𝒏 [
] + $1,000 [
𝟏
(𝟏+𝒊)𝒏
𝟏
(𝟏+𝟎.𝟎𝟔)𝟏𝟎
= $1,000 (0.665) + $1,000 (0.558)
= $665 + $558
= $1223
]
]
Present Value Factors
Present Value of $1 for Different
Periods and Discount Rates
Future Value and Present Value
Compared
Present Value and Discounting
o CALCULATOR EXAMPLE
• Present Value
What is the present value of $1,000 to be received 10
years from now if the discount rate is 9%?
Enter
Answer
10
9
N
i
PV
-422.41
0
1,000
PMT
FV
Finding the Interest Rate
o TIME VALUE OF MONEY CALCULATIONS
• Many situations require using a time value of
money calculation to determine a rate of
change or growth rate
• An investor or analyst may want
the growth rate in sales
the rate-of-return on an investment
the effective interest rate on a loan
Compound Growth Rates
o CALCULATOR EXAMPLE
• Compound Growth Rate
A firm’s sales increased from $20 million to $35 million
in three years. What was the average annual growth
rate in sales?
Enter
3
N
Answer
i
20.51
-20
0
35
PV
PMT
FV
Compound Growth Rates
o CALCULATOR EXAMPLE
• Compound Growth Rate
The house at 1245 Maple St. was appraised at
$247,000 in 2006 and at $173,000 in 2011. What is the
average annual change in its value?
Enter
5
N
Answer
i
-6.874
-247000
0
173000
PV
PMT
FV
The Rule of 72
o ESTIMATE THE NUMBER OF PERIODS
• The Rule of 72 is used to estimate the time
(number of periods) it takes for an amount to
double.
The time it takes for the amount to double is
approximately equal to 72/i, where i equals the
percentage earned each period.
The Rule of 72 is fairly accurate for interest rates
between 5% and 20%.
The Rule of 72
o CALCULATOR EXAMPLE
• Time required for an amount to double
If you can earn 8% compounded annually, how long
will it take for your money to double?
Enter
N
Answer
9.006
8
-1
0
2
i
PV
PMT
FV
The Rule of 72
o CALCULATOR EXAMPLE
• Time required for an amount to double
If you can earn 8% compounded monthly
(.667%/month), how many months will it take for an
amount to double?
Enter
N
Answer
104.32
.667
-1
0
2
i
PV
PMT
FV
Chapter 6: Discounted Cash Flows and
Valuation
Learning Objectives
1. EXPLAIN WHY CASH FLOWS OCCURRING AT
DIFFERENT TIMES MUST BE ADJUSTED TO
REFLECT THEIR VALUE AS OF A COMMON DATE
BEFORE THEY CAN BE COMPARED, AND
COMPUTE THE PRESENT VALUE AND FUTURE
VALUE FOR MULTIPLE CASH FLOWS.
2. DESCRIBE HOW TO CALCULATE THE PRESENT
VALUE AND THE FUTURE VALUE OF AN
ORDINARY ANNUITY AND HOW AN ORDINARY
ANNUITY DIFFERS FROM AN ANNUITY DUE.
Learning Objectives
3. EXPLAIN WHAT A PERPETUITY IS AND WHERE
WE SEE THEM IN BUSINESS AND CALCULATE THE
VALUE OF A PERPETUITY.
4. DISCUSS GROWING ANNUITIES AND
PERPETUITIES, AS WELL AS THEIR APPLICATION
IN BUSINESS, AND CALCULATE THEIR VALUES.
5. DISCUSS WHY THE EFFECTIVE ANNUAL INTEREST
RATE (EAR) IS THE APPROPRIATE WAY TO
ANNUALIZE INTERESTS RATES, AND CALCULATE
THE EAR.
Multiple Cash Flows
o FUTURE VALUE OF MULTIPLE CASH FLOWS
1. Draw a timeline to determine the number of
periods for which each cash flow will earn the
rate-of-return
2. Calculate the future value of each cash flow
using Equation 5.1
3. Add the future values
Future Value of Two Cash Flows
Exhibit 6.1 Future Value of Two Cash Flows
This exhibit shows a timeline for two cash flows invested in a
savings account that pays 10 percent interest annually. The
total amount in the savings account after two years is
$2,310, which is the sum of the future values of the two cash
flows.
5
Future Value of Three Cash Flows
Exhibit 6.2 Future Value of Three Cash Flows
The exhibit shows a timeline for an investment program
with a three-year horizon. The value of the investment at
the end of three years is $3,641, the sum of the future
values of the three separate cash flows.
Present Value of Three Cash Flows
7
Kronka, Inc., is expecting cash flows of $13,000, $11,500, $12,750, and $9,635 over
the next four years. What is the present value of these cash flows if the appropriate
discount rate is 8 percent?
Level Cash Flows: Annuities and
Perpetuities
o ANNUITY
• A series of equally-spaced and level cash flows
extending over a finite number of periods
o PERPETUITY
• A series of equally-spaced and level cash flows
that continue forever
Level Cash Flows: Annuities and
Perpetuities
o ORDINARY ANNUITY
• cash flows occur at the end of a period
mortgage payment
interest payment to bondholder
Exhibits 6.1, 6.2, and 6.3
o ANNUITY DUE
• cash flows occur at the beginning of a period
lease
Exhibit 6.7
Level Cash Flows: Annuities and
Perpetuities
o CALCULATE PRESENT VALUE OF AN ANNUITY
• To calculate a future value or a present value is
to calculate an equivalent amount
• The amount reflects an adjustment to account
for the effect of compounding
Level Cash Flows: Annuities and
Perpetuities
o CALCULATE PRESENT VALUE OF AN ANNUITY
Present value of an annuity
• amount needed produce the annuity
• current fair value or market price of the annuity
• amount of a loan that can be repaid with the annuity
How to calculate present value of an
annuity
o 𝑃𝑉𝑜𝑓 𝑎𝑛 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 = 𝑃𝑀𝑇
o 𝑃𝑉𝑜𝑓 𝑎𝑛 𝑎𝑛𝑛𝑢𝑖𝑡𝑦 = 𝑃𝑀𝑇
1−𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑟
1−(𝟏+𝒊−𝒏
𝑟
PVA CF PVFA
0
1 PVFA
CF
i
1
1 (1 i )
CF
i
n
(6.1)
13
Level Cash Flows: Annuities and
Perpetuities
o PRESENT VALUE OF AN ANNUITY EXAMPLE
• A contract will pay $2,000 at the end of each
year for three years and the appropriate discount
rate is 8%. What is a fair price for the contract?
(1 1/(1 0.08)
PVA $2000
$5,154.19
0.08
3
3
Refer Table B-4
14
Present Value Annuity Factors
15
Example 1
WHAT IS THE VALUE OF 10-YEAR $1,000 ANNUITY
DISCOUNTED BACK TO THE PRESENT AT 5 PERCENT?
𝟏 − (𝟏 + 𝒊)−𝒏
𝑷𝑽𝒐𝒇 𝒂𝒏 𝒂𝒏𝒏𝒖𝒊𝒕𝒚 = 𝑷𝑴𝑻
𝒊
o
o
𝟏 − (𝟏 + 𝟎. 𝟎𝟓)−𝟏𝟎
𝑷𝑽 = $𝟏, 𝟎𝟎𝟎
𝟎. 𝟎𝟓
= $1,000 (7.722)
= $7,722
Example 2
o
TRANSIT INSURANCE COMPANY HAS MADE AN INVESTMENT IN ANOTHER COMPANY THAT
WILL GUARANTEE IT A CASH FLOW OF $37,250 EACH YEAR FOR THE NEXT FIVE YEARS. IF
THE COMPANY USES A DISCOUNT RATE OF 15 PERCENT ON ITS INVESTMENTS, WHAT IS THE
PRESENT VALUE OF THIS INVESTMENT? (ROUND TO THE NEAREST DOLLAR.)
Annual payment = PMT = $37,250
No. of payments = n = 5
Required rate of return = 15%
1
1
(1 i ) n
PVAn PMT
i
1
1
(1.15)5
$37, 250
$37, 250 3.3522
0.15
$124, 867.78
Example 4
Myers, Inc., will be making lease payments of $3,895.50 for a 10-year period,
starting at the end of this year. If the firm uses a 9 percent discount rate, what is
the present value of this annuity? (Round to the nearest dollar.)
1
1
(1 i ) n
PVAn PMT
i
1
1
(1.09)10
$3,895.50
$3,895.50 6.4177
0.09
$24, 999.99
Level Cash Flows: Annuities and
Perpetuities
o CALCULATOR EXAMPLE
• Present Value of Annuity
Enter
Answer
3
8
N
i
PV
2,000
0
PMT
FV
-5,154.19
19
Example 2
Jackson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5
percent. It plans to repay the loan in eight equal installments, beginning in a year.
What is its annual loan payment? (Round to the nearest dollar.)
PVAn = $27,850
1
1
(1 i ) n
PVAn PMT
i
$27,850
$27,850
PMT
1
5.6392
1
(1.085)8
0.085
$4, 938.66
n = 8;
i = 8.5%
Loan Amortization
• How borrowed funds are repaid over the life of
a loan
• Each payment includes less interest and more
principal; the loan is paid off with the last
payment
• Amortization schedule shows interest and
principal in each payment, and amount of
principal still owed after each payment
Amortization Table for a 5-Yr, $10,000
Loan at 5% Interest
22
Using Excel – Loan Amortization Table
Using Excel – Calculating the Interest
Rate for an Annuity
Level Cash Flows: Annuities and
Perpetuities
o FINDING THE INTEREST RATE
• The present value of an annuity equation can be
used to find the interest rate or discount rate for
an annuity
• To determine the rate-of-return for an annuity,
solve the equation for i
• Using a calculator is easier than a trial-and-error
approach
Level Cash Flows: Annuities and
Perpetuities
o CALCULATOR EXAMPLE
• Finding the Interest Rate
An insurer requires $350,000 to provide a guaranteed
annuity of $50,000 per year for 10 years. What is the
rate-of-return for the annuity?
Enter
10
N
Answer
i
-350,000
50,000
0
PV
PMT
FV
7.073
26
Level Cash Flows: Annuities and
Perpetuities
o FUTURE VALUE OF AN ANNUITY
• The future value of an annuity equation is
derived from Equation 6.1
FVA PVA Future Value Factor
n
n
Future Value Factor - 1
CF
i
(1 i) 1
CF
i
n
(6.2)
27
HOW MUCH WE DEPOSIT IN AN 8% SAVINGS
ACCOUNT AT THE END OF EACH YEAR TO
ACCUMULATE $5,000 AT THE END OF 10 YEARS?
(𝟏 + 𝒊)𝒏 −𝟏
𝑭𝑽 = 𝑪𝑭
𝒊
$5000 = CF
(𝟏+𝟎.𝟎𝟖)𝟏𝟎 −𝟏
𝟎.𝟎𝟖
$5000 = CF (14.487)
$𝟓𝟎𝟎𝟎
= CF
𝟏𝟒.𝟒𝟖𝟕
PMT = $345.15
REFER TABLE B-2
Future Value of 4-Yr Annuity: Colnago
C50 Bicycle
Exhibit 6.6
The exhibit shows a timeline for a savings plan to buy a Colnago
C50 bicycle. Under this savings plan, $1,000 is invested at the end
of each year for four years at an annual interest rate of 8 percent.
We find the value at the end of the four-year period by adding the
future values of the separate cash flows, just as in Exhibits 6.1 and
6.2.
29
Example 2
Carlos Menendez is planning to invest $3,500 every year for the next six years in
an investment paying 12 percent annually. What will be the amount he will have at
the end of the six years? (Round to the nearest dollar.)
Example 3
You plan to save $1,250 at the end of each of the next three years to pay for a
vacation. If you can invest it at 7 percent, how much will you have at the end of
three years? (Round to the nearest dollar.)
Example 4:
Maricela Sanchez needs to have $25,000 in five years. If she can earn 8 percent on
any investment, what is the amount that she will have to invest every year at the
end of each year for the next five years? (Round to the nearest dollar.)
Level Cash Flows: Annuities and
Perpetuities
o CALCULATOR EXAMPLE
• Future Value of an Annuity
Colnago Bicycle C50
Enter
Answer
4
8
0
1,000
N
i
PV
PMT
FV
-4,506.11
33
Level Cash Flows: Annuities and
Perpetuities
o PERPETUITY
• A stream of equal cash flows that goes on
forever
• Preferred stock and some bonds are perpetuities
• Equation for the present value of a perpetuity
can be derived from the present value of an
annuity equation
34
Level Cash Flows: Annuities and
Perpetuities
o PRESENT VALUE OF A PERPETUITY
PVP CF Pr esent value factor for an annuity
0
1
1 ( 1 i)
(1 0 )
CF
CF
i
i
CF
i
( 6.3 )
35
Valuing Perpetuity
Example 1
• Suppose you decide to endow a chair in finance.
The goal of the endowment is to provide
$100,000 of financial support per year forever. If
the endowment earns a rate of 8%, how much
money will you have to donate to provide the
desired level of support?
PVP
0
CF $100,000
$1,250,000
i
0.08
36
Example 2
o WHAT IS THE VALUE OF A $500 PERPETUITY
DISCOUNTED BACK TO THE PRESENT AT 8
PERCENT?
𝑪𝑭
𝑷𝑽 =
𝒊
$𝟓𝟎𝟎
𝑷𝑽 =
= $6250
𝟎.𝟎𝟖
Example 3
Your father is 60 years old and wants to set up a cash flow stream that would be
forever. He would like to receive $20,000 every year, beginning at the end of this
year. If he could invest in account earning 9 percent, how much would he have to
invest today to receive his perpetual cash flow? (Round to the nearest dollar.)
Annual payment needed = PMT = $20,000
Investment rate of return = i = 9%
Term of payment = Perpetuity
Present value of investment needed = PV
PMT $20, 000
PV of Perpetuity
i
0.09
$222, 222.22
Example 4
A lottery winner was given a perpetual payment of $11, 444. She could invest the
cash flows at 7 percent. What is the present value of this perpetuity? (Round to
the nearest dollar.)
Annual payment needed = PMT =
$11,444
Investment rate of return = i = 7%
Term of payment = Perpetuity
Present value of investment needed = PV
PMT $11, 444
PV of Perpetuity
i
0.07
$163, 485.71
Ordinary Annuity versus Annuity Due
• Present Value of Annuity Due
Cash flows are discounted for one period less than in an
ordinary annuity.
• Future Value of Annuity Due
Cash flows are earn compound interest for one period
more than in an ordinary annuity.
43
Ordinary Annuity versus Annuity Due
• The present value or future value of an annuity
due is always higher than that of an ordinary
annuity that is otherwise identical.
PVA PVA (1 i )
1
Due
(6.4)
FVA FVA (1 i )
1
Due
44
Ordinary Annuity versus Annuity
Due
45
Cash Flows That Grow at a Constant
Rate
o GROWING ANNUITY
• equally-spaced cash flows that increase in size
at a constant rate for a finite number of periods
o GROWING PERPETUITY
• equally-spaced cash flows that increase in size
at a constant rate forever
Cash Flows That Grow at a Constant
Rate
o GROWING ANNUITY
• Multiyear product or service contract with
periodic cash flows that increase at a constant
rate for a finite number of years
o GROWING PERPETUITY
• Common stock whose dividend is expected to
increase at a constant rate forever
47
Cash Flows That Grow at a Constant
Rate
o GROWING ANNUITY
• Calculate the present value of growing annuity
(only) when the growth rate is less than the
discount rate.
CF
1 g
PVA
1
i - g 1 i
n
1
n
(6.5)
48
Growing Annuity Example
• A coffee shop will operate for fifty more years.
Cash flow was $300,000 last year and increases
by 2.5% each year. The discount rate for similar
firms is 15%. Estimate the value of the firm.
CF
1 g
PVA
1
i - g 1 i
n
1
n
(6.5)
CF1 $300,000 (1 0.025) $307,500
$307,500
1.025
PVA
1
0.15 0.025 1.15
50
0
$2,460,000 0.9968
$2,452,128
Cash Flows That Grow at a Constant
Rate
o GROWING PERPETUITY
• Use Equation 6.6 to calculate the present value
of growing perpetuity (only) when the growth
rate is less than discount rate.
• It is derived from equation 6.5 when the number
of periods approaches infinity
CF
PVP
i - g
1
0
(6.6)
50
Cash Flows That Grow at a Constant
Rate
o GROWING PERPETUITY EXAMPLE
• A firm’s cash flow was $450,000 last year. You
expect the cash flow to increase by 5% per year
forever. If you use a discount rate of 18%, what
is the value of the firm?
PVP
0
CF
i - g
1
(6.6)
CF1 $450,000 (1 0.05) $307,500
PVP
0
$472,500 $472,500
0.18 0.05
0.13
$3,634,615
51
The Effective Annual Interest Rate
o DESCRIBING INTEREST RATES
• The most common way to quote interest rates is
in terms of annual percentage rate (APR). It
does not incorporate the effects of
compounding.
• The most appropriate way to quote interest rates
is in terms of effective annual rate (EAR). It
incorporates the effects of compounding.
52
The Effective Annual Interest Rate
o CALCULATE ANNUAL PERCENTAGE RATE (APR)
• APR = (periodic rate) x m
m is the # of periods in a year
• APR does not account for the number of
compounding periods or adjust the annualized
interest rate for the time value of money
• APR is not a precise measure of the rates
involved in borrowing and investing
53
The Effective Annual Interest Rate
o ANNUAL PERCENTAGE RATE (APR) EXAMPLE
• Anna is charged 1% interest when she borrows
$2000 for one week. What is the annual
percentage interest rate (APR) on the loan?
APR = (periodic rate) x m
APR (0.01) x 52 0.52 or 52%
54
The Effective Annual Interest Rate
o EFFECTIVE ANNUAL INTEREST RATE (EAR)
• EAR accounts for the number of compounding
periods and adjusts the annualized interest rate
for the time value of money
• EAR is a more accurate measure of the rates
involved in lending and investing
55
The Effective Annual Interest Rate
o EFFECTIVE ANNUAL RATE (EAR) EXAMPLE
• Anna is charged 1% interest when she borrows
$2000 for one week. What is the effective annual
interest rate (EAR)?
EAR (1 0.01) - 1
52
1.6777 - 1
0.6777 or 67.77%
56
The Effective Annual Interest Rate
o EFFECTIVE ANNUAL RATE (EAR) EXAMPLE
• Your credit card has an APR of 12 % (1% per
month). What is the EAR?
EAR (1 0.12/12) - 1
12
(1 0.01) - 1
12
1.1268 - 1
0.1268 or 12.68%
57
Consumer Protection and Information
o CONSUMER PROTECTION AND INFORMATION
• Truth-in-Lending Act (1968) requires that
borrowers be told the actual cost of credit
• Truth-in-Savings Act (1991) requires that the
actual return on savings be disclosed to
consumers
• Credit Card Act (2009) limits credit card fees
and interest rate increases, and requires better
disclosure of contract details
58
Chapter 7: Risk and Return
Learning Objectives
1. EXPLAIN THE RELATION BETWEEN RISK AND
RETURN.
2. DESCRIBE THE TWO COMPONENTS OF A
TOTAL HOLDING PERIOD RETURN, AND
CALCULATE THIS RETURN FOR AN ASSET.
3. EXPLAIN WHAT AN EXPECTED RETURN IS
AND CALCULATE THE EXPECTED RETURN FOR
AN ASSET.
Learning Objectives
4. EXPLAIN WHAT THE STANDARD DEVIATION
OF RETURNS IS AND WHY IT IS VERY USEFUL
IN FINANCE AND CALCULATE IT FOR AN
ASSET.
5. EXPLAIN THE CONCEPT OF DIVERSIFICATION.
6. DISCUSS WHICH TYPE OF RISK MATTERS TO
INVESTORS AND WHY.
Learning Objectives
7. DESCRIBE WHAT THE CAPITAL ASSET PRICING
MODEL (CAPM) TELLS US AND HOW TO USE
IT TO EVALUATE WHETHER THE EXPECTED
RETURN OF AN ASSET IS SUFFICIENT TO
COMPENSATE AN INVESTOR FOR THE RISKS
ASSOCIATED WITH THAT ASSET.
Risk and Return
o PEOPLE DO NOT WANT TO LOSE MONEY
• Why would a person choose an investment with
a higher risk of loss when there is a lower-risk
opportunity available?
Risk and Return
o PEOPLE DO NOT WANT TO LOSE MONEY
• A person will prefer a higher-risk opportunity if
the probability of an adequate reward is high
enough
A higher-risk investment must offer a potential return
high enough to make it as attractive as the lower-risk
alternative.
The potential return a person requires depends on the
amount of risk – the probability of being dissatisfied
with an outcome.
Risk and Return
o RISK/RETURN RELATIONSHIP
• The higher the risk, the higher the required
rate-of-return (possible/expected return)
This is the risk/return relationship.
Risk and Return
o INSIGHT INTO THE RISK/RETURN
RELATIONSHIP
• Most people are risk averse – they do not like
risk
• People vary in their risk tolerance –the amount
of risk they will accept
Risk and Return
o INSIGHT INTO THE RISK/RETURN
RELATIONSHIP
• An optimal combination of risk and return is
the highest expected return for a given amount
of risk
• An optimal combination of risk and return is
the lowest level of risk for a given expected
return
Risk and Return
o RISK
• default
• misuse
• slow pay
• theft
o RISK
• cost increase
• price decline
• missed opportunity
• not enough
• ….. many others
Risk and Return
o RETURN
• Refers to expected return.
“Expected” means there is some uncertainty about
what the return will actually be.
– “I expect to earn around 9%.”
• The higher the risk, the higher the required rate
of (expected) return
Quantitative Measures of Return
o EXPECTED RETURN AND REALIZED RETURN
• Expected return
estimated or predicted before the outcome is known
• Realized return
calculated after the outcome is known
– Both are important in financial decision-making.
Quantitative Measures of Return
o HOLDING PERIOD RETURN
• Total holding period return consists of capital
appreciation (Rca) and income (Ri)
capital appreciation P P P
R
initial price
P
P
1
0
ca
0
0
cash flow
CF
CF
R
initial price initial price P
1
1
i
0
Quantitative Measures of Return
o TOTAL HOLDING PERIOD RETURN
P CF P CF
R R R
P
P
P
1
1
t
ca
i
0
0
0
(7.1)
Quantitative Measures of Return
o TOTAL HOLDING PERIOD RETURN EXAMPLE 1
• Ella buys a stock for $26.00. After one year, the
stock price is $29.00 and she receives a dividend
of $0.80. What is her return for the period?
Rt Rca Ri
P CF1
P0
($29.00 $26.00) $0.80
$26.00
$3.80
0.14615 or 14.62%
$26.00
Example 2
o GEORGE WILSON PURCHASED BRIGHT LIGHT INDUSTRIES
COMMON STOCK FOR $47.50 ON JANUARY 31, 2010. THE
FIRM PAID DIVIDENDS OF $1.10 DURING THE LAST 12
MONTHS. GEORGE SOLD THE STOCK TODAY (JANUARY 30,
2011) FOR $54.00. WHAT IS GEORGE’S HOLDING PERIOD
RETURN? ROUND OFF THE NEAREST 0.01%.
R1
P1 P 0 CF 1 $54.00 $47.50 $1.10
.1600 16.00%
P0
$47.50
o AHMET PURCHASED A STOCK FOR $45 ONE YEAR AGO. THE STOCK IS
NOW WORTH $65. DURING THE YEAR, THE STOCK PAID A DIVIDEND OF
$2.50. WHAT IS THE TOTAL RETURN TO AHMET FROM OWNING THE
STOCK? (ROUND YOUR ANSWER TO THE NEAREST WHOLE PERCENT.)
$65 $45 $2.50
0.5 50%
$45
Quantitative Measures of Return
o EXPECTED RETURN
• E(RAsset), is the weighted average of the
possible investment returns. Multiply each
return by the probability that it will occur,
then add.
E (R ) ( p R ) ( p R ) ( p R ) ... ( p R ) (7.2)
n
asset
i 1
i
i
1
1
2
2
n
n
Quantitative Measures of Return
o EXPECTED RETURN EXAMPLE
• There is 30% chance the total return on Dell
stock will be -3.45%, a 30% chance it will be
+5.17% , a 30% chance it will be +12.07% and a
10% chance that it will be +24.14%. Calculate
the expected return.
E (R ) .30 ( 0.0345) (.30 0.0517)
Dell
(.30 0.1207) (.10 0.2414)
0.010305 0.01551 0.03621 0.02414
0.0655 or 6.55%
Example 2
o Use the following Table to calculate the Expected Return for
the asset
Return
Probability
0.05
0.1
0.15
0.25
0.1
0.15
0.5
0.25
Feedback:
(0.5)(0.1) + (0.1)(0.15) + (0.15)(0.5) + (0.25)(0.25) = 0.1575
Quantitative Measures of Return
o EXPECTED RETURN
• If each possible outcome is equally likely (p1
= p2 = p3 = … = pn = p = 1/n), the expected
return formula reduces to
(R )
n
E (R )
asset
i
i 1
n
R R R ... R
n
1
2
3
n
Variance and Standard Deviation
as Measures of Risk
o CALCULATE VARIANCE
1. Square the difference between each possible
outcome and the mean
2. Multiply each squared difference by its
probability of occurring
3. Add
n
Var ( R ) pi Ri E ( R)
2
R
i 1
2
(7.3)
Variance and Standard Deviation
as Measures of Risk
o CALCULATE VARIANCE
• If all possible outcomes are equally likely, the
formula becomes
n
R E ( R)
i 1
2
R
2
i
n
Variance and Standard Deviation
as Measures of Risk
o CALCULATE STANDARD DEVIATION
• Standard deviation is the square root of the
variance
2
R
Variance and Standard Deviation
as Measures of Risk
o VARIANCE AND STANDARD DEVIATION
• Variance and Standard Deviation for Dell Stock
2
Dell
.30 (0.0345 .0655) 2 .30 (0.0517 0.0655) 2
.30 (0.1207 0.0655) 2 .10 (0.2414 0.0655) 2
0.0030 0.0009 0.00006 0.0031
0.0071
Dell 0.0071 0.084
Example 2
o Tommie has made an investment that will generate returns that
are subject to the state of the economy during the year. Use the
following information to calculate the standard deviation of the
return distribution for tommie's investment.
State
Return Probabilit
y
Weak
OK
Great
0.13
0.2
0.25
0.3
0.4
0.3
E ( R) (0.3)(0.13) (0.4)(0.2) (0.3)(0.25) 0.194
Var ( R) 0.3(0.13 0.194) 2 0.4(0.2 0.194) 2 0.3(0.25 0.194) 2 0.002184
1
2
Std ( R) (0.002184) 0.046733
Example 3
o Elrond has made an investment that will generate returns that are
subject to the state of the economy. Use the following
information to calculate the variance of the return distribution for
elrond's investment.
State
Return Probabilit
y
Weak
OK
Great
0.10
0.17
0.28
0.8
0.1
0.1
Variance and Standard Deviation
as Measures of Risk
o NORMAL DISTRIBUTION
• A symmetric distribution completely described
by its mean (average) and standard deviation
Completely described by its mean and standard
deviation says they are all we need to draw conclusions
about its shape and the location of items in the
distribution.
Variance and Standard Deviation
as Measures of Risk
o NORMAL DISTRIBUTION
• Mean (average) is at the center
• Areas to the left and right of the mean are
mirror images of each other
• Values less than the mean are on the left and
values greater than the mean are on the right
Variance and Standard Deviation
as Measures of Risk
o NORMAL DISTRIBUTION
• The mean is the reference point to which all
other values in the distribution are compared
• To use standard deviation as a distance
measure, consider how many standard
deviations are between a value in the
distribution and the mean
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• For a normal distribution, the standard
deviation tells us, based on what has happened
in the past, the probability that an outcome will
occur
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• Is used in a context similar to “The average
return on the S&P 500 is 3%. What is the
probability of it being between 3% and 1%?”
When the difference between 3% and 1% is converted to
a standard deviation, it becomes a distance.
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• For a normal distribution, the standard
deviation distance between 3% and 1% is the
same as between 3% and 5%
• Outcomes that occur most often are closest to
the mean – convert to fewer standard deviations.
Outcomes that rarely occur are farthest from the
mean – convert to more standard deviations
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• A unit of measure or distance
“Forty-three percent of the time, the number is more
than the average but less than 62.”
• A measure of frequency
“A professional makes that put more than 99% of the
time.”
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• For a normal distribution, a standard deviation
is associated with the probability that an
outcome occurs within a certain distance from
the mean
Variance and Standard Deviation
as Measures of Risk
o STANDARD DEVIATION
• For a normal distribution
90% of outcomes are not more than 1.645 standard
deviations from the mean
95% of outcomes are not more than 1.960 standard
deviations from the mean
99% of outcomes are not more than 2.575 standard
deviations from the mean
Normal Distribution
Standard Deviation and Width of the
Normal Distribution
Variance and Standard Deviation
as Measures of Risk
o HISTORICAL MARKET PERFORMANCE
• On average, annual returns have been higher for
riskier securities
• Exhibit 7.3 shows that small stocks have the
largest standard deviation of returns and the
largest average return
• On other end of spectrum, Treasury bills have
the smallest standard deviation and the smallest
average return
Distributions of Annual Total Returns
for U.S. Stocks & Bonds
Monthly Returns for Apple Inc. Stock
and the S&P 500 Index
Cumulative Value of $1 Invested in
1926
Exhibit 7.5
Risk and Diversification
o DIVERSIFICATION
• By investing in two or more assets whose
returns do not always move in same direction at
the same time, investors can reduce the risk in
their investment portfolios
o PORTFOLIO: The collection of assets an investor
owns.
Risk and Diversification
o SINGLE-ASSET PORTFOLIOS
• Returns for individual stocks are largely independent of each
other and approximately normally distributed.
• A simple tool for comparing risk and return for individual
stocks is the coefficient of variation (CV).
• CV is a measure that can help us in making
comparisons i.e between Stocks A and C.
CVi
Ri
E ( Ri )
(7.4)
• CV is a measure of the risk associated with an
investment for each 1percent of expected return.
Risk and Diversification
o COEFFICIENT OF VARIATION EXAMPLE 1
• Stock A has an expected return of 12% and a standard
deviation of 12% while Stock B has an expected return
of 16% and a standard deviation of 20%. What is the
coefficient of variation for these stocks?
Ri
CVi
E ( Ri )
0.12
CV ( RA )
1
0.12
.20
CV ( RB )
1.25
.16
Example 2
o Braniff ground services stock has an expected return of 9 percent and a
variance of 0.25 percent. What is the coefficient of variation for braniff?
Example 3
Sayers purchased a stock with a coefficient of variation equal to
0.125. The expected return on the stock is 20 percent. What is
the variance of the stock?
Coefficient
of
Variation
E ( R)
1
2 2
0.125, 0.000625
2
0.20
Risk and Diversification
o SHARPE RATIO
• A modified version of the coefficient of
variation.
• A measure of the return per unit of risk for an
investment.
Sharpe Ratio S
E ( Ri ) Rrf
Ri
(7.5)
Example
o You have decided to invest in the stock that has the highest expected
return per unit of total risk. If the expected return and standard
deviation of returns for stock A are 10 percent and 25 percent,
respectively, and the expected return and standard deviation of returns
for stock B are 15 percent and 40 percent, respectively, which should you
choose? Assume that the risk free rate is 5 percent .
Sharpe Ratio S
E ( Ri ) Rrf
Ri
S ( A)
0.10 0.05
0.20
0.25
S ( B)
0.15 0.05
0.25
0.40
o STOCK B HAS THE HIGHEST EXPECTED RETURN PER UNIT OF RISK.
Risk and Diversification
o PORTFOLIOS OF MORE THAN ONE ASSET
• The coefficient of variation and Sharpe Ratio have a
critical shortcoming when applied to a portfolio of assets –
they cannot account for the interaction of assets’ risks
when they are grouped into a portfolio
• Expected return for portfolio made up of two assets.
E (R
Portfolio
) x E (R ) x E (R )
1
1
2
2
• where xi represents the fraction of the portfolio invested in
asset i.
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• Expected return for portfolio made up of
multiple assets
E (R
) ( x E (R ) ( x E (R ) ( x E (R ) ...
n
Portfolio
i
i 1
i
( x E (R )
n
n
1
( 7 .6 )
1
2
2
Risk and Diversification
o EXPECTED RETURN FOR PORTFOLIO EXAMPLE
• A portfolio consists of $100,000 in Treasury bills that yield
4.5%; $150,000 in Proctor and Gamble stock with an
expected return of 7.5%; and $150,000 in Exxon Mobil stock
with an expected return of 9.0%. What is the expected
return for this $400,000 portfolio?
$100,000
0.25
$400,000
$150,000
x P&G x EM
0.375
$400,000
x TB
E ( RPortfolio ) (0.25 0.045) (0.375 0.075) (0.375 0.09)
0.0731or 7.3%
Monthly Returns for Netflix &
Southwest Airlines (1 of 2)
Exhibit 7.6
Monthly Returns for Netflix &
Southwest Airlines (2 of 2)
Exhibit 7.7
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• When stock prices move in opposite directions,
the price change of one stock offsets some of
the price change of another stock
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• Risk for a portfolio of two stocks is less than the
average of the risks associated with the individual
stocks. The portfolio’s risk is:
22Asset Portfolio x 12 R21 x 22 R2 2 2x 1x 2 R1,2
(7.7)
• where xi represents the fraction of the portfolio
invested in stock i, σ2R i is the variance of the return of
stock i, and σR1,2 is the covariance of the returns
between stocks 1 and 2. The covariance of returns is a
measure of how the returns on two assets covary, or
move together.
Risk and Diversification
o PORTFOLIO VARIANCE EXAMPLE
• The variance of the annual returns of CSX and
Wal-Mart stock are 0.03949 and 0.02584
respectively. The covariance between returns is
0.00782. Calculate the variance of a portfolio
consisting of 50% CSX and 50% Wal-Mart.
22Asset Portfolio x 12 R21 x 22 R2 2 2x 1x 2 R1, 2
(0.5) 2 (0.03949) (0.5) 2 (0.02584) 2(0.5)(0.5)(0.00782)
0.02024
Example
o BATMAN STOCK HAS EXHIBITED A STANDARD DEVIATION IN STOCK
RETURNS OF 0.5, WHEREAS SUPERMAN STOCK HAS EXHIBITED A
STANDARD DEVIATION OF 0.6. THE CORRELATION COEFFICIENT BETWEEN
THE STOCK RETURNS IS 0.5. WHAT IS THE VARIANCE OF A PORTFOLIO
COMPOSED OF 70 PERCENT BATMAN AND 30 PERCENT SUPERMAN?
Var ( port ) x1212 x22 22 2 x1 x21 2 12
(0.7)2 (0.5)2 (0.3)2 (0.6)2 2(0.7)(0.3)(0.5)(0.6)(0.5) 0.2179
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• In the variance equation, R1, 2 is the covariance
between stocks 1 and 2.
• Covariance indicates whether stocks’ returns
tend to move in the same direction at the same
time. If so, the covariance is positive. If not, it
is negative or zero.
n
COV ( R1 , R2 ) pi ( R1,i E ( R1 ) ( R2,i E ( R2 )
i1
(7.8)
Example
GIVEN THE RETURNS FOR TWO STOCKS WITH THE FOLLOWING
INFORMATION, CALCULATE THE COVARIANCE OF THE RETURNS FOR THE
TWO STOCKS. ASSUME THE EXPECTED RETURN IS 10.8 PERCENT FOR STOCK
1 AND 9.7 PERCENT FOR STOCK 2.
Prob Stock 1Stock 2
0.4
0.5
0.1
0.09
0.11
0.17
0.11
0.08
0.13
Cov(R1,R2)=
[0.4*(0.09-0.108)*(0.11-0.097)]
+
0.108)*(0.08-0.097)] + [0.1*(0.17-0.108)*(0.13-0.097)]
= (-0.0000936) + (-0.000017) + (0.0002046)
= 0.000094
[0.5*(0.11-
Example
o Given the returns for two stocks with the following information, calculate
the covariance of the returns for the two stocks. Assume the expected
return is 14.4 percent for stock 1 and 15.9 percent for stock 2.
Prob Stock 1 Stock 2
0.5
0.3
0.2
0.11
0.17
0.19
0.18
0.15
0.12
Cov( R1 , R2 ) PState1 ( RState1,1 E ( R1 )( RState1,2 E ( R2 )) PState 2) ( RState 2,1 E ( R1 ))(RState 2,2 E (R2 ))
PState3 ( RState3,1 E ( R1 ))( RState3,2 E ( R2 )) 0.00007192
Cov(R1,R2) = .
(0.5*(0.11-0.144)*(0.18-0.159)+0.3*(0.17-0.144)*(0.15-0.159)+0.2*(0.19-0.144)*(0.120.159)
= -0.00079
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
o To measure the strength of the covariance
relationship, divide the covariance by the product
of the standard deviations of the assets’ returns.
This result is the correlation coefficient that
measures the strength of the relationship between
the assets’ returns.
R1, 2
R1, 2
R1 R 2
(7.9)
CORRELATION COEFFICIENT EXAMPLE
• The variance of the annual returns of CSX and
Wal-Mart stock are 0.03949 and 0.02584
respectively. The covariance between returns is
0.00782. Calculate the variance of a portfolio
consisting of 50% CSX and 50% Wal-Mart.
CSX 0.03949 0.1987
W alMart 0.02584 0.1607
CSX ,W almart
0.00782
CSX ,W almart
0.2449
CSX W alMart 0.1987 0.1607
Example
o THE COVARIANCE OF THE RETURNS BETWEEN EINSTEIN STOCK AND BOHR STOCK
IS 0.0087. THE STANDARD DEVIATION OF EINSTEIN IS 0.26, AND THE STANDARD
DEVIATION OF BOHR IS 0.37. WHAT IS THE CORRELATION COEFFICIENT BETWEEN
THE RETURNS OF THE TWO STOCKS?
Cov( R1 , R2 )
1 2
0.0087
0.090437
(0.26)(0.37)
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• A correlation coefficient cannot be greater than +1
or less than -1.
• Negative correlation
stock X is higher when stock Y is lower; stock X is lower when
stock Y is higher
• Positive correlation
stock X is higher when stock Y is higher; stock X is lower
when stock Y is lower
• Zero Correlation
no relationship or pattern linking returns on the stocks.
Risk and Diversification
o PORTFOLIOS WITH MORE THAN ONE ASSET
• If assets are not perfectly correlated, risk can be
reduced by creating a portfolio using assets
having different risk characteristics
• For each asset, account for the covariance
between that asset and every other asset in the
portfolio
Risk and Diversification
o LIMITS ON DIVERSIFICATION BENEFITS
• Adding an asset whose returns do not replicate
the returns on an asset already in the portfolio
will reduce the standard deviation of the
portfolio returns
The amount by which the standard deviation of
portfolio returns is reduced gets smaller with each
asset added
Risk and Diversification
o LIMITS OF DIVERSIFICATION
• When the number of assets in a portfolio is
large, adding another stock has almost no effect
on the standard deviation
• Most risk-reduction from diversification may be
achieved with 15-20 assets
• Diversification can virtually eliminate risk
unique to individual assets, but the risk
common to all assets in the market remains
Risk and Diversification
o THE LIMITS OF DIVERSIFICATION
• Firm-specific risk relevant for a particular firm
can be diversified away and is called
diversifiable, unsystematic, or unique risk.
• Risk that cannot be diversified away is nondiversifiable, or systematic risk. This is the risk
inherent in the market or economy.
Firm-specific risk is, in effect, reduced to zero in a
diversified portfolio but some systematic risk remains.
Total Risk in a Portfolio as the
Number of Assets Increases
Exhibit 7.8
Systematic Risk
o WHY SYSTEMATIC RISK IS ALL THAT MATTERS
• Investors do not like risk and will not bear risk
they can avoid by diversification
• Well-diversified portfolios contain only systematic
risk.
• Portfolios that are not well-diversified face
systematic risk plus unsystematic risk.
• No one compensates investors for bearing
unsystematic risk, and investors will not accept risk
that they are not paid to take.
Systematic Risk
o MEASURING SYSTEMATIC RISK
• Systematic risk of an individual asset depends
on how the behavior of the market influences
the return on that asset. Systematic risk cannot
be eliminated by diversification.
• Standard deviation measures total risk of an
asset. It cannot be used to measure the risk of a
diversified portfolio.
Monthly General Electric Company
Stock and S&P 500 Index Returns
Exhibit 7.9
Slope of Relation Between GE
Returns and S&P 500 Returns
Exhibit 7.10
Systematic Risk
o MEASURING SYSTEMATIC RISK
• If the average return for all assets (the market
return) is used as the benchmark and its
influence on the return for a specific stock can
be quantified, the expected return on that stock
can be calculated
• The market’s influence on a stock’s return is
quantified in the stock’s beta
Systematic Risk
o MEASURING SYSTEMATIC RISK
• If the beta of an asset is
• zero, the market has no measurable effect on the
asset’s return
• positive, the market has a positive effect on the
asset’s return
• negative, the market has a negative effect on the
asset’s return
Systematic Risk
o MEASURING SYSTEMATIC RISK
• If the beta of an asset is
• 0, the asset has no measurable systematic risk.
• > 1, the systematic risk for the asset is greater than
the average for assets in the market.
• < 1, the systematic risk for the asset is less than the
average for assets in the market.
Compensation for Bearing Systematic
Risk
o MEASURING SYSTEMATIC RISK
• The risk premium is the difference between the
market rate of return and the risk-free rate of
return
• The difference between the required return on a
risky asset (Ri) and the return on a risk-free
asset Rrf is an investor’s compensation for risk
• E(Ri) = Rrf + Compensation for bearing
Systematic risk
Compensation for Bearing Systematic
Risk
o MEASURING SYSTEMATIC RISK
• Since compensation for bearing systematic risk
depends on the asset
E(Ri) = Rrf + (Amount of Systematic Risk)
(Compensation/Unit of Systematic Risk)
Compensation for Bearing Systematic
Risk
o MEASURING SYSTEMATIC RISK
• Beta is the number of units of systematic risk
• Compensation for Risk = β (Compensation
per Unit of Systematic Risk)
• Compensation per Unit of Systematic Risk =
E(Rm) – Rrf
• Equation 7.10 is the Capital Asset Pricing Model
E(R ) R E(R ) – R
i
rf
i
m
rf
(7.10)
Compensation for Bearing Systematic
Risk
o CAPITAL ASSET PRICING MODEL
• The Capital Asset Pricing Model (CAPM)
describes the relationship between risk and
required expected return for an asset
E(R ) R E(R ) – R
i
rf
i
m
rf
Compensation for Bearing Systematic
Risk
o CAPITAL ASSET PRICING MODEL EXAMPLE
• A stock has a beta of 1.5. The expected return
on the market is 10% and the risk-free rate is
4%. What is the expected return for the stock?
E(R ) R (E(R ) – R )
i
rf
i
m
rf
0.04 1.500.10 - 0.04
0.13 or 13%
Compensation for Bearing Systematic
Risk
o THE SECURITY MARKET LINE
• The graph of the CAPM equation is known as
the Security Market Line (SML)
• The SML illustrates the CAPM’s prediction for
the required expected total return for various
values of beta. The expected total return
depends on an asset’s current price.
P CF
E (R )
P
1
T
0
Compensation for Bearing Systematic
Risk
Exhibit 7.11 The Security Market Line
Compensation for Bearing Systematic
Risk
o THE SECURITY MARKET LINE
• If the expected return is greater than the required
return estimated with the CAPM, the expected
return will plot above the SML
• If the expected return is less than the required
return estimated with the CAPM, the expected
return will plot below the SML
• If an asset’s expected return plots above the SML,
the asset is considered underpriced
• If an asset’s expected return plots below the SML,
the asset is considered overpriced
Compensation for Bearing Systematic
Risk
o THE CAPM AND PORTFOLIO RETURNS
• The expected return for a portfolio is the
weighted average of the expected returns of the
assets in the portfolio
• The beta of a portfolio is the weighted average
of the betas of the assets in the portfolio
( x ) ( x ) ( x ) ... ( x )
n
n asset portfolio
i 1
i
i
1
1
2
2
n
n
(7.10)
Compensation for Bearing Systematic
Risk
o PORTFOLIO BETA EXAMPLE
• You invest 25% of your retirement savings in a
fully diversified market fund, 25% in risk-free
Treasury bills, and 50% in a house with twice as
much systematic risk as the market. What is the
beta of your portfolio?
(x ) (x ) (x ) (x
n
portfolio
i 1
i
i
Fund
Fund
TB
TB
House
)
House
(0.25 1.0) (0.25 0.00) (0.50 2.00)
1.25
Compensation for Bearing Systematic
Risk
o EXPECTED PORTFOLIO RETURN EXAMPLE
• In the previous problem, what rate of return
would you expect to earn from the portfolio if
the risk-free rate is 4% and the expected return
on the market 10%?
E(R
n Asset Portf olio
)R
rf
n Asset Portf olio
E (R ) R
m
rf
0.04 1.250.10 0.04
0.04 1.25 (0.06)
0.115, or 11.5 %
Bond Valuation and the Structure of
Interest Rates
Learning Objectives...

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