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Introduction to Corporate Finance

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Title: Introduction to Corporate Finance


1
Introduction to Corporate Finance
  • Chapter 1

2
Corporate Finance addresses the following three
questions
  • What long-term investments should the firm
    choose?
  • How should the firm raise funds for the selected
    investments?
  • How should short-term assets be managed and
    financed?

3
Balance Sheet Model of the Firm
4
The Capital Budgeting Decision
Current Liabilities
Current Assets
Long-Term Debt
Fixed Assets 1 Tangible 2 Intangible
Shareholders Equity
What long-term investments should the firm choose?
5
The Capital Structure Decision
Current Liabilities
Current Assets
Long-Term Debt
How should the firm raise funds for the selected
investments?
Fixed Assets 1 Tangible 2 Intangible
Shareholders Equity
6
Short-Term Asset Management
Current Liabilities
Current Assets
Net Working Capital
Long-Term Debt
  • How should short-term assets be managed and
    financed?

Fixed Assets 1 Tangible 2 Intangible
Shareholders Equity
7
Capital Structure
The value of the firm can be thought of as a pie.
8
Capital Structure
The value of the firm can be thought of as a pie.
The goal of the manager is to increase the size
of the pie. Where should the firm invest?
9
Capital Structure
The value of the firm can be thought of as a pie.
The goal of the manager is to increase the size
of the pie. Where should the firm invest?
Capital Structure decision can be viewed as how
the pie is sliced. How do we raise funds?
10
The Financial Manager
  • The Financial Managers primary goal is to
    increase the value of the firm by
  • Selecting value creating projects
  • Capital Budgeting Decision
  • Making smart financing decisions
  • Capital Structure Decision

11
The Firm and the Markets
Firm issues securities
Retained cash flows
Investsin assets(B)
Cash flowfrom firm
Div and debt payments
Short-term debt Long-term debt Equity shares
Current assetsFixed assets
Taxes
The cash flows from the firm must exceed the cash
flows from the financial markets.
Ultimately, the firm must be a cash generating
activity.
12
1.2 Forms of Business Organization
  • The Sole Proprietorship
  • The owner of the firm also runs the firm
  • The Partnership
  • General Partnership
  • Like a sole proprietorship, but with several
    owners
  • Limited Partnership
  • Some partner bears limited financial risk, and do
    not participate in running the company
  • The Corporation
  • Generally used when need to raise a large amount
    of capital
  • Separates ownership and control

13
A Comparison
14
1.3 The Goal of Financial Management
  • What is the correct goal?
  • Maximize profit?
  • Minimize costs?
  • Maximize market share?
  • Maximize shareholder wealth?

15
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
  • Other Ex. Real Estate Agents, Mutual Funds
  • Agency problem
  • Conflict of interest between principal and agent
  • Agents goals may not be the same as Principals

16
Managerial Goals
  • Managerial goals may be different from
    shareholder goals
  • Expensive perquisites
  • Private jet, golf memberships, cars, etc.
  • Company Survival,
  • Independence

17
Managing Managers
  • Managerial compensation
  • Incentives are used to align management and
    stockholder interests
  • Ex. Stock Options, Performance Bonuses
  • The incentives need to be structured carefully to
    make sure that they achieve their intended goal
  • Corporate control
  • The threat of a takeover force managers to act in
    stockholder interest

18
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
  • Some Financial Markets NYSE, NASDAQ, London
    Tokyo Stock Exchanges

19
Financial Markets
Investors
Firms
Sue
Bob
20
Quick Quiz
  • What are the three basic questions Financial
    Managers must answer?
  • What are the three major forms of business
    organization?
  • What is the goal of financial management?
  • What are agency problems, and why do they exist
    within a corporation?
  • What is the difference between a primary market
    and a secondary market?

21
Financial Statements and Cash Flow
  • Chapter 2

22
2.1 The Balance Sheet
  • A snapshot of the firms accounting value at a
    specific point in time
  • What does the company look like today
  • The Balance Sheet Identity is
  • Assets Liabilities Stockholders Equity
  • Left Hand Side of the balance sheet must equal
    the Right Hand Side

23
Balance Sheet
24
U.S. Composite Corporation Balance Sheet
The assets are listed in order by the length of
time it would normally take a firm with ongoing
operations to convert them into cash. Clearly,
cash is much more liquid than property, plant,
and equipment.
2007
2006
Current Liabilities
Accounts payable
213
197
Notes payable
50
53
Accrued expenses
223
205
Total current liabilities
486
455
Long-term liabilities
Deferred taxes
117
104
Long-term debt
471
458
Total long-term liabilities
588
562
Stockholder's equity
Preferred stock
39
39
Common stock (1 per value)
55
32
Capital surplus
347
327
Accumulated retained earnings
390
347
Less treasury stock
(26)
(20)
Total equity
805
725
Total liabilities and stockholder's equity
1,879
1,742
25
Balance Sheet Analysis
  • When analyzing a balance sheet, the Finance
    Manager should be aware of three concerns
  • Liquidity
  • Debt versus Equity
  • Value versus Cost

26
Liquidity
  • Refers to the ease and quickness with which
    assets can be converted to cashwithout a
    significant loss in value
  • Generally the more liquid the asset the lower the
    rate of return
  • Current assets are more liquid than fixed assets
  • The more liquid a firms assets, the less likely
    the firm is to experience problems meeting
    short-term cash obligations (Ex. payroll)

27
Debt versus Equity
  • Debt ? Liability
  • Promise to payout cash, an IOU
  • Equity is the residual
  • Assets Liabilities Equity
  • Debt represents a senior claim on firm assets
  • If the firm goes bankrupt debt holders get paid
    before equity holders

28
Value versus Cost
  • Accountants are historians, they care about what
    something cost when purchase
  • Under GAAP, financial statements carry assets at
    cost
  • Market value is the price at which assets,
    liabilities, and equity could actually be bought
    or sold, TODAY
  • Cost and Market Value are two completely
    different concepts
  • What did we pay for it, versus what can we sell
    it for

29
2.2 The Income Statement
  • Measures financial performance over a specific
    period of time
  • How has the company performed?
  • The accounting definition of income is
  • Revenue Expenses Income
  • Generally the Income Statement is comprised of
    several parts

30
U.S.C.C. Income Statement
Total operating revenues
2,262
The operations section of the income statement
reports the firms revenues and expenses from
principal operations.
Cost of goods sold
1,655
Selling, general, and administrative expenses
327
Depreciation
90
Operating income
190
Other income
29
Earnings before interest and taxes
219
Interest expense
49
Pretax income
170
Taxes
84
Current 71
Deferred 13
Net income
86
31
U.S.C.C. Income Statement
Total operating revenues
2,262
The non-operating section of the income statement
includes all financing costs, such as interest
expense.
Cost of goods sold
1,655
Selling, general, and administrative expenses
327
Depreciation
90
Operating income
190
29
Other income
Earnings before interest and taxes
219
Interest expense
49
Pretax income
170
Taxes
84
Current 71
Deferred 13
Net income
86
32
U.S.C.C. Income Statement
Total operating revenues
2,262
Cost of goods sold
1,655
Selling, general, and administrative expenses
327
Depreciation
90
Operating income
190
Other income
29
Earnings before interest and taxes
219
Usually a separate section reports the amount of
taxes levied on income.
Interest expense
49
Pretax income
170
Taxes
84
Current 71
Deferred 13
Net income
86
33
U.S.C.C. Income Statement
Total operating revenues
2,262
Cost of goods sold
1,655
Selling, general, and administrative expenses
327
Depreciation
90
Operating income
190
Other income
29
Earnings before interest and taxes
219
Interest expense
49
Net income is the bottom line.
Pretax income
170
Taxes
84
Current 71
Deferred 13
Net income
86
34
Income Statement Analysis
  • There are three things to keep in mind when
    analyzing an income statement
  • Generally Accepted Accounting Principles (GAAP)
  • Non-Cash Items
  • Time and Costs

35
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.

36
Non-Cash Items
  • The income statements also makes allowances for
    expense where no money changes hands
  • Depreciation is the most apparent example. 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.

37
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.

38
2.3 Taxes
  • In this world nothing is certain but death and
    taxes. Ben Franklin
  • Taxes represent a major cost to the firm
  • Taxes rules change, and are subject to political,
    not economic forces
  • What this means is that taxes do not need to make
    economic sense
  • Company is subject to two different tax rates
  • Marginal the percentage paid on the next dollar
    earned
  • Average the tax bill / taxable income

39
Marginal versus Average Rates
  • Suppose your firm earns 4 million in taxable
    income.
  • What is the firms tax liability?
  • .15(50,000) .25(75,000 50,000) .34(100,000
    75,000) .39(335,000 100,000)
    .34(4,000,000 335,000) 1,356,100
  • Rate from table 2.3
  • What is the average tax rate?
  • What is the marginal tax rate?
  • If you are considering a project that will
    increase the firms taxable income by 1 million,
    what tax rate should you use in your analysis?

40
2.4 Net Working Capital
  • Net Working Capital (NWC)
  • Current Assets Current Liabilities
  • NWC is usually positive for a growing firm
  • Why?

41
U.S.C.C. Balance Sheet
42
2.5 Financial Cash Flow
  • As finance people what we are really interested
    in is the firms actual cash flow
  • Since there is no magic in finance, it must be
    the case that the cash flow received from the
    firms assets must equal the cash flows to the
    firms creditors and stockholders.
  • CF(A) CF(B) CF(S)

43
U.S.C.C. Financial Cash Flow
Cash Flow of the Firm
Operating cash flow
238
(Earnings before interest and taxes
plus depreciation minus taxes)
Capital spending
-173
(Acquisitions of fixed assets
minus sales of fixed assets)
Additions to net working capital
-23
Total
42
Cash Flow of Investors in the Firm
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
44
2.5 The Statement of Cash Flows
  • There is a third accounting statement called the
    statement of cash flows.
  • The three components are
  • Cash flow from operating activities
  • Cash flow from investing activities
  • Cash flow from financing activities

45
U.S.C.C. Cash Flow from Operations
To calculate cash flow from operations, start
with net income, add back non-cash items like
depreciation and adjust for changes in current
assets and liabilities (other than cash).
46
U.S.C.C. Cash Flow from Investing
Cash flow from investing activities involves
changes in capital assets acquisition of fixed
assets and sales of fixed assets (i.e., net
capital expenditures). The cash from sales of
our buildings/machinery minus the cost of
buildings/machinery we bought
47
U.S.C.C. Cash Flow from Financing
Cash flows to and from creditors and owners
include changes in equity and debt.
48
U.S.C.C. Statement of Cash Flows
The statement of cash flows is the addition of
cash flows from operations, investing, and
financing.
49
Quick Quiz
  • What is the difference between book value and
    market value? Which should we use for decision
    making purposes?
  • What is the difference between accounting income
    and cash flow? Which do we need to use when
    making decisions?
  • What is the difference between average and
    marginal tax rates? Which should we use when
    making financial decisions?
  • How do we determine a firms cash flows? What are
    the equations, and where do we find the
    information?

50
Financial Statements Analysis and Long-Term
Planning
  • Chapter 3

51
3.1 Financial Statements Analysis
  • 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.

52
3.2 Ratio Analysis
  • Ratios allow for a better comparison through time
    and/or between companies
  • Give a sense for how the firm is doing
  • 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 companys ratio?

53
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

54
Liquidity Ratios
  • These measure the ability of the firm to meet
    its short term obligations
  • Why is this important?
  • Current Ratio CA / CL
  • 708 / 540 1.31 times
  • Quick Ratio (Acid Test) (CA Inventory) / CL
  • (708 - 422) / 540 0.53 times
  • Cash Ratio Cash / CL
  • 98 / 540 0.18 times
  • Where do the raw numbers come from?

55
Leverage Ratios
  • These measure the ability of the firm to meet
    its long term obligations
  • Why is this important?
  • 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
  • Where do the raw numbers come from?

56
Coverage Ratios
  • These measure the ability of the firm to pay its
    debt holders
  • Why do we care about paying the debt holders?
  • Times Interest Earned EBIT / Interest
  • 691 / 141 4.9 times
  • Cash Coverage (EBIT Depreciation) / Interest
  • (691 276) / 141 6.9 times
  • Where do the raw numbers come from?

57
Inventory Ratios
  • These tell else how efficiently the firm manages
    its inventory
  • Why do we care about this?
  • Do we want these ratios to be high or low?
  • Where do the raw numbers come from?
  • Inventory Turnover Cost of Goods Sold /
    Inventory
  • 1344 / 422 3.2 times
  • Days Sales in Inventory 365 / Inventory
    Turnover
  • 365 / 3.2 114 days

58
Receivables Ratios
  • These tell else how quickly the firm is paid?
  • Why do we care about this?
  • Do we want these ratios to be high or low?
  • Where do the raw numbers come from?
  • Receivables Turnover Sales / Accounts
    Receivable
  • 2311 / 188 12.3 times
  • Days Sales in Receivables 365 / Receivables
    Turnover
  • 365 / 12.3 30 days

59
Total Asset Turnover
  • This tells us how efficiently the firm is turning
    assets into sales
  • Why do we care about this?
  • Total Asset Turnover Sales / Total Assets
  • 2311 / 3588 0.64 times
  • It is not unusual for TAT lt 1, especially if a
    firm has a large amount of fixed assets.

60
Profitability Measures
  • These measure how efficiently the firm operates
  • Why do we care about these?
  • Where do the raw numbers come from?
  • 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

61
Market Value Measures
  • These tell us how the market (people) feel about
    the firm
  • Where do these raw numbers come from?
  • 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

62
3.3 The Du Pont Identity
  • Breaking down ROE into it component parts
  • 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

63
What does it mean?
  • ROE PM TAT EM
  • Profit margin is a measure of the firms
    operating efficiency how well it controls
    costs.
  • Total asset turnover is a measure of the firms
    asset use efficiency how well it manages its
    assets.
  • Equity multiplier is a measure of the firms
    financial leverage.

64
The Du Pont Identity in action
  • 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

65
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 firms performance is
    changing through time
  • Peer Group Analysis
  • Compare to similar companies or within industries
  • SIC and NAICS codes

66
Potential Problems to Remember when Analyzing
Financial Statement
  • There is no underlying theory, so there is no
    definitive way to know which ratios are most
    relevant
  • Benchmarking is difficult
  • Especially for diversified firms
  • Firms use varying accounting procedures
  • Ex. LIFO versus FIFO
  • Globalization means different accounting
    regulations
  • Firms have different fiscal years
  • Extraordinary, or one-time, events

67
3.5 Long-Term Financial Planning
  • These are the big decisions
  • Planning where the company is heading
  • Investment in new assets (Capital budgeting
    decisions)
  • Does Nike start a magazine?
  • Degree of financial leverage (Capital structure
    decisions)
  • Should we issue more bonds?
  • Generally we make these decisions based on pro
    forma financial statement

68
Percent of Sales Approach
  • Relatively quick and simple way to generate pro
    forma financial statements
  • Which can also be used to estimate where the
    company is heading
  • Remember that some items vary directly with
    sales, while others do not
  • Costs may vary directly with sales
  • Depreciation and interest expense generally do
    not vary directly with sales
  • Dividends are a management decision and generally
    do not vary directly with sales

69
Pro Forma Income Statement
70
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.

71
The Internal Growth Rate
  • The internal growth rate tells us how fast the
    firm can grow assets using only retained earnings
    for financing
  • The Internal Growth Rate can be calculated with
    ROA and Plowback
  • Plowback ratio how much of net income is being
    reinvested in the company
  • b Addition to Retained Earnings / Net Income

72
Calculating the Internal Growth Rate
  • Using the information from the Hoffman Co.
  • ROA 66 / 500 0.132
  • b 44/ 66 .66700
  • Internal Growth Rate
  • (ROA b )/ (1 ROA b)
  • (0.132 0.667) / (1 0.132 0.667 ) 0.0965
  • Hoffman Co. can grow at 9.65 using only internal
    funds

73
The Sustainable Growth Rate
  • The sustainable growth rate tells us how fast the
    firm can grow by using internally generated funds
    and issuing debt, without changing the firms
    leverage
  • Do you expect this be higher or lower than the
    internal growth rate?
  • The Sustainable Growth Rate can be calculated
    with ROE and Plowback

74
Calculating the Sustainable Growth Rate
  • Using the Hoffman Co.
  • ROE 66 / 250 0.264
  • b 0.667
  • Sustainable Growth Rate
  • (ROE b )/ (1 ROE b)
  • (0.264 0.667) / (1 0.264 0.667 ) 0.214
  • Hoffman Co. can grow at 21.4 using only internal
    funds

75
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

76
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.

77
Quick Quiz
  • How do you standardize balance sheets and income
    statements?
  • Why is standardization useful?
  • What are the major categories of financial
    ratios?
  • How do you compute the ratios within each
    category?
  • What are some of the problems associated with
    financial statement analysis?

78
Quick Quiz
  • What is the purpose of long-range planning?
  • What are the major decision areas involved in
    developing a plan?
  • What is the percentage of sales approach?
  • What is the internal growth rate?
  • What is the sustainable growth rate?
  • What are the major determinants of growth?

79
Discounted Cash Flow Valuation
  • Chapter 4

80
BASIC PRINCIPAL
  • Is a dollar today worth more or less than a
    dollar in 30 years?
  • Why?
  • Or would you rather have 1,000 today or 1,000
    in 30 years?
  • FYI this is one of those fundamental building
    blocks of finance

81
Present Value
  • Present Value is the value of a future payment
    today
  • Find this by discounting
  • In order to find the present value, we need to
    know the discount rate, r
  • Also know as the hurdle rate or the opportunity
    cost of capital

82
One Period Discounting
  • PV Future Value / (1 Discount Rate)
  • V0 C1 / (1r)
  • Alternatively
  • PV Future Value Discount Factor
  • V0 C1 (1/ (1r))
  • Discount factor is 1/ (1r)

83
PV Example
  • What is the value today of 100 in one year, if
    r15?

84
Future Value
  • In the one-period case, the formula for FV can be
    written as
  • FV C0(1 r)
  • Where C0 is cash flow today (time zero), and
  • r is the appropriate discount rate.

85
FV Example
  • What is the value in one year of 100, invested
    today at 15?

86
NPV
  • NPV Present Value of all expected cash flows
  • Represents how much value the project is
    contributing to the firm
  • To compute NPV we need to know two components
    appropriate discount rate and the expected cash
    flows (timing and magnitude).

87
Net Present Value (NPV)
  • NPV PV (Costs) PV (Benefit)
  • Costs are negative cash flows
  • Benefits are positive cash flows
  • One period example
  • NPV C0 C1 / (1r)
  • For investments C0 will be negative, and C1 will
    be positive
  • Reverse for loan

88
Net Present Value Example
  • Suppose you can buy an investment that promises
    to pay 10,000 in one year for 9,500. Should you
    invest?

89
Net Present Value
  • We cannot simply compare the two cash flows
  • They occur at different times
  • We need to find the NPV of the investment
  • If the NPV is positive then we buy
  • Your interest rate is 5.
  • NPV
  • At what price are we indifferent?

90
Coffee Shop Example
  • If you build a coffee shop on campus, you can
    sell it to Starbucks in one year for 300,000
  • Costs of building a coffee shop is 275,000
  • Should you build the coffee shop?

91
Step 1 Draw it out
92
Step 2 Discount Rate
  • Assume that the Starbucks offer is guaranteed
  • US T-Bills are risk-free and currently pay 7
    interest
  • This is known as rf
  • Thus, the appropriate discount rate is 7
  • Why

93
Example Continues
  • Step 3 Find the present value of future cash
    flows, our money from Starbucks
  • Step 4 Use the NPV rule
  • So do we build or not?

94
If we are unsure about future?
  • Is the appropriate discount rate
  • rd rf
  • rd gt rf
  • rd lt rf

95
Note on Discount Rates
  • The discount rate should take into account
  • Time value of money
  • Riskiness of cash flow
  • The appropriate discount rate is the opportunity
    cost of capital
  • The opportunity cost of capital is the rate of
    return offered by comparable investment
    opportunities.

96
Risky Coffee Shop
  • Assume that the risk of the coffee shop is
    equivalent to an investment in the stock market
    which is currently paying 12
  • Should we still build the coffee shop?

97
Calculations?
  • Need to recalculate PV and NPV
  • PV
  • NPV
  • Does the project still add value?

98
Expected Cash Flows
  • Future cash flows are generally not certain
  • Therefore need to form expectations
  • Need to identify the factors that affect cash
    flows (ex. Weather etc).
  • Determine the various scenarios for this factor
    (ex. rainy or sunny)
  • Estimate cash flows under the various scenarios
    (sensitivity analysis)
  • Assign probabilities to each scenario

99
Expectation Calculation
  • Expected value of X is the weighted sum of the
    possible values of X where the weight is given by
    the probability of its occurrence, p.
  • E(X) p1X1 p2X2 . psXs
  • E(X) p1X1 p2X2 . psXs
  • E(X) Expected Value of X
  • Xi ? Outcome of X in state i
  • pi Probability of state i
  • s Number of possible states
  • Note that p1 p2 . ps 1

100
Dice Example
  • What is the expected value of the role of a dice?
  • What are the possible states?
  • What is the probability of anyone state occurring?

101
Coffee Shop Expected Future Value
  • If the value of the coffee shop depends on the
    state of the economy, what is the expected future
    value?

102
Calculations
  • Discount Rate 12
  • Expected Future Cash Flow
  • NPV
  • Do we still build the coffee shop?

103
Valuing a Project Summary
  • Step 1 Forecast cash flows
  • Step 2 Draw out the cash flows
  • Step 3 Determine the opportunity cost of
    capital
  • Step 4 Discount future cash flows
  • Step 5 Apply the NPV rule

104
Reminder
  • Important to set up problem correctly
  • Keep track of
  • Magnitude and timing of the cash flows
  • TIMELINES
  • You cannot compare cash flows _at_ t3 and _at_ t2 if
    they are not in present value terms!!

105
Discounted Cash Flow Analysis
  • A method of evaluating an investment by
    estimating future cash flows and taking into
    consideration the time value of money
  • Provides us with the present value of the
    investment (NPV)
  • This allows for the comparison of investments
  • If capital is limited allows for the selection of
    the more valuable investment

106
General Formula
  • PV0 FVN/(1 r)N OR FVN PVo(1 r)N
  • Given any three, you can solve for the fourth
  • Present value (PV)
  • Future value (FV)
  • Time period
  • Discount rate

107
Four Related Questions
  • How much must you deposit today to have 1
    million in 25 years? (r12)
  • If a 58,823.31 investment yields 1 million in
    25 years, what is the rate of interest?
  • How many years will it take 58,823.31 to grow to
    1 million if r12?
  • What will 58,823.31 grow to after 25 years if
    r12?

108
FV Example
  • Suppose a stock is currently worth 10, and is
    expected to grow at 40 per year for the next
    five years.
  • What is the stock worth in five years?

109
PV Example
  • 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?

20,000
PV
110
Simple vs. Compound Interest
  • Simple Interest Where interest accumulates only
    on the principal
  • Compound Interest Where interest is accumulated
    on the principal as well as the interest already
    accumulated
  • What will 100 grow to after 2 periods at 10?
  • Compounded interest
  • FV2 PV0 (1r) (1r) PV0 (1r)2
  • Simple interest
  • FV2 (PV0 (r) PV0 (r)) PV0 PV0 (1 2r)

111
Compounding Periods
  • We have been assuming that compounding and
    discounting occurs annually, this does not need
    to be the case

112
Non-Annual Compounding
  • Cash flows are usually compounded over periods
    shorter than a year
  • The relationship between PV FV when interest is
    not compounded annually for N years
  • FVN PV ( 1 r / M) MN
  • PV FVN / ( 1 r / M) MN
  • M is number of compounding periods per year

113
Compound Interest
114
Interest Rates
  • In the table the 6 interest is known as the
    Stated Annual Interest Rate (more popularly known
    as the Annual Percentage Rate)
  • This is the rate that will generally be quoted
  • Ex Car loan, mortgage
  • However, this does not tell us the interest rate
    earned on our investment over the year
  • The interest rate that the investment actually
    earns over the year, is the Effective Annual Rate

115
Continuous Compounding
  • The general formula for the future value of an
    investment compounded continuously over many
    periods can be written as
  • FV C0erT
  • e is a transcendental number approximately equal
    to 2.718. ex is a key on your calculator.
  • Example The future value of 100 continuously
    compounded at 10 for one year is 100e.10
    110.52

116
Power of compounding
117
Compounding Example
  • What is the FV of 500 in 5 years, if the
    discount rate is 12, compounded monthly?
  • FV
  • What is the PV of 500 received in 5 years, if
    the discount rate is 12 compounded monthly?
  • PV

118
Compounding Example 2
  • If you invest 50 for 3 years at 12 compounded
    semi-annually, your investment will grow to
    ___________

119
Alternative Calculating the EAR
  • EAR (1 R/m)m 1
  • Earlier example 12 semi-annual
  • EAR
  • Using the EAR
  • FV
  • So, investing at _____ compounded annually is
    the same as investing at 12 compounded
    semi-annually.

120
EAR Example
  • Find the Effective Annual Rate (EAR) of an 18
    APR loan that is compounded weekly.
  • EAR

121
Present Value Of a Cash Flow Stream
  • The present value of a stream of cash flows can
    be found using the following general valuation
    formula.
  • In other words, discount each cash flow back to
    the present using the appropriate discount rate
    and then sum the present values.

122
Insight Example
Which project is more valuable? Why?
123
Example (Given)
  • 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?

124
Multiple Cash Flows (Given)
0
1
2
3
4
200
400
600
800
178.57
318.88
427.07
508.41
1,432.93
125
Common Cash Flows
  • Perpetuity, Growing Perpetuity
  • A constant stream of cash flows that lasts
    forever
  • A stream of cash flows that grows at a constant
    rate forever
  • Annuity, Growing Annuity
  • A stream of constant cash flows that lasts for a
    fixed number of periods
  • A stream of cash flows that grows at a constant
    rate for a fixed number of periods
  • All of the following formulas assume the first
    payment is next year, and payments occur annually

126
Perpetuity
  • A constant stream of cash flows that lasts
    forever
  • Since we arent able to spend forever calculating
    a perpetuitys PV
  • PVC/r
  • What is PV if C100 and r10


127
Growing Perpetuities
  • Annual payments grow at a constant rate, g
  • PV C1/(1r) C1(1g)/(1r)2 C1(1g)2(1r)3
  • PV C1/(r-g)
  • What is PV if C100, r10, and g2?

128
Growing Perpetuity Example (Given)
  • 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 (1.05)2 1.43
1.30(1.05) 1.37

2
3
  • PV 1.30 / (0.10 0.05) 26

129
Example
  • An investment in a growing perpetuity costs
  • 5,000 and is expected to pay 200 next year.
  • If the interest is 10, what is the growth rate
  • of the annual payment?

130
Annuity
  • A constant stream of cash flows with a fixed
    maturity

131
Annuity Example 1
  • Compute the present value of a 3 year ordinary
    annuity with payments of 100 at r10
  • Answer

132
An Alternative to the Formulas, is a Financial
Calculator
  • Texas Instruments BA-II Plus, basic
  • N number of periods
  • 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
  • PV present value
  • PMT payments received periodically
  • FV future value
  • Remember to clear the registers (CLR TVM) after
    each problem
  • Other calculators are similar in format

133
Annuity Example 2
  • You agree to lease a car for 4 years at 300 per
    month. You
  • are not required to pay any money up front or at
    the end of
  • your agreement. If your opportunity cost of
    capital is 0.5
  • per month, what is the cost of the lease?
  • Work through on financial calculators

134
Annuity Example 3
  • What is the value today of a 10-year annuity that
    pays 600 every other year? Assume that the
    stated annual discount rate is 10.
  • What do the payments look like?
  • What is the discount rate?

135
Annuity Example 4
  • 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?

136
Annuity Example 5
  • What is the value today of a 10-pymt annuity that
    pays 300 a year (at year-end) if the annuitys
    first cash flow is at the end of year 6. The
    interest rate is 15 for years 1-5 and 10
    thereafter?
  • Steps
  • Get value of annuity at t 5 (year end)
  • Bring value in step 1 to t0

137
Delayed first payment Perpetuity
  • What is the present value of a growing
    perpetuity, that pays 100 per year, growing at
    6, when the discount rate is 10, if the first
    payment is in 12 years?

138
Growing Annuity
  • A growing stream of cash flows with a fixed
    maturity

139
Growing Annuity Example
  • A defined-benefit retirement plan offers to pay
    20,000 per year for 40 years and increase the
    annual payment by 3 each year. What is the
    present value at retirement if the discount rate
    is 10?

140
Growing Annuity Example (Given)
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? PV (8,500/(.12-.07)) 1-
1.07/1.125 34,706.26
141
Valuation Formulas
142
Remember
  • That when you use one of these formulas or the
    calculator the assumptions are that
  • PV is right now, and the first payment is next
    year

143
What Is a Firm Worth?
  • A firm is worth the present value of the firms
    cash flows.
  • PV (Equity) PV of their expected cash flows
  • PV (Debt) PV of their expected cash flows
  • The tricky part is determining the size, timing,
    and risk of those cash flows.

144
Quick Quiz
  • How is the future value of a single cash flow
    computed?
  • How is the present value of a series of cash
    flows computed.
  • What is the Net Present Value of an investment?
  • What is an EAR, and how is it computed?
  • What is a perpetuity? An annuity?

145
Why We Care
  • The Time Value of Money is the basic foundation
    of knowledge that people will assume that you know

146
How to Value Bonds and Stocks
  • Chapter 5

147
What is a Bond?
  • A bond is a legally binding agreement between a
    borrower and a lender
  • IOU

148
Bond Terminology
  • Face value (F) or Principal
  • For a corporate bond this is generally 1,000
  • Coupon rate
  • This is a Stated Annual rate
  • However, coupons are generally paid semi-annually
  • Coupon payment (C )
  • Zero- coupon bond
  • Yield to maturity
  • Rating

149
Yield to Maturity
  • YTM is the interest that the bond is offering at
    its current price, if held till maturity
  • R for the previous slide
  • It is determined by
  • Time to maturity
  • Longer term bonds should have higher yields
  • Risk of default
  • Risk is measured by bond ratings

150
Valuing a Bond
  • The value of a bond is just the present value of
    its future cash flows
  • Bonds are valued like a package of two
    investments
  • Present value of the coupon (interest) payments
  • Present value of the principal payment

151
Pure Discount Bonds
  • This is a bond that makes no coupon payments
  • Sometimes called zeroes, deep discount bonds, or
    original issue discount bonds (OIDs)
  • Example T-Bill
  • Yield to maturity (return) comes only from the
    difference between the purchase price and face
    (par) value
  • A pure discount bond cannot sell for more than
    par value. WHY?

152
Pure Discount Bonds
  • Information needed for valuing pure discount
    bonds
  • Time to maturity (T) Maturity date - todays
    date
  • Face value (F)
  • Discount rate (r)

Present value of a pure discount bond at time 0
153
Pure Discount Bond Example
  • Find the value of a 30-year zero-coupon bond with
    a 1,000 par value and a YTM of 6.

154
Coupon Bonds
  • Make periodic coupon payments in addition to the
    principal value
  • The coupon payments are the same each period.
  • Coupon payments are typically semi-annual.
  • Effective annual rate
  • EAR (1 R/m)m 1
  • The bond is just a combination of an annuity and
    a terminal (maturity) value.

155
Coupon Bond Pricing Equation
  • Simply an annuity with a lump sum payment at the
    end

156
Coupon Bond Pricing BA II plus
  • N This is the number of coupon payments
  • I/Y This is the rate discount rate for the
    coupon period
  • PV The price of the bond today
  • PMT this is the amount of the coupon payment
  • FV This is the principal that will be repaid

157
Valuing a Corporate Bond
  • Dupont issued a 30 year maturity bonds with a
    coupon rate of 7.95.
  • Interest is paid semi-annually
  • These bonds currently have 28 years remaining to
    maturity and are rated AA.
  • The bonds have a par value of 1,000
  • Newly issued AA bonds with maturities greater
    than 10 years are currently yielding 7.73
  • What is the value of Dupont bond today?

158
Dupont example (continued)
  • Annual interest ()
  • Semiannual coupon payment
  • Semiannual discount rate
  • Number of semiannual periods
  • PV

159
Level Coupon Bond Example (Given)
  • Consider a U.S. government bond with a 6 3/8
    coupon that expires in December 2010.
  • 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, 2006 the size and timing of cash
    flows are
  • The require annual rate is 5

160
Level Coupon Bond Example (Given)
  • Coupon Rate 6 3/8, pay semi-annually
  • 10 Semi-Annual Payments of 31.875.
  • Maturity December 2010, Start Jan. 2006
  • The Par Value of the bond is 1,000.
  • The require annual rate is 5
  • N 10, I/Y 2.5, PV???, PMT 31.875,
    FV1,000 PV 1,060.17

161
Valuing a Corporate Bond (Given)
  • Value a bond with the following characteristics
    (calculator)
  • Face value 1,000
  • Coupon rate (C ) 8
  • Time to maturity 4 years
  • Discount rate 9
  • Present Value 967.02
  • You should know how to get any one of these
    numbers given the other 4.

162
YTM and bond prices
  • When coupon rate YTM, price par value
  • When coupon rate gt YTM, price gt par value
    (premium bond)
  • When coupon rate lt YTM, price lt par value
    (discount bond)
  • What will a zero sell at?
  • Bond prices and market interest rates move in
    opposite directions.

163
YTM and Bond Value
When the YTM lt coupon, the bond trades at a
premium.
1300
1200
Bond Value
When the YTM coupon, the bond trades at par.
1100
1000
800
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Discount Rate
Coupon Rate
When the YTM gt coupon, the bond trades at a
discount.
164
Computing Yield to Maturity
  • Finding the YTM requires trial and error if you
    do not have a financial calculator
  • 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

165
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?
  • What is the YTM?

166
YTM with Annual Coupons (Given)
  • 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 YTM be more or less than 10?
  • MORE
  • What is the YTM?
  • N 15
  • I/Y ???? 11
  • PV 928.09
  • PMT 100
  • FV 1000

167
The effect of changes in interest rates on bond
prices
  • Known as interest rate risk
  • Consider two identical 8 coupon bonds except
    that one matures in 4 years, the other matures in
    10 years
  • Calculate the change in the price of each bond if
    interest rates fall from 8 to 6, if interest
    rates rise from 8 to 10

168
Interest Rates and Time to Maturity
  • The longer a bond has till maturity, the greater
    the price impact of a change in interest rates
  • WHY?

169
Interest Rates and Bond Prices
  • Bond Prices and Interest Rates have an Inverse
    Relationship

170
Bond Market Reporting
  • 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

171
Pricing Stocks
  • Remember The value of any asset is the present
    value of its expected future cash flows.
  • Bond Cash flows are ________ ________
  • Stock produces cash flows from
  • ___________
  • ___________

172
Types of Stock
  • Preferred stock
  • Does not grant voting rights
  • Holders receive cash in the form of fixed
    dividend payment, or by selling (illiquid)
  • Common stock
  • Grants voting rights to holder
  • Cash flow from fluctuating dividends and selling
    shares

173
Stock Valuation Terminology
  • Dt or Divt expected dividend at time t
  • P0 market price of stock at time 0
  • Pt expected price of stock at time t
  • g- expected growth rate of dividends
  • rs or re- required rate of return on equity
  • D1 / P0 expected one-year dividend yield
  • (P1 - P0)/ P0 expected one year capital gain
  • The stocks total return div yield cap. gain

174
Valuing Common stock
  • The return on a share of stock is
  • rs is also known as the capitalization rate
  • If the investor requires a return of rs, then the
    price he is willing to pay today will depend on
    the cash flow he expects to receive _at_ t1

175
P0 ?
  • R
  • P1

176
With Substitution
  • This process can be repeated into the future, for
    example to period H, so that
  • Using summation
  • P0 ?H Dh / (1 r)h PH / (1 r)H
  • What happens to the last term as the time horizon
    gets long (as H approaches infinity)

177
Dividend Valuation model
  • As H approaches infinity the last term goes to
    zero
  • Because of this we can value a stock using just
    there dividends and an assumption about the
    companys growth rate
  • Dividend Valuation Model- the price of a stock is
    equal to the present value of the stream of
    expected future dividends

178
Constant Dividend (No Growth)
  • How do you value a stock that will pay a constant
    dividend?
  • Hint what does the cash flow stream look similar
    to?

179
No Growth Example
  • What is the value of a share of a firm that is
    expected to pay constant dividend of 2 per share
    forever?
  • The required rate of return is 10

180
Constant Dividend Growth
  • If the dividend payments on a stock are expected
    to grow at a constant rate, g, and the discount
    rate is rs, the value of the stock at time 0
    is______, similar to a __________

181
Constant Growth Example
  • Geneva steel just paid a dividend of 2.10.
    Dividend payments are expected to grow at a
    constant rate of 6. The appropriate discount
    rate is 12. What is the price of Geneva stock?
  • Div1
  • P0

182
Valuation of stocks with variable dividend growth
  • Steps
  • Find the PV of dividends during the period of
    non-constant growth, PA
  • Find the price of the stock at the end of the
    non-constant growth period, PN
  • Discount the price found in 2 back to the
    present, PB
  • Add the two present values (13) to find the
    intrinsic value (price) of the stock P0 PA PB

183
Generic Differential Growth
  • Dividends will grow at g1 for N years and g2
    thereafter
  • Step 1 An N-year annuity growing at rate g1
  • Step 2 A growing perpetuity at rate g2
  • PN DivN1 / (R-g2)
  • Step 3 PB PN / (1R)N
  • Step 4 P0 PA PB

184
Non-Constant Growth Example (Given)
  • Websurfers Inc, a new internet firm is expected
    to do very well during its initial growth period.
    Investors expect its dividends to grow at 25 for
    the next 3 years. Obviously one cannot expect
    such extraordinary growth to continue forever,
    and it is expected that dividends will grow at 5
    after year 3 in perpetuity. Its current dividend
    is 1/share. Required rate of return on the stock
    10. Calculate what the current price should be.

185
Websurfer Inc, Example (Given)
  • PA(11.25)/(0.10-0.25)1-1.25/1.103
    3.90
  • PN 11.2531.05/(0.10-0.05) 41.00
  • PB 41.00/(1.103) 30.80
  • P0 PA PB 3.90 30.80 34.70

186
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.

187
Solution
  • PA
  • PN
  • PB
  • P0 PA PB

188
Important Parameters
  • The value of a firm depends on the discount rate,
    R, and the growth rate, g.

189
Market Capitalization Rate
  • R is the market consensus of the appropriate
    discount rate
  • This is known as the Market Capitalization Rate
  • Return that is expected by an investor buying the
    stock today
  • This is similar to what for a bond?

190
Where does R come from?
  • We generally estimate R from one of the dividend
    valuation models
  • Using constant dividend growth model
  • In practice, estimates of R have a lot of
    estimation error

191
Where does R come from?
  • What is D1/P0?
  • What is g?

192
Where does R come from?
  • What is D1/P0?
  • What is g?

193
Decomposing R
  • Stocks are often classified based on this split
  • Income/Value stocks have a higher dividend
    yield
  • Growth stocks have a higher growth component
  • As long as both are equally risky, the return
    should be the same

194
Where does g come from?
  • From analysts' estimates
  • I/B/E/S, Google, Yahoo, or WSJ
  • From earnings re-investment
  • g Retention ratio Return on equity
  • How much net income is reinvested in the company
    times what the firm can make on the money
  • This is an estimate of how fast the company can
    grow its dividends, which is?

195
Plowback Ratio
  • The portion of a dollar earned that is reinvested
  • 1 - Payout Ratio
  • 1 - DIV/EPS
  • ROE Net Income / Book Equity
  • Net Income/ Number of shares
  • Book Equity / Number of shares
  •   EPS / Book Equity per share
  •   g plowback ratio ROE

196
Earnings Re-Investment
  • g Retained Earnings Net Income
  • Net Income Book Equity
  • g Plowback Ratio Return on Equity

197
Link between stock prices and earnings
  • A new valuation model
  • Consider a firm with a 100 payout ratio, so Div
    EPS in each period and earnings remain flat.

198
Link between stock prices and earnings
  • Since the firm is paying out all of its earnings
    as dividends, the expected return is simply the
    earnings per share divided by the share price
    (earnings-price ratio)
  • r EPS/P0

199
Present Value of all Future Growth Opportunities
(PVGO)
  • The stock price is composed of the value of the
    co
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