SMO 3 Financial Management

Chapter 1
Introduction to Corporate Finance
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Key Concepts and Skills
 Know the basic types of financial management
decisions and the role of the Financial Manager
 Know the financial implications of the various
forms of business organization
 Know the goal of financial management
 Understand the conflicts of interest that can
arise between owners and managers
 Understand the various types of financial
markets
Chapter Outline
1.1 What is Corporate Finance?
1.2 The Corporate Firm
1.3 The Goal of Financial Management
1.4 The Agency Problem and Control of the
Corporation
1.5 Financial Markets
1.1 What is Corporate Finance?
Corporate Finance addresses the following
three questions:
1. What long-term investments should the firm
choose?
2. How should the firm raise funds for the selected
investments?
3. How should short-term assets be managed and
financed?
Balance Sheet Model of the Firm
Total Value of Assets: Total Firm Value to Investors:
Current
Liabilities
Current Assets
Long-Term
Debt
Fixed Assets
1 Tangible
Shareholders’
2 Intangible Equity
The Capital Budgeting Decision
Current
Liabilities
Current Assets
Long-Term
Debt
Fixed Assets
What long-term
1 Tangible investments Shareholders’
should the firm
2 Intangible Equity
choose?
The Capital Structure Decision
Current
Liabilities
Current Assets
Long-Term
How should the Debt
firm raise funds
for the selected
Fixed Assets
investments?
1 Tangible Shareholders’
2 Intangible Equity
Short-Term Asset Management
Current
Liabilities
Current Assets
Net
Working Long-Term
Capital Debt
How should
Fixed Assets
short-term assets
1 Tangible be managed and
financed? Shareholders’
2 Intangible Equity
Capital Structure
The value of the firm can be
thought of as a pie.
The goal of the manager is 70%50%30%
25%
to increase the size of the DebtDebt
Equity
pie.
75%
50%
The Capital Structure Equity
decision can be viewed as
how best to slice the pie.
If how you slice the pie affects the size of the pie,
then the capital structure decision matters.
The Financial Manager
The Financial Manager’s primary goal is to
increase the value of the firm by:
1. Selecting value creating projects
2. Making smart financing decisions
Hypothetical Organization Chart
Board of Directors
Chairman of the Board and

Chief Executive Officer (CEO)
President and Chief

Operating Officer (COO)
Vice President and

Chief Financial Officer (CFO)
Treasurer Controller
Cash Manager Credit Manager Tax Manager Cost Accounting
Capital Expenditures Financial Planning Financial Accounting Data Processing
The Firm and the Financial Markets
Firm Firm issues securities (A) Financial

markets
Invests
Retained
in assets cash flows (F)
(B)
Short-term debt
Current assets Cash flow Dividends and Long-term debt
Fixed assets from firm (C) debt payments (E)
Equity shares
Taxes (D)
Ultimately, the firm The cash flows from

must be a cash the firm must exceed
Government
the cash flows from
generating activity.
the financial markets.
1.2 The Corporate Firm
 The corporate form of business is the standard
method for solving the problems encountered
in raising large amounts of cash.
 However, businesses can take other forms.
Forms of Business Organization
 The Sole Proprietorship
 The Partnership
 General Partnership
 Limited Partnership
 The Corporation
A Comparison
Corporation Partnership
Liquidity Shares can be easily Subject to substantial

exchanged restrictions
Voting Rights Usually each share gets one General Partner is in charge;
vote limited partners may have
some voting rights
Taxation Double Partners pay taxes on

distributions
Reinvestment and dividend Broad latitude All net cash flow is
payout distributed to partners
Liability Limited liability General partners may have

unlimited liability; limited
partners enjoy limited
liability
Continuity Perpetual life Limited life
1.3 The Goal of Financial Management
 What is the correct goal?
 Maximize profit?
 Minimize costs?
 Maximize market share?
 Maximize shareholder wealth?
1.4 The Agency Problem
 Agency relationship
 Principal hires an agent to represent his/her interest
 Stockholders (principals) hire managers (agents) to
run the company
 Agency problem
 Conflict of interest between principal and agent
Managerial Goals
 Managerial goals may be different from
shareholder goals
 Expensive perquisites
 Survival
 Independence
 Increased growth and size are not necessarily
equivalent to increased shareholder wealth
Managing Managers
 Managerial compensation
 Incentivescan be used to align management and
stockholder interests
 The incentives need to be structured carefully to
make sure that they achieve their intended goal
 Corporate control
 The
threat of a takeover may result in better
management
 Other stakeholders
1.5 Financial Markets
 Primary Market
 Issuance of a security for the first time
 Secondary Markets
 Buying and selling of previously issued securities
 Securities may be traded in either a dealer or
auction market
 NYSE
 NASDAQ
Financial Markets
Stocks and
Investors
Bonds
Firms securities
Money Bob Sue
money
Primary Market
Secondary
Market
Chapter 2
Financial Statements and Cash Flow
 Understand the information provided by
financial statements
 Differentiate between book and market values
 Know the difference between average and

marginal tax rates
 Know the difference between accounting
income and cash flow
 Calculate a firm’s cash flow
Chapter Outline
2.1 The Balance Sheet
2.2 The Income Statement
2.3 Taxes
2.4 Net Working Capital
2.5 Financial Cash Flow
2.6 The Accounting Statement of Cash Flows
2.1 The Balance Sheet
 An accountant’s snapshot of the firm’s
accounting value at a specific point in time
 The Balance Sheet Identity is:
Assets ≡ Liabilities + Stockholder’s Equity
U.S. Composite Corporation Balance Sheet
2006 2005
The assets are listed in2006 order2005by
Current assets:
Cash and equivalents $140 $107
the length
Current Liabilities: of time it would
Accounts payable $213 $197
Accounts receivable 294 270 normally
Notes payable take a firm with 50 53
Inventories 269 280 Accrued expenses 223 205
Other 58 50 ongoing
Total currentoperations
liabilities to convert
$486 $455
Total current assets $761 $707
them into
Long-term cash.
liabilities:
Fixed assets: Deferred taxes $117 $104
Property, plant, and equipment $1,423 $1,274 Long-term debt 471 458
Less accumulated depreciation (550) (460) Total long-term liabilities $588 $562
Net property, plant, and equipment 873 814
Intangible assets and other 245 221 Stockholder's equity:
Total fixed assets $1,118 $1,035 Preferred stock $39 $39
Clearly, cash is much more
Common stock ($1 per value) 55 32
liquid than property, plant, and
Capital surplus
Accumulated retained earnings
347
390
327
347
equipment.
Less treasury stock (26) (20)
Total equity $805 $725
Total assets $1,879 $1,742 Total liabilities and stockholder's equity $1,879 $1,742
Balance Sheet Analysis
 When analyzing a balance sheet, the Finance
Manager should be aware of three concerns:
1. Accounting liquidity
2. Debt versus equity
3. Value versus cost
Accounting Liquidity
 Refers to the ease and quickness with which
assets can be converted to cash—without a
significant loss in value
 Current assets are the most liquid.
 Some fixed assets are intangible.
 The more liquid a firm’s assets, the less likely
the firm is to experience problems meeting short-
term obligations.
 Liquid assets frequently have lower rates of
return than fixed assets.
Debt versus Equity
 Creditors generally receive the first claim on
the firm’s cash flow.
 Shareholder’s equity is the residual difference
between assets and liabilities.
Value versus Cost
 Under Generally Accepted Accounting
Principles (GAAP), audited financial
statements of firms in the U.S. carry assets at
cost.
 Market value is the price at which the assets,
liabilities, and equity could actually be bought
or sold, which is a completely different
concept from historical cost.
2.2 The Income Statement
 Measures financial performance over a
specific period of time
 The accounting definition of income is:
Revenue – Expenses ≡ Income
U.S.C.C. Income Statement
Total operating revenues $2,262
The operations Cost of goods sold 1,655
section of the Selling, general, and administrative expenses 327
Depreciation 90
income statement
Operating income $190
reports the firm’s Other income 29
revenues and Earnings before interest and taxes $219
Interest expense 49
expenses from Pretax income $170
principal Taxes 84
operations. Current: $71
Deferred: $13
Net income $86
Addition to retained earnings $43
Dividends: $43
The non-operating Cost of goods sold 1,655
section of the Selling, general, and administrative expenses 327
Depreciation 90
income statement
includes all Other income 29
financing costs, Earnings before interest and taxes $219
Interest expense 49
such as interest Pretax income $170
expense. Taxes 84
Current: $71
Deferred: $13
Net income $86
Addition to retained earnings: $43
Dividends: $43
Cost of goods sold 1,655
Selling, general, and administrative expenses 327
Depreciation 90
Other income 29
Earnings before interest and taxes $219
Usually a separate Interest expense 49
section reports the Pretax income $170
Taxes 84
amount of taxes Current: $71
levied on income. Deferred: $13
Net income $86
Addition to retained earnings: $43
Dividends: $43
Cost of goods sold 1,655
Selling, general, and administrative expenses 327
Depreciation 90
Other income 29
Earnings before interest and taxes $219
Interest expense 49
Net income is the Pretax income $170
“bottom line.” Taxes 84
Current: $71
Deferred: $13
Net income $86
Retained earnings: $43
Dividends: $43
Income Statement Analysis
 There are three things to keep in mind when
analyzing an income statement:
1. Generally Accepted Accounting Principles
(GAAP)
2. Non-Cash Items
3. Time and Costs
GAAP
 The matching principal of GAAP dictates that
revenues be matched with expenses.
 Thus, income is reported when it is earned,
even though no cash flow may have occurred.
Non-Cash Items
 Depreciation is the most apparent. No firm
ever writes a check for “depreciation.”
 Another non-cash item is deferred taxes,
which does not represent a cash flow.
 Thus, net income is not cash.
Time and Costs
 In the short-run, certain equipment, resources, and
commitments of the firm are fixed, but the firm can
vary such inputs as labor and raw materials.
 In the long-run, all inputs of production (and hence
costs) are variable.
 Financial accountants do not distinguish between
variable costs and fixed costs. Instead, accounting
costs usually fit into a classification that
distinguishes product costs from period costs.
2.3 Taxes
 The one thing we can rely on with taxes is
that they are always changing
 Marginal vs. average tax rates
 Marginal – the percentage paid on the next dollar
earned
 Average – the tax bill / taxable income
 Other taxes
Marginal versus Average Rates
 Suppose your firm earns $4 million in taxable
income.
 What is the firm’s tax liability?
 What is the average tax rate?
 What is the marginal tax rate?
 If you are considering a project that will
increase the firm’s taxable income by $1
million, what tax rate should you use in your
analysis?
2.4 Net Working Capital
 Net Working Capital ≡

Current Assets – Current Liabilities
 NWC usually grows with the firm
U.S.C.C. Balance Sheet
$252m = $707- $455
2006 2005 2006 2005

Current assets: Current Liabilities:
Cash and equivalents $140 $107 Accounts payable $213 $197
Accounts receivable 294 270 Notes payable 50 53
Inventories 269 280 Accrued expenses 223 205
Other 58 50 Total current liabilities $486 $455
Total current assets $761 $707
Long-term liabilities:
Fixed assets: Here we see NWC grow
Deferred taxes $117 to $104
Property, plant, and equipment $1,423 $1,274 Long-term debt 471 458
Less accumulated depreciation (550) (460 $275 million in 2006 from
Total long-term liabilities $588 $562
Net property, plant, and equipment
Intangible assets and other
873
245
814
221
$252 million in 2005.
Stockholder's equity:
Total fixed assets $1,118 $1,035
$23 million
Preferred stock
Common stock ($1 par value)
$39
55
$39
32
$275m = $761m- $486m This increase

Capital surplus of
Accumulated retained earnings
$23 million
347
390
is
327
347
anLessinvestment
treasury stock of the firm.
(26) (20)
Total equity $805 $725
Total assets $1,879 $1,742 Total liabilities and stockholder's equity $1,879 $1,742
2.5 Financial Cash Flow
 In finance, the most important item that can
be extracted from financial statements is the
actual cash flow of the firm.
 Since there is no magic in finance, it must be
the case that the cash flow received from the
firm’s assets must equal the cash flows to
the firm’s creditors and stockholders.
CF(A)≡ CF(B) + CF(S)
U.S.C.C. Financial Cash Flow
Cash Flow of the Firm Operating Cash Flow:
Operating cash flow $238
(Earnings before interest and taxes
plus depreciation minus taxes) EBIT $219
Capital spending -173
(Acquisitions of fixed assets Depreciation $90
minus sales of fixed assets)
Additions to net working capital -23 Current Taxes -$71
Total $42
Cash Flow of Investors in the Firm OCF $238
Debt $36
(Interest plus retirement of debt
minus long-term debt financing)
Equity 6
(Dividends plus repurchase of
equity minus new equity financing)
Total $42
Cash Flow of the Firm
plus depreciation minus taxes)
Capital Spending
Capital spending -173 Purchase of fixed assets $198
(Acquisitions of fixed assets
minus sales of fixed assets) Sales of fixed assets -$25
Additions to net working capital -23
Total $42 Capital Spending $173
Cash Flow of Investors in the Firm
Debt $36
Equity 6
Total $42
NWC grew from $275
Capital spending -173 million in 2006 from $252
minus sales of fixed assets) million in 2005.
Total $42 This increase of $23
Cash Flow of Investors in the Firm million is the addition to
Debt $36
(Interest plus retirement of debt NWC.
Equity 6
Total $42
Total $42
Debt $36
Equity 6
Total $42
Cash Flow to Creditors
(Acquisitions of fixed assets Interest $49
Additions to net working capital -23 Retirement of debt 73
Total $42
Cash Flow of Investors in the Firm Debt service 122
Debt $36
(Interest plus retirement of debt Proceeds from new debt
Equity 6 sales -86
equity minus new equity financing) Total $36
Total $42
(Earnings before interest and taxes Cash Flow to Stockholders
Capital spending -173 Dividends $43
minus sales of fixed assets) Repurchase of stock 6
Cash to Stockholders 49
Total $42
Cash Flow of Investors in the Firm Proceeds from new stock issue
Debt $36 -43
minus long-term debt financing) Total $6
Equity 6
Total $42
Operating cash flow $238 The cash flow received
from the firm’s assets
Capital spending -173 must equal the cash flows
to the firm’s creditors and
Additions to net working capital -23 stockholders:
Total $42
Debt $36
Equity 6
Total $42
2.6 The Statement of Cash Flows
 There is an official accounting statement called the
statement of cash flows.
 This helps explain the change in accounting cash,
which for U.S. Composite is $33 million in 2006.
 The three components of the statement of cash
flows are:
 Cash flow from operating activities
 Cash flow from investing activities
 Cash flow from financing activities
U.S.C.C. Cash Flow from Operations
Operations
To calculate cash Net Income $86
flow from operations, Depreciation 90
Deferred Taxes 13
start with net income,
Changes in Assets and Liabilities
add back non-cash Accounts Receivable -24
items like Inventories 11
Accounts Payable 16
depreciation and Accrued Expenses 18
adjust for changes in Notes Payable -3
current assets and Other -8
liabilities (other than Total Cash Flow from Operations $199

cash).
U.S.C.C. Cash Flow from Investing
Cash flow from Acquisition of fixed assets -$198

investing activities Sales of fixed assets 25
Total Cash Flow from Investing Activities -$173
involves changes in
capital assets:
acquisition of fixed
assets and sales of
fixed assets (i.e., net
capital expenditures).
U.S.C.C. Cash Flow from Financing
Cash flows to and Retirement of debt (includes notes) -$73

from creditors and Proceeds from long-term debt sales 86
Dividends -43
owners include
Repurchase of stock -6
changes in equity and Proceeds from new stock issue 43
debt.
Total Cash Flow from Financing $7
U.S.C.C. Statement of Cash Flows
Operations
Net Income $86
The statement of Depreciation 90
Deferred Taxes 13
cash flows is the Changes in Assets and Liabilities
Accounts Receivable -24
addition of cash Inventories
Accounts Payable
11
16
Accrued Expenses 18
flows from Notes Payable -3
Other -8
operations, Total Cash Flow from Operations
Investing Activities
$199
investing, and Acquisition of fixed assets

Sales of fixed assets
-$198
25
Total Cash Flow from Investing Activities -$173
financing. Financing Activities
Retirement of debt (includes notes) -$73
Proceeds from long-term debt sales 86
Dividends -43
Repurchase of stock -6
Proceeds from new stock issue 43
Total Cash Flow from Financing $7
Change in Cash (on the balance sheet) $33
Chapter 3
Financial Statements Analysis and Long-Term
Planning
 Know how to standardize financial statements
for comparison purposes
 Know how to compute and interpret important
financial ratios
 Be able to develop a financial plan using the
percentage of sales approach
 Understand how capital structure and dividend
policies affect a firm’s ability to grow
Chapter Outline
3.1 Financial Statements Analysis
3.2 Ratio Analysis
3.3 The Du Pont Identity
3.4 Using Financial Statement Information
3.5 Long-Term Financial Planning
3.6 External Financing and Growth
3.7 Some Caveats Regarding Financial Planning Models
3.1 Standardizing Financial Statements
 Common-Size Balance Sheets
 Compute all accounts as a percent of total assets
 Common-Size Income Statements
 Compute all line items as a percent of sales
 Standardized statements make it easier to compare
financial information, particularly as the company
grows.
 They are also useful for comparing companies of
different sizes, particularly within the same industry.
3.2 Ratio Analysis
 Ratios also allow for better comparison
through time or between companies
 As we look at each ratio, ask yourself:
 How is the ratio computed?
 What is the ratio trying to measure and why?
 What is the unit of measurement?
 What does the value indicate?
 How can we improve the company’s ratio?
Categories of Financial Ratios
 Short-term solvency or liquidity ratios
 Long-term solvency, or financial leverage,
ratios
 Asset management or turnover ratios
 Profitability ratios
 Market value ratios
Computing Liquidity Ratios
 Current Ratio = CA / CL
 708 / 540 = 1.31 times
 Quick Ratio = (CA – Inventory) / CL
 (708 - 422) / 540 = .53 times
 Cash Ratio = Cash / CL
 98 / 540 = .18 times
Computing Leverage Ratios
 Total Debt Ratio = (TA – TE) / TA
 (3588 - 2591) / 3588 = 28%
 Debt/Equity = TD / TE
 (3588 – 2591) / 2591 = 38.5%
 Equity Multiplier = TA / TE = 1 + D/E
 1 + .385 = 1.385
Computing Coverage Ratios
 Times Interest Earned = EBIT / Interest
 691 / 141 = 4.9 times
 Cash Coverage = (EBIT + Depreciation) /
Interest
 (691 + 276) / 141 = 6.9 times
Computing Inventory Ratios
 Inventory Turnover = Cost of Goods Sold /
Inventory
 1344 / 422 = 3.2 times
 Days’ Sales in Inventory = 365 / Inventory
Turnover
 365 / 3.2 = 114 days
Computing Receivables Ratios
 Receivables Turnover = Sales / Accounts
Receivable
 2311 / 188 = 12.3 times
 Days’ Sales in Receivables = 365 /
Receivables Turnover
 365 / 12.3 = 30 days
Computing Total Asset Turnover
 Total Asset Turnover = Sales / Total Assets
 2311 / 3588 = .64 times
 It is not unusual for TAT < 1, especially if a firm
has a large amount of fixed assets.
Computing Profitability Measures
 Profit Margin = Net Income / Sales
 363 / 2311 = 15.7%
 Return on Assets (ROA) = Net Income / Total
Assets
 363 / 3588 = 10.1%
 Return on Equity (ROE) = Net Income / Total
Equity
 363 / 2591 = 14.0%
Computing Market Value Measures
 Market Price = $88 per share
 Shares outstanding = 33 million
 PE Ratio = Price per share / Earnings per share

 88 / 11 = 8 times
 Market-to-book ratio = market value per share
/ book value per share
 88 / (2591 / 33) = 1.12 times
3.3 The Du Pont Identity
 ROE = NI / TE
 Multiply by 1 and then rearrange:
 ROE = (NI / TE) (TA / TA)
 ROE = (NI / TA) (TA / TE) = ROA * EM
 Multiply by 1 again and then rearrange:

 ROE = (NI / TA) (TA / TE) (Sales / Sales)
 ROE = (NI / Sales) (Sales / TA) (TA / TE)
 ROE = PM * TAT * EM
Using the Du Pont Identity
 ROE = PM * TAT * EM
 Profit margin is a measure of the firm’s operating
efficiency – how well it controls costs.
 Total asset turnover is a measure of the firm’s
asset use efficiency – how well it manages its
assets.
 Equity multiplier is a measure of the firm’s
financial leverage.
Calculating the Du Pont Identity
 ROA = 10.1% and EM = 1.39
 ROE = 10.1% * 1.385 = 14.0%
 PM = 15.7% and TAT = 0.64
 ROE = 15.7% * 0.64 * 1.385 = 14.0%
3.4 Using Financial Statements
 Ratios are not very helpful by themselves: they
need to be compared to something
 Time-Trend Analysis
 Used to see how the firm’s performance is
changing through time
 Peer Group Analysis
 Compare to similar companies or within industries
 SIC and NAICS codes
Potential Problems
 There is no underlying theory, so there is no way to
know which ratios are most relevant.
 Benchmarking is difficult for diversified firms.
 Globalization and international competition makes
comparison more difficult because of differences in
accounting regulations.
 Firms use varying accounting procedures.
 Firms have different fiscal years.
 Extraordinary, or one-time, events
3.5 Long-Term Financial Planning
 Investment in new assets – determined by
capital budgeting decisions
 Degree of financial leverage – determined by
capital structure decisions
 Cash paid to shareholders – determined by
dividend policy decisions
 Liquidity requirements – determined by net
working capital decisions
Financial Planning Ingredients
 Sales Forecast – many cash flows depend directly on the level of
sales (often estimate sales growth rate)
 Pro Forma Statements – setting up the plan as projected (pro
forma) financial statements allows for consistency and ease of
interpretation
 Asset Requirements – the additional assets that will be required
to meet sales projections
 Financial Requirements – the amount of financing needed to pay
for the required assets
 Plug Variable – determined by management decisions about what
type of financing will be used (makes the balance sheet balance)
 Economic Assumptions – explicit assumptions about the coming
economic environment
Percent of Sales Approach
 Some items vary directly with sales, others do not.
 Income Statement
 Costs may vary directly with sales - if this is the case, then
the profit margin is constant
 Depreciation and interest expense may not vary directly
with sales – if this is the case, then the profit margin is not
constant
 Dividends are a management decision and generally do not
vary directly with sales – this affects additions to retained
earnings
Percent of Sales Approach
 Balance Sheet
 Initially assume all assets, including fixed, vary directly
with sales.
 Accounts payable also normally vary directly with sales.
 Notes payable, long-term debt, and equity generally do not
vary with sales because they depend on management
decisions about capital structure.
 The change in the retained earnings portion of equity will
come from the dividend decision.
 External Financing Needed (EFN)
 The difference between the forecasted increase in assets
and the forecasted increase in liabilities and equity.
Percent of Sales and EFN
 External Financing Needed (EFN) can also be
calculated as:
3.6 External Financing and Growth
 At low growth levels, internal financing
(retained earnings) may exceed the required
investment in assets.
 As the growth rate increases, the internal
financing will not be enough, and the firm will
have to go to the capital markets for financing.
 Examining the relationship between growth
and external financing required is a useful tool
in long-range planning.
The Internal Growth Rate
 The internal growth rate tells us how much the
firm can grow assets using retained earnings
as the only source of financing.
 Using the information from the Hoffman Co.
 ROA = 66 / 500 = .132
 b = 44/ 66 = .667
ROA  b
Internal Growth Rate 
1 - ROA  b
.132 .667
  .0965
1  .132 .667
 9.65%
The Sustainable Growth Rate
 The sustainable growth rate tells us how much
the firm can grow by using internally
generated funds and issuing debt to maintain a
constant debt ratio.
 Using the Hoffman Co.
 ROE = 66 / 250 = .264
ROE  b
 b = .667 Sustainabl e Growth Rate 
1 - ROE  b
.264 .667
  .214
1  .264 .667
 21.4%
Determinants of Growth
 Profit margin – operating efficiency
 Total asset turnover – asset use efficiency
 Financial leverage – choice of optimal debt
ratio
 Dividend policy – choice of how much to pay
to shareholders versus reinvesting in the firm
3.7 Some Caveats
 Financial planning models do not indicate
which financial polices are the best.
 Models are simplifications of reality, and the
world can change in unexpected ways.
 Without some sort of plan, the firm may find
itself adrift in a sea of change without a rudder
for guidance.
Chapter 4
Discounted Cash Flow Valuation
 Be able to compute the future value and/or
present value of a single cash flow or series of
cash flows
 Be able to compute the return on an
investment
 Be able to use a financial calculator and/or
spreadsheet to solve time value problems
 Understand perpetuities and annuities
Chapter Outline
4.1 Valuation: The One-Period Case
4.2 The Multiperiod Case
4.3 Compounding Periods
4.4 Simplifications
4.5 What Is a Firm Worth?
4.1 The One-Period Case
 If you were to invest $10,000 at 5-percent interest
for one year, your investment would grow to
$10,500.
$500 would be interest ($10,000 × .05)

$10,000 is the principal repayment ($10,000 × 1)
$10,500 is the total due. It can be calculated as:
$10,500 = $10,000×(1.05)
 The total amount due at the end of the investment is
call the Future Value (FV).
Future Value
 In the one-period case, the formula for FV can
be written as:
FV = C0×(1 + r)T
Where C0 is cash flow today (time zero), and

r is the appropriate interest rate.
Present Value
 If you were to be promised $10,000 due in one year
when interest rates are 5-percent, your investment
would be worth $9,523.81 in today’s dollars.
The amount that a borrower would need to set aside

today to be able to meet the promised payment of
$10,000 in one year is called the Present Value (PV).
Note that $10,000 = $9,523.81×(1.05).

Present Value
 In the one-period case, the formula for PV can
be written as:
Where C1 is cash flow at date 1, and

r is the appropriate interest rate.
Net Present Value
 The Net Present Value (NPV) of an
investment is the present value of the
expected cash flows, less the cost of the
investment.
 Suppose an investment that promises to pay
$10,000 in one year is offered for sale for
$9,500. Your interest rate is 5%. Should you
buy?
Net Present Value
The present value of the cash inflow is greater

than the cost. In other words, the Net Present
Value is positive, so the investment should be
purchased.
Net Present Value
In the one-period case, the formula for NPV can be
written as:
NPV = –Cost + PV
If we had not undertaken the positive NPV project
considered on the last slide, and instead invested our
$9,500 elsewhere at 5 percent, our FV would be less
than the $10,000 the investment promised, and we
would be worse off in FV terms :
$9,500×(1.05) = $9,975 < $10,000

4.2 The Multiperiod Case
 The general formula for the future value of an
investment over many periods can be written
as:
FV = C0×(1 + r)T
Where
C0 is cash flow at date 0,
r is the appropriate interest rate, and
T is the number of periods over which the cash is
invested.
Future Value
 Suppose a stock currently pays a dividend of
$1.10, which is expected to grow at 40% per
year for the next five years.
 What will the dividend be in five years?
FV = C0×(1 + r)T
$5.92 = $1.10×(1.40)5
Future Value and Compounding
 Notice that the dividend in year five, $5.92,
is considerably higher than the sum of the
original dividend plus five increases of 40-
percent on the original $1.10 dividend:
$5.92 > $1.10 + 5×[$1.10×.40] = $3.30
This is due to compounding.
Future Value and Compounding
0 1 2 3 4 5
Present Value and Discounting
 How much would an investor have to set
aside today in order to have $20,000 five
years from now if the current rate is 15%?
PV $20,000
0 1 2 3 4 5
How Long is the Wait?
If we deposit $5,000 today in an account paying 10%,
how long does it take to grow to $10,000?
What Rate Is Enough?
Assume the total cost of a college education will be
$50,000 when your child enters college in 12 years.
You have $5,000 to invest today. What rate of interest
must you earn on your investment to cover the cost of
your child’s education? About 21.15%.
Calculator Keys
 Texas Instruments BA-II Plus
 FV = future value
 PV = present value
 I/Y = periodic interest rate
 P/Y must equal 1 for the I/Y to be the periodic rate
 Interest is entered as a percent, not a decimal
 N = number of periods
 Remember to clear the registers (CLR TVM) after
each problem
 Other calculators are similar in format
Multiple Cash Flows
 Consider an investment that pays $200 one
year from now, with cash flows increasing by
$200 per year through year 4. If the interest
rate is 12%, what is the present value of this
stream of cash flows?
 If the issuer offers this investment for $1,500,
should you purchase it?
Multiple Cash Flows
0 1 2 3 4
200 400 600 800

178.57
318.88
427.07
508.41
1,432.93
Present Value < Cost → Do Not Purchase
Valuing “Lumpy” Cash Flows
First, set your calculator to 1 payment per year.
Then, use the cash flow menu:
CF0 0 CF3 600 I 12
CF1 200 F3 1 NPV 1,432.93
F1 1 CF4 800
CF2 400 F4 1
F2 1
4.3 Compounding Periods
Compounding an investment m times a year for
T years provides for future value of wealth:
Compounding Periods
 For example, if you invest $50 for 3 years at
12% compounded semi-annually, your
investment will grow to
Effective Annual Rates of Interest
A reasonable question to ask in the above
example is “what is the effective annual rate of
interest on that investment?”
The Effective Annual Rate (EAR) of interest is

the annual rate that would give us the same
end-of-investment wealth after 3 years:
So, investing at 12.36% compounded annually

is the same as investing at 12% compounded
semi-annually.
 Find the Effective Annual Rate (EAR) of an
18% APR loan that is compounded monthly.
 What we have is a loan with a monthly
interest rate rate of 1½%.
 This is equivalent to a loan with an annual
interest rate of 19.56%.
EAR on a Financial Calculator
Texas Instruments BAII Plus

keys: description:
[2nd] [ICONV] Opens interest rate conversion menu
[↑] [C/Y=] 12 [ENTER] Sets 12 payments per year
[↓][NOM=] 18 [ENTER] Sets 18 APR.
[↓] [EFF=] [CPT] 19.56
Continuous Compounding
 The general formula for the future value of an
investment compounded continuously over many
periods can be written as:
FV = C0×erT
Where
C0 is cash flow at date 0,
r is the stated annual interest rate,
T is the number of years, and
e is a transcendental number approximately equal
to 2.718. ex is a key on your calculator.
4.4 Simplifications
 Perpetuity
 A constant stream of cash flows that lasts forever
 Growing perpetuity
 A stream of cash flows that grows at a constant rate
forever
 Annuity
 A stream of constant cash flows that lasts for a fixed
number of periods
 Growing annuity
 A stream of cash flows that grows at a constant rate for
a fixed number of periods
Perpetuity
A constant stream of cash flows that lasts forever
C C C
…
0 1 2 3
Perpetuity: Example
What is the value of a British consol that
promises to pay £15 every year for ever?
The interest rate is 10-percent.
£15 £15 £15
…
0 1 2 3
Growing Perpetuity
A growing stream of cash flows that lasts forever
C C×(1+g) C ×(1+g)2
…
0 1 2 3
Growing Perpetuity: Example
The expected dividend next year is $1.30, and
dividends are expected to grow at 5% forever.
If the discount rate is 10%, what is the value of this
promised dividend stream?
$1.30 $1.30×(1.05) $1.30 ×(1.05)2
…
0 1 2 3
Annuity
A constant stream of cash flows with a fixed maturity
C C C C
0 1 2 3 T
Annuity: Example
If you can afford a $400 monthly car payment, how
much car can you afford if interest rates are 7% on 36-
month loans?
$400 $400 $400 $400
0 1 2 3 36
What is the present value of a four-year annuity of $100
per year that makes its first payment two years from today if the
discount rate is 9%?
$297.22 $323.97 $100 $100 $100 $100
0 1 2 3 4 5
Growing Annuity
A growing stream of cash flows with a fixed maturity
C C×(1+g) C ×(1+g)2 C×(1+g)T-1
0 1 2 3 T
Growing Annuity: Example
A defined-benefit retirement plan offers to pay $20,000 per
year for 40 years and increase the annual payment by three-
percent each year. What is the present value at retirement if the
discount rate is 10 percent?
$20,000 $20,000×(1.03) $20,000×(1.03)39
0 1 2 40
Growing Annuity: Example
You are evaluating an income generating property. Net rent is
received at the end of each year. The first year's rent is
expected to be $8,500, and rent is expected to increase 7%
each year. What is the present value of the estimated income
stream over the first 5 years if the discount rate is 12%?
0 1 2 3 4 5
$34,706.26
4.5 What Is a Firm Worth?
 Conceptually, a firm should be worth the
present value of the firm’s cash flows.
 The tricky part is determining the size, timing
and risk of those cash flows.
Chapter 5
Interest Rates and Bond Valuation
 Know the important bond features and bond types
 Understand bond values and why they fluctuate
 Understand bond ratings and what they mean
 Understand the impact of inflation on interest

rates
 Understand the term structure of interest rates and
the determinants of bond yields
Chapter Outline
5.1 Bonds and Bond Valuation
5.2 More on Bond Features
5.3 Bond Ratings
5.4 Some Different Types of Bonds
5.5 Bond Markets
5.6 Inflation and Interest Rates
5.7 Determinants of Bond Yields
5.1 Bonds and Bond Valuation
 A bond is a legally binding agreement between
a borrower and a lender that specifies the:
 Par (face) value
 Coupon rate
 Coupon payment
 Maturity Date
 The yield to maturity is the required market

interest rate on the bond.
Bond Valuation
 Primary Principle:
 Value of financial securities = PV of expected
future cash flows
 Bond value is, therefore, determined by the
present value of the coupon payments and par
value.
 Interest rates are inversely related to present
(i.e., bond) values.
The Bond-Pricing Equation
 1 
1 -
 (1  r)T  F
Bond Value  C  
 (1  r)
T
 r
 
Bond Example
 Consider a U.S. government bond with as 6 3/8%
coupon that expires in December 2009.
 The Par Value of the bond is $1,000.
 Coupon payments are made semi-annually (June 30 and
December 31 for this particular bond).
 Since the coupon rate is 6 3/8%, the payment is $31.875.
 On January 1, 2005 the size and timing of cash flows are:
Bond Example
 On January 1, 2005, the required yield is 5%.
 The size and timing of the cash flows are:
Bond Example: Calculator
Find the present value (as of January 1, 2005), of a 6 3/8% coupon
bond with semi-annual payments, and a maturity date of
December 2009 if the YTM is 5%.
N 10
I/Y 2.5
PV – 1,060.17
1,000×0.06375
PMT 31.875 =
2
FV 1,000
Bond Example
 Now assume that the required yield is 11%.
 How does this change the bond’s price?
YTM and Bond Value
When the YTM < coupon, the bond
1300 trades at a premium.
Bond Value
1200
1100 When the YTM = coupon, the

bond trades at par.
1000
800
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
6 3/8 Discount Rate
When the YTM > coupon, the bond trades at a discount.
Bond Concepts
 Bond prices and market interest rates move
in opposite directions.
 When coupon rate = YTM, price = par
value
 When coupon rate > YTM, price > par
value (premium bond)
 When coupon rate < YTM, price < par
value (discount bond)
Interest Rate Risk
 Price Risk
 Change in price due to changes in interest rates
 Long-term bonds have more price risk than short-term bonds
 Low coupon rate bonds have more price risk than high
coupon rate bonds.
 Reinvestment Rate Risk
 Uncertainty concerning rates at which cash flows can be
reinvested
 Short-term bonds have more reinvestment rate risk than long-term
bonds.
 High coupon rate bonds have more reinvestment rate risk than low
coupon rate bonds.
Maturity and Bond Price Volatility
Bond Value
Consider two otherwise identical bonds.

The long-maturity bond will have much more
volatility with respect to changes in the
discount rate.
Par
Short Maturity Bond
C Long Maturity Discount Rate

Bond
Coupon Rates and Bond Prices
Bond Value
Consider two otherwise identical bonds.

The low-coupon bond will have much more
volatility with respect to changes in the
discount rate.
Par
High Coupon Bond
C Discount Rate
Low Coupon Bond
Computing Yield to Maturity
 Yield-to-maturity is the rate implied by the
current bond price.
 Finding the YTM requires trial and error if you
do not have a financial calculator and is similar
to the process for finding r with an annuity.
 If you have a financial calculator, enter N, PV,
PMT, and FV, remembering the sign
convention (PMT and FV need to have the
same sign, PV the opposite sign).
YTM with Annual Coupons
 Consider a bond with a 10% annual coupon
rate, 15 years to maturity, and a par value of
$1,000. The current price is $928.09.
 Will the yield be more or less than 10%?
 N = 15; PV = -928.09; FV = 1,000; PMT = 100
 CPT I/Y = 11%
YTM with Semiannual Coupons
 Suppose a bond with a 10% coupon rate and
semiannual coupons has a face value of
$1,000, 20 years to maturity, and is selling for
$1,197.93.
 Is the YTM more or less than 10%?
 What is the semi-annual coupon payment?
 How many periods are there?
 N = 40; PV = -1,197.93; PMT = 50; FV = 1,000;
CPT I/Y = 4% (Is this the YTM?)
 YTM = 4%*2 = 8%
Current Yield vs. Yield to Maturity
 Current Yield = annual coupon / price
 Yield to maturity = current yield + capital gains yield
 Example: 10% coupon bond, with semi-annual
coupons, face value of 1,000, 20 years to maturity,
$1,197.93 price
 Current yield = 100 / 1197.93 = .0835 = 8.35%
 Price in one year, assuming no change in YTM = 1,193.68
 Capital gain yield = (1193.68 – 1197.93) / 1197.93 =
-.0035 = -.35%
 YTM = 8.35 - .35 = 8%, which is the same YTM computed
earlier
Bond Pricing Theorems
 Bonds of similar risk (and maturity) will be
priced to yield about the same return,
regardless of the coupon rate.
 If you know the price of one bond, you can
estimate its YTM and use that to find the price
of the second bond.
 This is a useful concept that can be transferred
to valuing assets other than bonds.
Bond Pricing with a Spreadsheet
 There are specific formulas for finding bond
prices and yields on a spreadsheet.
 PRICE (Settlement, Maturity, Rate, Yld, Redemption,
Frequency, Basis)
 YIELD (Settlement, Maturity, Rate, Pr, Redemption,
Frequency, Basis)
 Settlement and maturity need to be actual dates
 The redemption and Pr need to given as % of par value
Debt versus Equity
 Debt  Equity
 Not an ownership interest  Ownership interest
 Creditors do not have voting  Common stockholders vote
rights for the board of directors and
 Interest is considered a cost of other issues
doing business and is tax  Dividends are not considered
deductible a cost of doing business and
 Creditors have legal recourse are not tax deductible
if interest or principal  Dividends are not a liability of
payments are missed the firm, and stockholders
 Excess debt can lead to have no legal recourse if
financial distress and dividends are not paid
bankruptcy  An all equity firm can not go
bankrupt
The Bond Indenture
 Contract between the company and the
bondholders that includes:
 The basic terms of the bonds
 The total amount of bonds issued
 A description of property used as security, if
applicable
 Sinking fund provisions
 Call provisions
 Details of protective covenants
Bond Classifications
 Registered vs. Bearer Forms
 Security
 Collateral – secured by financial securities
 Mortgage – secured by real property, normally
land or buildings
 Debentures – unsecured
 Notes – unsecured debt with original maturity less
than 10 years
 Seniority
Required Yields
 The coupon rate depends on the risk
characteristics of the bond when issued.
 Which bonds will have the higher coupon, all
else equal?
 Secured debt versus a debenture
 Subordinated debenture versus senior debt
 A bond with a sinking fund versus one without
 A callable bond versus a non-callable bond
5.3 Bond Ratings – Investment Quality
 High Grade
 Moody’s Aaa and S&P AAA – capacity to pay is
extremely strong
 Moody’s Aa and S&P AA – capacity to pay is very
strong
 Medium Grade
 Moody’s A and S&P A – capacity to pay is strong, but
more susceptible to changes in circumstances
 Moody’s Baa and S&P BBB – capacity to pay is
adequate, adverse conditions will have more impact on
the firm’s ability to pay
Bond Ratings - Speculative
 Low Grade
 Moody’s Ba and B
 S&P BB and B
 Considered speculative with respect to capacity to pay.
 Very Low Grade
 Moody’s C and S&P C – income bonds with no
interest being paid
 Moody’s D and S&P D – in default with principal and
interest in arrears
Government Bonds
 Treasury Securities
 Federal government debt
 T-bills – pure discount bonds with original maturity less
than one year
 T-notes – coupon debt with original maturity between one
and ten years
 T-bonds – coupon debt with original maturity greater than
ten years
 Municipal Securities
 Debt of state and local governments
 Varying degrees of default risk, rated similar to corporate
debt
 Interest received is tax-exempt at the federal level
After-tax Yields
 A taxable bond has a yield of 8%, and a
municipal bond has a yield of 6%.
 If you are in a 40% tax bracket, which bond do
you prefer?
 8%(1 - .4) = 4.8%
 The after-tax return on the corporate bond is 4.8%,
compared to a 6% return on the municipal
 At what tax rate would you be indifferent between
the two bonds?
 8%(1 – T) = 6%
 T = 25%
Zero Coupon Bonds
 Make no periodic interest payments (coupon rate =
0%)
 The entire yield to maturity comes from the
difference between the purchase price and the par
value
 Cannot sell for more than par value
 Sometimes called zeroes, deep discount bonds, or
original issue discount bonds (OIDs)
 Treasury Bills and principal-only Treasury strips are
good examples of zeroes
Pure Discount Bonds
Information needed for valuing pure discount bonds:
 Time to maturity (T) = Maturity date - today’s date
 Face value (F)
 Discount rate (r)
Present value of a pure discount bond at time 0:
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond
with a $1,000 par value and a YTM of 6%.
Floating Rate Bonds
 Coupon rate floats depending on some index value
 Examples – adjustable rate mortgages and inflation-
linked Treasuries
 There is less price risk with floating rate bonds.
 The coupon floats, so it is less likely to differ
substantially from the yield to maturity.
 Coupons may have a “collar” – the rate cannot go
above a specified “ceiling” or below a specified
“floor.”
Other Bond Types
 Income bonds
 Convertible bonds
 Put bonds
 There are many other types of provisions that

can be added to a bond, and many bonds have
several provisions – it is important to
recognize how these provisions affect required
returns.
5.5 Bond Markets
 Primarily over-the-counter transactions with
dealers connected electronically
 Extremely large number of bond issues, but
generally low daily volume in single issues
 Makes getting up-to-date prices difficult,
particularly on a small company or municipal
issues
 Treasury securities are an exception
Treasury Quotations
 What is the coupon rate on the bond?
 When does the bond mature?
 What is the bid price? What does this mean?
 What is the ask price? What does this mean?
 How much did the price change from the

previous day?
 What is the yield based on the ask price?
Clean versus Dirty Prices
 Clean price: quoted price
 Dirty price: price actually paid = quoted price plus accrued
interest
 Example: Consider T-bond in previous slide, assume today is
July 15, 2005
 Number of days since last coupon = 61
 Number of days in the coupon period = 184
 Accrued interest = (61/184)(.04*1,000) = 13.26
 Prices (based on ask):
 Clean price = 1,327.50
 Dirty price = 1,327.50 + 13.26 = 1,340.76
 So, you would actually pay $1,340.76 for the bond.
5.6 Inflation and Interest Rates
 Real rate of interest – change in purchasing
power
 Nominal rate of interest – quoted rate of
interest, change in purchasing power and
inflation
 The ex ante nominal rate of interest includes
our desired real rate of return plus an
adjustment for expected inflation.
The Fisher Effect
 The Fisher Effect defines the relationship
between real rates, nominal rates, and inflation.
 (1 + R) = (1 + r)(1 + h), where
 R = nominal rate
 r = real rate
 h = expected inflation rate
 Approximation
 R=r+h
The Fisher Effect: Example
 If we require a 10% real return and we expect
inflation to be 8%, what is the nominal rate?
 R = (1.1)(1.08) – 1 = .188 = 18.8%
 Approximation: R = 10% + 8% = 18%
 Because the real return and expected inflation

are relatively high, there is a significant
difference between the actual Fisher Effect and
the approximation.
5.7 Determinants of Bond Yields
 Term structure is the relationship between time
to maturity and yields, all else equal.
 It is important to recognize that we pull out the
effect of default risk, different coupons, etc.
 Yield curve – graphical representation of the
term structure
 Normal – upward-sloping, long-term yields are
higher than short-term yields
 Inverted – downward-sloping, long-term yields are
lower than short-term yields
Factors Affecting Required Return
 Default risk premium – remember bond ratings
 Taxability premium – remember municipal
versus taxable
 Liquidity premium – bonds that have more
frequent trading will generally have lower
required returns
 Anything else that affects the risk of the cash
flows to the bondholders will affect the
required returns.
Chapter 6
Stock Valuation
 Understand how stock prices depend on future
dividends and dividend growth
 Be able to compute stock prices using the
dividend growth model
 Understand how growth opportunities affect
stock values
 Understand the PE ratio
 Understand how stock markets work
Chapter Outline
6.1 The Present Value of Common Stocks
6.2 Estimates of Parameters in the Dividend-Discount
Model
6.3 Growth Opportunities
6.4 The Dividend Growth Model and the NPVGO
Model
6.5 Price-Earnings Ratio
6.6 Some Features of Common and Preferred Stock
6.7 The Stock Markets
6.1 The PV of Common Stocks
 The value of any asset is the present value of its
expected future cash flows.
 Stock ownership produces cash flows from:
 Dividends
 Capital Gains
 Valuation of Different Types of Stocks
 Zero Growth
 Constant Growth
 Differential Growth
Case 1: Zero Growth
 Assume that dividends will remain at the same level
forever
 Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:
Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g,
forever, i.e.,
Since future cash flows grow at a constant rate forever,

the value of a constant growth stock is the present value
of a growing perpetuity:
Constant Growth Example
 Suppose Big D, Inc., just paid a dividend of
$.50. It is expected to increase its dividend by
2% per year. If the market requires a return of
15% on assets of this risk level, how much
should the stock be selling for?
 P0 = .50(1+.02) / (.15 - .02) = $3.92
Case 3: Differential Growth
 Assume that dividends will grow at different rates
in the foreseeable future and then will grow at a
constant rate thereafter.
 To value a Differential Growth Stock, we need to:
 Estimate future dividends in the foreseeable future.
 Estimate the future stock price when the stock
becomes a Constant Growth Stock (case 2).
 Compute the total present value of the estimated
future dividends and future stock price at the
appropriate discount rate.
 Assume that dividends will grow at rate g1 for N
years and grow at rate g2 thereafter.
..
.
..
.
Dividends will grow at rate g1 for N years and grow
at rate g2 thereafter
…
0 1 2
… …
N N+1
We can value this as the sum of:
 an N-year annuity growing at rate g1
 plus the discounted value of a perpetuity growing at

rate g2 that starts in year N+1
Consolidating gives:
Or, we can “cash flow” it out.
A Differential Growth Example
A common stock just paid a dividend of $2. The
dividend is expected to grow at 8% for 3 years,
then it will grow at 4% in perpetuity.
What is the stock worth? The discount rate is 12%.
With the Formula
With Cash Flows
…
0 1 2 3 4
The constant
growth phase
beginning in year 4
can be valued as a
0 1 2 3 growing perpetuity
at time 3.
6.2 Estimates of Parameters
 The value of a firm depends upon its growth
rate, g, and its discount rate, R.
 Where does g come from?
g = Retention ratio × Return on retained earnings
Where does R come from?
 The discount rate can be broken into two parts.
 The dividend yield
 The growth rate (in dividends)
 In practice, there is a great deal of estimation

error involved in estimating R.
Using the DGM to Find R
 Start with the DGM:
D 0 (1  g) D1
P0  
R -g R -g
Rearrange and solve for R:
D 0 (1  g) D1
R g g
P0 P0
6.3 Growth Opportunities
 Growth opportunities are opportunities to
invest in positive NPV projects.
 The value of a firm can be conceptualized as
the sum of the value of a firm that pays out
100-percent of its earnings as dividends and
the net present value of the growth
opportunities.
6.4 The NPVGO Model
 We have two ways to value a stock:
 The dividend discount model
 The sum of its price as a “cash cow” plus the per
share value of its growth opportunities
The NPVGO Model: Example
Consider a firm that has EPS of $5 at the end of the
first year, a dividend-payout ratio of 30%, a discount
rate of 16%, and a return on retained earnings of
20%.
 The dividend at year one will be $5 × .30 = $1.50 per share.
 The retention ratio is .70 ( = 1 -.30), implying a growth rate in
dividends of 14% = .70 × 20%.
From the dividend growth model, the price of a share is:
The NPVGO Model: Example
First, we must calculate the value of the firm as a
cash cow.
Second, we must calculate the value of the growth

opportunities.
Finally,
6.5 Price-Earnings Ratio
 Many analysts frequently relate earnings per share to
price.
 The price-earnings ratio is calculated as the current
stock price divided by annual EPS.
 The Wall Street Journal uses last 4 quarter’s earnings
6.6 Features of Common Stock
 Voting rights (Cumulative vs. Straight)
 Proxy voting
 Classes of stock
 Other rights
 Share proportionally in declared dividends
 Share proportionally in remaining assets during
liquidation
 Preemptive right – first shot at new stock issue to
maintain proportional ownership if desired
Features of Preferred Stock
 Dividends
 Stated dividend must be paid before dividends can
be paid to common stockholders.
 Dividends are not a liability of the firm, and
preferred dividends can be deferred indefinitely.
 Most preferred dividends are cumulative – any
missed preferred dividends have to be paid before
common dividends can be paid.
 Preferred stock generally does not carry voting
rights.
6.7 The Stock Markets
 Dealers vs. Brokers
 New York Stock Exchange (NYSE)
 Largest stock market in the world
 Members
 Own seats on the exchange
 Commission brokers
 Specialists
 Floor brokers
 Floor traders
 Operations
 Floor activity
NASDAQ
 Not a physical exchange – computer-based
quotation system
 Multiple market makers
 Electronic Communications Networks
 Three levels of information
 Level 1 – median quotes, registered representatives
 Level 2 – view quotes, brokers & dealers
 Level 3 – view and update quotes, dealers only
 Large portion of technology stocks
Stock Market Reporting
52 WEEKS YLD VOL NET
HI LO STOCK SYM DIV % PE 100s CLOSE CHG
25.72 18.12 Gap Inc GPS 0.18 0.8 18 39961 21.35 …
Gap pays a
dividend of 18
Gap has cents/share. Gap ended trading at
been as high $21.35, which is
as $25.72 in unchanged from yesterday.
the last year. Given the current
price, the dividend
yield is .8%.
3,996,100 shares traded

Gap has been as Given the current hands in the last day’s
low as $18.12 in price, the PE ratio is trading.
the last year. 18 times earnings.
Chapter 7
Net Present Value and Other Investment Rules
 Be able to compute payback and discounted
payback and understand their shortcomings
 Understand accounting rates of return and their
shortcomings
 Be able to compute the internal rate of return and
profitability index, understanding the strengths
and weaknesses of both approaches
 Be able to compute the net present value and
understand why it is the best decision criterion
Chapter Outline
7.1 Why Use Net Present Value?
7.2 The Payback Period Method
7.3 The Discounted Payback Period Method
7.4 The Average Accounting Return Method
7.5 The Internal Rate of Return
7.6 Problems with the IRR Approach
7.7 The Profitability Index
7.8 The Practice of Capital Budgeting
7.1 Why Use Net Present Value?
 Accepting positive NPV projects benefits
shareholders.
 NPV uses cash flows
 NPV uses all the cash flows of the project
 NPV discounts the cash flows properly
 Reinvestment assumption: the NPV rule

assumes that all cash flows can be reinvested
at the discount rate.
The Net Present Value (NPV) Rule
 Net Present Value (NPV) =
Total PV of future CF’s + Initial Investment
 Estimating NPV:
1. Estimate future cash flows: how much? and when?
2. Estimate discount rate
3. Estimate initial costs
 Minimum Acceptance Criteria: Accept if NPV > 0
 Ranking Criteria: Choose the highest NPV
Calculating NPV with Spreadsheets
 Spreadsheets are an excellent way to compute
NPVs, especially when you have to compute
the cash flows as well.
 Using the NPV function:
 The first component is the required return entered
as a decimal.
 The second component is the range of cash flows
beginning with year 1.
 Add the initial investment after computing the
NPV.
7.2 The Payback Period Method
 How long does it take the project to “pay
back” its initial investment?
 Payback Period = number of years to recover
initial costs
 Minimum Acceptance Criteria:
 Set by management
 Ranking Criteria:
 Set by management
The Payback Period Method
 Disadvantages:
 Ignores the time value of money
 Ignores cash flows after the payback period
 Biased against long-term projects
 Requires an arbitrary acceptance criteria
 A project accepted based on the payback
criteria may not have a positive NPV
 Advantages:
 Easy to understand
 Biased toward liquidity
7.3 The Discounted Payback Period
 How long does it take the project to “pay
back” its initial investment, taking the time
value of money into account?
 Decision rule: Accept the project if it pays
back on a discounted basis within the specified
time.
 By the time you have discounted the cash
flows, you might as well calculate the NPV.
7.4 Average Accounting Return
 Another attractive, but fatally flawed,

approach
 Ranking Criteria and Minimum Acceptance
Criteria set by management
Average Accounting Return
 Disadvantages:
 Ignores the time value of money
 Uses an arbitrary benchmark cutoff rate
 Based on book values, not cash flows and market
values
 Advantages:
 The accounting information is usually available
 Easy to calculate
7.5 The Internal Rate of Return
 IRR: the discount rate that sets NPV to zero
 Accept if the IRR exceeds the required return
 Select alternative with the highest IRR
 Reinvestment assumption:
 All future cash flows assumed reinvested at the
IRR
Internal Rate of Return (IRR)
 Disadvantages:
 Does not distinguish between investing and
borrowing
 IRR may not exist, or there may be multiple IRRs
 Problems with mutually exclusive investments
 Advantages:
 Easy to understand and communicate
IRR: Example
Consider the following project:
$50 $100 $150
0 1 2 3
-$200
The internal rate of return for this project is 19.44%
NPV Payoff Profile
If we graph NPV versus the discount rate, we can see the IRR
as the x-axis intercept.
0% $100.00 $120.00
4% $73.88 $100.00
8% $51.11 $80.00
12% $31.13 $60.00
16% $13.52 $40.00 IRR = 19.44%
NPV
20% ($2.08) $20.00

24% ($15.97) $0.00
28% ($28.38) ($20.00)
-1% 9% 19% 29% 39%
32% ($39.51) ($40.00)
36% ($49.54) ($60.00)
40% ($58.60) ($80.00)
44% ($66.82)
Discount rate
Calculating IRR with Spreadsheets
 You start with the cash flows the same as you
did for the NPV.
 You use the IRR function:
 You first enter your range of cash flows, beginning
with the initial cash flow.
 You can enter a guess, but it is not necessary.
 The default format is a whole percent – you will
normally want to increase the decimal places to at
least two.
7.6 Problems with IRR
 Multiple IRRs
 Are We Borrowing or Lending
 The Scale Problem
 The Timing Problem
Mutually Exclusive vs. Independent
 Mutually Exclusive Projects: only ONE of several
potential projects can be chosen, e.g., acquiring an
accounting system.
 RANK all alternatives, and select the best one.
 Independent Projects: accepting or rejecting one

project does not affect the decision of the other
projects.
 Must exceed a MINIMUM acceptance criteria
Multiple IRRs
There are two IRRs for this project:
$200 $800 Which one should
we use?
0 1 2 3
-$200 - $800
NPV
$100.00
$50.00
100% = IRR2
$0.00
-50% 0% 50% 100% 150% 200%
($50.00) 0% = IRR1 Discount rate
($100.00)
Modified IRR
 Calculate the net present value of all cash
outflows using the borrowing rate.
 Calculate the net future value of all cash
inflows using the investing rate.
 Find the rate of return that equates these
values.
 Benefits: single answer and specific rates
The Scale Problem
Would you rather make 100% or 50% on your
investments?
What if the 100% return is on a $1
investment, while the 50% return is on a
$1,000 investment?
The Timing Problem
$10,000 $1,000 $1,000
Project A
0 1 2 3
-$10,000
$1,000 $1,000 $12,000
Project B
0 1 2 3
-$10,000
The Timing Problem
$5,000.00 Project A
$4,000.00 Project B
$3,000.00
$2,000.00
10.55% = crossover rate
$1,000.00
NPV
$0.00
($1,000.00) 0% 10% 20% 30% 40%
($2,000.00)
($3,000.00)
($4,000.00)
12.94% = IRRB 16.04% = IRRA
($5,000.00)
Discount rate
Calculating the Crossover Rate
Compute the IRR for either project “A-B” or “B-A”
Year Project A Project B Project A-B Project B-A
0 ($10,000) ($10,000) $0 $0
1 $10,000 $1,000 $9,000 ($9,000)
2 $1,000 $1,000 $0 $0
3 $1,000 $12,000 ($11,000) $11,000
$3,000.00
$2,000.00
10.55% = IRR
$1,000.00
NPV
A-B
$0.00
B-A
($1,000.00) 0% 5% 10% 15% 20%
($2,000.00)
($3,000.00)
Discount rate
NPV versus IRR
 NPV and IRR will generally give the same
decision.
 Exceptions:
 Non-conventional cash flows – cash flow signs
change more than once
 Mutually exclusive projects
 Initial
investments are substantially different
 Timing of cash flows is substantially different
7.7 The Profitability Index (PI)

 Accept if PI > 1
 Select alternative with highest PI
The Profitability Index
 Disadvantages:
 Problems with mutually exclusive investments
 Advantages:
 May be useful when available investment funds
are limited
 Easy to understand and communicate
 Correct decision when evaluating independent
projects
7.8 The Practice of Capital Budgeting
 Varies by industry:
 Some firms use payback, others use accounting
rate of return.
 The most frequently used technique for large
corporations is IRR or NPV.
Example of Investment Rules
Compute the IRR, NPV, PI, and payback period
for the following two projects. Assume the
required return is 10%.
Year Project A Project B
0 -$200 -$150
1 $200 $50
2 $800 $100
3 -$800 $150
Project A Project B
CF0 -$200.00 -$150.00
PV0 of CF1-3 $241.92 $240.80
NPV = $41.92 $90.80

IRR = 0%, 100% 36.19%
PI = 1.2096 1.6053
Payback Period:
Project A Project B
Time CF Cum. CF CF Cum. CF
0 -200 -200 -150 -150
1 200 0 50 -100
2 800 800 100 0
3 -800 0 150 150
Payback period for project B = 2 years.

Payback period for project A = 1 or 3 years?
NPV and IRR Relationship
Discount rate NPV for A NPV for B
-10% -87.52 234.77
0% 0.00 150.00
20% 59.26 47.92
40% 59.48 -8.60
60% 42.19 -43.07
80% 20.85 -65.64
100% 0.00 -81.25
120% -18.93 -92.52
NPV Profiles
$400
NPV
$300
IRR 1(A) IRR (B) IRR 2(A)
$200
$100
$0
-15% 0% 15% 30% 45% 70% 100% 130% 160% 190%
($100)
($200)
Project A
Discount rates
Cross-over Rate Project B
Summary – Discounted Cash Flow
 Net present value
 Difference between market value and cost
 Accept the project if the NPV is positive
 Has no serious problems
 Preferred decision criterion
 Internal rate of return
 Discount rate that makes NPV = 0
 Take the project if the IRR is greater than the required return
 Same decision as NPV with conventional cash flows
 IRR is unreliable with non-conventional cash flows or mutually exclusive
projects
 Profitability Index
 Benefit-cost ratio
 Take investment if PI > 1
 Cannot be used to rank mutually exclusive projects
 May be used to rank projects in the presence of capital rationing
Summary – Payback Criteria
 Payback period
 Length of time until initial investment is recovered
 Take the project if it pays back in some specified period
 Doesn’t account for time value of money, and there is an
arbitrary cutoff period
 Discounted payback period
 Length of time until initial investment is recovered on a
discounted basis
 Take the project if it pays back in some specified period
 There is an arbitrary cutoff period
Summary – Accounting Criterion
 Average Accounting Return
 Measure of accounting profit relative to book
value
 Similar to return on assets measure
 Take the investment if the AAR exceeds some
specified return level
 Serious problems and should not be used
Chapter 8
Making Capital Investment Decisions
 Understand how to determine the relevant cash
flows for various types of capital investments
 Be able to compute depreciation expense for
tax purposes
 Incorporate inflation into capital budgeting
 Understand the various methods for computing
operating cash flow
 Apply the Equivalent Annual Cost approach
Chapter Outline
8.1 Incremental Cash Flows
8.2 The Baldwin Company: An Example
8.3 Inflation and Capital Budgeting
8.4 Alternative Definitions of Cash Flow
8.5 Investments of Unequal Lives: The
Equivalent Annual Cost Method
8.1 Incremental Cash Flows
 Cash flows matter—not accounting earnings.
 Sunk costs don’t matter.
 Incremental cash flows matter.
 Opportunity costs matter.
 Side effects like cannibalism and erosion matter.
 Taxes matter: we want incremental after-tax

cash flows.
 Inflation matters.
Cash Flows—Not Accounting
 Consider depreciation expense.
 Younever write a check made out to
“depreciation.”
 Much of the work in evaluating a project
lies in taking accounting numbers and
generating cash flows.
Incremental Cash Flows
 Sunk costs are not relevant
 Just because “we have come this far” does not
mean that we should continue to throw good
money after bad.
 Opportunity costs do matter. Just because a
project has a positive NPV, that does not mean
that it should also have automatic acceptance.
Specifically, if another project with a higher NPV
would have to be passed up, then we should not
proceed.
Incremental Cash Flows
 Side effects matter.
 Erosion and cannibalism are both bad
things. If our new product causes existing
customers to demand less of current
products, we need to recognize that.
 If, however, synergies result that create
increased demand of existing products, we
also need to recognize that.
Estimating Cash Flows
 Cash Flow from Operations
 Recall that:
OCF = EBIT – Taxes + Depreciation
 Net Capital Spending
 Don’t forget salvage value (after tax, of course).
 Changes in Net Working Capital
 Recall that when the project winds down, we enjoy
a return of net working capital.
Interest Expense
 Later chapters will deal with the impact
that the amount of debt that a firm has in
its capital structure has on firm value.
 For now, it’s enough to assume that the
firm’s level of debt (and, hence, interest
expense) is independent of the project at
hand.
8.2 The Baldwin Company
 Costs of test marketing (already spent):
$250,000
 Current market value of proposed factory site
(which we own): $150,000
 Cost of bowling ball machine: $100,000
(depreciated according to MACRS 5-year)
 Increase in net working capital: $10,000
 Production (in units) by year during 5-year
life of the machine: 5,000, 8,000, 12,000,
10,000, 6,000
The Baldwin Company
 Price during first year is $20; price increases
2% per year thereafter.
 Production costs during first year are $10 per
unit and increase 10% per year thereafter.
 Annual inflation rate: 5%
 Working Capital: initial $10,000 changes with
sales
The Baldwin Company
($ thousands) (All cash flows occur at the end of the year.)
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Investments:
(1) Bowling ball machine –100.00 21.76*
(2) Accumulated 20.00 52.00 71.20 82.72 94.24
depreciation
(3) Adjusted basis of 80.00 48.00 28.80 17.28 5.76
machine after
depreciation (end of year)
(4) Opportunity cost –150.00 150.00
(warehouse)
(5) Net working capital 10.00 10.00 16.32 24.97 21.22 0
(end of year)
(6) Change in net –10.00 –6.32 –8.65 3.75 21.22
working capital
(7) Total cash flow of –260.00 –6.32 –8.65 3.75 192.98
investment
[(1) + (4) + (6)]
The Baldwin Company
Investments:
(1) Bowling ball machine –100.00 21.76*
(2) Accumulated 20.00 52.00 71.20 82.72 94.24
depreciation
(3) Adjusted basis of 80.00 48.00 28.80 17.28 5.76
machine after
depreciation (end of year)
(4) Opportunity cost –150.00 150.00
(warehouse)
(5) Net working capital 10.00 10.00 16.32 24.97 21.22 0
(end of year)
(6) Change in net –10.00 –6.32 –8.65 3.75 21.22
working capital
(7) Total cash flow of –260.00 –6.32 –8.65 3.75 192.98
investment
[(1) + (4) + (6)]
At the end of the project, the warehouse is unencumbered, so we can sell it if we want to.
The Baldwin Company
Income:
(8) Sales Revenues 100.00 163.20 249.72 212.20 129.90
Recall that production (in units) by year during the 5-year life of the machine is
given by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Price during the first year is $20 and increases 2% per year thereafter.
Sales revenue in year 3 = 12,000×[$20×(1.02)2] = 12,000×$20.81 = $249,720.
The Baldwin Company
Income:
(8) Sales Revenues 100.00 163.20 249.72 212.20 129.90
(9) Operating costs 50.00 88.00 145.20 133.10 87.84
Again, production (in units) by year during 5-year life of the machine is given
by:
(5,000, 8,000, 12,000, 10,000, 6,000).
Production costs during the first year (per unit) are $10, and they increase
10% per year thereafter.
Production costs in year 2 = 8,000×[$10×(1.10)1] = $88,000
The Baldwin Company
Income:
(8) Sales Revenues 100.00 163.20 249.72 212.20 129.90
(9) Operating costs 50.00 88.00 145.20 133.10 87.84
(10) Depreciation 20.00 32.00 19.20 11.52 11.52
Depreciation is calculated using the Accelerated Year ACRS %

Cost Recovery System (shown at right). 1 20.00%
Our cost basis is $100,000. 2 32.00%
Depreciation charge in year 4 3 19.20%
= $100,000×(.1152) = $11,520. 4 11.52%
5 11.52%
6 5.76%
Total 100.00%
The Baldwin Company
Income:
(8) Sales Revenues 100.00 163.20 249.72 212.20 129.90
(9) Operating costs 50.00 88.00 145.20 133.10 87.84
(10) Depreciation 20.00 32.00 19.20 11.52 11.52
(11) Income before taxes 30.00 43.20 85.32 67.58 30.54
[(8) – (9) - (10)]
(12) Tax at 34 percent 10.20 14.69 29.01 22.98 10.38
(13) Net Income 19.80 28.51 56.31 44.60 20.16
Incremental After Tax Cash Flows
(1) Sales $100.00 $163.20 $249.72 $212.20 $129.90

Revenues
(2) Operating -50.00 -88.00 -145.20 133.10 -87.84
costs
(3) Taxes -10.20 -14.69 -29.01 -22.98 -10.38
(4) OCF 39.80 60.51 75.51 56.12 31.68

(1) – (2) – (3)
(5) Total CF of –260. –6.32 –8.65 3.75 192.98
Investment
(6) IATCF –260. 39.80 54.19 66.86 59.87 224.66
[(4) + (5)]
NPV of Baldwin Company
CF0 –260 F3 1
CF1 CF4 59.87 I 10

39.80
F1 1 NPV
F4 1 51.588
CF2 54.19
CF5 224.66
F2 1
F5 1
CF3 66.86
8.3 Inflation and Capital Budgeting
 Inflation is an important fact of economic life
and must be considered in capital budgeting.
 Consider the relationship between interest
rates and inflation, often referred to as the
Fisher equation:
(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)
Inflation and Capital Budgeting
 For low rates of inflation, this is often approximated:
Real Rate  Nominal Rate – Inflation Rate
 While the nominal rate in the U.S. has fluctuated
with inflation, the real rate has generally exhibited
far less variance than the nominal rate.
 In capital budgeting, one must compare real cash
flows discounted at real rates or nominal cash flows
discounted at nominal rates.
Other Methods for Computing OCF
 Bottom-Up Approach
 Works only when there is no interest expense
 OCF = NI + depreciation
 Top-Down Approach
 OCF = Sales – Costs – Taxes
 Don’t subtract non-cash deductions
 Tax Shield Approach

 OCF = (Sales – Costs)(1 – T) + Depreciation*T
8.5 Investments of Unequal Lives
 There are times when application of the NPV
rule can lead to the wrong decision. Consider a
factory that must have an air cleaner that is
mandated by law. There are two choices:
 The “Cadillac cleaner” costs $4,000 today, has
annual operating costs of $100, and lasts 10 years.
 The “Cheapskate cleaner” costs $1,000 today, has
annual operating costs of $500, and lasts 5 years.
 Assuming a 10% discount rate, which one
should we choose?
Investments of Unequal Lives
Cadillac Air Cleaner Cheapskate Air Cleaner
CF0 – 4,000 CF0 –1,000
CF1 –100 CF1 –500
F1 10 F1 5
I 10 I 10
NPV –4,614.46 NPV –2,895.39

At first glance, the Cheapskate cleaner has a higher NPV.
 This overlooks the fact that the Cadillac
cleaner lasts twice as long.
 When we incorporate that, the Cadillac
cleaner is actually cheaper (i.e., has a
higher NPV).
 Replacement Chain
 Repeat projects until they begin and end at the
same time.
 Compute NPV for the “repeated projects.”
 The Equivalent Annual Cost Method
Replacement Chain Approach
The Cadillac cleaner time line of cash flows:
-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -100
0 1 2 3 4 5 6 7 8 9 10
The Cheapskate cleaner time line of cash flows

over ten years:
-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -500
0 1 2 3 4 5 6 7 8 9 10
Replacement Chain Approach
Cadillac Air Cleaner Cheapskate Air Cleaner
CF0 –4,000 CF0 –1,000

CF1 –500
CF1 –100
F1 4
F1 10 CF2 –1,500
I 10 F2 1
CF3 –500 I 10
NPV –4,614
F3 5 NPV –4,693
Equivalent Annual Cost (EAC)
 Applicable to a much more robust set of
circumstances than the replacement chain
 The EAC is the value of the level payment
annuity that has the same PV as our original set
of cash flows.
 For example, the EAC for the Cadillac air cleaner is
$750.98.
 The EAC for the Cheapskate air cleaner is $763.80,
which confirms our earlier decision to reject it.
Cadillac EAC with a Calculator
CF0 –4,000 N 10
CF1 –100 I/Y 10
F1 10 PV –4,614.46
I 10 PMT 750.98
NPV –4,614.46 FV
Cheapskate EAC with a Calculator
CF0 –1,000 N 5
CF1 –500 I/Y 10
F1 5 PV -2,895.39
I 10 PMT 763.80
NPV –2,895.39 FV
Chapter 9
Risk Analysis, Real Options, and Capital
Budgeting
 Understand decision trees
 Understand and be able to apply scenario and
sensitivity analysis
 Understand the various forms of break-even
analysis
 Understand Monte Carlo simulation
 Understand the importance of real options in

capital budgeting
Chapter Outline
9.1 Decision Trees
9.2 Sensitivity Analysis, Scenario Analysis,
and Break-Even Analysis
9.3 Monte Carlo Simulation
9.4 Real Options
9.1 Decision Trees
 Allow us to graphically represent the
alternatives available to us in each period
and the likely consequences of our
actions
 This graphical representation helps to
identify the best course of action.
Example of a Decision Tree
Squares represent decisions to be made. Circles represent
“A” receipt of information,
e.g., a test score.
Study
“B”
finance
“C”
The lines leading away
from the squares
Do not “D” represent the alternatives.
study
“F”
Stewart Pharmaceuticals
 Stewart Pharmaceuticals Corporation is considering investing
in the development of a drug that cures the common cold.
 A corporate planning group, including representatives from
production, marketing, and engineering, has recommended
that the firm go ahead with the test and development phase.
 This preliminary phase will last one year and cost $1 billion.
Furthermore, the group believes that there is a 60% chance
that tests will prove successful.
 If the initial tests are successful, Stewart Pharmaceuticals can
go ahead with full-scale production. This investment phase
will cost $1.6 billion. Production will occur over the
following 4 years.
NPV Following Successful Test
Investment Year 1 Years 2-5 Note that the NPV is
calculated as of date 1, the
Revenues $7,000 date at which the
investment of $1,600
Variable Costs (3,000) million is made. Later we
Fixed Costs (1,800) bring this number back to
date 0. Assume a cost of
Depreciation (400) capital of 10%.
Pretax profit $1,800

Tax (34%) (612)
Net Profit $1,188
Cash Flow -$1,600 $1,588
NPV Following Unsuccessful Test
Investment Year 1 Years 2-5 Note that the NPV is
calculated as of date 1,
Revenues $4,050 the date at which the
investment of $1,600
Variable Costs (1,735) million is made. Later
we bring this number
Fixed Costs (1,800) back to date 0. Assume a
cost of capital of 10%.
Depreciation (400)
Pretax profit $115
Tax (34%) (39.10)
Net Profit $75.90
Cash Flow -$1,600 $475.90
Decision Tree for Stewart
The firm has two decisions to make: Invest
NPV = $3.4 b
To test or not to test. Success
To invest or not to invest.
Test Do not
NPV = $0
invest
Failure
Do not Invest
test NPV = –$91.46 m
Decision to Test
 Let’s move back to the first stage, where the decision boils
down to the simple question: should we invest?
 The expected payoff evaluated at date 1 is:
The NPV evaluated at date 0 is:
So, we should test.

9.2 Sensitivity, Scenario, and Break-Even
 Each allows us to look behind the NPV
number to see how firm our estimates
are.
 When working with spreadsheets, try to
build your model so that you can adjust
variables in a single cell and have the
NPV calculations update accordingly.
Sensitivity Analysis: Stewart
 We can see that NPV is very sensitive to changes in revenues.
In the Stewart Pharmaceuticals example, a 14% drop in
revenue leads to a 61% drop in NPV.
For every 1% drop in revenue, we can expect roughly a

4.26% drop in NPV:
Scenario Analysis: Stewart
 A variation on sensitivity analysis is scenario analysis.
 For example, the following three scenarios could apply
to Stewart Pharmaceuticals:
1. The next years each have heavy cold seasons, and sales
exceed expectations, but labor costs skyrocket.
2. The next years are normal, and sales meet expectations.
3. The next years each have lighter than normal cold
seasons, so sales fail to meet expectations.
 Other scenarios could apply to FDA approval.
 For each scenario, calculate the NPV.
Break-Even Analysis
 Common tool for analyzing the relationship
between sales volume and profitability
 There are three common break-even measures
 Accounting break-even: sales volume at which net
income = 0
 Cash break-even: sales volume at which operating
cash flow = 0
 Financial break-even: sales volume at which net
present value = 0
Break-Even Analysis: Stewart
 Another way to examine variability in
our forecasts is break-even analysis.
 In the Stewart Pharmaceuticals example,
we could be concerned with break-even
revenue, break-even sales volume, or
break-even price.
 To find either, we start with the break-
even operating cash flow.
Break-Even Analysis: Stewart
 The project requires an N 4
investment of $1,600.
 In order to cover our cost I/Y
of capital (break even), the
10
project needs to generate a
cash flow of $504.75 each PV 1,600
year for four years.
 This is the project’s break-
PMT − 504.75
even operating cash flow,
OCFBE. FV 0
Break-Even Revenue: Stewart
Work backwards from OCFBE to Break-Even Revenue
Revenue $5,358.71
+ VC
Variable cost $3,000
Fixed cost $1,800
Depreciation +D $400
+FC
EBIT $158.71
$104.75
Tax (34%) 0.66 $53.96
Net Income $104.75
OCF =$104.75 + $400 $504.75
Break-Even Analysis: PBE
 Now that we have break-even revenue of $5,358.71
million, we can calculate break-even price.
 The original plan was to generate revenues of $7
billion by selling the cold cure at $10 per dose and
selling 700 million doses per year,
 We can reach break-even revenue with a price of
only:
$5,358.71 million = 700 million × PBE
$5,378.71
PBE = = $7.68 / dose
700
9.3 Monte Carlo Simulation
 Monte Carlo simulation is a further
attempt to model real-world uncertainty.
 This approach takes its name from the
famous European casino, because it
analyzes projects the way one might
analyze gambling strategies.
Monte Carlo Simulation
 Imagine a serious blackjack player who wants to
know if she should take the third card whenever her
first two cards total sixteen.
 She could play thousands of hands for real money to
find out.
 This could be hazardous to her wealth.
 Or, she could play thousands of practice hands.
 Monte Carlo simulation of capital budgeting projects
is in this spirit.
Monte Carlo Simulation
 Monte Carlo simulation of capital budgeting projects
is often viewed as a step beyond either sensitivity
analysis or scenario analysis.
 Interactions between the variables are explicitly
specified in Monte Carlo simulation, so, at least
theoretically, this methodology provides a more
complete analysis.
 While the pharmaceutical industry has pioneered
applications of this methodology, its use in other
industries is far from widespread.
9.4 Real Options
 One of the fundamental insights of modern
finance theory is that options have value.
 The phrase “We are out of options” is surely a
sign of trouble.
 Because corporations make decisions in a
dynamic environment, they have options that
should be considered in project valuation.
Real Options
 The Option to Expand
 Has value if demand turns out to be higher than
expected
 The Option to Abandon
 Has value if demand turns out to be lower than
expected
 The Option to Delay
 Has value if the underlying variables are
changing with a favorable trend
Discounted CF and Options
 We can calculate the market value of a project as the
sum of the NPV of the project without options and
the value of the managerial options implicit in the
project.
M = NPV + Opt
A good example would be comparing the desirability

of a specialized machine versus a more versatile
machine. If they both cost about the same and last
the same amount of time, the more versatile machine
is more valuable because it comes with options.
The Option to Abandon: Example
 Suppose we are drilling an oil well. The
drilling rig costs $300 today, and in one year
the well is either a success or a failure.
 The outcomes are equally likely. The
discount rate is 10%.
 The PV of the successful payoff at time one
is $575.
 The PV of the unsuccessful payoff at time
one is $0.
Traditional NPV analysis would indicate rejection of the project.
Expected = Prob. × Successful + Prob. × Failure

Payoff Success Payoff Failure Payoff
Expected
= (0.50×$575) + (0.50×$0) = $287.50
Payoff
$287.50
NPV = –$300 + = –$38.64
1.10
Traditional NPV analysis overlooks the option to abandon.
Success: PV = $500
Drill Sit on rig; stare

at empty hole:
PV = $0.
Failure
Do not Sell the rig;

drill salvage value
= $250
The firm has two decisions to make: drill or not, abandon or stay.
 When we include the value of the option to abandon, the
drilling project should proceed:
Expected = Prob. × Successful + Prob. × Failure

Payoff Success Payoff Failure Payoff
Expected
= (0.50×$575) + (0.50×$250) = $412.50
Payoff
$412.50
NPV = –$300 + = $75.00
1.10
Valuing the Option to Abandon
 Recall that we can calculate the market value of
a project as the sum of the NPV of the project
without options and the value of the managerial
options implicit in the project.
M = NPV + Opt
$75.00 = –$38.64 + Opt
$75.00 + $38.64 = Opt
Opt = $113.64
The Option to Delay: Example
Year
Year Cost
Cost PVPV NPV NPVt t
NPV 0
0 0 $ 20,000
$ 20,000$ 25,000
$ 25,000$ 5,000
$ 5,000$ 5,000
1 1 $ 18,000
$ 18,000$ 25,000
$ 25,000$ 7,000
$ 7,000$ 6,364
2 2 $ 17,100
$ 17,100$ 25,000
$ 25,000$ 7,900
$ 7,900$ 6,529
3 3 $ 16,929
$ 16,929$ 25,000
$ 25,000$ 8,071
$ 8,071$ 6,064
4 4 $ 16,760
$ 16,760$ 25,000
$ 25,000$ 8,240
$ 8,240$ 5,628
 Consider the above project, which can be undertaken in any of the
next 4 years. The discount rate is 10 percent. The present value of the
benefits at the time the project is launched remains constant at
$25,000, but since costs are declining, the NPV at the time of launch
steadily rises.
 The best time to launch the project is in year 2—this schedule yields
the highest NPV when judged today.
Chapter 10
Risk and Return Lessons from Market History
 Know how to calculate the return on an investment
 Know how to calculate the standard deviation of an
investment’s returns
 Understand the historical returns and risks on various
types of investments
 Understand the importance of the normal distribution
 Understand the difference between arithmetic and
geometric average returns
Chapter Outline
10.1 Returns
10.2 Holding-Period Returns
10.3 Return Statistics
10.4 Average Stock Returns and Risk-Free
Returns
10.5 Risk Statistics
10.6 More on Average Returns
10.1 Returns
 Dollar Returns Dividends
the sum of the cash received
and the change in value of the Ending
asset, in dollars. market value
Time 0 1
Percentage Returns
–the sum of the cash received and the
Initial change in value of the asset divided by
investment the initial investment.
Returns
Dollar Return = Dividend + Change in Market Value
Returns: Example
 Suppose you bought 100 shares of Wal-Mart
(WMT) one year ago today at $25. Over the last
year, you received $20 in dividends (20 cents per
share × 100 shares). At the end of the year, the
stock sells for $30. How did you do?
 Quite well. You invested $25 × 100 = $2,500. At
the end of the year, you have stock worth $3,000
and cash dividends of $20. Your dollar gain was
$520 = $20 + ($3,000 – $2,500).
$520
 Your percentage gain for the year is: 20.8% =
$2,500
Returns: Example
Dollar Return: $20
$520 gain
$3,000
Time 0 1
Percentage Return:
$520
-$2,500 20.8% =
$2,500
10.2 Holding-Period Returns
 The holding period return is the return
that an investor would get when holding
an investment over a period of n years,
when the return during year i is given as
ri :
Holding-Period Return: Example
 Suppose your investment provides the
following returns over a four-year
period:
Year Return
1 10%
2 -5%
3 20%
4 15%
Holding-Period Returns
 A famous set of studies dealing with rates of returns
on common stocks, bonds, and Treasury bills was
conducted by Roger Ibbotson and Rex Sinquefield.
 They present year-by-year historical rates of return
starting in 1926 for the following five important types
of financial instruments in the United States:
 Large-company Common Stocks
 Small-company Common Stocks
 Long-term Corporate Bonds
 Long-term U.S. Government Bonds
 U.S. Treasury Bills
10.3 Return Statistics
 The history of capital market returns can be
summarized by describing the:
 average return
 the standard deviation of those returns
 the frequency distribution of the returns

Historical Returns, 1926-2004
Average Standard
Series Annual Return Deviation Distribution
Large Company Stocks 12.4% 20.3%
Small Company Stocks 17.5 33.1
Long-Term Corporate Bonds 6.2 8.6
Long-Term Government Bonds 5.8 9.3
U.S. Treasury Bills 3.8 3.1
Inflation 3.1 4.3
– 90% 0% + 90%
Source: © Stocks, Bonds, Bills, and Inflation 2005 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
10.4 Average Stock Returns and Risk-Free Returns
 The Risk Premium is the added return (over and above the
risk-free rate) resulting from bearing risk.
 One of the most significant observations of stock market
data is the long-run excess of stock return over the risk-free
return.
 The average excess return from large company common stocks
for the period 1926 through 2004 was: 8.6% = 12.4% – 3.8%
 The average excess return from small company common stocks
for the period 1926 through 2004 was: 13.7% = 17.5% – 3.8%
 The average excess return from long-term corporate bonds for
the period 1926 through 2004 was: 2.4% = 6.2% – 3.8%
Risk Premia
 Suppose that The Wall Street Journal announced that
the current rate for one-year Treasury bills is 5%.
 What is the expected return on the market of small-
company stocks?
 Recall that the average excess return on small
company common stocks for the period 1926
through 2004 was 13.7%.
 Given a risk-free rate of 5%, we have an expected
return on the market of small-company stocks of
18.7% = 13.7% + 5%
The Risk-Return Tradeoff
18%
Small-Company Stocks
16%
Annual Return Average
14%
12% Large-Company Stocks

10%
8%
6%
T-Bonds
4%
T-Bills
2%
0% 5% 10% 15% 20% 25% 30% 35%
Annual Return Standard Deviation
10.5 Risk Statistics
 There is no universally agreed-upon
definition of risk.
 The measures of risk that we discuss are
variance and standard deviation.
 The standard deviation is the standard statistical
measure of the spread of a sample, and it will be
the measure we use most of this time.
 Its interpretation is facilitated by a discussion of
the normal distribution.
Normal Distribution
 A large enough sample drawn from a normal
distribution looks like a bell-shaped curve.
Probability
The probability that a yearly return

will fall within 20.3 percent of the
mean of 12.4 percent will be
approximately 2/3.
– 3s – 2s – 1s 0 + 1s + 2s + 3s
– 48.5% – 28.2% – 7.9% 12.4% 32.7% 53.0% 73.3% Return on
large company common
68.26% stocks
95.44%
99.74%
Normal Distribution
 The 20.3% standard deviation we found
for large stock returns from 1926
through 2004 can now be interpreted in
the following way: if stock returns are
approximately normally distributed, the
probability that a yearly return will fall
within 20.3 percent of the mean of
12.4% will be approximately 2/3.
Example – Return and Variance
Year Actual Average Deviation from the Squared
Return Return Mean Deviation
1 .15 .105 .045 .002025
2 .09 .105 -.015 .000225
3 .06 .105 -.045 .002025
4 .12 .105 .015 .000225
Totals .00 .0045
Variance = .0045 / (4-1) = .0015 Standard Deviation = .03873
Arithmetic vs. Geometric Mean
 Arithmetic average – return earned in an average
period over multiple periods
 Geometric average – average compound return per
period over multiple periods
 The geometric average will be less than the arithmetic
average unless all the returns are equal
 Which is better?
 The arithmetic average is overly optimistic for long
horizons.
 The geometric average is overly pessimistic for short
horizons.
Geometric Return: Example
 Recall our earlier example:
Year Return
1 10%
2 -5%
3 20%
4 15%
So, our investor made an average of 9.58% per year,
realizing a holding period return of 44.21%.
Geometric Return: Example
 Note that the geometric average is not
the same as the arithmetic average:
Year Return
1 10%
2 -5%
3 20%
4 15%
Forecasting Return
 To address the time relation in forecasting returns,
use Blume’s formula:
 T 1   N T 
R (T )     GeometricAverage    ArithmeticAverage
 N  1  N 1 
where, T is the forecast horizon and N is the number of
years of historical data we are working with. T must be
less than N.
Chapter 11
Return and Risk: The Capital Asset Pricing
Model (CAPM)
 Know how to calculate expected returns
 Know how to calculate covariances,
correlations, and betas
 Understand the impact of diversification
 Understand the systematic risk principle
 Understand the security market line
 Understand the risk-return tradeoff
 Be able to use the Capital Asset Pricing Model
Chapter Outline
11.1 Individual Securities
11.2 Expected Return, Variance, and Covariance
11.3 The Return and Risk for Portfolios
11.4 The Efficient Set
11.5 Riskless Borrowing and Lending
11.6 Announcements, Surprises, and Expected Return
11.7 Risk: Systematic and Unsystematic
11.8 Diversification and Portfolio Risk
11.9 Market Equilibrium
11.10 Relationship between Risk and Expected Return (CAPM)
11.1 Individual Securities
 The characteristics of individual securities
that are of interest are the:
 Expected Return
 Variance and Standard Deviation
 Covariance and Correlation (to another security
or index)
11.2 Expected Return, Variance, and Covariance
Consider the following two risky asset world.

There is a 1/3 chance of each state of the
economy, and the only assets are a stock
fund and a bond fund.
Rate of Return
Scenario Probability Stock Fund Bond Fund
Recession 33.3% -7% 17%
Normal 33.3% 12% 7%
Boom 33.3% 28% -3%
Expected Return
Stock Fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Expected return 11.00% 7.00%
Variance 0.0205 0.0067
Standard Deviation 14.3% 8.2%
Expected Return
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Variance 0.0205 0.0067
Variance
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Variance 0.0205 0.0067
Variance
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Variance 0.0205 0.0067
Standard Deviation
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Variance 0.0205 0.0067
Covariance
Stock Bond
Scenario Deviation Deviation Product Weighted
Recession -18% 10% -0.0180 -0.0060
Normal 1% 0% 0.0000 0.0000
Boom 17% -10% -0.0170 -0.0057
Sum -0.0117
Covariance -0.0117
Deviation compares return in each state to the expected return.

Weighted takes the product of the deviations multiplied by the
probability of that state.
Correlation
Cov(a, b)

s as b
 .0117
  0.998
(.143)(.082)
11.3 The Return and Risk for Portfolios
Recession -7% 0.0324 17% 0.0100
Normal 12% 0.0001 7% 0.0000
Boom 28% 0.0289 -3% 0.0100
Variance 0.0205 0.0067
Note that stocks have a higher expected return than bonds

and higher risk. Let us turn now to the risk-return tradeoff
of a portfolio that is 50% invested in bonds and 50%
invested in stocks.
Portfolios
Rate of Return
Scenario Stock fund Bond fund Portfolio squared deviation
Recession -7% 17% 5.0% 0.0016
Normal 12% 7% 9.5% 0.0000
Boom 28% -3% 12.5% 0.0012
Expected return 11.00% 7.00% 9.0%

Variance 0.0205 0.0067 0.0010
Standard Deviation 14.31% 8.16% 3.08%
The rate of return on the portfolio is a weighted average of

the returns on the stocks and bonds in the portfolio:
Portfolios
Rate of Return
Recession -7% 17% 5.0% 0.0016
Normal 12% 7% 9.5% 0.0000
Boom 28% -3% 12.5% 0.0012

Variance 0.0205 0.0067 0.0010
The expected rate of return on the portfolio is a weighted
average of the expected returns on the securities in the
portfolio.
Portfolios
Rate of Return
Recession -7% 17% 5.0% 0.0016
Normal 12% 7% 9.5% 0.0000
Boom 28% -3% 12.5% 0.0012

Variance 0.0205 0.0067 0.0010
The variance of the rate of return on the two risky assets
portfolio is
where BS is the correlation coefficient between the returns

on the stock and bond funds.
Portfolios
Rate of Return
Recession -7% 17% 5.0% 0.0016
Normal 12% 7% 9.5% 0.0000
Boom 28% -3% 12.5% 0.0012

Variance 0.0205 0.0067 0.0010
Observe the decrease in risk that diversification offers.

An equally weighted portfolio (50% in stocks and 50%
in bonds) has less risk than either stocks or bonds held
in isolation.
11.4 The Efficient Set
% in stocks Risk Return
0% 8.2% 7.0% Portfolo Risk and Return Combinations
Portfolio Return
5% 7.0% 7.2%
10% 5.9% 7.4% 12.0%
100%
15% 4.8% 7.6% 11.0%
stocks
20% 3.7% 7.8% 10.0%
25% 2.6% 8.0% 9.0% 100%
30% 1.4% 8.2% 8.0% bonds
35% 0.4% 8.4%
7.0%
40% 0.9% 8.6%
6.0%
45% 2.0% 8.8%
5.0%
50.00% 3.08% 9.00%
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
55% 4.2% 9.2%
60% 5.3% 9.4% Portfolio Risk (standard deviation)
65% 6.4% 9.6%
70% 7.6% 9.8% We can consider other
75%
80%
8.7%
9.8%
10.0%
10.2%
portfolio weights besides
85% 10.9% 10.4% 50% in stocks and 50% in
90%
95%
12.1%
13.2%
10.6%
10.8%
bonds …
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11.0%
The Efficient Set
% in stocks Risk Return
0% 8.2% 7.0% Portfolo Risk and Return Combinations
Portfolio Return
5% 7.0% 7.2%
10% 5.9% 7.4% 12.0%
15% 4.8% 7.6% 11.0%
20% 3.7% 7.8% 10.0% 100%
25% 2.6% 8.0% 9.0% stocks
30% 1.4% 8.2% 8.0%
35% 0.4% 8.4% 7.0% 100%
40% 0.9% 8.6% 6.0%
45% 2.0% 8.8%
bonds
5.0%
50% 3.1% 9.0%
0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0%
55% 4.2% 9.2%
60% 5.3% 9.4% Portfolio Risk (standard deviation)
65% 6.4% 9.6%
70% 7.6% 9.8% Note that some portfolios are
75%
80%
8.7%
9.8%
10.0%
10.2%
“better” than others. They have
85% 10.9% 10.4% higher returns for the same level of
90% 12.1% 10.6%
95% 13.2% 10.8%
risk or less.
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Portfolios with Various Correlations
 Relationship depends
on correlation
return
100%
 = -1.0 stocks coefficient
-1.0 <  < +1.0
 If  = +1.0, no risk
 = 1.0 reduction is possible
100%
 = 0.2  If  = –1.0, complete
bonds risk reduction is
s possible
The Efficient Set for Many Securities
return
Individual Assets
sP
Consider a world with many risky assets; we can
still identify the opportunity set of risk-return
combinations of various portfolios.
The Efficient Set for Many Securities
return
minimum
variance
portfolio
Individual Assets
sP
The section of the opportunity set above the
minimum variance portfolio is the efficient
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Optimal Portfolio with a Risk-Free Asset
return
100%
stocks
rf
100%
bonds
s
In addition to stocks and bonds, consider a world
that also has risk-free securities like T-bills.
11.5 Riskless Borrowing and Lending
return
100%
stocks
Balanced
fund
rf
100%
bonds
s
Now investors can allocate their money across
the T-bills and a balanced mutual fund.
Riskless Borrowing and Lending
return
rf
sP
With a risk-free asset available and the efficient
frontier identified, we choose the capital
allocation line with the steepest slope.
Expected vs. Unexpected Returns
 Realized returns are generally not equal to
expected returns.
 There is the expected component and the
unexpected component.
 At any point in time, the unexpected return can be
either positive or negative.
 Over time, the average of the unexpected
component is zero.
11.6 Announcements and News
 Announcements and news contain both an
expected component and a surprise
component.
 It is the surprise component that affects a
stock’s price and, therefore, its return.
 This is very obvious when we watch how stock
prices move when an unexpected
announcement is made or earnings are
different than anticipated
11.7 Risk: Systematic
 Risk factors that affect a large number of
assets
 Also known as non-diversifiable risk or market
risk
 Includes such things as changes in GDP,
inflation, interest rates, etc.
Risk: Unsystematic
 Risk factors that affect a limited number of
assets
 Also known as unique risk and asset-specific
risk
 Includes such things as labor strikes, part
shortages, etc.
Returns
 Total Return = expected return + unexpected
return
 Unexpected return = systematic portion +
unsystematic portion
 Therefore, total return can be expressed as
follows:
 Total Return = expected return + systematic
portion + unsystematic portion
11.8 Diversification and Portfolio Risk
 Diversification can substantially reduce the
variability of returns without an equivalent
reduction in expected returns.
 This reduction in risk arises because worse
than expected returns from one asset are offset
by better than expected returns from another.
 However, there is a minimum level of risk that
cannot be diversified away, and that is the
systematic portion.
Portfolio Risk and Number of Stocks
In a large portfolio the variance terms are effectively
s diversified away, but the covariance terms are not.
Diversifiable Risk;
Nonsystematic Risk;
Firm Specific Risk;
Unique Risk
Portfolio risk
Nondiversifiable risk;
Systematic Risk;
Market Risk
n
Diversifiable Risk
 The risk that can be eliminated by combining
assets into a portfolio
 Often considered the same as unsystematic,
unique, or asset-specific risk
 If we hold only one asset, or assets in the same
industry, then we are exposing ourselves to
risk that we could diversify away.
Total Risk
 Total risk = systematic risk + unsystematic risk
 The standard deviation of returns is a measure
of total risk.
 For well-diversified portfolios, unsystematic
risk is very small.
 Consequently, the total risk for a diversified
portfolio is essentially equivalent to the
systematic risk.
11.9 Market Equilibrium
return
rf
sP
With the capital allocation line identified, all investors choose a
point along the line—some combination of the risk-free asset
and the market portfolio M. In a world with homogeneous
expectations, M is the same for all investors.
Market Equilibrium
return
100%
stocks
Balanced
fund
rf
100%
bonds
s
Just where the investor chooses along the Capital Market
Line depends on his risk tolerance. The big point is that
all investors have the same CML.
Risk When Holding the Market Portfolio
 Researchers have shown that the best measure
of the risk of a security in a large portfolio is
the beta (b)of the security.
 Beta measures the responsiveness of a
security to movements in the market portfolio
(i.e., systematic risk).
Estimating b with Regression
Security Returns
Slope = bi
Return on
market %
Ri = a i + biRm + ei
The Formula for Beta
Clearly, your estimate of beta will

depend upon your choice of a proxy
for the market portfolio.
11.10 Risk and Return (CAPM)
 Expected Return on the Market:
• Expected return on an individual security:
Market Risk Premium

This applies to individual securities held within well-
diversified portfolios.
Expected Return on a Security
 This formula is called the Capital Asset
Pricing Model (CAPM):
Expected
Risk- Beta of the Market risk
return on = + ×
free rate security premium
a security
• Assume bi = 0, then the expected return is RF.

• Assume bi = 1, then
Relationship Between Risk & Return
Expected return
1.0 b
Relationship Between Risk & Return
Expected
return
1.5 b
Chapter 12
Risk, Cost of Capital, and Capital Budgeting
 Know how to determine a firm’s cost of equity
capital
 Understand the impact of beta in determining
the firm’s cost of equity capital
 Know how to determine the firm’s overall cost
of capital
Chapter Outline
12.1 The Cost of Equity Capital
12.2 Estimation of Beta
12.3 Determinants of Beta
12.4 Extensions of the Basic Model
12.5 Estimating Eastman Chemical’s Cost of
Capital
Where Do We Stand?
 Earlier chapters on capital budgeting
focused on the appropriate size and
timing of cash flows.
 This chapter discusses the appropriate
discount rate when cash flows are risky.
12.1 The Cost of Equity Capital
Shareholder
Firm with invests in
Pay cash dividend financial
excess cash
asset
A firm with excess cash can either pay a
dividend or make a capital investment
Shareholder’s
Invest in project Terminal
Value
Because stockholders can reinvest the dividend in risky financial assets, the
expected return on a capital-budgeting project should be at least as great as the
expected return on a financial asset of comparable risk.
The Cost of Equity Capital
 From the firm’s perspective, the expected
return is the Cost of Equity Capital:
• To estimate a firm’s cost of equity capital, we need

to know three things:
1. The risk-free rate, RF
2. The market risk premium,
3. The company beta,

Example
 Suppose the stock of Stansfield Enterprises, a
publisher of PowerPoint presentations, has a beta
of 2.5. The firm is 100 percent equity financed.
 Assume a risk-free rate of 5 percent and a market
risk premium of 10 percent.
 What is the appropriate discount rate for an
expansion of this firm?
Example
Suppose Stansfield Enterprises is evaluating the following
independent projects. Each costs $100 and lasts one year.
Project Project b Project’s IRR NPV at
Estimated Cash 30%
Flows Next
Year
A 2.5 $150 50% $15.38
B 2.5 $130 30% $0
C 2.5 $110 10% -$15.38
Using the SML
IRR
Project
Good A
project
30% B
C Bad project
5%
Firm’s risk (beta)
2.5
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects whose
IRRs fall short of the cost of capital.
Market Portfolio - Portfolio of all assets in the

economy. In practice, a broad stock market
index, such as the S&P Composite, is used to
represent the market.
Beta - Sensitivity of a stock’s return to the return

on the market portfolio.
• Problems
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.
• Solutions
– Problems 1 and 2 can be moderated by more sophisticated statistical
techniques.
– Problem 3 can be lessened by adjusting for changes in business and
financial risk.
– Look at average beta estimates of comparable firms in the industry.
Stability of Beta
 Most analysts argue that betas are generally
stable for firms remaining in the same
industry.
 That’s not to say that a firm’s beta can’t
change.
 Changes in product line
 Changes in technology
 Deregulation
 Changes in financial leverage
Using an Industry Beta
 It is frequently argued that one can better estimate a
firm’s beta by involving the whole industry.
 If you believe that the operations of the firm are
similar to the operations of the rest of the industry,
you should use the industry beta.
 If you believe that the operations of the firm are
fundamentally different from the operations of the
rest of the industry, you should use the firm’s beta.
 Don’t forget about adjustments for financial
leverage.
12.3 Determinants of Beta
 Business Risk
 Cyclicality of Revenues
 Operating Leverage
 Financial Risk
 Financial Leverage
Cyclicality of Revenues
 Highly cyclical stocks have higher betas.
 Empirical evidence suggests that retailers and
automotive firms fluctuate with the business cycle.
 Transportation firms and utilities are less dependent
upon the business cycle.
 Note that cyclicality is not the same as
variability—stocks with high standard deviations
need not have high betas.
 Movie studios have revenues that are variable,
depending upon whether they produce “hits” or “flops,”
but their revenues may not especially dependent upon
the business cycle.
Operating Leverage
 The degree of operating leverage measures how
sensitive a firm (or project) is to its fixed costs.
 Operating leverage increases as fixed costs rise
and variable costs fall.
 Operating leverage magnifies the effect of
cyclicality on beta.
 The degree of operating leverage is given by:
DOL = D EBIT Sales

×
EBIT D Sales
Operating Leverage
D EBIT
Total
$ costs
Fixed costs
D Sales
Fixed costs
Sales
Operating leverage increases as fixed costs rise

and variable costs fall.
Financial Leverage and Beta
 Operating leverage refers to the sensitivity to the
firm’s fixed costs of production.
 Financial leverage is the sensitivity to a firm’s
fixed costs of financing.
 The relationship between the betas of the firm’s
debt, equity, and assets is given by:
bAsset = Debt × bDebt + Equity × bEquity

Debt + Equity Debt + Equity
• Financial leverage always increases the equity beta relative
to the asset beta.
Example
Consider Grand Sport, Inc., which is currently all-equity
financed and has a beta of 0.90.
The firm has decided to lever up to a capital structure of
1 part debt to 1 part equity.
Since the firm will remain in the same industry, its asset
beta should remain 0.90.
However, assuming a zero beta for its debt, its equity
beta would become twice as large:
1
bAsset = 0.90 = × bEquity
1+1
bEquity = 2 × 0.90 = 1.80
12.4 Extensions of the Basic Model
 The Firm versus the Project
 The Cost of Capital with Debt
The Firm versus the Project
 Any project’s cost of capital depends on
the use to which the capital is being
put—not the source.
 Therefore, it depends on the risk of the
project and not the risk of the company.
Capital Budgeting & Project Risk
Project IRR
The SML can tell us why:

Incorrectly accepted
negative NPV projects
Hurdle RF  βFIRM ( R M  RF )
rate
Incorrectly rejected
rf positive NPV projects
Firm’s risk (beta)
bFIRM
A firm that uses one discount rate for all projects may over time
increase the risk of the firm while decreasing its value.
Suppose the Conglomerate Company has a cost of capital, based on
the CAPM, of 17%. The risk-free rate is 4%, the market risk
premium is 10%, and the firm’s beta is 1.3.
17% = 4% + 1.3 × 10%
This is a breakdown of the company’s investment projects:
1/3 Automotive Retailer b = 2.0
1/3 Computer Hard Drive Manufacturer b = 1.3
1/3 Electric Utility b = 0.6
average b of assets = 1.3
When evaluating a new electrical generation investment,
which cost of capital should be used?
SML
24%
Project IRR
Investments in hard
drives or auto retailing
17%
should have higher
10% discount rates.
Project’s risk (b)

0.6 1.3 2.0
r = 4% + 0.6×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investment
in electrical generation, given the unique risk of the project.
The Cost of Capital with Debt
 The Weighted Average Cost of Capital is given by:
Equity Debt
rWACC = × rEquity + × rDebt ×(1 – TC)
Equity + Debt Equity + Debt
S B
rWACC = × rS + × rB ×(1 – TC)
S+B S+B
• Because interest expense is tax-deductible, we

multiply the last term by (1 – TC).
Example: International Paper
 First, we estimate the cost of equity and
the cost of debt.
 We estimate an equity beta to estimate the
cost of equity.
 We can often estimate the cost of debt by
observing the YTM of the firm’s debt.
 Second, we determine the WACC by
weighting these two costs appropriately.
 The industry average beta is 0.82, the
risk free rate is 3%, and the market risk
premium is 8.4%.
 Thus, the cost of equity capital is:
rS = RF + bi × ( RM – RF)
= 3% + 0.82×8.4%
= 9.89%
 The yield on the company’s debt is 8%,
and the firm has a 37% marginal tax rate.
 The debt to value ratio is 32%
S B
rWACC = × rS + × rB ×(1 – TC)
S+B S+B
= 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37)
= 8.34%
8.34 percent is International’s cost of capital. It should be used
to discount any project where one believes that the project’s
risk is equal to the risk of the firm as a whole and the project
has the same leverage as the firm as a whole.
Chapter 13
Corporate Financing Decisions and Efficient
Capital Markets
 Understand the importance of capital market
efficiency
 Be able to define the forms of efficiency
 Know the various empirical tests of market
efficiency
 Understand the implications of efficiency for
corporate finance managers
Chapter Outline
13.1 Can Financing Decisions Create Value?
13.2 A Description of Efficient Capital Markets
13.3 The Different Types of Efficiency
13.4 The Evidence
13.5 The Behavioral Challenge to Market Efficiency
13.6 Empirical Challenges to Market Efficiency
13.7 Reviewing the Differences
13.8 Implications for Corporate Finance
13.1 Can Financing Decisions Create Value?
 Earlier parts of the book show how to evaluate
investment projects according to the NPV criterion.
 The next four chapters concern financing decisions,
such as:
 How much debt and equity to sell
 When to sell debt and equity
 When (or if) to pay dividends
 We can use NPV to evaluate financing decisions.
Creating Value through Financing
1. Fool Investors
 Empirical evidence suggests that it is hard to fool
investors consistently.
2. Reduce Costs or Increase Subsidies
 Certain forms of financing have tax advantages or
carry other subsidies.
3. Create a New Security
 Sometimes a firm can find a previously-unsatisfied
clientele and issue new securities at favorable prices.
 In the long-run, this value creation is relatively small.
13.2 A Description of Efficient Capital Markets
 An efficient capital market is one in which stock
prices fully reflect available information.
 The EMH has implications for investors and firms.
 Since information is reflected in security prices
quickly, knowing information when it is released does
an investor little good.
 Firms should expect to receive the fair value for
securities that they sell. Firms cannot profit from
fooling investors in an efficient market.
Foundations of Market Efficiency
 Investor Rationality
 Independence of events
 Arbitrage
Stock Price Reactions
Stock
Price Overreaction to “good
news” with reversion
Delayed
response to
“good news”
Efficient market
response to “good news”
-30 -20 -10 0 +10 +20 +30

Days before (-) and after (+) announcement
Stock Price Reactions
Efficient market
Stock Delayed
response to “bad news”
Price response to
“bad news”
-30 -20 -10 0 +10 +20 +30

Overreaction to “bad news” with Days before (-) and after (+)
reversion announcement
13.3 The Different Types of Efficiency
 Weak Form
 Security prices reflect all historical information.
 Semistrong Form
 Security prices reflect all publicly available
information.
 Strong Form
 Security prices reflect all information—public
and private.
Weak Form Market Efficiency
 Security prices reflect all information
found in past prices and volume.
 If the weak form of market efficiency
holds, then technical analysis is of no
value.
 Since stock prices only respond to new
information, which by definition arrives
randomly, stock prices are said to follow a
random walk.
Why Technical Analysis Fails
Investor behavior tends to eliminate any profit
opportunity associated with stock price patterns.
Stock Price
If it were possible to make

Sell
big money simply by
Sell finding “the pattern” in the
stock price movements,
Buy everyone would do it, and
the profits would be
Buy
competed away.
Time
Semistrong Form Market Efficiency
 Security prices reflect all publicly
available information.
 Publicly available information includes:
 Historical price and volume information
 Published accounting statements
 Information found in annual reports
Strong Form Market Efficiency
 Security prices reflect all information—
public and private.
 Strong form efficiency incorporates
weak and semistrong form efficiency.
 Strong form efficiency says that
anything pertinent to the stock and
known to at least one investor is already
incorporated into the security’s price.
Information Sets
All information
relevant to a stock
Information set
of publicly available
information
Information
set of
past prices
What the EMH Does and Does NOT Say
 Investors can throw darts to select stocks.
 This is almost, but not quite, true.
 An investor must still decide how risky a portfolio he
wants based on risk aversion and expected return.
 Prices are random or uncaused.
 Prices reflect information.
 The price CHANGE is driven by new information,
which by definition arrives randomly.
 Therefore, financial managers cannot “time” stock and
bond sales.
13.4 The Evidence
 The record on the EMH is extensive, and, in large
measure, it is reassuring to advocates of the
efficiency of markets.
 Studies fall into three broad categories:
1. Are changes in stock prices random? Are there
profitable “trading rules?”
2. Event studies: does the market quickly and accurately
respond to new information?
3. The record of professionally managed investment
firms.
Are Changes in Stock Prices Random?
 Can we really tell?
 Many psychologists and statisticians believe that most
people want to see patterns even when faced with pure
randomness.
 People claiming to see patterns in stock price
movements are probably seeing optical illusions.
 A matter of degree
 Even if we can spot patterns, we need to have returns
that beat our transactions costs.
 Random stock price changes support weak form
efficiency.
What Pattern Do You See?
Randomly Selected Numbers
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1 3 5 7 9 11 13 15 17 19 21 23 25
Event Studies
 Event Studies are one type of test of the semistrong
form of market efficiency.
 Recall, this form of the EMH implies that prices should
reflect all publicly available information.
 To test this, event studies examine prices and returns
over time—particularly around the arrival of new
information.
 Test for evidence of underreaction, overreaction,
early reaction, or delayed reaction around the event.
Event Studies
 Returns are adjusted to determine if they are
abnormal by taking into account what the rest of the
market did that day.
 The Abnormal Return on a given stock for a
particular day can be calculated by subtracting the
market’s return on the same day (RM) from the actual
return (R) on the stock for that day:
AR= R – RM
 The abnormal return can be calculated using the
Market Model approach:
AR= R – (a + bRM)
Event Studies: Dividend Omissions
Cumulative Abnormal Returns for Companies Announcing
Cumulative abnormal returns
Dividend Omissions
0.146 0.108
(%)
0.032 0
-0.244
-8 -6 -4
-0.72 -2 -0.483 0 2 4 6 8
-1
-2
Efficient market
-3
-3.619
response to “bad news”
-4
-4.563-4.747-4.685-4.49
-5 -5.015 -4.898
-5.183
-5.411
-6
Days relative to announcement of dividend omission

Event Study Results
 Over the years, event study methodology has been
applied to a large number of events including:
 Dividend increases and decreases
 Earnings announcements
 Mergers
 Capital Spending
 New Issues of Stock
 The studies generally support the view that the
market is semistrong form efficient.
 Studies suggest that markets may even have some
foresight into the future, i.e., news tends to leak out in
advance of public announcements.
The Record of Mutual Funds
 If the market is semistrong form efficient, then
no matter what publicly available information
mutual fund managers rely on to pick stocks,
their average returns should be the same as those
of the average investor in the market as a whole.
 We can test efficiency by comparing the
performance of professionally managed mutual
funds with the performance of a market index.
The Record of Mutual Funds
All funds Small- Other- Growth Income Growth and Maximum Sector
company aggressive income capital gains
-1.06%
growth growth -0.39% -0.51%
-2.13% -2.17% -2.29%
-5.41%
-8.45%
Taken from Lubos Pastor and Robert F. Stambaugh, “Mutual Fund Performance and Seemingly Unrelated Assets,” Journal
of Financial Exonomics, 63 (2002).
The Strong Form of the EMH
 One group of studies of strong form
market efficiency investigates insider
trading.
 A number of studies support the view
that insider trading is abnormally
profitable.
 Thus, strong form efficiency does not
seem to be substantiated by the evidence.
13.5 The Behavioral Challenge
 Rationality
 People are not always rational.
 Many investors fail to diversify, trade too much,
and seem to try to maximize taxes by selling
winners and holding losers.
The Behavioral Challenge
 Independent Deviations from Rationality
 Psychologists argue that people deviate from
rationality in predictable ways:
 Representativeness: drawing conclusions from too
little data
 This can lead to bubbles in security prices.
 Conservativism: people are too slow in adjusting their
beliefs to new information.
 Security prices seem to respond too slowly to earnings
surprises.
The Behavioral Challenge
 Arbitrage
 Suppose that your superior, rational, analysis shows that
company ABC is overpriced.
 Arbitrage would suggest that you should short the shares.
 After the rest of the investors come to their senses, you
make money because you were smart enough to “sell high
and buy low.”
 But what if the rest of the investment community
doesn’t come to their senses in time for you to cover
your short position?
 This makes arbitrage risky.
13.6 Empirical Challenges
 Limits to Arbitrage
 “Markets can stay irrational longer than you can stay
insolvent.” John Maynard Keynes
 Earnings Surprises
 Stock prices adjust slowly to earnings announcements.
 Behavioralists claim that investors exhibit conservatism.
 Size
 Small cap stocks seem to outperform large cap stocks.
 Value versus Growth
 High book value-to-stock price stocks and/or high E/P
stocks outperform growth stocks.
Empirical Challenges
 Crashes
 On October 19, 1987, the stock market dropped
between 20 and 25 percent on a Monday
following a weekend during which little
surprising news was released.
 A drop of this magnitude for no apparent reason
is inconsistent with market efficiency.
 Bubbles
 Consider the tech stock bubble of the late 1990s.
13.7 Reviewing the Differences
 Financial Economists have sorted themselves
into three camps:
1. Market efficiency
2. Behavioral finance
3. Those that admit that they don’t know
 This is perhaps the most contentious area in
the field.
13.8 Implications for Corporate Finance
 Because information is reflected in security
prices quickly, investors should only expect to
obtain a normal rate of return.
 Awareness of information when it is released does an
investor little good. The price adjusts before the investor
has time to act on it.
 Firms should expect to receive the fair value for
securities that they sell.
 Fair means that the price they receive for the securities
they issue is the present value.
 Thus, valuable financing opportunities that arise from
fooling investors are unavailable in efficient markets.
Implications for Corporate Finance
 The EMH has three implications for corporate
finance:
1. The price of a company’s stock cannot be affected by a
change in accounting.
2. Financial managers cannot “time” issues of stocks and
bonds using publicly available information.
3. A firm can sell as many shares of stocks or bonds as it
desires without depressing prices.
 There is conflicting empirical evidence on all three
points.
Why Doesn’t Everybody Believe?
 There are optical illusions, mirages, and apparent
patterns in charts of stock market returns.
 The truth is less interesting.
 There is some evidence against market efficiency:
 Seasonality
 Small versus large stocks
 Value versus growth stocks
 The tests of market efficiency are weak.
Chapter 14
Capital Structure: Basic Concepts
 Understand the effect of financial leverage
(i.e., capital structure) on firm earnings
 Understand homemade leverage
 Understand capital structure theories with and
without taxes
 Be able to compute the value of the unlevered
and levered firm
Chapter Outline
14.1 The Capital Structure Question and The Pie
Theory
14.2 Maximizing Firm Value versus Maximizing
Stockholder Interests
14.3 Financial Leverage and Firm Value: An
Example
14.4 Modigliani and Miller: Proposition II (No
Taxes)
14.5 Taxes
14.1 Capital Structure and the Pie
 The value of a firm is defined to be the sum of the
value of the firm’s debt and the firm’s equity.
V=B+S
• If the goal of the firm’s

management is to make the S B
firm as valuable as possible,
then the firm should pick the
debt-equity ratio that makes
the pie as big as possible.
Value of the Firm
Stockholder Interests
There are two important questions:
1.Why should the stockholders care about maximizing
firm value? Perhaps they should be interested in
strategies that maximize shareholder value.
2.What is the ratio of debt-to-equity that maximizes the
shareholder’s value?
As it turns out, changes in capital structure

benefit the stockholders if and only if the value
of the firm increases.
14.3 Financial Leverage, EPS, and ROE
Consider an all-equity firm that is considering going into
debt. (Maybe some of the original shareholders want to cash
out.)
Current Proposed
Assets $20,000 $20,000
Debt $0 $8,000
Equity $20,000 $12,000
Debt/Equity ratio 0.00 2/3
Interest rate n/a 8%
Shares outstanding 400 240
Share price $50 $50
EPS and ROE Under Current Structure
Recession Expected Expansion
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
Net income $1,000 $2,000 $3,000
EPS $2.50 $5.00 $7.50
ROA 5% 10% 15%
ROE 5% 10% 15%
Current Shares Outstanding = 400 shares
EPS and ROE Under Proposed Structure
EBIT $1,000 $2,000 $3,000
Interest 640 640 640
Net income $360 $1,360 $2,360
EPS $1.50 $5.67 $9.83
ROA 1.8% 6.8% 11.8%
ROE 3.0% 11.3% 19.7%
Proposed Shares Outstanding = 240 shares
Financial Leverage and EPS
12.00
10.00 Debt
8.00 No Debt
6.00 Break-even Advantage

EPS
point to debt
4.00
2.00
0.00
1,000 2,000 3,000
(2.00) Disadvantage EBIT in dollars, no taxes
to debt
Assumptions of the M&M Model
 Homogeneous Expectations
 Homogeneous Business Risk Classes
 Perpetual Cash Flows
 Perfect Capital Markets:
 Perfect competition
 Firms and investors can borrow/lend at the same rate
 Equal access to all relevant information
 No transaction costs
 No taxes
Homemade Leverage: An Example
EPS of Unlevered Firm $2.50 $5.00 $7.50
Earnings for 40 shares $100 $200 $300
Less interest on $800 (8%) $64 $64 $64
Net Profits $36 $136 $236
ROE (Net Profits / $1,200) 3.0% 11.3% 19.7%
We are buying 40 shares of a $50 stock, using $800 in margin.
We get the same ROE as if we bought into a levered firm.
Our personal debt-equity ratio is:

Homemade (Un)Leverage: An Example
EPS of Levered Firm $1.50 $5.67 $9.83
Earnings for 24 shares $36 $136 $236
Plus interest on $800 (8%) $64 $64 $64
Net Profits $100 $200 $300
ROE (Net Profits / $2,000) 5% 10% 15%
Buying 24 shares of an otherwise identical levered firm along
with some of the firm’s debt gets us to the ROE of the unlevered
firm.
This is the fundamental insight of M&M
MM Proposition I (No Taxes)
 We can create a levered or unlevered position
by adjusting the trading in our own account.
 This homemade leverage suggests that capital
structure is irrelevant in determining the value
of the firm:
VL = VU
14.4 MM Proposition II (No Taxes)
 Proposition II
 Leverage increases the risk and return to stockholders
Rs = R0 + (B / SL) (R0 - RB)
RB is the interest rate (cost of debt)
Rs is the return on (levered) equity (cost of equity)
R0 is the return on unlevered equity (cost of capital)
B is the value of debt
SL is the value of levered equity
MM Proposition II (No Taxes)
The derivation is straightforward:
MM Proposition II (No Taxes)
Cost of capital: R (%)
R0
RB RB
Debt-to-equity Ratio
14.5 MM Propositions I & II (With Taxes)
 Proposition I (with Corporate Taxes)
 Firm value increases with leverage
VL = VU + TC B
 Proposition II (with Corporate Taxes)
 Some of the increase in equity risk and return is
offset by the interest tax shield
RS = R0 + (B/S)×(1-TC)×(R0 - RB)
RB is the interest rate (cost of debt)
RS is the return on equity (cost of equity)
R0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity
MM Proposition I (With Taxes)
The present value of this stream of cash flows is VL
The present value of the first term is VU

The present value of the second term is TCB
MM Proposition II (With Taxes)
Start with M&M Proposition I with taxes:
Since
The cash flows from each side of the balance sheet must equal:
Divide both sides by S
Which quickly reduces to

The Effect of Financial Leverage
Cost of capital: R
(%)
R0
RB
Debt-to-equity
ratio (B/S)
Total Cash Flow to Investors
EBIT $1,000 $2,000 $3,000
Interest 0 0 0
All Equity
EBT $1,000 $2,000 $3,000

Taxes (Tc = 35%) $350 $700 $1,050
Total Cash Flow to S/H $650 $1,300 $1,950

EBIT $1,000 $2,000 $3,000
Interest ($800 @ 8% ) 640 640 640
Levered
EBT $360 $1,360 $2,360

Taxes (Tc = 35%) $126 $476 $826
Total Cash Flow $234+640 $884+$640 $1,534+$640
(to both S/H & B/H): $874 $1,524 $2,174
EBIT(1-Tc)+TCRBB $650+$224 $1,300+$224 $1,950+$224
$874 $1,524 $2,174
Total Cash Flow to Investors
All-equity firm Levered firm
S G S G
The levered firm pays less in taxes than does the all-equity firm.
Thus, the sum of the debt plus the equity of the levered firm is
greater than the equity of the unlevered firm.
This is how cutting the pie differently can make the pie “larger.”
-the government takes a smaller slice of the pie!
Summary: No Taxes
 In a world of no taxes, the value of the firm is unaffected by
capital structure.
 This is M&M Proposition I:
VL = VU
 Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
 In a world of no taxes, M&M Proposition II states that
leverage increases the risk and return to stockholders.
Summary: Taxes
 In a world of taxes, but no bankruptcy costs, the value of the
firm increases with leverage.
 This is M&M Proposition I:
VL = VU + TC B
 Proposition I holds because shareholders can achieve any
pattern of payouts they desire with homemade leverage.
 In a world of taxes, M&M Proposition II states that leverage
increases the risk and return to stockholders.
Chapter 15
Capital Structure: Limits to the Use of Debt
 Define the costs associated with bankruptcy
 Understand the theories that address the level of debt
a firm carries
 Tradeoff
 Signaling
 Agency Cost
 Pecking Order
 Know real world factors that affect the debt to equity
ratio
Chapter Outline
15.1 Costs of Financial Distress
15.2 Can Costs of Debt Be Reduced?
15.3 Integration of Tax Effects and Financial Distress Costs
15.4 Signaling
15.5 Shirking, Perquisites, and Bad Investments: A Note on Agency
Cost of Equity
15.6 The Pecking-Order Theory
15.7 Growth and the Debt-Equity Ratio
15.8 How Firms Establish Capital Structure
15.9 A Quick Look at the Bankruptcy Process
15.1 Costs of Financial Distress
 Direct Costs
 Legal and administrative costs
 Indirect Costs
 Impaired ability to conduct business (e.g., lost
sales)
 Agency Costs
 Selfish Strategy 1: Incentive to take large risks
 Selfish Strategy 2: Incentive toward underinvestment
 Selfish Strategy 3: Milking the property
Example: Company in Distress
Assets BV MV Liabilities BV MV
Cash $200 $200 LT bonds $300 $200
Fixed Asset $400 $0 Equity $300 $0
Total $600 $200 Total $600 $200
What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get

nothing.
Selfish Strategy 1: Take Risks
The Gamble Probability Payoff
Win Big 10% $1,000
Lose Big 90% $0
Cost of investment is $200 (all the firm’s cash)
Required return is 50%
Expected CF from the Gamble = $1000 × 0.10 + $0 =
$100 $100
NPV = –$200 +
(1.50)
NPV = –$133
Selfish Strategy 1: Take Risks
 Expected CF from the Gamble
 To Bondholders = $300 × 0.10 + $0 = $30
 To Stockholders = ($1000 – $300) × 0.10 + $0 = $70
 PV of Bonds Without the Gamble = $200
 PV of Stocks Without the Gamble = $0
$30
• PV of Bonds With the Gamble: $20 =
(1.50)
$70
• PV of Stocks With the Gamble: $47 =
(1.50)
Selfish Strategy 2: Underinvestment
 Consider a government-sponsored project that
guarantees $350 in one period.
 Cost of investment is $300 (the firm only has $200
now), so the stockholders will have to supply an
additional $100 to finance the project.
 Required return is 10%.
$350
NPV = –$300 +
(1.10)
NPV = $18.18
Should we accept or reject?

Selfish Strategy 2: Underinvestment
Expected CF from the government sponsored project:
To Bondholder = $300
To Stockholder = ($350 – $300) = $50
PV of Bonds Without the Project = $200

PV of Stocks Without the Project = $0
$300
PV of Bonds With the Project: $272.73 =
(1.10)
$50
PV of Stocks With the Project: – $54.55 = – $100
(1.10)
Selfish Strategy 3: Milking the Property
 Liquidating dividends
 Suppose our firm paid out a $200 dividend to the
shareholders. This leaves the firm insolvent, with
nothing for the bondholders, but plenty for the
former shareholders.
 Such tactics often violate bond indentures.
 Increase perquisites to shareholders and/or
management
15.2 Can Costs of Debt Be Reduced?
 Protective Covenants
 Debt Consolidation:
 If we minimize the number of parties, contracting
costs fall.
15.3 Tax Effects and Financial Distress
 There is a trade-off between the tax
advantage of debt and the costs of financial
distress.
 It is difficult to express this with a precise
and rigorous formula.
Tax Effects and Financial Distress
Value of firm (V) Value of firm under
MM with corporate
Present value of tax taxes and debt
shield on debt
VL = VU + TCB
Maximum Present value of

firm value financial distress costs
V = Actual value of firm
VU = Value of firm with no debt
0 Debt (B)
B*
Optimal amount of debt
The Pie Model Revisited
 Taxes and bankruptcy costs can be viewed as just
another claim on the cash flows of the firm.
 Let G and L stand for payments to the government
and bankruptcy lawyers, respectively.
 VT = S + B + G + L S
B
L G
 The essence of the M&M intuition is that VT depends on the

cash flow of the firm; capital structure just slices the pie.
15.4 Signaling
 The firm’s capital structure is optimized where the
marginal subsidy to debt equals the marginal cost.
 Investors view debt as a signal of firm value.
 Firms with low anticipated profits will take on a low level
of debt.
 Firms with high anticipated profits will take on a high
level of debt.
 A manager that takes on more debt than is optimal in
order to fool investors will pay the cost in the long
run.
15.5 The Agency Cost of Equity
 An individual will work harder for a firm if he is one of the
owners than if he is one of the “hired help.”
 While managers may have motive to partake in perquisites,
they also need opportunity. Free cash flow provides this
opportunity.
 The free cash flow hypothesis says that an increase in
dividends should benefit the stockholders by reducing the
ability of managers to pursue wasteful activities.
 The free cash flow hypothesis also argues that an increase in
debt will reduce the ability of managers to pursue wasteful
activities more effectively than dividend increases.
15.6 The Pecking-Order Theory
 Theory stating that firms prefer to issue debt rather
than equity if internal financing is insufficient.
 Rule 1
 Use internal financing first.
 Rule 2
 Issue debt next, new equity last.
 The pecking-order theory is at odds with the tradeoff

theory:
 There is no target D/E ratio.
 Profitable firms use less debt.
 Companies like financial slack.
15.7 Growth and the Debt-Equity Ratio
 Growth implies significant equity financing,
even in a world with low bankruptcy costs.
 Thus, high-growth firms will have lower
debt ratios than low-growth firms.
 Growth is an essential feature of the real
world. As a result, 100% debt financing is
sub-optimal.
15.8 How Firms Establish Capital Structure
 Most corporations have low Debt-Asset ratios.
 Changes in financial leverage affect firm value.
 Stock price increases with increases in leverage and
vice-versa; this is consistent with M&M with taxes.
 Another interpretation is that firms signal good news
when they lever up.
 There are differences in capital structure across
industries.
 There is evidence that firms behave as if they had a
target Debt-Equity ratio.
Factors in Target D/E Ratio
 Taxes
 Since interest is tax deductible, highly profitable firms
should use more debt (i.e., greater tax benefit).
 Types of Assets
 The costs of financial distress depend on the types of
assets the firm has.
 Uncertainty of Operating Income
 Even without debt, firms with uncertain operating income
have a high probability of experiencing financial distress.
 Pecking Order and Financial Slack
 Theory stating that firms prefer to issue debt rather than
equity if internal financing is insufficient.
15.9 The Bankruptcy Process
 Business failure – business has terminated
with a loss to creditors
 Legal bankruptcy – petition federal court for
bankruptcy
 Technical insolvency – firm is unable to meet
debt obligations
 Accounting insolvency – book value of equity
is negative
The Bankruptcy Process
 Liquidation
 Chapter 7 of the Federal Bankruptcy Reform Act
of 1978
 Trustee takes over assets, sells them, and
distributes the proceeds according to the absolute
priority rule
 Reorganization
 Chapter 11 of the Federal Bankruptcy Reform Act
of 1978
 Restructure the corporation with a provision to
repay creditors
Chapter 16
Dividends and Other Payouts
 Understand dividend types and how they are
paid
 Understand the issues surrounding dividend
policy decisions
 Understand why share repurchases are an
alternative to dividends
 Understand the difference between cash and
stock dividends
Chapter Outline
16.1 Different Types of Dividends
16.2 Standard Method of Cash Dividend Payment
16.3 The Benchmark Case: An Illustration of the Irrelevance of
Dividend Policy
16.4 Repurchase of Stock
16.5 Personal Taxes, Issuance Costs, and Dividends
16.6 Real World Factors Favoring a High Dividend Policy
16.7 The Clientele Effect: A Resolution of Real-World Factors?
16.8 What We Know and Do Not Know About Dividend Policy
16.9 Stock Dividends and Stock Splits
16.1 Different Types of Dividends
 Many companies pay a regular cash dividend.
 Public companies often pay quarterly.
 Sometimes firms will pay an extra cash dividend.
 The extreme case would be a liquidating dividend.
 Companies will often declare stock dividends.
 No cash leaves the firm.
 The firm increases the number of shares outstanding.
 Some companies declare a dividend in kind.
 Wrigley’s Gum sends a box of chewing gum.
 Dundee Crematoria offers shareholders discounted
cremations.
16.2 Standard Method of Cash Dividend
Cash Dividend - Payment of cash by the firm
to its shareholders.
Ex-Dividend Date - Date that determines

whether a stockholder is entitled to a dividend
payment; anyone holding stock immediately
before this date is entitled to a dividend.
Record Date – Date on which company

determines existing shareholders.
Procedure for Cash Dividend
25 Oct. 1 Nov. 2 Nov. 5 Nov. 7 Dec.
…
Declaration Cum- Ex- Record Payment

Date dividend dividend Date Date
Date Date
Declaration Date: The Board of Directors declares a payment

of dividends.
Cum-Dividend Date: Buyer of stock still receives the dividend.
Ex-Dividend Date: Seller of the stock retains the dividend.
Record Date: The corporation prepares a list of all individuals
believed to be stockholders as of 5 November.
Price Behavior
 In a perfect world, the stock price will fall by the
amount of the dividend on the ex-dividend date.
-t … -2 -1 0 +1 +2 …
$P
$P - div
The price drops Ex-
by the amount of dividend
the cash Date
dividend. Taxes complicate things a bit. Empirically, the
price drop is less than the dividend and occurs
within the first few minutes of the ex-date.
16.3 The Irrelevance of Dividend Policy
 A compelling case can be made that dividend
policy is irrelevant.
 Since investors do not need dividends to
convert shares to cash; they will not pay
higher prices for firms with higher dividends.
 In other words, dividend policy will have no
impact on the value of the firm because
investors can create whatever income stream
they prefer by using homemade dividends.
Homemade Dividends
 Bianchi Inc. is a $42 stock about to pay a $2 cash
dividend.
 Bob Investor owns 80 shares and prefers a $3 dividend.
 Bob’s homemade dividend strategy:
 Sell 2 shares ex-dividend
homemade dividends $3 Dividend
Cash from dividend $160 $240
Cash from selling stock $80 $0
Total Cash $240 $240
Value of Stock Holdings $40 × 78 = $39 × 80 =
$3,120 $3,120
Dividend Policy is Irrelevant
 In the above example, Bob Investor began with a
total wealth of $3,360:
 After a $3 dividend, his total wealth is still $3,360:
 After a $2 dividend and sale of 2 ex-dividend shares, his

total wealth is still $3,360:
Dividends and Investment Policy
 Firms should never forgo positive NPV
projects to increase a dividend (or to pay a
dividend for the first time).
 Recall that one of the assumptions underlying
the dividend-irrelevance argument is: “The
investment policy of the firm is set ahead of
time and is not altered by changes in dividend
policy.”
16.4 Repurchase of Stock
 Instead of declaring cash dividends, firms can
rid themselves of excess cash through buying
shares of their own stock.
 Recently, share repurchase has become an
important way of distributing earnings to
shareholders.
Stock Repurchase versus Dividend
Consider a firm that wishes to distribute $100,000 to its
shareholders.
Assets Liabilities & Equity
A.Original balance sheet
Cash $150,000 Debt 0
Other Assets 850,000 Equity 1,000,000
Value of Firm 1,000,000 Value of Firm 1,000,000
Shares outstanding = 100,000
Price per share= $1,000,000 /100,000 = $10
If they distribute the $100,000 as a cash dividend, the balance
sheet will look like this:
Assets Liabilities & Equity
B. After $1 per share cash dividend
Cash $50,000 Debt 0
Other Assets 850,000 Equity 900,000
Value of Firm 900,000 Value of Firm 900,000
Shares outstanding = 100,000
Price per share = $900,000/100,000 = $9
If they distribute the $100,000 through a stock repurchase, the
balance sheet will look like this:
Assets Liabilities& Equity
C. After stock repurchase
Cash $50,000 Debt 0
Other Assets 850,000 Equity 900,000
Value of Firm 900,000 Value of Firm 900,000
Shares outstanding= 90,000
Price pershare = $900,000 / 90,000 = $10
Share Repurchase
 Flexibility for shareholders
 Keeps stock price higher
 Good for insiders who hold stock options
 As an investment of the firm
 Tax benefits
16.5 Personal Taxes, Issuance Costs,
and Dividends
 To get the result that dividend policy is irrelevant,
we needed three assumptions:
 No taxes
 No transactions costs
 No uncertainty
 In the United States, both cash dividends and capital
gains are taxed at a maximum rate of 15 percent.
 Since capital gains can be deferred, the tax rate on
dividends is greater than the effective rate on capital
gains.
Firms without Sufficient Cash
Investment Bankers The direct costs of
stock issuance will
add to this effect.
Cash: stock issue

Stock
Firm
Holders
Cash: dividends
Taxes In a world of personal

taxes, firms should not
issue stock to pay a
Gov. dividend.
Firms with Sufficient Cash
 The above argument does not necessarily apply
to firms with excess cash.
 Consider a firm that has $1 million in cash after
selecting all available positive NPV projects.
 Select additional capital budgeting projects (by
assumption, these are negative NPV).
 Acquire other companies
 Purchase financial assets
 Repurchase shares
Taxes, Issuance Costs, and Dividends
 In the presence of personal taxes:
1. A firm should not issue stock to pay a dividend.
2. Managers have an incentive to seek alternative
uses for funds to reduce dividends.
3. Though personal taxes mitigate against the
payment of dividends, these taxes are not
sufficient to lead firms to eliminate all dividends.
16.6 Real-World Factors Favoring
High Dividends
 Desire for Current Income
 Behavioral Finance
 It forces investors to be disciplined.
 Tax Arbitrage
 Investors can create positions in high dividend
yield securities that avoid tax liabilities.
 Agency Costs
 High dividends reduce free cash flow.
16.7 The Clientele Effect
 Clienteles for various dividend payout policies
are likely to form in the following way:
Group Stock Type
High Tax Bracket Individuals Zero-to-Low payout

Low Tax Bracket Individuals Low-to-Medium payout
Tax-Free Institutions Medium payout
Corporations High payout
Once the clienteles have been satisfied, a corporation is
unlikely to create value by changing its dividend policy.
16.8 What We Know and Do Not Know
 Corporations “smooth” dividends.
 Dividends provide information to the market.
 Firms should follow a sensible dividend
policy:
 Don’t forgo positive NPV projects just to pay a
dividend.
 Avoid issuing stock to pay dividends.
 Consider share repurchase when there are few
better uses for the cash.
16.9 Stock Dividends
 Pay additional shares of stock instead of cash
 Increases the number of outstanding shares
 Small stock dividend

 Less than 20 to 25%
 If you own 100 shares and the company declared a
10% stock dividend, you would receive an
additional 10 shares.
 Large stock dividend – more than 20 to 25%
Stock Splits
 Stock splits – essentially the same as a stock
dividend except it is expressed as a ratio
 For example, a 2 for 1 stock split is the same as a
100% stock dividend.
 Stock price is reduced when the stock splits.
 Common explanation for split is to return price
to a “more desirable trading range.”
Chapter 17
Options and Corporate Finance
 Understand option terminology
 Be able to determine option payoffs and profits
 Understand the major determinants of option
prices
 Understand and apply put-call parity
 Be able to determine option prices using the
binomial and Black-Scholes models
Chapter Outline
17.1 Options
17.2 Call Options
17.3 Put Options
17.4 Selling Options
17.5 Option Quotes
17.6 Combinations of Options
17.7 Valuing Options
17.8 An Option Pricing Formula
17.9 Stocks and Bonds as Options
17.10 Options and Corporate Decisions: Some Applications
17.11 Investment in Real Projects and Options
17.1 Options
 An option gives the holder the right, but not the
obligation, to buy or sell a given quantity of an asset on
(or before) a given date, at prices agreed upon today.
 Exercising the Option
 The act of buying or selling the underlying asset
 Strike Price or Exercise Price
 Refers to the fixed price in the option contract at which the
holder can buy or sell the underlying asset.
 Expiry (Expiration Date)
 The maturity date of the option
Options
 European versus American options
 European options can be exercised only at expiry.
 American options can be exercised at any time up to expiry.
 In-the-Money
 Exercising the option would result in a positive payoff.
 At-the-Money
 Exercising the option would result in a zero payoff (i.e.,
exercise price equal to spot price).
 Out-of-the-Money
 Exercising the option would result in a negative payoff.
17.2 Call Options
 Call options gives the holder the right,
but not the obligation, to buy a given
quantity of some asset on or before
some time in the future, at prices
agreed upon today.
 When exercising a call option, you
“call in” the asset.
Call Option Pricing at Expiry
 At expiry, an American call option is worth
the same as a European option with the same
characteristics.
 If the call is in-the-money, it is worth ST – E.
 If the call is out-of-the-money, it is worthless:
C = Max[ST – E, 0]
Where
ST is the value of the stock at expiry (time T)
E is the exercise price.
C is the value of the call option at expiry
Call Option Payoffs
60
Option payoffs ($)
40
20
20 40 60 80 100 120
50
Stock price ($)
–20
–40 Exercise price = $50

Call Option Profits
60
Option payoffs ($)
40 Buy a call
20
10
20 40 50 60 80 100 120
–10 Stock price ($)
–20
Exercise price = $50; option premium = $10

–40 3EA Global Academy | Copyright © 2021 3EA Limited | All rights reserved.
17.3 Put Options
 Put options gives the holder the right,
but not the obligation, to sell a given
quantity of an asset on or before some
time in the future, at prices agreed
upon today.
 When exercising a put, you “put” the
asset to someone.
Put Option Pricing at Expiry
 At expiry, an American put option is
worth the same as a European option
with the same characteristics.
 If the put is in-the-money, it is worth
E – ST.
 If the put is out-of-the-money, it is
worthless.
P = Max[E – ST, 0]
Put Option Payoffs
60
Option payoffs ($)
50
40
20
0 Buy a put
0 20 40 60 80 100
50
Stock price ($)
–20

Put Option Profits
60
Option payoffs ($)
40
20
10
Stock price ($)
20 40 50 60 80 100
–10
Buy a put
–20
–40 Exercise price

3EA Global Academy = $50;
| Copyright option
© 2021 3EA Limited | All premium
rights reserved. = $10
Option Value
 Intrinsic Value
 Call: Max[ST – E, 0]
 Put: Max[E – ST , 0]
 Speculative Value
 The difference between the option premium and
the intrinsic value of the option.
Option Intrinsic + Speculative
=
Premium Value Value
17.4 Selling Options
 The seller (or writer) of an option has an
obligation.
 The seller receives the option premium in
exchange.
Call Option Payoffs
60
Option payoffs ($)
40
20
20 40 60 80 100 120
50
Stock price ($)
–20

Put Option Payoffs
40
Option payoffs ($)
20
Sell a put
0
0 20 40 60 80 100
50
Stock price ($)
–20

–50
Option Diagrams Revisited
Option payoffs ($)
40 Buy a call
Sell a call
10 Sell a put
Stock price ($)

Buy a call 40 50 60 100
–10 Buy a put
Exercise price = $50;

–40 Sell a call
option premium = $10
17.5 Option Quotes
--Call-- --Put--
Option/Strike Exp. Vol. Last Vol. Last
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
Option Quotes
This option has a strike price of $135;
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
a recent price for the stock is $138.25;
July is the expiration month.
Option Quotes
This makes a call option with this exercise price in-the-
money by $3.25 = $138¼ – $135.
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
Puts with this exercise price are out-of-the-money.
Option Quotes
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
On this day, 2,365 call options with this exercise price were
traded.
Option Quotes
The CALL option with a strike price of $135 is trading for $4.75.
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
Since the option is on 100 shares of stock, buying this option
would cost $475 plus commissions.
Option Quotes
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
On this day, 2,431 put options with this exercise price were
traded.
Option Quotes
The PUT option with a strike price of $135 is trading for $.8125.
--Call-- --Put--
IBM 130 Oct 364 15¼ 107 5¼
138¼ 130 Jan 112 19½ 420 9¼
138¼ 135 Jul 2365 4¾ 2431 13/16
138¼ 135 Aug 1231 9¼ 94 5½
138¼ 140 Jul 1826 1¾ 427 2¾
138¼ 140 Aug 2193 6½ 58 7½
Since the option is on 100 shares of stock, buying this
option would cost $81.25 plus commissions.
17.6 Combinations of Options
 Puts and calls can serve as the
building blocks for more complex
option contracts.
 If you understand this, you can
become a financial engineer,
tailoring the risk-return profile to
meet your client’s needs.
Protective Put Strategy (Payoffs)
Value at Protective Put payoffs
expiry
$50
Buy the
stock Buy a put with an exercise
price of $50
$0
Value of stock at
$50 expiry
Protective Put Strategy (Profits)
Value at Buy the stock at $40
expiry
$40 Protective Put
strategy has
downside protection
and upside potential
$0
-$10
$40 $50
Buy a put with exercise price of $50
for $10 Value of
stock at
-$40 expiry
Covered Call Strategy
Value at Buy the stock at $40
expiry
$10 Covered Call strategy

$0
Value of stock at expiry
$40 $50
Sell a call with exercise price
of $50 for $10
-$30
-$40
Long Straddle
Option payoffs ($)
40 Buy a call with exercise

price of $50 for $10
30
Stock price ($)

30 40 60 70
Buy a put with exercise
price of $50 for $10
–20
$50
A Long Straddle only makes money if the stock price moves
$20 away from
3EA Global $50.
Academy | Copyright © 2021 3EA Limited | All rights reserved.
Short Straddle
This Short Straddle only loses money if the stock
price moves $20 away from $50.
Option payoffs ($)
20
Sell a put with exercise price of
$50 for $10
Stock price ($)
30 40 60 70
$50
–30 Sell a call with an

exercise price of $50 for $10
–40 3EA Global Academy | Copyright © 2021 3EA Limited | All rights reserved.
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
E Portfolio payoff
Portfolio value today = c0 +
(1+ r)T
Option payoffs ($)
Call
25 bond
25 Stock price ($)

Consider the payoffs from holding a portfolio consisting of a call with a
strike price of $25 and a bond with a future value of $25.
Put-Call Parity
Portfolio payoff
Portfolio value today = p0 + S0
Option payoffs ($)
25
Stock price ($)

25
Consider the payoffs from holding a portfolio consisting of a
share of stock and a put with a $25 strike.
Put-Call Parity
Portfolio value today
Option payoffs ($)
Option payoffs ($)

Portfolio value today
E = p0 + S0
= c0 +
(1+ r)T
25 25
25 Stock price ($) Stock price ($)

25
Since these portfolios have identical payoffs, they must have the same
value today: hence Put-Call Parity: c0 + E/(1+r)T = p0 + S0
17.7 Valuing Options
 The last section  This section
concerned itself considers the
with the value of value of an option
an option at prior to the
expiry. expiration date.
 A much more
interesting
question.
American Call
Profit ST
Option payoffs ($)
Call
25
Market Value
Time value
Intrinsic value
ST
E
Out-of-the-money In-the-money
loss
C0 must fall within max (S0 – E, 0) < C0 < S0.
Option Value Determinants
Call Put
1. Stock price + –
2. Exercise price – +
3. Interest rate + –
4. Volatility in the stock price + +
5. Expiration date + +
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on these factors.
17.8 An Option Pricing Formula
 We will start with  Then we will
a binomial option graduate to the
pricing formula to normal
build our approximation to
intuition. the binomial for
some real-world
option valuation.
Binomial Option Pricing Model
Suppose a stock is worth $25 today and in one period will either
be worth 15% more or 15% less. S0= $25 today and in one year
S1is either $28.75 or $21.25. The risk-free rate is 5%. What is the
value of an at-the-money call option?
S0 S1
$28.75 = $25×(1.15)
$25
$21.25 = $25×(1 –.15)

1. A call option on this stock with exercise price of $25 will
have the following payoffs.
2. We can replicate the payoffs of the call option with a levered
position in the stock.
S0 S1 C1
$28.75 $3.75
$25
$21.25 $0
Borrow the present value of $21.25 today and buy 1 share. The net payoff for
this levered equity portfolio in one period is either $7.50 or $0. The levered
equity portfolio has twice the option’s payoff, so the portfolio is worth twice the
call option value.
S0 ( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50 $3.75
$25
$21.25 – $21.25 = $0 $0
The value today of the levered equity
portfolio is today’s value of one share
less the present value of a $21.25 debt:
$28.75 – $21.25 = $7.50 $3.75
$25
$21.25 – $21.25 = $0 $0
We can value the call option today
as half of the value of the levered
equity portfolio:
$28.75 – $21.25 = $7.50 $3.75
$25
$21.25 – $21.25 = $0 $0
If the interest rate is 5%, the call is worth:
C0 S0 ( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50 $3.75
$2.38 $25
$21.25 – $21.25 = $0 $0
The most important lesson (so far) from the
binomial option pricing model is:
the replicating portfolio intuition.

Many derivative securities can be valued by
valuing portfolios of primitive securities when
those portfolios have the same payoffs as the
derivative securities.
Delta
 This practice of the construction of a
riskless hedge is called delta hedging.
 The delta of a call option is positive.
 Recall from the example:
Swing of call
D
Swing of stock
• The delta of a put option is negative.
Delta
 Determining the Amount of Borrowing:
Value of a call = Stock price × Delta

– Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12
The Risk-Neutral Approach
S(U), V(U)
q
S(0), V(0)
1- q
S(D), V(D)
We could value the option, V(0), as the value of the

replicating portfolio. An equivalent method is risk-neutral
valuation:
S(U), V(U)
q
q is the risk-neutral
S(0), V(0) probability of an
“up” move.
1- q
S(0) is the value of the underlying S(D), V(D)
asset today.
S(U) and S(D) are the values of the asset in the next period
following an up move and a down move, respectively.
V(U) and V(D) are the values of the option in the next period
following an up move and a down move, respectively.
S(U), V(U)
q
S(0), V(0)
1- q
S(D), V(D)
 The key to finding q is to note that it is already impounded

into an observable security price: the value of S(0):
A minor bit of algebra yields:

Example of Risk-Neutral Valuation
Suppose a stock is worth $25 today and in one period will
either be worth 15% more or 15% less. The risk-free rate is
5%. What is the value of an at-the-money call option?
The binomial tree would look like this:
q $28.75,C(U)
$25,C(0)
1- q
$21.25,C(D)
The next step would be to compute the risk neutral
probabilities
2/3 $28.75,C(U)
$25,C(0)
1/3
$21.25,C(D)
After that, find the value of the call in the up
state and down state.
2/3 $28.75, $3.75
$25,C(0)
1/3
$21.25, $0
Finally, find the value of the call at time 0:
2/3 $28.75,$3.75
$25,$2.38
$25,C(0)
1/3
$21.25, $0
Risk-Neutral Valuation and the
Replicating Portfolio
This risk-neutral result is consistent with valuing the
call using a replicating portfolio.
The Black-Scholes Model
Where
C0 = the value of a European option at time t = 0
r = the risk-free interest rate.
N(d) = Probability that a
standardized, normally
distributed, random
variable will be less than
or equal to d.
The Black-Scholes Model allows us to value options in the
real world just as we have done in the 2-state world.
Find the value of a six-month call option on Microsoft
with an exercise price of $150.
The current value of a share of Microsoft is $160.
The interest rate available in the U.S. is r = 5%.
The option maturity is 6 months (half of a year).
The volatility of the underlying asset is 30% per annum.
Before we start, note that the intrinsic value of the
option is $10—our answer must be at least that
amount.
Let’s try our hand at using the model. If you
have a calculator handy, follow along.
First calculate d1 and d2
Then,
N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401
17.9 Stocks and Bonds as Options
 Levered equity is a call option.
 The underlying asset comprises the assets of the firm.
 The strike price is the payoff of the bond.
 If at the maturity of their debt, the assets of the
firm are greater in value than the debt, the
shareholders have an in-the-money call. They will
pay the bondholders and “call in” the assets of the
firm.
 If at the maturity of the debt the shareholders have
an out-of-the-money call, they will not pay the
bondholders (i.e. the shareholders will declare
bankruptcy) and let the call expire.
Stocks and Bonds as Options
 Levered equity is a put option.
 The underlying asset comprises the assets of the firm.
 The strike price is the payoff of the bond.
 If at the maturity of their debt, the assets of the firm
are less in value than the debt, shareholders have an
in-the-money put.
 They will put the firm to the bondholders.
 If at the maturity of the debt the shareholders have an
out-of-the-money put, they will not exercise the option
(i.e. NOT declare bankruptcy) and let the put expire.
Stocks and Bonds as Options
 It all comes down to put-call parity.
E
c0 = S0 + p0 –
(1+ r)T
Value of a Value of a Value of a
call on the =
Value of + put on the – risk-free
firm the firm firm bond
Stockholder’s Stockholder’s
position in terms position in terms
of call options of put options
Mergers and Diversification
 Diversification is a frequently mentioned reason for
mergers.
 Diversification reduces risk and, therefore, volatility.
 Decreasing volatility decreases the value of an option.
 Assume diversification is the only benefit to a merger:
 Since equity can be viewed as a call option, should the merger
increase or decrease the value of the equity?
 Since risky debt can be viewed as risk-free debt minus a put
option, what happens to the value of the risky debt?
 Overall, what has happened with the merger and is it a good
decision in view of the goal of stockholder wealth
maximization?
Example
 Consider the following two merger candidates.
 The merger is for diversification purposes only with no
synergies involved.
 Risk-free rate is 4%.
Company A Company B
Market value of assets $40 million $15 million
Face value of zero coupon $18 million $7 million
debt
Debt maturity 4 years 4 years
Asset return standard 40% 50%
deviation
Example
 Use the Black and Scholes OPM (or an options
calculator) to compute the value of the equity.
 Value of the debt = value of assets – value of equity
Company A Company B
Market Value of Equity 25.72 9.88
Market Value of Debt 14.28 5.12
Example
 The asset return standard deviation for the combined firm is 30%
 Market value assets (combined) = 40 + 15 = 55
 Face value debt (combined) = 18 + 7 = 25
Combined Firm
Market value of equity 34.18
Market value of debt 20.82
Total MV of equity of separate firms = 25.72 + 9.88 = 35.60

Wealth transfer from stockholders to bondholders = 35.60 – 34.18 = 1.42
(exact increase in MV of debt)
M&A Conclusions
 Mergers for diversification only transfer
wealth from the stockholders to the
bondholders.
 The standard deviation of returns on the assets
is reduced, thereby reducing the option value
of the equity.
 If management’s goal is to maximize
stockholder wealth, then mergers for reasons
of diversification should not occur.
Options and Capital Budgeting
 Stockholders may prefer low NPV projects to high
NPV projects if the firm is highly leveraged and the
low NPV project increases volatility.
 Consider a company with the following
characteristics:
 MV assets = 40 million
 Face Value debt = 25 million
 Debt maturity = 5 years
 Asset return standard deviation = 40%
 Risk-free rate = 4%
Example: Low NPV
 Current market value of equity = $22.706 million
 Current market value of debt = $17.294 million
Project I Project II
NPV $3 $1
MV of assets $43 $41
Asset return standard deviation 30% 50%
MV of equity $23.831 $25.381
MV of debt $19.169 $15.169
Example: Low NPV
 Which project should management take?
 Even though project B has a lower NPV, it is
better for stockholders.
 The firm has a relatively high amount of
leverage:
 With project A, the bondholders share in the NPV
because it reduces the risk of bankruptcy.
 With project B, the stockholders actually
appropriate additional wealth from the
bondholders for a larger gain in value.
Example: Negative NPV
 We’ve seen that stockholders might prefer a
low NPV to a high one, but would they ever
prefer a negative NPV?
 Under certain circumstances, they might.
 If the firm is highly leveraged, stockholders
have nothing to lose if a project fails, and
everything to gain if it succeeds.
 Consequently, they may prefer a very risky
project with a negative NPV but high potential
rewards.
 Consider the previous firm.
 They have one additional project they are
considering with the following characteristics
 Project NPV = -$2 million
 MV of assets = $38 million
 Asset return standard deviation = 65%
 Estimate the value of the debt and equity

 MV equity = $25.453 million
 MV debt = $12.547 million
 In this case, stockholders would actually prefer
the negative NPV project to either of the
positive NPV projects.
 The stockholders benefit from the increased
volatility associated with the project even if
the expected NPV is negative.
 This happens because of the large levels of
leverage.
Options and Capital Budgeting
 As a general rule, managers should not accept
low or negative NPV projects and pass up high
NPV projects.
 Under certain circumstances, however, this
may benefit stockholders:
 The firm is highly leveraged
 The low or negative NPV project causes a
substantial increase in the standard deviation of
asset returns
17.12 Investment in Real Projects and Options
 Classic NPV calculations generally ignore
the flexibility that real-world firms typically
have.
Chapter 18
Short-Term Finance and Planning
 Understand the components of the cash cycle
and why it is important
 Understand the pros and cons of the various
short-term financing policies
 Be able to prepare a cash budget
 Understand the various options for short-term

financing
Chapter Outline
18.1 Tracing Cash and Net Working Capital
18.2 The Operating Cycle and the Cash Cycle
18.3 Some Aspects of Short-Term Financial
Policy
18.4 The Cash Budget
18.5 Short-Term Borrowing
18.6 A Short-Term Financial Plan
Balance Sheet Model of the Firm
Current
Liabilities
Current Assets
Net
Working
Long-Term
Capital Debt
How much short-

Fixed Assets
term cash flow
1 Tangible does a company
Shareholders’
need to pay its
2 Intangible bills? Equity
18.1 Tracing Cash and Net Working Capital
 Current Assets are cash and other assets that are
expected to be converted to cash within the year.
 Cash
 Marketable securities
 Accounts receivable
 Inventory
 Current Liabilities are obligations that are expected
to require cash payment within the year.
 Accounts payable
 Accrued wages
 Taxes
Defining Cash in Terms of Other Elements
Long-
Net Working Fixed
+ = Term + Equity
Capital Assets
Debt
Other
Net Working Current
= Cash + Current –
Capital Liabilities
Assets
Long- Net Working

Fixed
Cash = Term + Equity – Capital –
Assets
Debt (excluding cash)
Defining Cash in Terms of Other Elements
Long- Net Working
Fixed
Cash = Term + Equity – Capital –
Assets
Debt (excluding cash)
 An increase in long-term debt and or equity

leads to an increase in cash—as does a
decrease in fixed assets or a decrease in the
non-cash components of net working
capital.
 The sources and uses of cash follow from
this reasoning.
18.2 The Operating Cycle and the Cash Cycle
Raw material
Cash
purchased Finished goods sold
received
Order Stock
Placed Arrives
Inventory period Accounts receivable period
Time
Accounts payable period
Firm receives invoice Cash paid for materials

Operating cycle
Cash cycle
The Operating Cycle and the Cash Cycle
Accounts
Cash cycle = Operating cycle – payable
period
 In practice, the inventory period, the accounts

receivable period, and the accounts payable
period are measured by days in inventory,
days in receivables, and days in payables.
Example
 Inventory:
 Beginning = 200,000
 Ending = 300,000
 Accounts Receivable:
 Ending = 200,000
 Accounts Payable:
 Ending = 100,000
 Net sales = 1,150,000
 Cost of Goods sold = 820,000
Example
 Inventory period
 Average inventory = (200,000+300,000)/2 = 250,000
 Inventory turnover = 820,000 / 250,000 = 3.28 times
 Inventory period = 365 / 3.28 = 112 days
 Receivables period
 Average receivables = (160,000+200,000)/2 = 180,000
 Receivables turnover = 1,150,000 / 180,000 = 6.39 times
 Receivables period = 365 / 6.39 = 57 days
 Operating cycle = 112 + 57 = 169 days
Example
 Payables Period
 Average payables = (75,000+100,000)/2 = 87,500
 Payables turnover = 820,000 / 87,500 = 9.37 times
 Payables period = 365 / 9.37 = 39 days
 Cash Cycle = 169 – 39 = 130 days
 We have to finance our inventory for 130 days.
 If we want to reduce our financing needs, we need to
look carefully at our receivables and inventory
periods – they both seem excessive.
18.3 Some Aspects of Short-Term
Financial Policy
 There are two elements of the policy that a firm
adopts for short-term finance.
 The size of the firm’s investment in current assets,
usually measured relative to the firm’s level of total
operating revenues.
 Flexible
 Restrictive
 Alternative financing policies for current assets,
usually measured as the proportion of short-term
debt to long-term debt.
 Flexible
 Restrictive
Size of Investment in Current Assets
 A flexible short-term finance policy would maintain
a high ratio of current assets to sales.
 Keeping large cash balances and investments in
marketable securities
 Large investments in inventory
 Liberal credit terms
 A restrictive short-term finance policy would
maintain a low ratio of current assets to sales.
 Keeping low cash balances, no investment in marketable
securities
 Making small investments in inventory
 Allowing no credit sales (thus no accounts receivable)
Carrying Costs and Shortage Costs
$ Total costs of holding current
Minimum
assets.
point
Carrying costs
Shortage costs
CA* Investment in
Current Assets ($)
Appropriate Flexible Policy
$
Minimum Carrying costs

point
Total costs of holding
current assets.
Shortage costs
CA* Investment in
Current Assets ($)
Appropriate Restrictive Policy
$ Minimum Total costs of holding current assets.
point
Carrying costs
Shortage
costs
CA* Investment in
Current Assets ($)
Alternative Financing Policies
 A flexible short-term finance policy means a low
proportion of short-term debt relative to long-term
financing.
 A restrictive short-term finance policy means a high
proportion of short-term debt relative to long-term
financing.
 In an ideal world, short-term assets are always
financed with short-term debt, and long-term assets
are always financed with long-term debt.
 In this world, net working capital is zero.
18.4 The Cash Budget
 A cash budget is a primary tool of short-run
financial planning.
 The idea is simple: Record the estimates of cash
receipts and disbursements.
 Cash Receipts
 Arise from sales, but we need to estimate when we
actually collect
 Cash Outflow
 Payments of Accounts Payable
 Wages, Taxes, and other Expenses
 Capital Expenditures
 Long-Term Financial Planning
Example
 Pet Treats Inc. specializes in gourmet pet treats and receives all income
from sales
 Sales estimates (in millions)
 Q1 = 500; Q2 = 600; Q3 = 650; Q4 = 800; Q1 next year = 550
 Accounts receivable
 Beginning receivables = $250
 Average collection period = 30 days
 Accounts payable
 Purchases = 50% of next quarter’s sales
 Beginning payables = 125
 Accounts payable period is 45 days
 Other expenses
 Wages, taxes and other expense are 30% of sales
 Interest and dividend payments are $50
 A major capital expenditure of $200 is expected in the second quarter
 The initial cash balance is $80 and the company maintains a minimum
balance of $50
Example
 ACP = 30 days, this implies that 2/3 of sales are collected
in the quarter made, and the remaining 1/3 are collected
the following quarter.
 Beginning receivables of $250 will be collected in the
first quarter.
Q1 Q2 Q3 Q4
Beginning Receivables 250 167 200 217
Sales 500 600 650 800
Cash Collections 583 567 633 750
Ending Receivables 167 200 217 267
Example
 Payables period is 45 days, so half of the
purchases will be paid for each quarter, and the
remaining will be paid the following quarter.
 Beginning payables = $125
Q1 Q2 Q3 Q4
Payment of accounts 275 313 362 338
Wages, taxes and other expenses 150 180 195 240
Capital expenditures 200
Interest and dividend payments 50 50 50 50
Total cash disbursements 475 743 607 628
Example
Q1 Q2 Q3 Q4
Total cash collections 583 567 633 750
Total cash disbursements 475 743 607 628
Net cash inflow 108 -176 26 122
Beginning Cash Balance 80 188 12 38
Net cash inflow 108 -176 26 122
Ending cash balance 188 12 38 160
Minimum cash balance -50 -50 -50 -50
Cumulative surplus (deficit) 138 -39 -12 110
18.5 Short-Term Borrowing
 The most common way to finance a temporary cash
deficit is to arrange a short-term loan.
 Unsecured Loans
 Line of credit (at the bank)
 Secured Loans
 Accounts receivable can be either assigned or factored.
 Inventory loans use inventory as collateral.
 Other Sources
 Banker’s acceptance
 Commercial paper
Chapter 19
Mergers and Acquisitions
 Be able to define the various terms associated
with M&A activity
 Understand the various reasons for mergers
and whether or not those reasons are in the
best interest of shareholders
 Understand the various methods for paying for
an acquisition
 Understand the various defensive tactics that
are available
Chapter Outline
19.1 The Legal Forms of Acquisitions
19.2 Taxes and Acquisitions
19.3 Accounting for Acquisitions
19.4 Gains from Acquisition
19.5 Some Financial Side Effects of Acquisitions
19.6 The Cost of an Acquisition
19.7 Defensive Tactics
19.8 Some Evidence on Acquisitions: Does M&A Pay?
19.9 Divestitures and Restructurings
19.1 The Legal Forms of Acquisitions
 There are three basic legal procedures that
one firm can use to acquire another firm:
 Merger or Consolidation
 Acquisition of Stock
 Acquisition of Assets
Merger versus Consolidation
 Merger
 One firm is acquired by another
 Acquiring firm retains name and acquired firm
ceases to exist
 Advantage – legally simple
 Disadvantage – must be approved by stockholders
of both firms
 Consolidation
 Entirely new firm is created from combination of
existing firms
Acquisitions
 A firm can be acquired by another firm or individual(s)
purchasing voting shares of the firm’s stock
 Tender offer – public offer to buy shares
 Stock acquisition
 No stockholder vote required
 Can deal directly with stockholders, even if management is unfriendly
 May be delayed if some target shareholders hold out for more money –
complete absorption requires a merger
 Classifications
 Horizontal – both firms are in the same industry
 Vertical – firms are in different stages of the production process
 Conglomerate – firms are unrelated
Varieties of Takeovers
Merger
Acquisition Acquisition of Stock
Takeovers Proxy Contest Acquisition of Assets
Going Private
(LBO)
19.2 Taxes and Acquisitions
 If it is a taxable acquisition, selling
shareholders need to figure their cost basis
and pay taxes on any capital gains.
 If it is not a taxable event, shareholders are
deemed to have exchanged their old shares for
new ones of equivalent value.
19.3 Accounting for Acquisitions
 The Purchase Method
 The source of much “goodwill”
 Pooling of Interests
 Pooling of interest is generally used when the
acquiring firm issues voting stock in exchange for
at least 90 percent of the outstanding voting stock
of the acquired firm.
 Purchase accounting is generally used under
other financing arrangements.
19.4 Gains from Acquisition
 Most acquisitions fail to create value for the
acquirer.
 The main reason why they do not lies in failures
to integrate two companies after a merger.
 Intellectual capital often walks out the door when
acquisitions aren't handled carefully.
 Traditionally, acquisitions deliver value when they
allow for scale economies or market power, better
products and services in the market, or learning from
the new firms.
Synergy
 Suppose firm A is contemplating acquiring
firm B.
 The synergy from the acquisition is
Synergy = VAB – (VA + VB)
 The synergy of an acquisition can be
determined from the standard discounted cash
flow model:
S
DCFt
T
Synergy = (1 + r)t
t=1
Sources of Synergy
 Revenue Enhancement
 Cost Reduction
 Replacement of ineffective managers
 Economies of scale or scope
 Tax Gains
 Net operating losses
 Unused debt capacity
 Incremental new investment required in
working capital and fixed assets
Calculating Value
 Avoiding Mistakes
 Do not ignore market values
 Estimate only Incremental cash flows
 Use the correct discount rate
 Don’t forget transactions costs
19.5 Some Financial Side Effects
 Earnings Growth
 If there are no synergies or other benefits to the
merger, then the growth in EPS is just an artifact of a
larger firm and is not true growth (i.e., an accounting
illusion).
 Diversification
 Shareholders who wish to diversify can accomplish
this at much lower cost with one phone call to their
broker than can management with a takeover.
19.6 The Cost of an Acquisition
 Typically, a firm would use NPV analysis
when making acquisitions.
 The analysis is straightforward with a cash
offer, but gets complicated when the
consideration is stock.
Cash Acquisition
 The NPV of a cash acquisition is:
 NPV = (VB + ΔV) – cash cost = VB* – cash cost
 Value of the combined firm is:
 VAB = VA + (VB* – cash cost)
 Often, the entire NPV goes to the target firm.
 Remember that a zero-NPV investment may
also be desirable.
Stock Acquisition
 Value of combined firm
 VAB = VA + VB + DV
 Cost of acquisition
 Depends on the number of shares given to the target
stockholders
 Depends on the price of the combined firm’s stock after the
merger
 Considerations when choosing between cash and
stock
 Sharing gains – target stockholders don’t participate in
stock price appreciation with a cash acquisition
 Taxes – cash acquisitions are generally taxable
 Control – cash acquisitions do not dilute control
19.7 Defensive Tactics
 Corporate charter
 Establishes conditions that allow for a takeover
 Supermajority voting requirement
 Targeted repurchase (a.k.a. greenmail)

 Standstill agreements
 Poison pills (share rights plans)
 Leveraged buyouts
More (Colorful) Terms
 Golden parachute
 Poison put
 Crown jewel
 White knight
 Lockup
 Shark repellent
 Bear hug
 Fair price provision
 Dual class capitalization
 Countertender offer
19.8 Evidence on Acquisitions
 Shareholders of target companies tend to earn excess
returns in a merger:
 Shareholders of target companies gain more in a tender
offer than in a straight merger.
 Target firm managers have a tendency to oppose mergers,
thus driving up the tender price.
Evidence on Acquisitions
 Shareholders of bidding firms earn a small excess
return in a tender offer, but none in a straight
merger:
 Anticipated gains from mergers may not be achieved.
 Bidding firms are generally larger, so it takes a larger
dollar gain to get the same percentage gain.
 Management may not be acting in stockholders’ best
interest.
 Takeover market may be competitive.
 Announcement may not contain new information about
the bidding firm.
19.9 Divestitures and Restructurings
 Divestiture – company sells a piece of itself to
another company
 Equity carve-out – company creates a new company
out of a subsidiary and then sells a minority interest
to the public through an IPO
 Spin-off – company creates a new company out of a
subsidiary and distributes the shares of the new
company to the parent company’s stockholders
 Split-up – company is split into two or more
companies and shares of all companies are distributed
to the original firm’s shareholders
Chapter 20
International Corporate Finance
 Understand how exchange rates are quoted and what
they mean
 Know the difference between spot and forward rates
 Understand purchasing power parity and interest rate
parity and the implications for changes in exchange
rates
 Understand the basics of international capital
budgeting
 Understand the impact of political risk on
international business investing
Chapter Outline
20.1 Terminology
20.2 Foreign Exchange Markets and Exchange Rates
20.3 Purchasing Power Parity
20.4 Interest Rate Parity, Unbiased Forward Rates, and
the International Fisher Effect
20.5 International Capital Budgeting
20.6 Exchange Rate Risk
20.7 Political Risk
20.1 Terminology
 American Depository Receipt (ADR): a security issued in the
U.S. to represent shares of a foreign stock
 Cross rate: the exchange rate between two foreign currencies,
e.g., the exchange rate between £ and ¥
 Euro (€): the single currency of the European Monetary
Union which was adopted by 11 Member States on 1 January
1999. These member states were: Belgium, Germany, Spain,
France, Ireland, Italy, Luxemburg, Finland, Austria, Portugal
and the Netherlands
 Eurobonds: bonds denominated in a particular currency and
issued simultaneously in the bond markets of several
countries
Terminology
 Eurocurrency: money deposited in a financial center
outside the home country. Eurodollars are dollar
deposits held outside the U.S.; Euroyen are yen
denominated deposits held outside Japan.
 Foreign bonds: bonds issued in another nation’s
capital market by a foreign borrower
 Gilts: British and Irish government securities
 LIBOR: the London Interbank Offer Rate is the rate
most international banks charge one another for
loans of Eurodollars overnight in the London market
20.2 Foreign Exchange Markets and
Exchange Rates
 Without a doubt, the foreign exchange market is the
world’s largest financial market.
 In this market, one country’s currency is traded for
another’s.
 Most of the trading takes place in a few currencies:
 U.S. dollar ($)
 British pound sterling (£)
 Japanese yen (¥)
 Euro (€)
FOREX Market Participants
 The FOREX market is a two-tiered market:
 Interbank Market (Wholesale)
 About 700 banks worldwide stand ready to make a
market in Foreign exchange.
 Nonbank dealers account for about 20% of the market.
 There are FX brokers who match buy and sell orders but
do not carry inventory and FX specialists.
 Client Market (Retail)
 Market participants include international banks,
their customers, nonbank dealers, FOREX
brokers, and central banks.
Exchange Rates
 The price of one country’s currency in terms of
another.
 Most currency is quoted in terms of dollars.
 Consider the following quote:
 Euro 1.3170 .7593
 The first number (1.3170) is how many U.S. dollars it
takes to buy 1 Euro
 The second number (.7593) is how many Euros it takes
to buy $1
 The two numbers are reciprocals of each other
(1/1.3170 = .7593)
Example
 Suppose you have $10,000. Based on the rates in
Figure 20.1, how many Swiss Francs can you buy?
 Exchange rate = 1.2146 Francs per dollar
 Buy 10,000(1.2146) = 12,146 Francs
 Suppose you are visiting Bombay and you want to
buy a souvenir that costs 1,000 Indian Rupees. How
much does it cost in U.S. dollars?
 Exchange rate = 43.384 rupees per dollar
 Cost = 1,000 / 43.384 = $23.05
Cross Rates
 Suppose that SDM(0) = .50
 i.e., $1 = 2 DM in the spot market
 and that S¥(0) = 100
 i.e., $1 = ¥100
 What must the DM/¥ cross rate be?
Triangular Arbitrage
Suppose we
observe these $
Credit
banks posting Barclays
Lyonnais
these exchange S¥(0) = 120
S£(0) = 1.50
rates.
First calculate the ¥ £

implied cross Credit Agricole
rates to see if an S¥/£(0) = 85
arbitrage exists.
The implied S(¥/£) cross rate is S(¥/£) = 80
$
Credit
£1.50 $1 £1 Barclays
× = Lyonnais
$1 ¥120 ¥80 S¥(0) = 120
S£(0) = 1.50
Credit Agricole has
posted a quote of ¥
S(¥/£)=85, so there £
is an arbitrage Credit Agricole
opportunity. S¥/£(0) = 85
So, how can we make money?

As easy as 1 – 2 – 3:
$
Credit
Barclays
Lyonnais
S¥(0) =120
S£(0) = 1.50
¥ £
1. Sell our $ for £, Credit Agricole
2. Sell our £ for ¥, S¥/£(0) = 85
3. Sell those ¥ for $.
Sell $100,000 for £ at S£(0) = 1.50
receive £150,000
Sell our £ 150,000 for ¥ at S¥/£(0) = 85
receive ¥12,750,000
Sell ¥ 12,750,000 for $ at S¥(0) = 120

receive $106,250
profit per round trip = $ 106,250 – $100,000 = $6,250
Types of Transactions
 Spot trade – exchange currency immediately
 Spot rate – the exchange rate for an immediate trade
 Forward trade – agree today to exchange currency at
some future date and some specified price (also
called a forward contract)
 Forward rate – the exchange rate specified in the
forward contract
 If the forward rate is higher than the spot rate, the
foreign currency is selling at a premium (when quoted
as $ equivalents).
 If the forward rate is lower than the spot rate, the
foreign currency is selling at a discount.
20.3 Absolute Purchasing Power Parity
 Price of an item is the same regardless of the
currency used to purchase it.
 Requirements for absolute PPP to hold:
 Transaction costs are zero
 No barriers to trade (no taxes, tariffs, etc.)
 No difference in the commodity between locations
 For most goods, Absolute PPP rarely holds in

practice.
Relative Purchasing Power Parity
 Provides information about what causes
changes in exchange rates.
 The basic result is that exchange rates depend
on relative inflation between countries:
 E(St ) = S0[1 + (hFC – hUS)]t
 Because absolute PPP doesn’t hold for many
goods, we will focus on relative PPP from here
on out.
Example
 Suppose the Canadian spot exchange rate is
1.18 Canadian dollars per U.S. dollar. U.S.
inflation is expected to be 3% per year, and
Canadian inflation is expected to be 2%.
 Do you expect the U.S. dollar to appreciate or
depreciate relative to the Canadian dollar?
 Since inflation is higher in the U.S., we would expect
the U.S. dollar to depreciate relative to the Canadian
dollar.
 What is the expected exchange rate in one year?
 E(S1) = 1.18[1 + (.02 - .03)]1 = 1.1682
20.4 Interest Rate Parity
 IRP is an arbitrage condition.
 If IRP did not hold, then it would be possible
for an astute trader to make unlimited
amounts of money exploiting the arbitrage
opportunity.
 Since we don’t typically observe persistent
arbitrage conditions, we can safely assume
that IRP holds.
Interest Rate Parity
Suppose you have $100,000 to invest for one year.
You can either
1. Invest in the U.S. at i$.
Future value = $100,000×(1 + i$)
2. Trade your dollars for yen at the spot rate, invest in
Japan at i¥ and hedge your exchange rate risk by selling
the future value of the Japanese investment forward.
F × (1 + i )
Future value = $100,000 × ¥
S
Since both of these investments have the same risk, they must
have the same future value:
F × (1 + i ) = (1 + i )
¥ $
S
Interest Rate Parity
F × (1 + i ) = (1 + i )
Formally, ¥ $
S
F (1 + i$)
or if you prefer, =
S (1 + i¥)
IRP is sometimes approximated as
i$ – i¥ = F–S
S
IRP and Covered Interest Arbitrage
If IRP failed to hold, an arbitrage opportunity would exist. It’s
easiest to see this in the form of an example.
Consider the following set of foreign and domestic interest rates
and spot and forward exchange rates.
Spot exchange rate S£(0) = $1.25/£
360-day forward F£(360) = $1.20/£
rate
U.S. discount rate i$ = 7.10%
British discount i£ = 11.56%
rate
A trader with $1,000 to invest could invest in the U.S.,
in one year his investment will be worth $1,071 =
$1,000(1+ i$) = $1,000(1.071)
Alternatively, this trader could:
1. exchange $1,000 for £800 at the prevailing spot rate,
(note that £800 = $1,000÷$1.25/£)
2. invest £800 at i£ = 11.56% for one year to achieve
£892.48.
3. Translate £892.48 back into dollars at F£(360) =
$1.20/£, the £892.48 will be exactly $1,071.
A trader with $1,000 to invest:
Can invest in the U.S.

In one year his investment
will be worth
$1,071 = $1,000(1.071)
= $1,000(1+ i$)
£800
$1.25 Invest £800
£800= $1,000×
£1 at i£ =
11.56%
$1,000
In one year £800
will be worth
£892.48 =
$1,000(1+ i£)
Domestic FV = Bring it on back

$1,071 and to the U.S.A. $1.20
British FV = $1,071 = £892.48 ×
£1
$1,071 3EA Global Academy | Copyright © 2021 3EA Limited | All rights reserved.
Reasons for Deviations from IRP
 Transactions Costs
 The interest rate available to an arbitrageur for
borrowing, ib,may exceed the rate he can lend at, il.
 There may be bid-ask spreads to overcome, Fb/Sa < F/S
 Thus
(Fb/Sa)(1 + i¥l)  (1 + i¥ b)  0
 Capital Controls
 Governments sometimes restrict import and export of
money through taxes or outright bans.
International Fisher Effect
 Combining PPP and UIP we can get the
International Fisher Effect:
 RUS – hUS = RFC – hFC
 The International Fisher Effect tells us that the
real rate of return must be constant across
countries.
 If it is not, investors will move their money to
the country with the higher real rate of return.
Equilibrium Exchange Rate Relationships
E(e)
IFE FP
PPP
i$ – i¥ IRP
F–S
S
FE FRPPP
h$ – h £
20.5 International Capital Budgeting
 Home Currency Approach
 Estimate cash flows in foreign currency
 Estimate future exchange rates using UIP
 Convert future cash flows to dollars
 Discount using domestic required return
 Foreign Currency Approach
 Estimate cash flows in foreign currency
 Use the IFE to convert domestic required return to foreign
required return
 Discount using foreign required return
 Convert NPV to dollars using current spot rate
Home Currency Approach
 Your company is looking at a new project in
Mexico. The project will cost 9 million pesos.
The cash flows are expected to be 2.25 million
pesos per year for 5 years. The current spot
exchange rate is 9.08 pesos per dollar. The
risk-free rate in the US is 4%, and the risk-free
rate in Mexico 8%. The dollar required return
is 15%.
 Should the company make the investment?
Foreign Currency Approach
 Use the same information as the previous
example to estimate the NPV using the
Foreign Currency Approach
 Mexican inflation rate from the International
Fisher Effect is 8% - 4% = 4%
 Required Return = 15% + 4% = 19%
 PV of future cash flows = 6,879,679
 NPV = 6,879,679 – 9,000,000 = -2,120,321 pesos
 NPV = -2,120,321 / 9.08 = -233,516
20.6 Exchange Rate Risk
 Short-Run Exposure
 Long-Run Exposure
 Translation Exposure
Short-Run Exposure
 Risk from day-to-day fluctuations in exchange
rates and the fact that companies have
contracts to buy and sell goods in the short-run
at fixed prices
 Managing risk
 Enter into a forward agreement to guarantee the
exchange rate.
 Use foreign currency options to lock in exchange
rates if they move against you, but benefit from
rates if they move in your favor.
Long-Run Exposure
 Long-run fluctuations come from
unanticipated changes in relative economic
conditions
 Could be due to changes in labor markets or
governments
 More difficult to hedge
 Try to match long-run inflows and outflows in
the currency
 Borrowing in the foreign country may mitigate
some of the problems
Translation Exposure
 Income from foreign operations must be translated
back to U.S. dollars for accounting purposes, even if
foreign currency is not actually converted back to
dollars.
 If gains and losses from this translation flowed
through directly to the income statement, there would
be significant volatility in EPS.
 Current accounting regulations require that all cash
flows be converted at the prevailing exchange rates,
with currency gains and losses accumulated in a
special account within shareholders equity.
Managing Exchange Rate Risk
 Large multinational firms may need to manage
the exchange rate risk associated with several
different currencies.
 The firm needs to consider its net exposure to
currency risk instead of just looking at each
currency separately.
 Hedging individual currencies could be
expensive and may actually increase exposure.
20.7 Political Risk
 Changes in value due to political actions in the foreign
country
 Investment in countries that have unstable governments
should require higher returns.
 The extent of political risk depends on the nature of the
business:
 The more dependent the business is on other operations
within the firm, the less valuable it is to others.
 Natural resource development can be very valuable to
others, especially if much of the ground work in
developing the resource has already been done.
 Local financing can often reduce political risk.
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Chapter 1

Introduction to Corporate Finance

2. Making smart financing decisions

Chairman of the Board and

President and Chief

Vice President and

Cash Manager Credit Manager Tax Manager Cost Accounting

Capital Expenditures Financial Planning Financial Accounting Data Processing

Firm Firm issues securities (A) Financial

Ultimately, the firm The cash flows from

Liquidity Shares can be easily Subject to substantial

Taxation Double Partners pay taxes on

Liability Limited liability General partners may have

 Know the difference between average and

 Net Working Capital ≡

 NWC usually grows with the firm

2006 2005 2006 2005

$275m = $761m- $486m This increase

liabilities (other than Total Cash Flow from Operations $199

Cash flow from Acquisition of fixed assets -$198

Cash flows to and Retirement of debt (includes notes) -$73

investing, and Acquisition of fixed assets

 Market value ratios

 PE Ratio = Price per share / Earnings per share

 Multiply by 1 again and then rearrange:

$500 would be interest ($10,000 × .05)

Where C0 is cash flow today (time zero), and

The amount that a borrower would need to set aside

Note that $10,000 = $9,523.81×(1.05).

Where C1 is cash flow at date 1, and

The present value of the cash inflow is greater

$9,500×(1.05) = $9,975 < $10,000

$5.92 > $1.10 + 5×[$1.10×.40] = $3.30

This is due to compounding.

200 400 600 800

CF1 200 F3 1 NPV 1,432.93

The Effective Annual Rate (EAR) of interest is

So, investing at 12.36% compounded annually

Texas Instruments BAII Plus

$297.22 $323.97 $100 $100 $100 $100

$20,000 $20,000×(1.03) $20,000×(1.03)39

 Understand bond ratings and what they mean

 Understand the impact of inflation on interest

 The yield to maturity is the required market

1100 When the YTM = coupon, the

Consider two otherwise identical bonds.

Short Maturity Bond

C Long Maturity Discount Rate

Consider two otherwise identical bonds.

High Coupon Bond

Present value of a pure discount bond at time 0:

 There are many other types of provisions that

 What is the bid price? What does this mean?

 What is the ask price? What does this mean?

 How much did the price change from the

 Approximation: R = 10% + 8% = 18%

 Because the real return and expected inflation

 Since future cash flows are constant, the value of a zero

Since future cash flows grow at a constant rate forever,

 plus the discounted value of a perpetuity growing at