An Alternative View of Risk and Return The Arbitrage Pricing Theory

1
An Alternative View of Risk and Return The
Arbitrage Pricing Theory

• Chapter 11

2
Arbitrage Pricing Theory

• Arbitrage arises if an investor can construct a
  zero investment portfolio with a guaranteed
  profit.
• The investor can make money with no risk
• No investment is required so small profit
  opportunities can be scale up
• In efficient markets, arbitrage opportunities
  will quickly disappear.

3
11.1 Factor Models Announcements, Surprises, and
Expected Returns

• We can break a securitys return into
• The expected return
• The un-expected return
• Therefore a stocks return can be written as

4
Surprises, and Expected Returns

• Any announcement can be broken down into two
  parts, the anticipated (or expected) part and the
  surprise (or innovation)
• Announcement Expected part Surprise.

5
11.2 Risk Systematic and Unsystematic

• Systematic risk is
• Unsystematic risk is
• Examples of systematic risk include
• Unsystematic risk,

6
Breaking Returns Down

• We defined returns as
• We can break down U further
• is what we expect the asset to return, based
  on our expectations of what the systematic risk
  will due
• is the return earned because of deviations
  between what we expected of the systematic risks,
  and what they actually did
• is the return from unsystematic risk

7
11.3 Systematic Risk and Betas

• The beta coefficient, b, tells us the response of
  the stocks return to a systematic risk.
• CAPM assumes that there is only one systematic
  risk factor, the return on the market portfolio

• We shall now consider other potential systematic
  risk factors

8
Systematic Risk and Betas

• For example, suppose we have identified three
  systematic risks inflation, GNP growth, and the
  dollar-euro spot exchange rate, S(,).
• Our model is

9
Systematic Risk and Betas Example

• Suppose we have made the following estimates
• bI -2.30
• bGNP 1.50
• bS 0.50
• Finally, the firm was able to attract a
  superstar CEO, and this unanticipated
  development contributes 1 to the return.

10
Systematic Risk and Betas Example

• We must decide what surprises took place in the
  systematic factors.
• If it were the case that the inflation rate was
  expected to be 3, but in fact was 8 during the
  time period, then
• FI Surprise in the inflation rate actual
  expected 8 3 5

11
Systematic Risk and Betas Example

• If it were the case that the rate of GNP growth
  was expected to be 4, but in fact was 1, then
• FGNP Surprise in the rate of GNP growth
• actual expected 1 4 3

12
Systematic Risk and Betas Example

• If it were the case that the dollar-euro spot
  exchange rate, S(,), was expected to increase
  by 10, but in fact remained stable during the
  time period, then
• FS Surprise in the exchange rate
• actual expected 0 10 10

13
Systematic Risk and Betas Example

• Finally, if it were the case that the expected
  return on the stock was 8, then

14
11.6 The Capital Asset Pricing Model and the
Arbitrage Pricing Theory

• APT is more general as it does not assume a
  market portfolio in order to get a relationship
  between ß and expected return
• APT is easily extended to multiple systematic
  risk factors

15
11.7 Empirical Approaches to Asset Pricing

• Both the CAPM and APT are risk-based models.
• Empirical methods are based less on theory and
  more on looking for some regularities in the
  historical record.
• However, a correlation does not imply causality.
• Related to empirical methods is the practice of
  classifying portfolios by style, e.g.,
• Value portfolio
• Growth portfolio

16
Quick Quiz

• Differentiate systematic risk from unsystematic
  risk. Which type is essentially eliminated with
  well diversified portfolios?
• Define arbitrage.
• Explain how the CAPM be considered a special case
  of Arbitrage Pricing Theory?

17
Why We Care

• Another investment rule
• Teaches the Law of 1 Price

18
Corporate Financing Decisions and Efficient
Capital Markets

• Chapter 13
• Overview of Market Efficiency

19
Efficient Markets Means

• Prices quickly incorporate information
• Prices move when new information deviates from
  expectations
• The purchase/sale of a security is a zero NPV
  investment
• The market price is correct, reflecting the
  assets fair value

20
Reactions to Beating Expectations

• Which of these lines indicates an efficient
  market?

21
Reaction to Not Meeting Expectations
22
Potential Causes of Efficient Markets

• Investor Rationality
• Everyone is rational ? makes the right decision
• Independent Deviation from Rationality
• No one is rational ? makes the wrong decision
  Diversification
• Arbitrage
• Only some people are rational

23
13.3 The Different Types of Efficiency
24
Weak Form Efficiency

• Stock prices reflect all information contained in
  past prices and volumes
• No investor is able to form a trading strategy
  based on historic prices and volumes and earn an
  excess return
• Stock prices follow a random walk
• Price tomorrow todays price random (/-)

25
Price Today and Tomorrow
26
Disbelievers

• Chartists, or Technical Analysts
• Analyze charts of a stock Price and/or Volume
• Chartist believe in identifiable and predictable
  patterns in these characteristics
• Make investment decisions based on these patterns
• Brokers tend to love chartists

27
Head and Shoulders
28
Semi-strong Form Market Efficiency

• Security prices reflect all publicly available
  information.
• Encompasses Weak form efficiency
• Publicly available information includes
• Historical price and volume information
• Published accounting statements
• Information found in the WSJ

29
Disbelievers

• Fundamental Analysts
• Use revenues, earnings, future growth forecasts,
  return on equity, profit margins, and other data
  to determine a company's underlying value and
  potential for future growth (Financial
  Statements)
• These guys make more sense than technical
  analysts. Why?

30
Strong Form Market Efficiency

• Security prices reflect all available information
• Public Private
• Implies Insider trading will not earn excess
  return
• Strong form efficiency incorporates weak and
  semi-strong form efficiency.
• Strong form efficiency says that anything
  pertinent to the stock price and known to at
  least one investor is already incorporated in the
  securitys price.

31
EMH Continuum
32
What EMH Does and Does NOT Say

• Investors can throw darts to select stocks.
• Kind of We still need to consider risk
• Prices are random or uncaused.
• Prices reflect information.
• Price CHANGES are driven by new information,
  which by is random
• Therefore, managers cannot time stock and bond
  sales.

33
Predictions of Efficient Markets

• New information is rapidly incorporated into
  prices AND cannot be used to generate future
  excess returns
• Technical analysis should provide no useful
  information
• Mutual fund managers cannot systematically
  outperform the market
• Asset prices remain at levels consistent with
  fundamentals

34
Implications of Efficient Markets

• Purchase or sale of any security can never be a
  positive NPV transaction.
• You can trust market prices
• Read the signs, price reflect market expectations
  
• There are no financial illusions
• Stocks with similar risk are substitutes

35
Investing Based on EMH

• Once an event happens the price of the stock
  adjusts accordingly
• If the announcement doesnt affect the systematic
  risk of the company then the expected return is
  unaffected by the announcement
• If the announcement changes the firms systematic
  risk then expected returns will change

36
The Evidence

• The record on the EMH is extensive, and, in large
  measure, it is reassuring to believers in
  efficient markets
• Studies fall into three broad categories
• Are changes in stock prices random?
• Are there profitable trading rules?
• Event studies does the market quickly and
  accurately respond to new information?
• The record of professionally managed investment
  firms.

37
Event Studies

• Event Studies are a test of the semi-strong form
  of market efficiency, by examining returns around
  the arrival of new information
• EX Earnings, Dividend announcements
• Looking for under-reaction, over-reaction, early
  reaction, or delayed reaction around the event.

38
Event Studies

• Returns are adjusted to determine if they are
  abnormal by taking into account what the rest of
  the market did that day.
• Market Adjusted Abnormal Return
• Calculated by subtracting the markets return on
  the same day (RM) from the actual return (R) on
  the stock for that day AR R RM
• Market Model Abnormal Return
• CAPM residual AR R (a bRM)

39
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 semi-strong 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.

40
Event Studies Dividend Omissions
Efficient market response to bad news
41
The Record of Mutual Funds

• If the market is semi-strong form efficient, then
  mutual fund managers, should not be able to
  consistently beat the average market return
• We can test market efficiency by comparing the
  performance of professionally managed mutual
  funds with the performance of a market index.

42
The Record of Mutual Funds
Taken from Lubos Pastor and Robert F. Stambaugh,
Mutual Fund Performance and Seemingly Unrelated
Assets, Journal of Financial Exonomics, 63
(2002).
43
Insider trading

• Strong form market efficiency implies that even
  insiders trading on private information cannot
  earn excess return
• A number of studies find that insiders are able
  to earn abnormal profits
• Violation of Strong form efficiency

44
Verdict on Market Efficiency

• Market is pretty efficient
• Opportunities for easy profits are rare.
• Financial managers should assume, at least as a
  starting point, that security prices are fair and
  that it is difficult to outguess the market.
• New information is rapidly incorporated into the
  prices.

45
EMH Exercises

• Indicate whether or not the EMH is contradicted,
  if so which form of EMH is contradicted
• An investor consistently earn an abnormal return
  over that expected by the market by examining
  charts of historical prices
• The acquisition of the latest annual report of a
  company enables an investor to earn an abnormal
  return.
• A stock which has been fluctuating between 25
  and 27 in the last three months suddenly rises
  to 40 per share right after management announces
  a new project that has a promising impact on the
  firm's expected future cash inflows.
• By subscribing to the Value Line Investment
  Survey, an investor can earn at least 5 over
  that earned by the market on comparable risk
  investments.

46
Why We Care

• Offering several points of view on how the market
  works, and the evidence for and against
• Using this you can form your own opinion about
  how the market works and invest accordingly

47
Risk, Cost of Capital, and Capital Budgeting

• Chapter 12

48
Valuing a Project

• In order to value a project we need to know both
  the expected cash flows, and the appropriate
  discount rate.
• Up till this point the discount rate has been
  given NOW we are going to focus on determining
  the appropriate discount rate
• How do we find the appropriate discount rate?

49
CAPM

• From CAPM we know that risk and return are
  related, and how that relationship works
• What is the relevant risk measure for a project?
• Why?
• How are they related?

50
Method 1 Matching

• Basic Idea Find another project with the same
  systematic risk characteristics, and use that
  projects return as the discount rate

51
Example

• Assume you need to find the discount rate for an
  apple picking machine, and you find that a pear
  picking machine offers a return on 15.
• Assume that pears and apples have the same
  systematic risk
• The appropriate discount rate for the apple
  picking machine is _____.

52
Method 2 CAPM

• CAPM E(ri) rf ßi (rM - rf)
• CAPM gives the expected return for a given level
  of systematic risk
• The expected return is what the investment should
  earn, we will use this to discount the projects
  cash flows

53
CAPM requirements

• Risk free rate
• Typically this is proxied for by the short term
  T-Bill rate
• Market risk premium
• This is generally found from historical data
  (8.4)
• The projects estimated ß
• You can use the ß from a company/project with the
  same risk

54
The ß of the project is

• Equal to the weighted average of the underlying
  assets ßs
• Equal to the weighted average of the financing
  ßs
• If the project is all equity financed then
• ßp
• If the project is all debt financed then
• ßp
• If the project is financed with equity and debt
• ßp

55
Estimating ße

• We generally estimate ße from historical data
  using a simple linear regression of stock return
  on the market return
• The beta estimate is what again?
• We use equity beta to get the expected return of
  equity

56
Estimating ßd ßa

• Similarly, if we use debt returns instead of
  stock returns, we get ?d.
• Or, if we use asset returns (cash
  flows/investment) instead, we will get ?a.
• ?a represents the systematic risk associated with
  the firm assets, and is the same as ?firm

57
Company Value

• Market Value of the Firm E D
• E Market Value of Equity Price of shares
  outstanding
• Equals the PV of the cash flows to all equity
  holders
• D Market Value of Debt Price of bonds
  outstanding
• Equals the PV of the cash flows to all debt
  holders
• What is the price?

58
Firm Beta (ßfirm)

• Can treat the firm as a portfolio of its
  financing
• So to get firm ß, we simple take a weighted
  average of the firms financing ßs
• ?firm D/V ?d E/V?e
• We can follow the same process with the firms
  assets, or division

59
Using ßa

• Once we have our estimate of ßa, we can plug it
  into the CAPM and find the appropriate discount
  rate
• ra rf ßa (rM - rf)

60
Method 3 Weighted Average Cost of Capital (WACC)

• Here we are going to work with the returns
  required by the firms investors (Equity, Debt,
  etc) to find the companys/projects cost of
  capital

61
Weighted Average Cost of Capital (WACC)

• If you own all of the debt and equity you own the
  whole firm, and the return you receive is simply
  the weighted average of the return on debt (rd)
  and equity (re)
• ra WACC

62
Equitys Expected Return

• We will generally use CAPM to get re
• re rf ße (rM - rf)

63
Debts expected return

• Generally we will not use CAPM to get rd
• Instead we will use the YTM of the firms public
  debt to get the appropriate rd
• If the firm has no public debt but it plans on
  issuing debt then the coupon rate offered will be
  rd
• Why?

64
Example

• Suppose the firm value is 100m and its equity is
  worth 40m. Given that the return on equity is
  20 and the return on debt is 10, calculate the
  firms WACC.
• WACC ra
• What does WACC represent?

65
Example Continued

• What would be the asset beta if we assume that ?d
  0.5, and ?e 1.5?
• What will ra be according to CAPM?
• rf 5, rm 15

66
Alternative WACC Calculations

• Using Returns
• WACC D/V rd E/V re
• Using Betas (Similar To CAPM)
• Use ?e and ?d to get ?a, then use CAPM to get
  WACC
• ?a D/V ?d E/V?e
• WACC Rf ?a E(Rm - Rf)
• Both methods give the same result

67
Alt Formula Proof Not on Test

• WACC Rf ?a(RmRf)
• WACC
• WACC D/Vrd E/Vre

68
What happens to WACC as the Firms Capital
Structure Changes

• Going back to our WACC example. Investors
  required a 14 return on the whole of the
  company. If the firm decides to issue debt and
  buyback equity, what will happen to the return
  required by
• An investor owning the entire company
• Equity investors
• Debt investors

69
The Investors

• Owner of the whole firm
• Equity and Debt investors

70
Equity versus Debt Investors

• Debt investors are paid according to the bond
  covenants, and they are paid off before the
  equity holders. Debt holders can also force a
  company into bankruptcy if it fails to pay them
• Equity holders are only entitled to the cash that
  is left after debt holders are paid, and cannot
  force the company into bankruptcy

71
Default Risk

• This is the risk associated with a company not
  being able to pay its debt holders and being
  force into bankruptcy
• How will issuing debt to buy back equity affect
  the firms default risk?

72
Default Risk and Required Returns

• As the default risk increases what happens to the
  required return of
• Equity
• Debt
• The whole firm

73
Changing Leverage WACC
74
WACC Graph
75
Changing Capital Structure

• What happens to the companys ? as the companys
  capital structure changes?

76
Example

• Suppose the firm decides to alter its capital
  structure by raising 20m in equity and using the
  cash to pay down debt. Do you expect the debt
  beta to increase or decrease? What about equity
  beta? Explain.

77
What about TAXES

• How will the inclusion of taxes affect our WACC
  formula? Why?
• No Taxes WACC D/V rd E/V re
• With Taxes

78
Order of Payment

• A company uses the money it makes to pay off
  three parties in the following order
• Bond holders
• Interest payments are tax deductible
• Government
• Equity holders
• Are only entitled to the residual cash flows

79
Discounting Projects with WACC

• The WACC is the discount rate for the entire
  company
• True/False
• Since we now have the companys WACC, are we able
  to value all of the firms potential projects.

80
Why we cannot use WACC for everything

• Using the WACC to value all potential projects is
  WRONG
• What happens if a firm does this?
• We need to consider each projects risk and then
  find the appropriate discount rate
• So, if we cannot use WACC to discount the
  potential projects why did we go over it?

81
Relative Discount Rates

• Project with same risk as firm
• Discount rate will ________ firms WACC
• Project with more risk than firm
• Discount rate will ________ firms WACC
• Project with less risk than firm
• Discount rate will ________ firms WACC

82
Boeing Example

• Boeing manufactures airplanes. It is planning to
  increase its capacity so that it can cater to
  increased demand. The firm currently has no debt
  in the capital structure. What is the appropriate
  discount rate for its expansion?
• Rf 5, Rm - Rf 10, ?e 1.5.

83
Levered Boeing

• Now, assume Boeing has debt in the capital
  structure. (Assume that ?e remains the same even
  though we know this is not true.) Its target
  debt-equity ratio is 30, and its debt has a
  beta of 0.2. What is the appropriate discount
  rate?

84
Levered Boeing Alt

• Now, assume Boeing has debt in the capital
  structure. (Assume that ?e remains the same even
  though we know it is not true.) Its target
  debt-equity ratio is 30. Also assume ?d was 0.2.
  What is the appropriate discount rate?

85
Project with different risk than firm

• When a project and a firm have different risk
  characteristics, the ?s will be different
• THEREFORE USING WACC IS WRONG
• So we find other publicly traded firms with
  systematic risk that is similar to the project
  being undertaken (surrogate firms).
• Beta is not firm specific

86
Calculating ßa

• ?a, i Di /Vi ?d, i Ei/Vi?e, i
• To get a better estimate of the projects ßa, you
  should estimate the ßa for as many companies as
  possible and then average them
• Use estimated ßa, and use CAPM to calculate WACC
• WACC Rf ßa (Rm Rf)

87
Lubbock Brewing Example

• Lubbock Brewings common stock has a market value
  of 40m, and its debt has a market value of 10m.
  Assume these values reflect the target D/E ratio.
• The beta of the stock is 1.2 and the expected
  risk premium on the market is 10.
• The current T-bill rate is 5.
• Assume debt is risk free.

88
Calculate

• The required return on Lubbock Brewery equity and
  debt
• re
• rd
• Asset beta
• ?a
• WACC using both methods
• WACC
• WACC
• Discount rate for an expansion project

89
Apparel Expansion

• Lubbock Brewery is considering diversifying into
  the apparel business. There are two apparel
  companies that are similar to the project being
  considered. These firms are not involved in any
  other business.
• Fashion Clothing, which has no debt in the
  capital structure, with an equity beta of 0.9.
• Tempe Trends has a debt-value ratio of 0.1, an
  equity beta of 0.9 and a debt beta of 0.1.
• What is the appropriate discount rate?

90
Apparel Expansion Calc.

• Fashion Clothing, which has no debt in the
  capital structure, has an equity beta of 0.9.
• Tempe Trends has a debt-firm value ratio of 0.1,
  an equity beta of 0.9 and a debt beta of 0.1.
• What is the appropriate discount rate?

91
Lingo Example

• Lingo Co. is currently involved in the
  manufacture of steel. It has a modernization plan
  which is expected to save 10m in cash flows each
  year over the next 3 years. The investment
  required is 20m. Should it take up the project?
• The following details are available Firm's
  current equity beta and debt beta are 1.2 and 0.3
  respectively. Risk free rate is 4. Expected
  market risk premium is 10. Firm's target
  debt-equity ratio is 0.5.

92
Lingo Expansion Calc
93
Lingo Computer Expansion

• Lingo Co is planning to diversify further into
  computers. It has identified two competitors
• While Compaq manufactures only computers, Toshiba
  manufactures other products as well.
• What is the discount rate for this
  diversification project?

94
Lingo Computer Expansion Calc
95
Summary

• The companys cost of capital is not the expected
  return on its stock or debt
• The company cost of capital is a weighted average
  of the returns that investors expect from the
  debt and equity issued by the firm.
• The company cost of capital is related to the
  firms asset beta, not to the beta of the common
  stock.

96
Summary Continued

• The asset beta can be calculated as a weighted
  average of the betas of the various securities.
• When the firm changes its financial leverage, the
  risk and expected returns of the individual
  securities change. The asset beta and the
  company cost of capital do NOT change.

97
Quick Quiz

• How do we determine the cost of equity capital?
• How can we estimate a firm or project beta?
• How does leverage affect beta?
• How do we determine the cost of capital with debt?

98
Why We Care

• Refinement of the time value of money, learning
  how to get the proper discount rate

99
Capital Structure

• Chapter 15

100
Corporate Financing

• We have been focusing on investment decision, now
  we are turning to financing decisions
• Investment decisions What do we buy?
• Financing decisions How do we pay for it?

101
Patterns of Corporate Financing

• Companies generally finance themselves and their
  investments with internally generated cash flows
  (70-90)
• What companies spend that cannot be met by these
  internally generated cash flows is financed by
  the sale of equity and debt
• The new sales of debt (net) are greater than the
  new sales of equity (net)

102
Stock

• Represents ownership of the company
• Limited Liability
• Owners of stock receive the following rights
• Right to vote for company directors, and other
  matters of great importance (Merger)
• Right to remaining assets once liabilities are
  paid off
• Right to dividends declared by company
• Can NOT force dividend payment
• Kind of, Why kind of?

103
Dividends

• None payment of a dividend cannot result in
  bankruptcy
• Dividends are not tax deductible
• Investors pay ordinary income tax on dividends
  they receive

104
Preferred Stock

• This is like a hybrid between stock bond
• Represents ownership in the company, but it
  receives a stated dividend before stockholders,
  and is entitled to a fixed claim in the event of
  bankruptcy
• Its dividends are NOT tax deductible
• Corporate investors do not pay taxes on 70 of
  the preferred stock dividends they receive
• No voting rights

105
Debt

• This is a IOU
• The bond indenture usually lists
• Amount of Issue, Date of Issue, Maturity
• Denomination (Par value)
• Annual Coupon, Dates of Coupon Payments
• Covenants
• Collateral, Sinking Funds, Call Provisions
• Features that may change over time
• Rating, Yield-to-Maturity, Market price
• Interest Payments are tax deductible

106
Seniority

• Seniority indicates preference in position over
  other lenders.
• Some debt is subordinated. In the event of
  default, holders of subordinated debt must give
  preference to other specified creditors who are
  paid first.
• Equity is subordinated to debt in bankruptcy

107
Corporate Debt

• Debt allows the borrower (firm) to walk away from
  its obligation, in exchange for the assets of
  the company (bankruptcy)
• Default Risk describe the likelihood that a firm
  will walk away from its obligation
• Bond Ratings are issued on debt to help
  investors assess the default risk of a firm

108
Summary and Conclusions

• The basic sources of long-term external financing
  are
• Debt, Common Stock, Preferred Stock
• Common shareholders have voting rights, limited
  liability, and a residual claim on the
  corporation.
• Bondholders have a contractual claim against the
  corporation.
• Preferred stock is a mix

109
Capital Structure

• Firm investments are financed with a mixture of
  securities, debt, equity, preferred stock
• We will focus our discussions to debt and equity
• Managers want to maximize firm value
• If capital structure influences firm value then
  managers will choose the capital structure that
  maximizes firm value

110
Firm Value

• The value of the firm is the market value of the
  firms equity the market value of the firms
  debt
• V E D

111
The Value of E and D

• E Equals the PV of the cash flows to all equity
  holders
• If a company pays 1.5 mil. in dividends each
  year (re8) E
• D Equals the PV of the cash flows to all debt
  holders
• If a company pays 0.75 mil. in interest each
  year (rd4) D
• V

112
Securitys Prices/Value

• What does the price of an asset tell us?

113
Modigliani-Miller Proposition 1

• The market value of a firm is independent of its
  capital structure
• Firm Value is determined by assets
• Capital Structure has no affect on firm value
• Cap. Struct. JUST DOESNT MATTER
• Implication Allows complete separation of
  financing and investment decisions
• Cap Struct will not affect the cash flows or the
  discount rate

114
MM 1 Assumptions

• Perfect Capital Markets
• No taxes, transactions costs, information
  asymmetry
• No Bankruptcy Costs
• Investment decisions are fixed
• Operating cash flow is independent of capital
  structure
• Everyone borrows and lends at the same interest
  rate

115
MM 1 Intuition

• Assume that there are two identical firms, except
  one has leverage and the other is un-levered
• MM1 states Vu Vl
• Intuition Investor can replicate the firms
  capital structure on his own so wont pay extra
  for it

116
MM 1 Proof

• Suppose Vl lt Vu
• Consider an investment of 1 Us equity
• Dollar investment 1 Vu
• Dollar payoff 1Profits
• Consider an investment of 1 of firm Ls equity
  and debt
• Dollar investment 1 EL 1 DL
• Dollar payoff
• From owning 0.01 DL 1 interest
• From owning 0.01 EL 1 ( profits interest)
• Total dollar payoff 1 Profits

117
MM 1 Proof

• Suppose Vl lt Vu, so Levered90 and
  Un-Levered100. Each makes profits of 50, but
  the levered firm has 50 of debt and owes 10 in
  interest
• Consider an investment of 1 U, own 1 of
  Un-Levereds equity
• Dollar investment 1 Vu, have invested 1
• Dollar payoff 1Profits, make 0.50
• Consider an investment of 1 of L, own 1 of
  Levereds equity and debt
• Dollar investment 1 EL 1 DL 0.400.50
  0.90
• Dollar payoff
• Debt 1 interest 0.0110 0.10
• Equity 1 ( profits interest)0.01400.40
• Total dollar payoff 0.100.400.50, or 1
  Profits

118
If Vl lt Vu then

• So if Vl lt Vu were true, an investor can
  purchase a claim in the levered firm with the
  same payoff as purchasing a claim in the
  un-levered firm, for a lower price!
• This situation is impossible in a well
  functioning capital market (arbitrage)
• Investors will buy Vl and sell it for Vu until
  Vl Vu

119
MM 1 Proof The Other Way

• Suppose Vl gt Vu
• Consider an investment of 1 of firm Ls equity
• Dollar investment 1 EL (VL - DL )
• Dollar payoff 1 (Profits Interest)
• Consider an investment of 1 of firm Us and
  borrowing 1 of DL
• Dollar investment 1 Vu - 1 DL
• Dollar payoff
• From borrowing owe 0.01 DL (1 interest)
• From owning 0.01 Vu 1 ( profits)
• Total dollar payoff 1 (Profits interest)

120
MM 1 Proof The Other Way

• Suppose Vl gt Vu, so Levered100 and
  Un-Levered90. Each makes profits of 50, but
  the levered firm has 50 of debt and owes 10 in
  interest
• Consider an investment of 1 of firm Ls equity
• Dollar investment 1 EL (VL - DL ) 0.50
• Dollar payoff 1 (Profits Interest)0.01400
  .40
• Consider an investment of 1 U, borrow1 of DL
• Dollar investment 1Vu-1DL0.90-0.500.40
• Dollar payoff
• Owe 1interest0.01100.10
• Receive 1Profits0.01500.50
• Total dollar payoff -0.100.500.40

121
If Vl gt Vu then

• In perfect capital markets the inequality cannot
  hold. Since both strategies have the same payoff,
  they should cost the same.

122
Cash flows and Firm Value 1

• A firm is only worth the PV of its cash flows to
  investors
• Consider an un-levered firm, which has an EBIT of
  1,500.
• The companys investors require a return on 12.
• Assume no taxes, what is the firm worth?

123
Cash flows and Firm Value 2

• Consider an levered firm, which has an EBIT of
  1,500.
• The firm owes 1,000 in interest
• The companys investors (equity and debt) require
  a return on 12.
• Assume no taxes, what is the firm worth?

124
MM1 and WACC

• If you owe the whole firm (all E D) then the
  return you get is the weighted average. The risk
  you are exposed to is the risk of the assets.
• Given that the assets do not change as D/E
  changes the risk and return for the whole firm
  will not change

125
How D/E Affects Shareholders

• While changes in the firms D/E ratio do not
  affect the firms value, ra, or ßa the higher the
  D/E the higher the risk faced by shareholders
• Debt influence financial risk
• Shareholders need to be compensated for two kinds
  of risks
• Business risk
• Financial risk

126
MM Proposition 2 D/E and re, ße

• As increasing a firms debt increase the
  riskiness (financial risk) of the equity
  investment
• Therefore, the return required by equity
  investors, re, will increase
• D/E relationship with re, ße
• ra D/V rd E/Vre which we can rearrange
• re ra D/E (ra - rd)
• ?a D /V ?d E/V?e
• ?e ?a D /E (?a - ?d)

127
ße Break-Down

• ?e ?a D /E (?a - ?d)
• ?a
• D /E (?a - ?d)

128
MM 2 Graph

• Look familiar?

129
Question 1

• Shareholders demand a higher rate of return than
  bondholders. As debt is cheaper, we should
  increase the D/E ratio as it reduces ra. True or
  False?

130
Question 2

• As the firm borrows more and debt becomes risky,
  both shareholders and bondholders demand a higher
  rate of return. Thus by reducing the debt-equity
  ratio, we can reduce the cost of debt and the
  cost of equity. This makes everybody better off.
  True or False?

131
More Realistic World

• MM showed us that in the theoretical world
  capital structure does not matter
• But by relaxing the MM assumptions and allowing
  for a more realistic world, capital structure
  can/will matter
• Here we are going to relax the MM assumptions, to
  see how D/E changes affect firm value
• Taxes, bankruptcy costs, agency costs

132
Corporate Taxes

• Corporations interest payments are tax
  deductible
• If less money is going to Uncle Sam, what will
  happen to firm value?
• Will cash flows to debt or equity investors
  increase?
• What happens to the discount rate?

133
Example

• There are two identical firms, each with an EBIT
  of 1,000. Firm U is unlevered, and firm L has
  5,000 in debt _at_6
• The tax shield provided by debt increases the
  cash available for investors
• If debt is a perpetuity, discount 120 to see
  increase in firm value

134
PV of Tax Shield

• Tax Shield Tax Rate Dollar Interest
• PV (Tax Shield) Tax Rate Interest / rd
• Tax Rate (Debt rd) / rd
• Tax Rate Debt
• 0.4 5,000 2,000

135
Vl with Corporate Taxes

• In the presence of corporate taxes, the value of
  a levered firm, increases by the PV of the tax
  shield
• Vl Vu PV(Tax Shield) Vu DTc
• As the tax shield increases company value how
  should the company be financed?

136
Cash flows and Firm Value 3

• Consider an un-levered firm, which has an EBIT of
  1,500.
• The companys investors require a return on 12.
• Taxes are 34, what is the firm worth?

137
Cash flows and Firm Value 4

• Consider an levered firm, which has an EBIT of
  1,500.
• The firm owes 1,000 in interest
• The companys investors (equity and debt) require
  a return on 12.
• Taxes are 34, what is the firm worth?

138
Cash flows and Firm Value 4 ALT

• Consider an levered firm, which has an EBIT of
  1,500.
• The firm owes 1,000 in interest
• The companys investors (equity and debt) require
  a return on 12.
• Taxes are 34, what is the firm worth?

139
MM 2 re with corporate taxes

• Earlier I showed you how re changes with debt,
  when we ignore taxes
• re ra D/E (ra - rd)
• What happens if we include corporate taxes?

140
Personal Taxes

• The firm wants to minimize the present value of
  all taxes paid (Corporate and Personal) WHY?

141
Including Personal Taxes

• Vl Vu D 1-(1-Tc)(1-Te)/(1-Td)
• The bracketed term is the total PV of the tax
  shield

142
Cash flows and Firm Value 5

• Consider an levered firm, which has an EBIT of
  1,500. The firm owes 1,000 in interest. The
  companys investors (equity and debt) require a
  return on 12.
• Taxes are Corp 34, Income 20, Equity 15
• E
• D
• Vl

143
Cash flows and Firm Value 5 cont.

• VU
• D
• TS
• Vl

144
Case 1 Te Td

• If all equity incomes is through dividends, the
  relationship is the same as when we did not
  consider personal taxes
• Vl Vu D 1-(1-Tc)(1-Td)/(1-Td)
• Vl
• Vl
• Vl

145
Case 2 (1-Tc)(1-Te) (1-Td)

• (1-Tc)(1-Te) Represents the after-tax return ()
  from 1 in equity income (Dividend or Capital
  Gain)
• (1-Td) Represents the after-tax return () from
  1 in debt income
• We are indifferent between equity and debt

146
Case 2 Cont. (1-Tc)(1-Te) (1-Td)

• Vl Vu D 1-(1-Tc)(1-Te)/(1-Td)
• Vl
• Vl
• Vl
• Vl
• Vl Vu

147
Case 3 Ti gt Te

• Generally some portion of equity income will come
  from capital gains
• The preferential tax treatment of capital gains
  reduces the value of the debt tax shield
• On the personal level the greater tax rate on
  debt income than equity income reduces the value
  of the tax shield
• PV(Tax Shield) lt DTc

148
Bankruptcy Costs

• Financial Distress this is when a firm struggles
  to honor its commitments
• Generally entered before bankruptcy
• Direct Costs Legal and Administrative costs
  associated with bankruptcy
• These are considered to be small
• Indirect Costs Impaired ability to conduct
  business
• These are considered to be significant

149
Bankruptcy Costs

• Increase as the firm takes on more leverage
• Make taking on more debt less attractive
• These costs are borne by the shareholders

150
Agency Costs

• When a firm becomes financially distressed the
  conflict between bondholders and stockholders
  increases
• This can result in managers playing games
• Who is the manager likely to be helping with
  these games?

151
Asset Substitution

• A firm has 6m in assets, and has 10m in debt
  outstanding ? Financial Distress
• The firm has a project requiring a 2m investment
  and pays 7m (PV) with a 10 probability or pays
  - 7m (PV) with a 90
• Will the firm take the project?
• Project NPV?

152
Projects Payoffs

• Equity holders want to take the project
• If dont bond holders force liquidation
• Equity gets ____, Debt gets ____
• If project turns out bad
• Equity gets ____, Debt gets ____
• If project turns out good
• Equity gets ____, Debt gets ____

153
Underinvestment

• Now instead of taking NPV projects the firm
  passes on NPV projects
• The same firm has a project requiring 2m
  investment and pays 5m (PV) with a 50
  probability or pays 1m (PV) with a 50
  probability
• What is the NPV?
• Will the firm take the project?

154
Project Payoffs

• Equity holders do not want the project
• If dont bond holders force liquidation
• Equity gets ______ , Debt gets ______
• If project turns out bad
• Equity gets ______ , Debt gets ______
• If project turns out good
• Equity gets ______, Debt gets ______

155
Milk the Property (Cash out)

• If the value of the firm is less than the value
  of the debt holders claims, then the shareholders
  have an incentive to sell off the assets and
  issue a cash dividends to themselves.
• However bond holders prevent this by using
  covenants

156
Intelligent Bondholders

• Bondholders know about agency costs and consider
  this when investing
• Requiring Higher rd, covenants
• Limit possible div payments, Restrict debt
  issuances or sales of assets
• All of this requires costly monitoring of the
  firm
• This is another agency costs borne by equity
  holders

157
Trade-off Theory of Cap Struct

• The debt-equity decision is a trade-off between
  interest tax shields and the costs associated
  with bankruptcy/financial distress and agency
  problems.
• Vl Vu PV (Tax shields) PV (Bankruptcy
  costs) PV (Agency costs)

158
Trade-off Theory Graph
Only Tax Shield
159
Trade-off Theory Implications

• Firms have an optimal D/E, which varies across
  firms
• Safe, highly profitable firms with lots of
  tangible assets should have lots of debt
• US studies finds that profitable firms have
  little debt
• Risky, marginally profitable firms with lots of
  intangible assets should have little debt

160
Another Cap Structure Theory Pecking Order

• Firms finance investments first with Retained
  Earnings, then Debt issuance, and lastly with
  stock
• This financing pecking order is driven by
  information asymmetry, and belief that managers
  will act in the interest of current shareholder