Title: Adrian Cheung
1Lecture 4
2Chapter
11
Risk and Return
3Key Concepts and Skills
- Know how to calculate expected returns
- Understand the impact of diversification
- Understand the systematic risk principle
- Understand the security market line
- Understand the risk-return trade-off
4Chapter Outline
- Expected Returns and Variances
- Portfolios
- Announcements, Surprises, and Expected Returns
- Risk Systematic and Unsystematic
- Diversification and Portfolio Risk
- Systematic Risk and Beta
- The Security Market Line
- The SML and the Cost of Capital A Preview
5Expected Returns
- Expected returns are based on the probabilities
of possible outcomes - In this context, expected means average if the
process is repeated many times - The expected return does not even have to be a
possible return
6Example Expected Returns
- Suppose you have predicted the following returns
for stocks C and T in three possible states of
nature. What are the expected returns? - State Probability C T
- Boom 0.3 0.15 0.25
- Normal 0.5 0.10 0.20
- Recession ??? 0.02 0.01
- RC .3(.15) .5(.10) .2(.02) .099 9.99
- RT .3(.25) .5(.20) .2(.01) .177 17.7
7Variance and Standard Deviation
- Variance and standard deviation still measure the
volatility of returns - Using unequal probabilities for the entire range
of possibilities - Weighted average of squared deviations
8Example Variance and Standard Deviation
- Consider the previous example. What are the
variance and standard deviation for each stock? - Stock C
- ?2 .3(.15-.099)2 .5(.1-.099)2 .2(.02-.099)2
.002029 - ? .045
- Stock T
- ?2 .3(.25-.177)2 .5(.2-.177)2 .2(.01-.177)2
.007441 - ? .0863
9Portfolios
- A portfolio is a collection of assets
- An assets risk and return is important in how it
affects the risk and return of the portfolio - The risk-return trade-off for a portfolio is
measured by the portfolio expected return and
standard deviation, just as with individual assets
10Example Portfolio Weights
- Suppose you have 15,000 to invest and you have
purchased securities in the following amounts.
What are your portfolio weights in each security? - 2000 of DCLK
- 3000 of KO
- 4000 of INTC
- 6000 of KEI
- DCLK 2/15 .133
- KO 3/15 .2
- INTC 4/15 .267
- KEI 6/15 .4
11Portfolio Expected Returns
- The expected return of a portfolio is the
weighted average of the expected returns for each
asset in the portfolio - You can also find the expected return by finding
the portfolio return in each possible state and
computing the expected value as we did with
individual securities
12Example Expected Portfolio Returns
- Consider the portfolio weights computed
previously. If the individual stocks have the
following expected returns, what is the expected
return for the portfolio? - DCLK 19.65
- KO 8.96
- INTC 9.67
- KEI 8.13
- E(RP) .133(19.65) .2(8.96) .167(9.67)
.4(8.13) 9.27
13Portfolio Variance
- Compute the portfolio return for each stateRP
w1R1 w2R2 wmRm - Compute the expected portfolio return using the
same formula as for an individual asset - Compute the portfolio variance and standard
deviation using the same formulas as for an
individual asset
14Example Portfolio Variance
- Consider the following information
- Invest 50 of your money in Asset A
- State Probability A B
- Boom .4 30 -5
- Bust .6 -10 25
- What is the expected return and standard
deviation for each asset? - What is the expected return and standard
deviation for the portfolio?
Portfolio 12.5 7.5
15Expected versus 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
16Announcements and News
- Announcements and news contain both an expected
component and a surprise component - It is the surprise component that affects a
stocks 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
17Efficient Markets
- Efficient markets are a result of investors
trading on the unexpected portion of
announcements - The easier it is to trade on surprises, the more
efficient markets should be - Efficient markets involve random price changes
because we cannot predict surprises
18Systematic Risk
- 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.
19Unsystematic Risk
- 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.
20Returns
- 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
21Diversification
- Portfolio diversification is the investment in
several different asset classes or sectors - Diversification is not just holding a lot of
assets - For example, if you own 50 internet stocks, you
are not diversified - However, if you own 50 stocks that span 20
different industries, then you are diversified
22Table 11.7
( 3) (2) Ratio of Portfolio
(1) Average Standard Standard Deviation to
Number of Stocks Deviation of Annual Standard
Deviation in Portfolio Portfolio Returns of a
Single Stock 1 49.24 1.00 10 23.93
0.49 50 20.20 0.41 100 19.69 0.40
300 19.34 0.39 500 19.27 0.39
1,000 19.21 0.39
23The Principle of Diversification
- 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
24Figure 11.1
Average annualstandard deviation ()
Diversifiable risk
Nondiversifiablerisk
Number of stocksin portfolio
25Diversifiable 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
26Total 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
27Systematic Risk Principle
- There is a reward for bearing risk
- There is not a reward for bearing risk
unnecessarily - The expected return on a risky asset depends only
on that assets systematic risk since
unsystematic risk can be diversified away
28Measuring Systematic Risk
- How do we measure systematic risk?
- We use the beta coefficient to measure systematic
risk - What does beta tell us?
- A beta of 1 implies the asset has the same
systematic risk as the overall market - A beta lt 1 implies the asset has less systematic
risk than the overall market - A beta gt 1 implies the asset has more systematic
risk than the overall market
29Total versus Systematic Risk
- Consider the following information
- Standard Deviation Beta
- Security C 20 1.25
- Security K 30 0.95
- Which security has more total risk?
- Which security has more systematic risk?
- Which security should have the higher expected
return?
30Example Portfolio Betas
- Consider the previous example with the following
four securities - Security Weight Beta
- DCLK .133 4.03
- KO .2 0.84
- INTC .167 1.05
- KEI .4 0.59
- What is the portfolio beta?
- .133(4.03) .2(.84) .167(1.05) .4(.59) 1.12
31Beta and the Risk Premium
- Remember that the risk premium expected return
risk-free rate - The higher the beta, the greater the risk premium
should be - Can we define the relationship between the risk
premium and beta so that we can estimate the
expected return? - YES!
32Example Portfolio Expected Returns and Betas
E(RA)
Rf
?A
33Reward-to-Risk Ratio Definition and Example
- The reward-to-risk ratio is the slope of the line
illustrated in the previous example - Slope (E(RA) Rf) / (?A 0)
- Reward-to-risk ratio for previous example (20
8) / (1.6 0) 7.5 - What if an asset has a reward-to-risk ratio of 8
(implying that the asset plots above the line)? - What if an asset has a reward-to-risk ratio of 7
(implying that the asset plots below the line)?
34Market Equilibrium
- In equilibrium, all assets and portfolios must
have the same reward-to-risk ratio and they all
must equal the reward-to-risk ratio for the
market
35Security Market Line
- The security market line (SML) is the
representation of market equilibrium - The slope of the SML is the reward-to-risk ratio
(E(RM) Rf) / ?M - But since the beta for the market is ALWAYS equal
to one, the slope can be rewritten - Slope E(RM) Rf market risk premium
36Capital Asset Pricing Model
- The capital asset pricing model (CAPM) defines
the relationship between risk and return - E(RA) Rf ?A(E(RM) Rf)
- If we know an assets systematic risk, we can use
the CAPM to determine its expected return - This is true whether we are talking about
financial assets or physical assets
37Factors Affecting Expected Return
- Pure time value of money measured by the
risk-free rate - Reward for bearing systematic risk measured by
the market risk premium - Amount of systematic risk measured by beta
38Example - CAPM
- Consider the betas for each of the assets given
earlier. If the risk-free rate is 6.15 and the
market risk premium is 9.5, what is the expected
return for each? - Security Beta Expected Return
- DCLK 4.03 6.15 4.03(9.5) 44.435
- KO 0.84 6.15 .84(9.5) 14.13
- INTC 1.05 6.15 1.05(9.5) 16.125
- KEI 0.59 6.15 .59(9.5) 11.755
39Chapter 11 Quick Quiz
- How do you compute the expected return and
standard deviation for an individual asset? For a
portfolio? - What is the difference between systematic and
unsystematic risk? - What type of risk is relevant for determining the
expected return? - Consider an asset with a beta of 1.2, a risk-free
rate of 5 and a market return of 13. - What is the reward-to-risk ratio in equilibrium?
- What is the expected return on the asset?
40Chapter
12
Cost of Capital
41Key Concepts and Skills
- Know how to determine a firms cost of equity
capital - Know how to determine a firms cost of debt
- Know how to determine a firms overall cost of
capital - Understand pitfalls of overall cost of capital
and how to manage them
42Chapter Outline
- The Cost of Capital Some Preliminaries
- The Cost of Equity
- The Costs of Debt and Preferred Stock
- The Weighted Average Cost of Capital
- Divisional and Project Costs of Capital
43Why Cost of Capital Is Important
- We know that the return earned on assets depends
on the risk of those assets - The return to an investor is the same as the cost
to the company - Our cost of capital provides us with an
indication of how the market views the risk of
our assets - Knowing our cost of capital can also help us
determine our required return for capital
budgeting projects
44Required Return
- The required return is the same as the
appropriate discount rate and is based on the
risk of the cash flows - We need to know the required return for an
investment before we can compute the NPV and make
a decision about whether or not to take the
investment - We need to earn at least the required return to
compensate our investors for the financing they
have provided
45Cost of Equity
- The cost of equity is the return required by
equity investors given the risk of the cash flows
from the firm - There are two major methods for determining the
cost of equity - Dividend growth model
- SML (or CAPM)
46The Dividend Growth Model Approach
- Start with the dividend growth model formula and
rearrange to solve for RE
47Dividend Growth Model Example
- Suppose that your company is expected to pay a
dividend of 1.50 per share next year. There has
been a steady growth in dividends of 5.1 per
year and the market expects that to continue. The
current price is 25. What is the cost of equity?
48Example Estimating the Dividend Growth Rate
- One method for estimating the growth rate is to
use the historical average - Year Dividend Percent Change
- 1995 1.23
- 1996 1.30
- 1997 1.36
- 1998 1.43
- 1999 1.50
(1.30 1.23) / 1.23 5.7 (1.36 1.30) / 1.30
4.6 (1.43 1.36) / 1.36 5.1 (1.50 1.43)
/ 1.43 4.9
Average (5.7 4.6 5.1 4.9) / 4 5.1
49Advantages and Disadvantages of Dividend Growth
Model
- Advantage easy to understand and use
- Disadvantages
- Only applicable to companies currently paying
dividends - Not applicable if dividends arent growing at a
reasonably constant rate - Extremely sensitive to the estimated growth rate
an increase in g of 1 increases the cost of
equity by 1 - Does not explicitly consider risk
50The SML Approach
- Use the following information to compute our cost
of equity - Risk-free rate, Rf
- Market risk premium, E(RM) Rf
- Systematic risk of asset, ?
51Example - SML
- Suppose your company has an equity beta of .58
and the current risk-free rate is 6.1. If the
expected market risk premium is 8.6, what is
your cost of equity capital? - RE 6.1 .58(8.6) 11.1
- Since we came up with similar numbers using both
the dividend growth model and the SML approach,
we should feel pretty good about our estimate
52Advantages and Disadvantages of SML
- Advantages
- Explicitly adjusts for systematic risk
- Applicable to all companies, as long as we can
compute beta - Disadvantages
- Have to estimate the expected market risk
premium, which does vary over time - Have to estimate beta, which also varies over
time - We are relying on the past to predict the future,
which is not always reliable
53Example Cost of Equity
- Suppose our company has a beta of 1.5. The market
risk premium is expected to be 9 and the current
risk-free rate is 6. We have used analysts
estimates to determine that the market believes
our dividends will grow at 6 per year and our
last dividend was 2. Our stock is currently
selling for 15.65. What is our cost of equity? - Using SML RE 6 1.5(9) 19.5
- Using DGM RE 2(1.06) / 15.65 .06 19.55
54Cost of Debt
- The cost of debt is the required return on our
companys debt - We usually focus on the cost of long-term debt or
bonds - The required return is best estimated by
computing the yield-to-maturity on the existing
debt - We may also use estimates of current rates based
on the bond rating we expect when we issue new
debt - The cost of debt is NOT the coupon rate
55Cost of Debt Example
- Suppose we have a bond issue currently
outstanding that has 25 years left to maturity.
The coupon rate is 9 and coupons are paid
semiannually. The bond is currently selling for
908.72 per 1000 bond. What is the cost of debt? - T 50 PMT 45 FV 1000 PV -908.75 Y
5 YTM 5(2) 10
56Cost of Preferred Stock
- Reminders
- Preferred generally pays a constant dividend
every period - Dividends are expected to be paid every period
forever - Preferred stock is an annuity, so we take the
annuity formula, rearrange and solve for RP - RP D / P0
57Cost of Preferred Stock - Example
- Your company has preferred stock that has an
annual dividend of 3. If the current price is
25, what is the cost of preferred stock? - RP 3 / 25 12
58Weighted Average Cost of Capital
- We can use the individual costs of capital that
we have computed to get our average cost of
capital for the firm. - This average is the required return on our
assets, based on the markets perception of the
risk of those assets - The weights are determined by how much of each
type of financing that we use
59Capital Structure Weights
- Notation
- E market value of equity outstanding shares
times price per share - D market value of debt outstanding bonds
times bond price - V market value of the firm D E
- Weights
- wE E/V percent financed with equity
- wD D/V percent financed with debt
60Example Capital Structure Weights
- Suppose you have a market value of equity equal
to 500 million and a market value of debt 475
million. - What are the capital structure weights?
- V 500 million 475 million 975 million
- wE E/D 500 / 975 .5128 51.28
- wD D/V 475 / 975 .4872 48.72
61Taxes and the WACC
- We are concerned with after-tax cash flows, so we
need to consider the effect of taxes on the
various costs of capital - Interest expense reduces our tax liability
- This reduction in taxes reduces our cost of debt
- After-tax cost of debt RD(1-TC)
- Dividends are not tax deductible, so there is no
tax impact on the cost of equity - WACC wERE wDRD(1-TC)
62Extended Example WACC - I
- Equity Information
- 50 million shares
- 80 per share
- Beta 1.15
- Market risk premium 9
- Risk-free rate 5
- Debt Information
- 1 billion in outstanding debt (face value)
- Current quote 110
- Coupon rate 9, semiannual coupons
- 15 years to maturity
- Tax rate 40
63Extended Example WACC - II
- What is the cost of equity?
- RE 5 1.15(9) 15.35
- What is the cost of debt?
- T 30 PV 1100 PMT 45 FV 1000 YTM
3.9268 - RD 3.927(2) 7.854
- What is the after-tax cost of debt?
- RD(1-TC) 7.854(1-.4) 4.712
64Extended Example WACC - III
- What are the capital structure weights?
- E 50 million (80) 4 billion
- D 1 billion (1.10) 1.1 billion
- V 4 1.1 5.1 billion
- wE E/V 4 / 5.1 .7843
- wD D/V 1.1 / 5.1 .2157
- What is the WACC?
- WACC .7843(15.35) .2157(4.712) 13.06
65Table 12.1
66Divisional and Project Costs of Capital
- Using the WACC as our discount rate is only
appropriate for projects that are the same risk
as the firms current operations - If we are looking at a project that is NOT the
same risk as the firm, then we need to determine
the appropriate discount rate for that project - Divisions also often require separatediscount
rates
67Pure Play Approach
- Find one or more companies that specialize in the
product or service that we are considering - Compute the beta for each company
- Take an average
- Use that beta along with the CAPM to find the
appropriate return for a project of that risk - Often difficult to find pure play companies
68Subjective Approach
- Consider the projects risk relative to the firm
overall - If the project is more risky than the firm, use a
discount rate greater than the WACC - If the project is less risky than the firm, use a
discount rate less than the WACC - You may still accept projects that you shouldnt
and reject projects you should accept, but your
error rate should be lower than not considering
differential risk at all
69Subjective Approach - Example
70Chapter 12 Quick Quiz
- What are the two approaches for computing the
cost of equity? - How do you compute the cost of debt and the
after-tax cost of debt? - How do you compute the capital structure weights
required for the WACC? - What is the WACC?
- What happens if we use the WACC for the discount
rate for all projects? - What are two methods that can be used to compute
the appropriate discount rate when WACC isnt
appropriate?
71Chapter
13
Leverage and Capital Structure
72Key Concepts and Skills
- Understand the effect of financial leverage on
cash flows and cost of equity - Understand the impact of taxes and bankruptcy on
capital structure choice - Understand the basic components of the bankruptcy
process
73Chapter Outline
- The Capital Structure Question
- The Effect of Financial Leverage
- Capital Structure and the Cost of Equity Capital
- Corporate Taxes and Capital Structure
- Bankruptcy Costs
- Optimal Capital Structure
- Observed Capital Structures
74Capital Restructuring
- We are going to look at how changes in capital
structure affect the value of the firm, all else
equal - Capital restructuring involves changing the
amount of leverage a firm has without changing
the firms assets - Increase leverage by issuing debt and
repurchasing outstanding shares - Decrease leverage by issuing new shares and
retiring outstanding debt
75Choosing a Capital Structure
- What is the primary goal of financial managers?
- Maximize stockholder wealth
- We want to choose the capital structure that will
maximize stockholder wealth - We can maximize stockholder wealth by maximizing
firm value or minimizing WACC
76The Effect of Leverage
- How does leverage affect the EPS and ROE of a
firm? - When we increase the amount of debt financing, we
increase the fixed interest expense - If we have a really good year, then we pay our
fixed cost and we have more left over for our
stockholders - If we have a really bad year, we still have to
pay our fixed costs and we have less left over
for our stockholders - Leverage amplifies the variation in both EPS and
ROE
77Example Financial Leverage, EPS and ROE
- We will ignore the effect of taxes at this stage
- What happens to EPS and ROE when we issue debt
and buy back shares of stock?
78Example Financial Leverage, EPS and ROE
- Variability in ROE
- Current ROE ranges from 6.25 to 18.75
- Proposed ROE ranges from 2.50 to 27.50
- Variability in EPS
- Current EPS ranges from 1.25 to 3.75
- Proposed EPS ranges from 0.50 to 5.50
- The variability in both ROE and EPS increases
when financial leverage is increased
79Break-Even EBIT
- Find EBIT where EPS is the same under both the
current and proposed capital structures - If we expect EBIT to be greater than the
break-even point, then leverage is beneficial to
our stockholders - If we expect EBIT to be less than the break-even
point, then leverage is detrimental to our
stockholders
80Example Break-Even EBIT
81Example Homemade Leverage and ROE
- Current Capital Structure
- Investor borrows 2000 and uses 2000 of their
own to buy 200 shares of stock - Payoffs
- Recession 200(1.25) - .1(2000) 50
- Expected 200(2.50) - .1(2000) 300
- Expansion 200(3.75) - .1(2000) 550
- Mirrors the payoffs from purchasing 100 shares
from the firm under the proposed capital structure
- Proposed Capital Structure
- Investor buys 1000 worth of stock (50 shares)
and 1000 worth of Trans Am bonds paying 10. - Payoffs
- Recession 50(.50) .1(1000) 125
- Expected 50(3.00) .1(1000) 250
- Expansion 50(5.50) .1(1000) 375
- Mirrors the payoffs from purchasing 100 shares
under the current capital structure
82Capital Structure Theory
- Modigliani and Miller Theory of Capital Structure
- Proposition I firm value
- Proposition II WACC
- The value of the firm is determined by the cash
flows to the firm and the risk of the assets - Changing firm value
- Change the risk of the cash flows
- Change the cash flows
83Capital Structure Theory Under Three Special Cases
- Case I Assumptions
- No corporate or personal taxes
- No bankruptcy costs
- Case II Assumptions
- Corporate taxes, but no personal taxes
- No bankruptcy costs
- Case III Assumptions
- Corporate taxes, but no personal taxes
- Bankruptcy costs
84Case I Propositions I and II
- Proposition I
- The value of the firm is NOT affected by changes
in the capital structure - The cash flows of the firm do not change,
therefore value doesnt change - Proposition II
- The WACC of the firm is NOT affected by capital
structure
85Case II Cash Flows
- Interest is tax deductible
- Therefore, when a firm adds debt, it reduces
taxes, all else equal - The reduction in taxes increases the cash flow of
the firm - How should an increase in cash flows affect the
value of the firm?
86Case II - Example
87Interest Tax Shield
- Annual interest tax shield
- Tax rate times interest payment
- 6250 in 8 debt 500 in interest expense
- Annual tax shield .34(500) 170
- Present value of annual interest tax shield
- Assume perpetual debt for simplicity
- PV 170 / .08 2125
- PV D(RD)(TC) / RD DTC 6250(.34) 2125
88Case II Proposition I
- The value of the firm increases by the present
value of the annual interest tax shield - Value of a levered firm value of an unlevered
firm PV of interest tax shield - Value of equity Value of the firm Value of
debt - Assuming perpetual cash flows
- VU EBIT(1-T) / RU
- VL VU DTC
89Case III
- Now we add bankruptcy costs
- As the D/E ratio increases, the probability of
bankruptcy increases - This increased probability will increase the
expected bankruptcy costs - At some point, the additional value of the
interest tax shield will be offset by the
expected bankruptcy cost - At this point, the value of the firm will start
to decrease and the WACC will start to increase
as more debt is added
90Bankruptcy Costs
- Direct costs
- Legal and administrative costs
- Ultimately cause bondholders to incur additional
losses - Disincentive to debt financing
- Financial distress
- Significant problems in meeting debt obligations
- Most firms that experience financial distress do
not ultimately file for bankruptcy
91More Bankruptcy Costs
- Indirect bankruptcy costs
- Larger than direct costs, but more difficult to
measure and estimate - Stockholders wish to avoid a formal bankruptcy
filing - Bondholders want to keep existing assets intact
so they can at least receive that money - Assets lose value as management spends time
worrying about avoiding bankruptcy instead of
running the business - Also have lost sales, interrupted operations and
loss of valuable employees
92Conclusions
- Case I no taxes or bankruptcy costs
- No optimal capital structure
- Case II corporate taxes but no bankruptcy costs
- Optimal capital structure is 100 debt
- Each additional dollar of debt increases the cash
flow of the firm - Case III corporate taxes and bankruptcy costs
- Optimal capital structure is part debt and part
equity - Occurs where the benefit from an additional
dollar of debt is just offset by the increase in
expected bankruptcy costs
93Additional Managerial Recommendations
- The tax benefit is only important if the firm has
a large tax liability - Risk of financial distress
- The greater the risk of financial distress, the
less debt will be optimal for the firm - The cost of financial distress varies across
firms and industries and as a manager you need to
understand the cost for your industry
94Observed Capital Structure
- Capital structure does differ by industries
- Differences according to Cost of Capital 2000
Yearbook by Ibbotson Associates, Inc. - Lowest levels of debt
- Drugs with 2.75 debt
- Computers with 6.91 debt
- Highest levels of debt
- Steel with 55.84 debt
- Department stores with 50.53 debt
95Chapter 13 Quick Quiz
- Explain the effect of leverage on EPS and ROE
- What is the break-even EBIT?
- How do we determine the optimal capital
structure? - What is the optimal capital structure in the
three cases that were discussed in this chapter?