COST OF CAPITALCHAPTER 14Copyright © 2019 McGraw-Hill Educat

COST OF CAPITAL
CHAPTER 14
Copyright © 2019 McGraw-Hill Education. All rights reserved.
No reproduction or distribution without the prior written
consent of McGraw-Hill Education.
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Determine a firm’s cost of equity capital
Determine a firm’s cost of debt
Determine a firm’s overall cost of capital and how to use it to
value a company
Explain how to correctly include flotation costs in capital
budgeting projects
Describe some of the pitfalls associated with a firm’s overall
cost of capital and what to do about them
Key Concepts and Skills

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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
Company Valuation with the WACC
Flotation Costs and the Weighted Average Cost of Capital
Chapter Outline
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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 budgeti ng projects.
Why Cost of Capital Is Important
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12.4
Section 14.1
Lecture Tip: Students often find it easier to grasp the intricacies
of cost of capital estimation when they understand why it is
important. A good estimate is required for:
-good capital budgeting decisions – neither the NPV rule nor
the IRR rule can be implemented without knowledge of the
appropriate discount rate
-financing decisions – the optimal/target capital structure
minimizes the cost of capital
-operating decisions – cost of capital is used by regulatory
agencies in order to determine the “fair” return in some
regulated industries (e.g. utilities)
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.
Required Return
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Section 14.1 (A)
12.5
The cost of equity is the return required by equity investors
given the risk of the cash flows from the firm.
Business risk
Financial risk
There are two major methods for determining the cost of equity.
Dividend growth model
SML, or CAPM
Cost of Equity
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Section 14.2
12.6

Start with the dividend growth model formula and rearrange to
solve for RE.
The Dividend Growth Model Approach
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12.7
Section 14.2 (A)
Remind students that D1 = D0(1+g).
You may also want to take this time to remind them that return
is comprised of the dividend yield (D1 / P0) and the capital
gains yield (g).
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?
Example: Dividend
Growth Model

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12.8
Section 14.2 (A)
One method for estimating the growth rate is to use the
historical average.
YearDividendPercent Change
20141.23-
20151.30
20161.36
20171.43
20181.50
Example: Estimating the Dividend Growth Rate
(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%
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12.9
Section 14.2 (A)

Our historical growth rates are fairly close, so we could feel
reasonably comfortable that the market will expect our dividend
to grow at around 5.1%. Note that when we are computing our
cost of equity, it is important to consider what the market
expects our growth rate to be, not what we may know it to be
internally. The market price is based on market expectations,
not our private information. So, another way to estimate the
market consensus estimate is to look at analysts’ forecasts and
take an average.
Lecture Tip: It is noted in the text that there are other ways to
compute g. Rather than use the arithmetic mean, as in the
example, the geometric mean (which implies a compound
growth rate) can be used. OLS regression with the log of the
dividends as the dependent variable and time as the independent
variable is also an option. Another way to estimate g is to
assume that the ROE and retention rate are constant. If this is
the case, then g = ROE × retention rate.
Advantage – easy to understand and use
Disadvantages
Only applicable to companies currently paying dividends
Not applicable if dividends aren’t 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
Advantages and Disadvantages of Dividend Growth Model

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12.10
Section 14.2 (A)
Point out that there is no allowance for the uncertainty about
the growth rate.
Lecture Tip: Some students may question how you value the
stock for a firm that doesn’t pay dividends. In the case of
growth-oriented, non-dividend-paying firms, analysts often look
at the trend in earnings or use similar firms to project the future
date of the first expected dividend and its future growth rate.
However, such processes are subject to greater estimation error,
and when companies fail to meet (or even exceed) estimates, the
stock price can experience a high degree of variability. It should
also be pointed out that no firm pays zero dividends forever – at
some point, every going concern will pay dividends. Microsoft
is a good example. Many people believed that Microsoft would
never pay dividends, but even it ran out of investments for all
of the cash that it generated and began paying dividends in
2003.
Use the following information to compute our cost of equity.
Risk-free rate, Rf
Market risk premium, E(RM) – Rf
Systematic
You can find data on betas and rates at Yahoo! Finance.
The SML Approach

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12.11
Section 14.2 (B)
You will often hear this referred to as the Capital Asset Pricing
Model Approach as well.
www: Click on the link to go to finance.yahoo.com. Both betas
and 3-month T-bills are available on this site. To get betas,
enter a ticker symbol to get the stock quote, then choose Key
Statistics. To get the T-bill rates, click on “Bonds” under
Investing on the home page.
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 good about
our estimate.
Example – SML
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12.12

Section 14.2 (B)
The similarity is completely dependent on estimates of the risk-
free rate and market risk premium.
Advantages
Explicitly adjusts for systematic risk
Applicable to all companies, as long as we can estimate 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 using the past to predict the future, which is not always
reliable.
Advantages and Disadvantages of SML
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12.13
Section 14.2 (B)
A good example to illustrate how beta estimates can lag changes
in the risk of equity, consider Citigroup (C), which was used in
an example in the slides in the previous chapter. In Sept. 2012,
(based on calculations on Yahoo) Citigroup had a beta of 2.6.
Yet, its capital gains return from Sept 2002 to Sept 2012 was
almost -90%!! On the positive side, in Sept. 2012, APPL had a
beta of .88, yet its capital gains return over the past 10 years
was over 9,000%!!!!!.

Lecture Tip: Students are often surprised when they find that
the two approaches typically result in different estimates.
Suggest that it would be more surprising if the results were
identical. Why? The underlying assumptions of the two
approaches are very different. The constant growth model is a
variant of a growing perpetuity model and requires that
dividends are expected to grow at a constant rate forever and
that the discount rate is greater than the growth rate. The SML
approach requires assumptions of normality of returns and/or
quadratic utility functions. It also requires the absence of taxes,
transaction costs, and other market imperfections.
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%
Example – Cost of Equity
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12.14
Section 14.2

Since the two models are reasonably close, we can assume that
our cost of equity is probably around 19.5%. Again, though, this
similarity is a function of the inputs selected and is not
indicative of the true similarity that could be expected.
The cost of debt is the required return on our company’s 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.
Cost of Debt
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12.15
Section 14.3 (A)
Point out that the coupon rate was the cost of debt for the
company when the bond was issued. We are interested in the
rate we would have to pay on newly issued debt, which could be
very different from past rates.
Lecture Tip: Consider what happens to corporate bond rates and

mortgage rates as the Federal Reserve board changes the fed
funds rate. If the Federal Reserve raises the fed funds rate by a
quarter point, virtually all bond rates, from government to
municipal to corporate, will increase after this action.
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 $1,000 bond.
What is the cost of debt?
N = 50; PMT = 45; FV = 1000; PV = -908.72; CPT I/Y = 5%;
YTM = 5(2) = 10%
Example: Cost of Debt
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12.16
Section 14.3 (A)
Remind students that it is a trial and error process to find the
YTM if they do not have a financial calculator or spreadsheet
application.
Reminders
Preferred stock generally pays a constant dividend each period.
Dividends are expected to be paid every period forever.
Preferred stock is a perpetuity, so we take the perpetuity
formula, rearrange and solve for RP.

RP = D / P0
Cost of Preferred Stock
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Section 14.3 (B)
12.17
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%
Example: Cost of Preferred Stock
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Section 14.3 (B)
12.18
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 the firm’s assets, based
on the market’s perception of the risk of those assets.
The weights are determined by how much of each type of
financing is used.
The Weighted Average Cost of Capital
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Section 14.4
12.19
Notation
E = market value of equity = # of outstanding shares times price
per share
D = market value of debt = # of 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
Capital Structure Weights

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12.20
Section 14.4 (A)
Note that for bonds we would find the market value of each
bond issue and then add them together.
Also note that preferred stock would just become another
component of the equation if the firm has issued it.
Finally, we generally ignore current liabilities in our
computations. However, if a company finances a substantial
portion of its assets with current liabilities, it should be
included in the process.
Lecture Tip: It may be helpful to mention and differentiate
between the three types of weightings in the capital structure
equation: book, market and target. It is also helpful to mention
that the total market value of equity incorporates the market
value of all three common equity accounts on the balance sheet
(common stock, additional paid-in capital and retained
earnings).
Lecture Tip: The cost of short-term debt is usually very
different from that of long-term debt. Some types of current
liabilities are interest-free, such as accruals. However, accounts
payable has a cost associated with it if the company forgoes
discounts. The cost of notes payable and other current liabilities
depends on market rates of interest for short-term loans. Since
these loans are often negotiated with banks, you can get
estimates of the short-term cost of capital from the company’s
bank. The market value and book value of current liabilities are

usually very similar, so you can use the book value as an
estimate of market value.
Suppose you have a market value of equity equal to $500
million and a market value of debt equal to $475 million.
What are the capital structure weights?
V = 500 million + 475 million = 975 million
wE = E/V = 500 / 975 = .5128 = 51.28%
wD = D/V = 475 / 975 = .4872 = 48.72%
Example: Capital Structure Weights
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12.21
Section 14.4 (A)
We are concerned with aftertax cash flows, so we also need to
consider the effect of taxes on the various costs of capital.
Interest expense reduces our tax liability (subject to limitation).
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)
Taxes and the WACC

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12.22
Section 14.4 (B)
Point out that if we have other financing that is a significant
part of our capital structure, we would just add additional terms
to the equation and consider any tax consequences.
The Tax Cuts and Jobs Act of 2017 placed limitations on the
amount of interest that can be deducted in certain situations. If
there is no deduction, then the pretax and aftertax cost of debt
would be equal. If any deduction is allowed, then the aftertax
cost would be lower.
Lecture Tip: With a lower tax rate and/or less deductibility, the
overall WACC would be higher, which would reduce
project/firm value. However, the lower tax rate also increases
cash flows, which would increase project/firm value. The latter
seems to be the dominant impact.
Lecture Tip: If the firm utilizes substantial amounts of current
liabilities, equation 14.7 from the text should be modified as
follows:
WACC = (E/V)RE + (D/V)RD(1-TC) + (P/V)RP +
(CL/V)RCL(1-TC)
where CL/V represents the market value of current liabilities in
the firm’s capital structure and V = E + D + P + CL.

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 = 21%
Extended Example: WACC - I
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12.23
Section 14.4 (B)
Remind students that bond prices are quoted as a percent of par
value.
What is the cost of equity?
RE = 5 + 1.15(9) = 15.35%
What is the cost of debt?
N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268
RD = 3.927(2) = 7.854%

What is the after-tax cost of debt?
RD(1-TC) = 7.854(1-.21) = 6.205%
Extended Example: WACC - II
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12.24
Section 14.4 (B)
Point out that students do not have to compute the YTM based
on the entire face amount. They can still use a single bond or
they could also base everything on 100 (PV = -110; FV = 100;
PMT = 4.5).
We assume that the interest expense remains fully deductible.
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(6.205%) = 13.38%
Extended Example: WACC - III

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12.25
Section 14.4 (B)
Go to Yahoo! Finance to get information on Eastman Chemical
(EMN).
Under Profile and Key Statistics, you can find the following
information:
# of shares outstanding
Book value per share
Price per share
Beta
Under analysts estimates, you can find analysts estimates of
earnings growth (use as a proxy for dividend growth).
The Bonds section at Yahoo! Finance can provide the T-bill
rate.
Use this information, along with the CAPM and DGM, to
estimate the cost of equity.
Eastman Chemical I
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Section 14.4 (C)
12.26

Go to FINRA to get market information on Eastman Chemical’s
bond issues.
Enter “Eastman Ch” to find the bond information.
Note that you may not be able to find information on all bond
issues due to the illiquidity of the bond market.
Go to the SEC website to get book value information from the
firm’s most recent 10Q.
Eastman Chemical II
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Section 14.4 (C)
12.27
Find the weighted average cost of the debt.
Use market values if you were able to get the information.
Use the book values if market information was not available.
They are often very close.
Compute the WACC.
Use market value weights if available.
Eastman Chemical III

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Section 14.4 (C)
12.28
Find estimates of WACC at ValuePro.
Look at the assumptions.
How do the assumptions impact the estimate of WACC?
Example: Work the Web
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Section 14.4 (C)
12.29
Table 14.1 Cost of Equity

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Section 14.4 (C)
12.30
Table 14.1 Cost of Debt
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Section 14.4 (C)
12.31
Table 14.1 WACC
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Section 14.4 (C)
12.32

Using the WACC as our discount rate is only appropriate for
projects that have the same risk as the firm’s current operations.
If we are looking at a project that does NOT have the same risk
as the firm, then we need to determine the appropriate discount
rate for that project.
Divisions also often require separate
discount rates.
Does every GE Business Unit have the same cost?
Divisional and Project Costs of Capital
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12.33
Section 14.5
It is important to point out that a single corporate WACC is not
very useful for companies that have several disparate divisions.
www: Click on the link and then go to “GE Businesses” to see
an index of businesses owned by General Electric. Ask the
students if they think that projects proposed by “GE Capital”
should have the same discount rate as projects proposed by the
“Energy” group. You can go through the list and illustrate why
the divisional cost of capital is important for a company like
GE.
If GE’s WACC was used for every division, then the riskier

divisions would get more investme nt capital and the less risky
divisions would lose the opportunity to invest in positive NPV
projects.
What would happen if we use the WACC for all projects
regardless of risk?
Assume the WACC = 15%
ProjectRequired ReturnIRR
A20%17%
B15%18%
C10%12%
Example: Using WACC
for All Projects
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12.34
Section 14.5 (B)
Ask students which projects would be accepted if they used the
WACC for the discount rate? Compare 15% to the IRR and
accept projects A and B.
Now ask students which projects should be accepted if you use
the required return based on the risk of the project? Accept B
and C.
So, what happened when we used the WACC? We accepted a

risky project that we shouldn’t have and rejected a less risky
project that we should have accepted. What will happen to the
overall risk of the firm if the company does this on a consistent
basis? Most students will see that the firm will become riskier.
What will happen to the firm’s cost of capital as the firm
becomes riskier? It will increase (adjusting for changes in
market returns in general) as well.
Lecture Tip: It may help students to distinguish between the
average cost of capital to the firm and the required return on a
given investment if the idea is turned around from the firm’s
point of view to the investor’s point of view. Consider an
investor who is holding a portfolio of T-bills, corporate bonds
and common stocks. Suppose there is an equal amount invested
in each. The T-bills have paid 5% on average, the corporate
bonds 10%, and the common stocks 15%. Thus, the average
portfolio return is 10%. Now suppose that the investor has some
additional money to invest and they can choose between T-bills
that are currently paying 7% and common stock that is expected
to pay 13%. What choice will the investor make if he uses the
10% average portfolio return as his cut-off rate? (Invest in
common stock 13%>10%, but not in T-bills 7%<10%.) What if
he uses the average return for each security as the cut-off rate?
(Invest in T-bills 7% > 5%, but not common stock 13%<15%.)
Lecture Tip: You may wish to point out here that the divisional
concept is no more than a firm-level application of the portfolio
concept introduced in the section on risk and return. And, not
surprisingly, the overall firm beta is therefore the weighted
average of the betas of the firm’s divisions.
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
The Pure Play Approach
14-‹#›
12.35
Section 14.5 (C)
Note that technically you need to unlever the beta for each
company before computing the average. Once the average of the
unlevered beta has been found, you then relever to match the
capital structure of the firm. This is done because the equity
beta contains both business risk and financial risk – what we
really need is the business risk and then we apply our own
financial risk.
Consider the project’s risk relative to the firm overall.
If the project has more risk than the firm, use a discount rate
greater than the WACC.
If the project has less risk than the firm, use a discount rate less
than the WACC.
You may still accept projects that you shouldn’t and reject

projects you should accept, but your error rate should be lower
than not considering differential risk at all.
Subjective Approach
14-‹#›
12.36
Section 14.5 (D)
Lecture Tip: Ask the class to consider a situation in which a
company maintains a large portfolio of marketable securities.
Now ask them to consider the impact this large security balance
would have on a company’s current and quick ratios and how
this might impact the company’s ability to meet short-term
obligations. The students should easily remember that a larger
liquidity ratio implies less risk (and less potential profit).
Although the revenue realized from the marketable securities
would be less than the interest expense on the company’s
comparable debt issues, these holdings would result in lowering
the firm’s beta and WACC. This example allows students to
recognize that the expected return and beta of an investment in
marketable securities would be below the company’s WACC,
and justification for such investments must be considered
relative to a benchmark other than the company’s overall
WACC.
International Note: The difficulty in arriving at an appropriate
estimate of the cost of capital for project analysis is magnified
for firms engaged in multinational investing. In Financial
Management for the Multinational Firm, Abdullah suggests that

adjustments to foreign project hurdle rates should reflect the
effects of the following:
-foreign exchange risk
-political risk
-capital market segmentation
-international diversification effects
Making these adjustments requires a great deal of judgment and
expertise, as well as an understanding of the underlying
financial theory. Most multinational firms find it expeditious to
adjust the hurdle rates subjectively, rather than attempting to
quantify precisely the effects of these factors for each foreign
project.
Risk LevelDiscount RateVery Low RiskWACC – 8%Low
RiskWACC – 3%Same Risk as FirmWACCHigh RiskWACC +
5%Very High RiskWACC + 10%
Example: Subjective Approach
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12.37
Section 14.5 (D)
Lecture Tip: What an individual firm considers a risky
investment and what the financial market considers a risky
investment may not be the same. Recall that the market is
concerned with systematic risk, or non-diversifiable risk. If a
firm is considering an investment’s total risk in assigning it to a
risk category, the risk categories may not line up with the SML.

The WACC can be useful for investment analysts when trying to
measure the value of a company.
If an analyst can predict future CFFA for the entire firm, WACC
becomes the firm’s discount rate.
To separate financing costs from the cash flows, the tax amount
should be the amount that would be paid if the firm used no
debt.
With no debt, Adjusted CFFA, or CFA*:
CFA* = EBIT × (1 – TC) + Depreciation – Change in NWC –
Capital spending
If these cash flows continue to grow at growth rate g
perpetually, the firm value today is:
V0 = CFA*1 / (WACC – g); CFA*1 is next year’s projected
value
Company Valuation with the WACC
14-‹#›
Section 14.6
See Example 14.6 in the book for an application of this
methodology.
12.38
The required return depends on the risk, not how the money is
raised.
However, the cost of issuing new securities should not just be
ignored either.

Basic Approach
Compute the weighted average flotation cost.
Use the target weights, because the firm will issue securities in
these percentages over the long term.
Flotation Costs
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Section 14.7 (A)
12.39
Your company is considering a project that will cost $1 million.
The project will generate aftertax cash flows of $250,000 per
year for 7 years. The WACC is 15%, and the firm’s target D/E
ratio is .6 The flotation cost for equity is 5%, and the flotation
cost for debt is 3%. What is the NPV for the project after
adjusting for flotation costs?
fA = (.375)(3%) + (.625)(5%) = 4.25%
PV of future cash flows = 1,040,105
NPV = 1,040,105 - 1,000,000/(1-.0425) = -4,281
The project would have a positive NPV of 40,105 without
considering flotation costs.
Once we consider the cost of issuing new securities, the NPV
becomes negative.
Example: NPV and

Flotation Costs
14-‹#›
12.40
Section 14.7 (B)
D/E = .6; Let E = 1; then D = .6
V = .6 + 1 = 1.6
D/V = .6 / 1.6 = .375; E/V = 1/1.6 = .625
PMT = 250,000; N = 7; I/y = 15; CPT PV = 1,040,105
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 isn’t appropriate?
How should we factor flotation costs into our analysis?

Quick Quiz
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Section 14.8
12.41
How could a project manager adjust the cost of capital (i.e.,
appropriate discount rate) to increase the likelihood of having
his/her project accepted?
Is this ethical or financially sound?
Ethics Issues
14-‹#›
12.42
A manager could assume that the project is less risky than the
typical firm project and therefore apply a lower discount rate,
which would increase the NPV. This illustrates the importance
of sensitivity analysis for corporate headquarters in evaluating
proposed projects.
A corporation has 10,000 bonds outstanding with a 6% annual
coupon rate, 8 years to maturity, a $1,000 face value, and a

$1,100 market price.
The company’s 100,000 shares of preferred stock pay a $3
annual dividend, and sell for $30 per share.
The company’s 500,000 shares of common stock sell for $25 per
share and have a beta of 1.5. The risk free rate is 4%, and the
market return is 12%.
Assuming a 21% tax rate, what is the company’s WACC?
Comprehensive Problem
14-‹#›
12.43
Section 14.8
MV of debt = 10,000 × $1,100 = $11,000,000
Cost of debt = YTM: 8 N; -1,100 PV; 60 PMT; 1,000 FV; CPT
I/Y = 4.48%
MV of preferred = 100,000 × $30 = $3,000,000
Cost of preferred = 3/30 = 10%
MV of common = 500,000 × $25 = $12,500,000
Cost of common = .04 + 1.5 × (.12 - .04) = 16%
Total MV of all securities = $11M + $3M + $12.5M = 26.5M
Weight of debt = 11M/26.5M = .4151

Weight of preferred = 3M/26.5M = .1132
Weight of common = 12.5M/26.5M = .4717
WACC = .4151 × .0448 × (1 - .21) + .1132 × .10 + .4717 × .16
= .0979 = 10.15%
End of Chapter
Chapter 14
14-‹#›
14-‹#›
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RETURN, RISK, AND THE SECURITY MARKET LINE
CHAPTER 13
1-‹#›
Show how to calculate expected returns, variance, and standard

deviation
Discuss the impact of diversification
Summarize the systematic risk principle
Describe the security market line and the risk-return trade-off
1-‹#›
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

Chapter Outline
1-‹#›
11.3
Lecture Tip: You may find it useful to emphasize the economic
foundations of the material in this chapter. Specifically, we
assume:
-Investor rationality: Investors are assumed to prefer more
money to less and less risk to more, all else equal. The result of
this assumption is that the ex ante risk-return trade-off will be
upward sloping.
-As risk-averse return-seekers, investors will take actions
consistent with the rationality assumptions. They will require
higher returns to invest in riskier assets and are willing to
accept lower returns on less risky assets.
-Similarly, they will seek to reduce risk while attaining the
desired level of return, or increase return without exceeding the
maximum acceptable level of risk.
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.

Expected Returns
1-‹#›
11.4
Section 13.1 (A)
Use the following example to illustrate the mathematical nature
of expected returns:
Consider a game where you toss a fair coin: If it is Heads, then
student A pays student B $1. If it is Tails, then student B pays
student A $1. Most students will remember from their statistics
that the expected value is $0 (=.5(1) + .5(-1)). That means that
if the game is played over and over then each student should
expect to break-even. However, if the game is only played once,
then one student will win $1 and one will lose $1.
Suppose you have predicted the following returns for stocks C
and T in three possible states of the economy. What are the
expected returns?
StateProbability C T___
Boom0.30.150.25
Normal0.50.100.20
Recession ???0.020.01
RC = .3(15) + .5(10) + .2(2) = 9.9%
RT = .3(25) + .5(20) + .2(1) = 17.7%

Example: Expected Returns
1-‹#›
11.5
Section 13.1 (A)
What is the probability of a recession? 1- 0.3 - 0.5 = 0.2
If the risk-free rate is 4.15%, what is the risk premium?
Stock C: 9.9 – 4.15 = 5.75%
Stock T: 17.7 – 4.15 = 13.55%
Variance and standard deviation measure the volatility of
returns.
Using unequal probabilities for the entire range of possibilities
Weighted average of squared deviations
Variance and Standard Deviation
1-‹#›

11.6
Section 13.1 (B)
It’s important to point out that these formulas are for
populations, unlike the formulas in chapter 12 that were for
samples (dividing by n-1 instead of n). Further, the probabilities
that are used account for the division.
Remind the students that standard deviation is the square root of
the variance.
Consider the previous example. What are the variance and
standard deviation for each stock?
Stock C
-0.099)2 + .5(0.10-0.099)2 + .2(0.02-0.099)2 =
0.002029
Stock T
-0.177)2 + .5(0.20-0.177)2 + .2(0.01-0.177)2 =
0.007441
Example: Variance and Standard Deviation
1-‹#›

11.7
Section 13.1 (B)
It is helpful to remind students that the standard deviation (but
not the variance) is expressed in the same units as the original
data, which is a percentage return in our example.
Consider the following information:
StateProbability ABC, Inc. Return
Boom.25 0.15
Normal.50 0.08
Slowdown.15 0.04
Recession.10-0.03
What is the expected return?
What is the variance?
What is the standard deviation?
Another Example
1-‹#›
11.8
Section 13.1 (B)
E(R) = .25(0.15) + .5(0.08) + .15(0.04) + .1(-0.03) = 8.05%
Variance = .25(.15-0.0805)2 + .5(0.08-0.0805)2 + .15(0.04-
0.0805)2 + .1(-0.03-0.0805)2 = 0.00267475

Standard Deviation = 5.17%
A portfolio is a collection of assets.
An asset’s risk and return are important in how they affect 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.
Portfolios
1-‹#›
11.9
Section 13.2
Lecture Tip: Each individual has their own level of risk
tolerance. Some people are just naturally more inclined to take
risk, and they will not require the same level of compensation
as others for doing so. Our risk preferences also change through
time. We may be willing to take more risk when we are young
and without a spouse or kids. But, once we start a family, our
risk tolerance may drop.
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 C
$3000 of KO
$4000 of INTC
$6000 of BP
Example: Portfolio Weights
C: 2/15 = .133
KO: 3/15 = .2
INTC: 4/15 = .267
BP: 6/15 = .4
1-‹#›
11.10
Section 13.2 (A)
C – Citigroup
KO – Coca-Cola
INTC – Intel
BP – BP
Show the students that the sum of the weights = 1
The expected return of a portfolio is the weighted average of the
expected returns of the respective assets 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.
Portfolio Expected Returns
1-‹#›
Section 13.2 (B)
11.11
Consider the portfolio weights computed previously. If the
individual stocks have the following expected returns, what is
the expected return for the portfolio?
C: 19.69%
KO: 5.25%
INTC: 16.65%
BP: 18.24%
E(RP) = .133(19.69%) + .2(5.25%) + .267(16.65%) +
.4(18.24%) = 15.41%
Example: Expected Portfolio Returns

1-‹#›
Section 13.2 (B)
11.12
Compute the portfolio return for each state:
RP = 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.
Portfolio Variance
1-‹#›
11.13
Section 13.2 (C)
Consider the following information on returns and probabilities:
Invest 50% of your money in Asset A.
StateProbabilityABPortfolio
Boom .430%-5%12.5%

Bust .6 -10%25%7.5%
What are the expected return and standard deviation for each
asset?
What are the expected return and standard deviation for the
portfolio?
Example: Portfolio Variance
1-‹#›
11.14
Section 13.2 (C)
If A and B are your only choices, what percent are you
investing in Asset B? 50%
Asset A: E(RA) = .4(30) + .6(-10) = 6%
Variance(A) = .4(30-6)2 + .6(-10-6)2 = 384
Std. Dev.(A) = 19.6%
Asset B: E(RB) = .4(-5) + .6(25) = 13%
Variance(B) = .4(-5-13)2 + .6(25-13)2 = 216
Std. Dev.(B) = 14.7%
Portfolio (solutions to portfolio return in each state appear with
mouse click after last question)
Portfolio return in boom = .5(30) + .5(-5) = 12.5
Portfolio return in bust = .5(-10) + .5(25) = 7.5
Expected return = .4(12.5) + .6(7.5) = 9.5 or
Expected return = .5(6) + .5(13) = 9.5

Variance of portfolio = .4(12.5-9.5)2 + .6(7.5-9.5)2 = 6
Standard deviation = 2.45%
Note that the variance is NOT equal to .5(384) + .5(216) = 300
and
Standard deviation is NOT equal to .5(19.6) + .5(14.7) =
17.17%
What would the expected return and standard deviation for the
portfolio be if we invested 3/7 of our money in A and 4/7 in B?
Portfolio return = 10% and standard deviation = 0
Portfolio variance using covariances:
COV(A,B) = .4(30-6)(-5-13) + .6(-10-6)(25-13) = -288
Variance of portfolio = (.5)2(384) + (.5)2(216) + 2(.5)(.5)( -288)
= 6
Consider the following information on returns and probabilities:
StateProbabilityXZ
Boom.2515%10%
Normal.6010%9%
Recession.155%10%
What are the expected return and standard deviation for a
portfolio with an investment of $6,000 in asset X and $4,000 in
asset Z?
Another Example: Portfolio Variance
1-‹#›

11.15
Section 13.2 (C)
Portfolio return in Boom: .6(15) + .4(10) = 13%
Portfolio return in Normal: .6(10) + .4(9) = 9.6%
Portfolio return in Recession: .6(5) + .4(10) = 7%
Expected return = .25(13) + .6(9.6) + .15(7) = 10.06%
Variance = .25(13-10.06)2 + .6(9.6-10.06)2 + .15(7-10.06)2 =
3.6924
Compare to return on X of 10.5% and standard deviation of
3.12%
And return on Z of 9.4% and standard deviation of .49%
Using covariances:
COV(X,Z) = .25(15-10.5)(10-9.4) + .6(10-10.5)(9-9.4) + .15(5-
10.5)(10-9.4) = .3
Portfolio variance = (.6 × 3.12)2 + (.4 × .49)2 + 2(.6)(.4)(.3) =
3.6868
Portfolio standard deviation = 1.92% (difference in variance due
to rounding)
Lecture Tip: Here are a few tips to pass along to students
suffering from “statistics overload”:
-The distribution is just the picture of all possible outcomes.
-The mean return is the central point of the distribution.
-The standard deviation is the average deviation from the mean.
-Assuming investor rationality (two-parameter utility
functions), the mean is a proxy for expected return and the
standard deviation is a proxy for total risk.

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.
Expected vs. Unexpected Returns
1-‹#›
Section 13.3 (A)
11.16
Announcements and news contain both an expected component
and a surprise component.
It is the surprise component that affects a stock’s price and
therefore its return.
This is very obvious when we watch how stock prices move
when an unexpected announcement is made or earnings are
different than anticipated.
Announcements and News

1-‹#›
11.17
Section 13.3 (B)
Lecture Tip: It is easy to see the effect of unexpected news on
stock prices and returns. Consider the following two cases:
(1) On November 17, 2004 it was announced that K-Mart would
acquire Sears in an $11 billion deal. Sears’ stock price jumped
from a closing price of $45.20 on November 16 to a closing
price of $52.99 (a 7.79% increase) and K-Mart’s stock price
jumped from $101.22 on November 16 to a closing price of
$109.00 on November 17 (a 7.69% increase). Both stocks traded
even higher during the day. Why the jump in price? Unexpected
news, of course. (2) On November 18, 2004, Williams-Sonoma
cut its sales and earnings estimates for the fourth quarter of
2004 and its share price dropped by 6%. There are plenty of
other examples where unexpected news causes a change in price
and expected returns.
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.

Efficient Markets
1-‹#›
Section 13.3 (B)
11.18
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.
Systematic Risk
1-‹#›
11.19
Section 13.4 (A)
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.
Unsystematic Risk
1-‹#›
11.20
Section 13.4 (A)
Lecture Tip: You can expand the discussion of the difference
between systematic and unsystematic risk by using the example
of a strike by employees. Students will generally agree that this
is unique or unsystematic risk for one company. However, what
if the UAW stages the strike against the entire auto industry.
Will this action impact other industries or the entire economy?
If the answer to this question is yes, then this becomes a
systematic risk factor. The important point is that it is not the
event that determines whether it is systematic or unsystematic
risk; it is the impact of the event.
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

Returns
1-‹#›
Section 13.4 (B)
11.21
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.
Diversification
1-‹#›

11.22
Section 13.5
Video Note: “Portfolio Management” looks at the value of
diversification.
Table 13.7
1-‹#›
Section 13.5 (A)
11.23
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.
The Principle of Diversification

1-‹#›
11.24
Section 13.5 (B)
A discussion of the potential benefits of international investing
may be helpful at this point.
Figure 13.1
1-‹#›
Section 13.5 (B)
11.25
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.
Diversifiable Risk
1-‹#›
Section 13.5 (C)
11.26
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.
Total Risk
1-‹#›
Section 13.5 (D)

11.27
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
asset’s systematic risk since unsystematic risk can be
diversified away.
Systematic Risk Principle
1-‹#›
11.28
Section 13.6 (A)
A discussion of diversification via mutual funds and ETFs may
add to the students’ understanding.
How do we measure systematic risk?
We use the beta coefficient.
What does beta tell us?
A beta of 1 implies the asset has the same systematic risk as the
overall market.
A beta < 1 implies the asset has less systematic risk than the

overall market.
A beta > 1 implies the asset has more systematic risk than the
overall market.
Measuring Systematic Risk
1-‹#›
11.29
Section 13.6 (B)
Lecture Tip: Remember that the cost of equity depends on both
the firm’s business risk and its financial risk. So, all else equal,
borrowing money will increase a firm’s equity beta because it
increases the volatility of earnings. Robert Hamada derived the
following equation to reflect the relationship between levered
and unlevered betas (excluding tax effects):
where:
D/E = debt-to-equity ratio
Table 13.8 – Selected Betas

1-‹#›
11.30
Section 13.6 (B)
Lecture Tip: Students sometimes wonder just how high a stock’s
beta can get. In earlier years, one would say that, while the
average beta for all stocks must be 1.0, the range of possible
values for any given beta is from -
Today, the Internet provides another way of addressing the
question. Go to the Yahoo! Finance stock screener site. This
site allows you to search many financial markets by
fundamental criteria.
Consider the following information:
Standard DeviationBeta
Security C20%1.25
Security K30%0.95
Which security has more total risk?
Which security has more systematic risk?
Which security should have the higher expected return?
Total vs. Systematic Risk

1-‹#›
11.31
Section 13.6 (B)
Security K has the higher total risk.
Security C has the higher systematic risk.
Security C should have the higher expected return.
Many sites provide betas for companies.
Yahoo! Finance provides beta, plus a lot of other information
under its Key Statistics section.
Enter a ticker symbol and get a basic quote.
Click on Key Statistics.
Work the Web Example
1-‹#›
Section 13.6 (B)
11.32

Consider the previous example with the following four
securities.
SecurityWeightBeta
C.1331.685
KO.20.195
INTC.2671.161
BP.41.434
What is the portfolio beta?
.133(1.685) + .2(.195) + .267(1.161) + .4(1.434) = 1.147
Example: Portfolio Betas
1-‹#›
11.33
Section 13.6 (C)
Which security has the highest systematic risk?
C
Which security has the lowest systematic risk?
KO
Is the systematic risk of the portfolio more or less than the
market?
more
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!
Beta and the Risk Premium
1-‹#›
Section 13.7 (A)
11.34
Example: Portfolio Expected Returns and Betas
Rf
E(RA)
1-‹#›

11.35
Section 13.7 (A)
Based on the example in the book:
Point out that there is a linear relationship between beta and
expected return. Ask if the students remember the form of the
equation for a line.
Y = mx + b
E(R) = slope (Beta) + y-intercept
The y-intercept is = the risk-free rate, so all we need is the
slope
Lecture Tip: The example in the book illustrates a greater than
100% investment in asset A. This means that the investor has
borrowed money on margin (technically at the risk-free rate)
and used that money to purchase additional shares of asset A.
This can increase the potential returns, but it also increases the
risk.
Expected
Return00.40.81.21.622.40.080.110.140000000000000010.170.2
0.230.2600.40.81.21.622.400.40.81.21.622.400.40.81.21.622.4
Beta
Expected Return
The reward-to-risk ratio is the slope of the line illustrated in the
previous example.
Slope = (E(RA) – – 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)?
Reward-to-Risk Ratio: Definition and Example
1-‹#›
11.36
Section 13.7 (A)
Ask students if they remember how to compute the slope of a
line: rise / run.
If the reward-to-risk ratio = 8, then investors will want to buy
the asset. This will drive the price up and the expected return
down (remember time value of money and valuation). When will
the flurry of trading stop? When the reward-to-risk ratio reaches
7.5.
If the reward-to-risk ratio = 7, then investors will want to sell
the asset. This will drive the price down and the expected return
up. When will the flurry of trading stop? When the reward-to-
risk ratio reaches 7.5.

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.
Market Equilibrium
1-‹#›
Section 13.7 (A)
11.37
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) /
But since the beta for the market is always equal to one, the
slope can be rewritten.
Slope = E(RM) – Rf = market risk premium

Security Market Line
1-‹#›
11.38
Section 13.7 (B)
Based on the discussion earlier, we now have all the
components of the line:
E(R) = [E(RM) –
Lecture Tip: Although the realized market risk premium has on
average been approximately 8.5%, the historical average should
not be confused with the anticipated risk premium for any
particular future period. There is abundant evidence that the
realized market return has varied greatly over time. The
historical average value should be treated accordingly. On the
other hand, there is currently no universally accepted means of
coming up with a good ex ante estimate of the market risk
premium, so the historical average might be as good a guess as
any. In the late 1990’s, there was evidence that the risk
premium had been shrinking. In fact, Alan Greenspan was
concerned with the reduction in the risk premium because he
was afraid that investors had lost sight of how risky stocks
actually are. Investors had a wake-up call in late 2000 and 2001
(and again in 2008 and 2009).
The capital asset pricing model defines the relationship between
risk and return.

– Rf)
If we know an asset’s 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.
The Capital Asset Pricing Model (CAPM)
1-‹#›
Section 13.7 (B)
11.39
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
Factors Affecting
Expected Return

1-‹#›
Section 13.7 (B)
11.40
Consider the betas for each of the assets given earlier. If the
risk-free rate is 4.15% and the market risk premium is 7.5%,
what is the expected return for each?Security BetaExpected
Return C2.6853.15 + 1.685(7.5) = 15.79% KO0.1953.15 +
0.195(7.5) = 4.61% INTC2.1613.15 + 1.161(7.5) = 11.86%
BP2.4343.15 + 1.434(7.5) = 13.93%
Example - CAPM
1-‹#›
11.41
Section 13.7 (B)
Lecture Tip: Students should remember that in an efficient
market, security investments have an NPV = 0, on average.
However, the NPV does not imply that a company’s investments
in new projects must have an NPV of zero. Firms attempt to
invest in projects with a positive NPV, and those that are
consistently successful will trade at higher prices, all else
equal. The ability to generate positive NPV projects reflects the
fundamental differences in physical asset markets and financial
asset markets. Physical asset markets are generally less efficient

than financial asset markets, and cash flows to physical assets
are often owner dependent.
Figure 13.4
1-‹#›
Section 13.7 (B)
11.42
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?

Quick Quiz
1-‹#›
11.43
Section 13.9
Reward-to-risk ratio = 13 – 5 = 8%
Expected return = 5 + 1.2(8) = 14.6%
The risk free rate is 4%, and the required return on the market is
12%.
What is the required return on an asset with a beta of 1.5?
What is the reward/risk ratio?
What is the required return on a portfolio consisting of 40% of
the asset above and the rest in an asset with an average amount
of systematic risk?
1-‹#›

11.44
Section 13.9
R = .04 + 1.5 × (.12 - .04) = .16
The reward/risk ratio is 8%
R = (.4 × .16) + (.6 × .12) = .136
End of Chapter
Chapter 13
1-‹#›
1-‹#›
n
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ii
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CHAPTER 12
SOME LESSONS FROM CAPITAL MARKET HISTORY

12-‹#›
Calculate the return on an investment
Discuss the historical returns on various types of investments
Discuss the historical risks on various important types of
investments
Explain the implications of market efficiency
12-‹#›
Returns
The Historical Record

Average Returns: The First Lesson
The Variability of Returns: The Second Lesson
More about Average Returns
Capital Market Efficiency
Chapter Outline
12-‹#›
We can examine returns in the financial markets to help us
determine the appropriate returns on non-financial assets.
Lessons from capital market history
There is a reward for bearing risk.
The greater the potential reward, the greater the risk.
Risk, Return, and Financial Markets
12-‹#›
Section 12.1
10.4

Total dollar return =
income from investment
+ capital gain (loss) due to change in price
Example:
You bought a bond for $950 one year ago. You have received
two coupons of $30 each. You can sell the bond for $975 today.
What is your total dollar return?
Income = 30 + 30 = 60
Capital gain = 975 – 950 = 25
Total dollar return = 60 + 25 = $85
Dollar Returns
12-‹#›
10.5
Section 12.1 (A)
Lecture Tip: The issues discussed in this section need to be
stressed. Many students feel that if you don’t sell a security,
you won’t have to consider the capital gain or loss involved.
(This is a common investor’s mistake – holding a loser too long
because of reluctance to admit a bad decision was made.) Point
out that non-recognition is relevant for tax purposes – only
realized income must be reported. However, whether or not you
have liquidated the asset is irrelevant when measuring a
security’s pre-tax performance. Also, we need to annualize total
returns so that we can compare the performance of different
securities available in the market.

It is generally more intuitive to think in terms of percentage
rather than dollar returns.
Dividend yield = income / beginning price
Capital gains yield =
(ending price – beginning price)/ beginning price
Total percentage return =
dividend yield + capital gains yield
Percentage Returns
12-‹#›
10.6
Section 12.1 (B)
Note that the “dividend” yield is really just the yield on cash
flows received from the security (other than the selling price).
You bought a stock for $35, and you received dividends of
$1.25. The stock is now selling for $40.
What is your dollar return?
Dollar return = 1.25 + (40 – 35) = $6.25
What is your percentage return?
Dividend yield = 1.25 / 35 = 3.57%

Capital gains yield = (40 – 35) / 35 = 14.29%
Total percentage return = 3.57 + 14.29 = 17.86%
Example: Calculating Returns
12-‹#›
10.7
Section 12.1 (B)
You might want to point out that total percentage return is also
equal to total dollar return / beginning price.
Total percentage return = 6.25 / 35 = 17.86%
Financial markets allow companies, governments and
individuals to increase their utility.
Savers have the ability to invest in financial assets so that they
can defer consumption and earn a return to compensate them for
doing so.
Borrowers have better access to the capital that is available so
that they can invest in productive assets.
Financial markets also provide us with information about the
returns that are required for various levels of risk.
The Importance of Financial Markets

12-‹#›
Section 12.2
10.8
Figure 12.4
12-‹#›
Section 12.2 (A)
10.9
Large-Company Stock Returns
Long-Term Government Bond Returns
U.S. Treasury Bill Returns
Year-to-Year Total Returns

12-‹#›
10.10
Click on each of the excel icons to see a chart of year -to-year
returns similar to the charts in the text.
The charts were created using the data in Table 12.1.
The annual total return for stocks has been quite volatile.
InvestmentAverage ReturnLarge Stocks12.0%Small
Stocks16.6%Long-term Corporate Bonds6.3%Long-term
Government Bonds6.0%U.S. Treasury Bills3.4%Inflation3.0%
Average Returns
12-‹#›
10.11
A brief review of statistical properties may be in order at this
point, particularly as it relates to the normal distribution.
The “extra” return earned for taking on risk
Treasury bills are considered to be risk-free.
The risk premium is the return over and above the risk-free rate.

Risk Premiums
12-‹#›
10.12
InvestmentAverage ReturnRisk PremiumLarge
Stocks12.0%8.6%Small Stocks16.6%13.2%Long-term Corporate
Bonds6.3%2.9%Long-term Government Bonds6.0%2.6%U.S.
Treasury Bills3.4%0.0%
Table 12.3: Average Annual Returns and Risk Premiums
12-‹#›
10.13
Ask the students to think about why the different investments
have different risk premiums.
Large stocks: 12.0 – 3.4 = 8.6
Small stocks: 16.6 – 3.4 = 13.2
LT Corp. bonds: 6.3 – 3.4 = 2.9
LT Gov’t. bonds: 6.0 – 3.4 = 2.6

Figure 12.9
12-‹#›
Section 12.4 (A)
10.14
Variance and standard deviation measure the volatility of asset
returns.
The greater the volatility, the greater the uncertainty.
Historical variance =
sum of squared deviations from
the mean / (number of observations – 1)
Standard deviation =
square root of the variance
Variance and Standard Deviation
12-‹#›
10.15

Lecture Tip: Occasionally, students ask why we include the
above-mean returns in measuring dispersion, since these are
desirable from the investor’s viewpoint. This question provides
a natural springboard for a discussion of alternative variability
measures. Here we discuss semivariance as an alternative to
variance.
In Portfolio Selection (1959), Harry Markowitz states:
“Analyses based on [semivariance] tend to produce better
portfolios than those based on [variance]. Variance considers
extremely high and extremely low returns equally undesirable.
An analysis based on [variance] seeks to eliminate extremes. An
analysis based on [semivariance] on the other hand,
concentrates on reducing losses.”
Semivariance is computed in a manner similar to the traditional
variance, except that if the deviation is positive, its value is
replaced by zero. We still tend to use variance instead of
semivariance because semivariance tends to complicate the risk-
return issue, and besides, if returns are symmetrically
distributed, then variance is two times semivariance.
YearActual ReturnAverage ReturnDeviation from the
MeanSquared Deviation1.15.105.045.0020252.09.105-
.015.0002253.06.105-
.045.0020254.12.105.015.000225Totals.42.00.0045
Example: Variance and
Standard Deviation
Variance = .0045 / (4-1) = .0015 Standard Deviation =
.03873

12-‹#›
10.16
Remind students that the variance for a sample is computed by
dividing the sum of the squared deviations by the number of
observations – 1.
The standard deviation is just the square root.
Lecture Tip: It is sometimes difficult to get students to
appreciate the risk involved in investing in common stocks.
They see the large average returns and miss the variance. A
simple exercise illustrating the risk of the different securities
can be performed using Table 12.1. Each student (or the entire
class) is given an initial investment. They are then all owed to
choose a security class. Use a random number generator and the
last two digits of the year to sample the distribution. The initial
investment is then increased or decreased based on the return.
This works best if the trials are limited to between one and five.
How volatile are mutual funds?
Morningstar provides information on mutual funds, including
volatility.
Go to the Morningstar site.
Pick a fund, such as the American Funds EuroPacific Growth
Fund (AEPGX).
Enter the ticker, press go, and then click “Ratings & Risk”.
Work the Web Example

12-‹#›
Section 12.4 (B)
10.17
Figure 12.10
12-‹#›
Section 12.4 (C)
10.18
The normal distribution is a symmetric, bell-shaped frequency
distribution.
It is completely defined by its mean and standard deviation.
As seen in Figure 12.10, the returns appear to be at least
roughly normally distributed.
Normal distribution
12-‹#›

Section 12.4 (D)
10.19
Figure 12.11
12-‹#›
10.20
2008 was one of the worst years for stock market investors in
history.
The S&P 500 plunged 37 percent.
The index lost 17 percent in October alone.
From March ‘09 to Feb ‘11, the S&P 500 doubled in value.
Long-term Treasury bonds gained over 40 percent in 2008.
They lost almost 26 percent in 2009.
Recent market volatility
12-‹#›

Two lessons for investors from this recent volatility:
Stocks have significant risk
Diversification matters
10.21
Arithmetic average – return earned in an average period over
multiple periods
Geometric average – average compound return per period over
multiple periods
The geometric average will be less than the arithmetic average
unless all the returns are equal.
Which is better?
The arithmetic average is overly optimistic for long horizons.
The geometric average is overly pessimistic for short horizons.
So, the answer depends on the planning period under
consideration.
15 – 20 years or less: use the arithmetic
20 – 40 years or so: split the difference between them
40 + years: use the geometric
Arithmetic vs. Geometric Mean
12-‹#›
10.22
The calculation of an appropriate average can be extended using

Blume’s formula as described in the text.
What is the arithmetic and geometric average for the following
returns?
Year 1 5%
Year 2-3%
Year 3 12%
Arithmetic average = (5 + (–3) + 12)/3 = 4.67%
Geometric average =
[(1+.05) × (1-.03) × (1+.12)]1/3 – 1 = .0449 = 4.49%
Example: Computing Averages
12-‹#›
Section 12.5 (B)
10.23
Stock prices are in equilibrium or are “fairly” priced.
If this is true, then you should not be able to earn “abnormal” or
“excess” returns.
Efficient markets DO NOT imply that investors cannot earn a
positive return in the stock market.
Efficient Capital Markets

12-‹#›
10.24
Consider asking the students if market efficiency has increased
over time.
Figure 12.14
12-‹#›
Section 12.6 (A)
10.25
There are many investors out there doing research.
As new information comes to market, this information is
analyzed and trades are made based on this information.
Therefore, prices should reflect all available public information.
If investors stop researching stocks, then the market will not be
efficient.
What Makes Markets Efficient?

12-‹#›
10.26
Point out that one consequence of the wider availability of
information and lower transaction costs is that the market will
be more volatile. It is easier to trade on “small” news instead of
just big events.
It is also important to remember that not all available
information is reliable information. It’s important to still do the
research and not just jump on everything that crosses the news
wire. The case of Emulex, discussed earlier, is an excellent
example.
Daniel Tully, Chairman Emeritus of Merrill Lynch: “I’m not
smart enough to know the top or the bottom of a market.”
Efficient markets do not mean that you can’t make money.
They do mean that, on average, you will earn a return that is
appropriate for the risk undertaken and there is not a bias in
prices that can be exploited to earn excess returns.
Market efficiency will not protect you from wrong choices if
you do not diversify – you still don’t want to “put all your eggs
in one basket.”
Common Misconceptions
about EMH

12-‹#›
10.27
Lecture tip: Claims of superior performance in stock picking are
very common and often hard to verify. However, if markets are
semistrong form efficient, the ability to consistently earn excess
returns is unlikely.
Lecture Tip: Even the experts get confused about the meaning
of capital market efficiency. Consider the following quote from
a column in Forbes magazine: “Popular delusion three: Markets
are efficient. The efficient market [sic] hypothesis, or EMH,
would do credit to medieval alchemists and is about as
scientific as their efforts to turn base metals into gold.” The
writer is definitely not a proponent of EMH. Now consider this
quote: “The truth is nobody can consistently predict the ups and
downs of the market.” This statement is clearly consistent with
the EMH. Ironically, the same person wrote both statements in
the same column with exactly nine lines of type separating
them.
Prices reflect all information, including public and private.
If the market is strong form efficient, then investors could not
earn abnormal returns regardless of the information they
possessed.
Empirical evidence indicates that markets are NOT strong form
efficient and that insiders could earn abnormal returns.
Strong Form Efficiency

12-‹#›
10.28
Students are often very interested in insider trading. The case of
Martha Stewart is one with which most students tend to be
familiar.
Prices reflect all publicly available information including
trading information, annual reports, press releases, etc.
If the market is semistrong form efficient, then investors cannot
earn abnormal returns by trading on public information.
Implies that fundamental analysis will not lead to abnormal
returns
Semistrong Form Efficiency
12-‹#›
10.29
Empirical evidence suggests that some stocks are semistrong
form efficient, but not all. Larger, more closely followed stocks
are more likely to be semistrong form efficient. Small, more
thinly traded stocks may not be semistrong form efficient, but
liquidity costs may wipe out any abnormal returns that are
available.

Prices reflect all past market information such as price and
volume.
If the market is weak form efficient, then investors cannot earn
abnormal returns by trading on market information.
Implies that technical analysis will not lead to abnormal returns
Empirical evidence indicates that markets are generally weak
form efficient.
Weak Form Efficiency
12-‹#›
10.30
Emphasize that just because technical analysis shouldn’t lead to
abnormal returns, that doesn’t mean that you won’t earn fair
returns using it – efficient markets imply that you will.
You might also want to point out that there are many technical
trading rules that have never been empirically tested; so it is
possible that one of them might lead to abnormal returns. But if
it is well publicized, then any abnormal returns that were
available will soon evaporate.
Which of the investments discussed has had the highest average
return and risk premium?
Which of the investments discussed has had the highest standard
deviation?

What is capital market efficiency?
What are the three forms of market efficiency?
Quick Quiz
12-‹#›
Section 12.7
10.31
Program trading is defined as automated trading generated by
computer algorithms designed to react rapidly to changes in
market prices. Is it ethical for investment banking houses to
operate such systems when they may generate trade activity
ahead of their brokerage customers, to which they owe a
fiduciary duty?
Suppose that you are an employee of a printing firm that was
hired to proofread proxies that contained unannounced tender
offers (and unnamed targets). Should you trade on this
information, and would it be considered illegal?
Ethics Issues

12-‹#›
10.32
Case 2: The court decided in Chiarella v. United States that an
employee of a printing firm, who was requested to proofread
proxies that contained unannounced tender offers (and unnamed
targets) was not guilty of insider trading because the employee
determined the identity of the target through his own expertise.
Your stock investments return 8%, 12%, and -4% in consecutive
years. What is the geometric return?
What is the sample standard deviation of the above returns?
Using the standard deviation and mean that you just calculated,
and assuming a normal probability distribution, what is the
probability of losing 3% or more?
12-‹#›
10.33
Section 12.7
(1.08 × 1.12 × .96)^.3333 – 1 = .0511
Mean = ( .08 + .12 + -.04) / 3 = .0533
Variance = (.08 - .0533)^2 + (.12 - .0533)^2 = (-.04 - .0533)^2 /
(3 - 1)= .00693

Standard deviation = .00693 ^ .5 = .0833
Probability: a 3% loss (return of -3%) lies one standard
deviation below the mean. There is 16% of the probability
falling below that point (68% falls between -3% and 13.66%, so
16% lies below -3% and 16% lies above 13.66%).
End of Chapter
Chapter 12
12-‹#›
12-‹#›
Large Companies
Long-Term Government Bonds
U.S. Treasury Bills
Large
Company192619271928192919301931193219331934193519361
93719381939194019411942194319441945194619471948194919
50195119521953195419551956195719581959196019611962196
31964196519661967196819691970197119721973197419751976
19771978197919801981198219831984198519861987198819891
99019911992199319941995199619971998199920002001200220
03200420052006200720082009201020112012201320142015201

6
Year
Total Return
Large Company Stocks
0.1375
0.357
0.4508
-0.088
-0.2513
-0.436
-0.0875
0.5295
-0.0231
0.4679
0.3249
-0.3545
0.3163
-0.0143
-0.1036
-0.1202
0.2075
0.2538
0.1949
0.3621
-0.0842
0.0505
0.0499
0.1781
0.3005
0.2379
0.1839
-0.0107
0.5223
0.3162
0.0691
-0.105

0.4357
0.1201
0.0047
0.2684
-0.0875
0.227
0.1643
0.1238
-0.1006
0.2398
0.1103
-0.0843
0.0394
0.143
0.1899
-0.1469
-0.2647
0.3723
0.2393
-0.0716
0.0657
0.1861
0.325
-0.0492
0.2155
0.2256
0.0627
0.3173
0.1867
0.0525
0.1661
0.3169
-0.031
0.3046
0.0762
0.1008

0.0132
0.3758
0.2296
0.3336
0.2858
0.2104
-0.091
-0.1189
-0.221
0.2889
0.1088
0.0491
0.1579
0.0549
-0.37
0.2646
0.1506
0.0211
0.16
0.3239
0.1369
0.0141
0.1198
Long-Term
Bonds19261927192819291930193119321933193419351936193
71938193919401941194219431944194519461947194819491950
19511952195319541955195619571958195919601961196219631
96419651966196719681969197019711972197319741975197619
77197819791980198119821983198419851986198719881989199
01991199219931994199519961997199819992000200120022003
2004200520062007200820092010201120122013201420152016
Long-Term Government Bonds
Year
Total Return
0.0569
0.0658

0.0115
0.0439
0.0447
-0.0215
0.0851
0.0192
0.0759
0.042
0.0513
0.0144
0.0421
0.0384
0.057
0.0047
0.018
0.0201
0.0227
0.0529
0.0054
-0.0102
0.0266
0.0458
-0.0098
-0.002
0.0243
0.0228
0.0308
-0.0073
-0.0172
0.0682
-0.0172
-0.0202
0.1121
0.022
0.0572
0.0179

0.0371
0.0093
0.0512
-0.0286
0.0225
-0.0563
0.1892
0.1124
0.0239
0.033
0.04
0.0552
0.1556
0.0038
-0.0126
0.0126
-0.0248
0.0404
0.4428
0.0129
0.1529
0.3227
0.2239
-0.0303
0.0684
0.1854
0.0774
0.1936
0.0734
0.1306
-0.0732
0.2594
0.0013
0.1202
0.1445
-0.0751

0.1722
0.0551
0.1515
0.0201
0.0812
0.0689
0.0028
0.1085
0.4178
-0.2561
0.0773
0.3575
0.018
-0.1469
0.2474
-0.0064
0.0176
T-
bills1926192719280.04470.02270.01150.00880.00520.00270.00
170.00170.00270.00060.00040.00040.00140.00340.00380.00380
.00380.00380.00620.01060.01120.01220.01560.01750.01870.00
930.0180.02660.03280.01710.03480.02810.0240.02820.03230.0
3620.04060.04940.04390.05490.0690.0650.04360.04230.07290.
07990.05870.05070.05450.07640.10560.1210.1460.10940.08990
.0990.07710.06090.05880.06940.08440.07690.05430.03480.030
30.04390.05610.05140.05190.04860.0480.05980.03330.01610.0
0940.01140.02790.04970.04520.01240.00150.00140.00060.0008
0.00050.00030.00040.0021
T-Bills
Year
Total Return
0.033
0.0315
0.0405
Sheet1YearLarge-Company StocksLong-Term Government
BondsU.S. Treasury BillsConsumer Price

Index19260.13750.05690.033-0.011219270.3570.06580.0315-
0.022619280.45080.01150.0405-0.01161929-
0.0880.04390.04470.00581930-0.25130.04470.0227-0.0641931-
0.436-0.02150.0115-0.09321932-0.08750.08510.0088-
0.102719330.52950.01920.00520.00761934-
0.02310.07590.00270.015219350.46790.0420.00170.029919360.
32490.05130.00170.01451937-
0.35450.01440.00270.028619380.31630.04210.0006-
0.02781939-0.01430.03840.000401940-
0.10360.0570.00040.00711941-
0.12020.00470.00140.099319420.20750.0180.00340.090319430.
25380.02010.00380.029619440.19490.02270.00380.02319450.3
6210.05290.00380.02251946-
0.08420.00540.00380.181319470.0505-
0.01020.00620.088419480.04990.02660.01060.029919490.1781
0.04580.0112-0.020719500.3005-
0.00980.01220.059319510.2379-
0.0020.01560.0619520.18390.02430.01750.00751953-
0.01070.02280.01870.007419540.52230.03080.0093-
0.007419550.3162-0.00730.0180.003719560.0691-
0.01720.02660.02991957-0.1050.06820.03280.02919580.4357-
0.01720.01710.017619590.1201-
0.02020.03480.017319600.00470.11210.02810.013619610.2684
0.0220.0240.00671962-
0.08750.05720.02820.013319630.2270.01790.03230.016419640.
16430.03710.03620.009719650.12380.00930.04060.01921966-
0.10060.05120.04940.034619670.2398-
0.02860.04390.030419680.11030.02250.05490.04721969-
0.0843-
0.05630.0690.06219700.03940.18920.0650.055719710.1430.112
40.04360.032719720.18990.02390.04230.03411973-
0.14690.0330.07290.08711974-
0.26470.040.07990.123419750.37230.05520.05870.069419760.2
3930.15560.05070.04861977-
0.07160.00380.05450.06719780.0657-
0.01260.07640.090219790.18610.01260.10560.132919800.325-

0.02480.1210.12521981-
0.04920.04040.1460.089219820.21550.44280.10940.038319830.
22560.01290.08990.037919840.06270.15290.0990.039519850.3
1730.32270.07710.03819860.18670.22390.06090.01119870.052
5-
0.03030.05880.044319880.16610.06840.06940.044219890.3169
0.18540.08440.04651990-
0.0310.07740.07690.061119910.30460.19360.05430.030619920.
07620.07340.03480.02919930.10080.13060.03030.027519940.0
132-
0.07320.04390.026719950.37580.25940.05610.025419960.2296
0.00130.05140.033219970.33360.12020.05190.01719980.28580.
14450.04860.016119990.2104-0.07510.0480.02682000-
0.0910.17220.05980.03392001-0.11890.05510.03330.01552002-
0.2210.15150.01610.02420030.28890.02010.00940.01920040.10
880.08120.01140.03320050.04910.06890.02790.03420060.1579
0.00280.04970.025420070.05490.10850.04520.04082008-
0.370.41780.01240.000920090.2646-
0.25610.00150.027220100.15060.07730.00140.01520110.02110.
35750.00060.029620120.160.0180.00080.017420130.3239-
0.14690.00050.01520140.13690.24740.00030.007520150.0141-
0.00640.00040.007420160.11980.01760.00210.02110.1176280.0
575090.0375890.030752
Sheet2
Sheet3
Large
Company192619271928192919301931193219331934193519361
93719381939194019411942194319441945194619471948194919
50195119521953195419551956195719581959196019611962196
31964196519661967196819691970197119721973197419751976
19771978197919801981198219831984198519861987198819891
990199119921993199419951996199719981999
Large-Company Stocks
Year
Total Return
Large Company Stocks

0.1375
0.357
0.4508
-0.088
-0.2513
-0.436
-0.0875
0.5295
-0.0231
0.4679
0.3249
-0.3545
0.3163
-0.0143
-0.1036
-0.1202
0.2075
0.2538
0.1949
0.3621
-0.0842
0.0505
0.0499
0.1781
0.3005
0.2379
0.1839
-0.0107
0.5223
0.3162
0.0691
-0.105
0.4357
0.1201
0.0047
0.2684

-0.0875
0.227
0.1643
0.1238
-0.1006
0.2398
0.1103
-0.0843
0.0394
0.143
0.1899
-0.1469
-0.2647
0.3723
0.2393
-0.0716
0.0657
0.1861
0.325
-0.0492
0.2155
0.2256
0.0627
0.3173
0.1867
0.0525
0.1661
0.3169
-0.031
0.3046
0.0762
0.1008
0.0132
0.3758
0.2296
0.3336

0.2858
0.2104
Long-Term
Bonds19261927192819291930193119321933193419351936193
71938193919401941194219431944194519461947194819491950
19511952195319541955195619571958195919601961196219631
96419651966196719681969197019711972197319741975197619
77197819791980198119821983198419851986198719881989199
01991199219931994199519961997199819992000200120022003
2004200520062007200820092010201120122013201420152016
Long-term Government Bonds
Year
Total Return
0.0569
0.0658
0.0115
0.0439
0.0447
-0.0215
0.0851
0.0192
0.0759
0.042
0.0513
0.0144
0.0421
0.0384
0.057
0.0047
0.018
0.0201
0.0227
0.0529
0.0054
-0.0102
0.0266

0.0458
-0.0098
-0.002
0.0243
0.0228
0.0308
-0.0073
-0.0172
0.0682
-0.0172
-0.0202
0.1121
0.022
0.0572
0.0179
0.0371
0.0093
0.0512
-0.0286
0.0225
-0.0563
0.1892
0.1124
0.0239
0.033
0.04
0.0552
0.1556
0.0038
-0.0126
0.0126
-0.0248
0.0404
0.4428
0.0129
0.1529

0.3227
0.2239
-0.0303
0.0684
0.1854
0.0774
0.1936
0.0734
0.1306
-0.0732
0.2594
0.0013
0.1202
0.1445
-0.0751
0.1722
0.0551
0.1515
0.0201
0.0812
0.0689
0.0028
0.1085
0.4178
-0.2561
0.0773
0.3575
0.018
-0.1469
0.2474
-0.0064
0.0176
T-
bills1926192719281929193019311932193319341935193619371
93819391940194119421943194419451946194719481949195019
51195219531954195519561957195819591960196119621963196

41965196619671968196919701971197219731974197519761977
19781979198019811982198319841985198619871988198919901
99119921993199419951996199719981999
U.S. Treasury Bills
Year
Total Return
0.033
0.0315
0.0405
0.0447
0.0227
0.0115
0.0088
0.0052
0.0027
0.0017
0.0017
0.0027
0.0006
0.0004
0.0004
0.0014
0.0034
0.0038
0.0038
0.0038
0.0038
0.0062
0.0106
0.0112
0.0122
0.0156
0.0175
0.0187
0.0093
0.018

0.0266
0.0328
0.0171
0.0348
0.0281
0.024
0.0282
0.0323
0.0362
0.0406
0.0494
0.0439
0.0549
0.069
0.065
0.0436
0.0423
0.0729
0.0799
0.0587
0.0507
0.0545
0.0764
0.1056
0.121
0.146
0.1094
0.0899
0.099
0.0771
0.0609
0.0588
0.0694
0.0844
0.0769
0.0543

0.0348
0.0303
0.0439
0.0561
0.0514
0.0519
0.0486
0.048
Sheet1YearLarge-Company StocksLong-Term Government
BondsU.S. Treasury BillsConsumer Price
Index19260.13750.05690.033-0.011219270.3570.06580.0315-
0.022619280.45080.01150.0405-0.01161929-
0.0880.04390.04470.00581930-0.25130.04470.0227-0.0641931-
0.436-0.02150.0115-0.09321932-0.08750.08510.0088-
0.102719330.52950.01920.00520.00761934-
0.02310.07590.00270.015219350.46790.0420.00170.029919360.
32490.05130.00170.01451937-
0.35450.01440.00270.028619380.31630.04210.0006-
0.02781939-0.01430.03840.000401940-
0.10360.0570.00040.00711941-
0.12020.00470.00140.099319420.20750.0180.00340.090319430.
25380.02010.00380.029619440.19490.02270.00380.02319450.3
6210.05290.00380.02251946-
0.08420.00540.00380.181319470.0505-
0.01020.00620.088419480.04990.02660.01060.029919490.1781
0.04580.0112-0.020719500.3005-
0.00980.01220.059319510.2379-
0.0020.01560.0619520.18390.02430.01750.00751953-
0.01070.02280.01870.007419540.52230.03080.0093-
0.007419550.3162-0.00730.0180.003719560.0691-
0.01720.02660.02991957-0.1050.06820.03280.02919580.4357-
0.01720.01710.017619590.1201-
0.02020.03480.017319600.00470.11210.02810.013619610.2684
0.0220.0240.00671962-
0.08750.05720.02820.013319630.2270.01790.03230.016419640.
16430.03710.03620.009719650.12380.00930.04060.01921966-

0.10060.05120.04940.034619670.2398-
0.02860.04390.030419680.11030.02250.05490.04721969-
0.0843-
0.05630.0690.06219700.03940.18920.0650.055719710.1430.112
40.04360.032719720.18990.02390.04230.03411973-
0.14690.0330.07290.08711974-
0.26470.040.07990.123419750.37230.05520.05870.069419760.2
3930.15560.05070.04861977-
0.07160.00380.05450.06719780.0657-
0.01260.07640.090219790.18610.01260.10560.132919800.325-
0.02480.1210.12521981-
0.04920.04040.1460.089219820.21550.44280.10940.038319830.
22560.01290.08990.037919840.06270.15290.0990.039519850.3
1730.32270.07710.03819860.18670.22390.06090.01119870.052
5-
0.03030.05880.044319880.16610.06840.06940.044219890.3169
0.18540.08440.04651990-
0.0310.07740.07690.061119910.30460.19360.05430.030619920.
07620.07340.03480.02919930.10080.13060.03030.027519940.0
132-
0.07320.04390.026719950.37580.25940.05610.025419960.2296
0.00130.05140.033219970.33360.12020.05190.01719980.28580.
14450.04860.016119990.2104-0.07510.0480.02682000-
0.0910.17220.05980.03392001-0.11890.05510.03330.01552002-
0.2210.15150.01610.02420030.28890.02010.00940.01920040.10
880.08120.01140.03320050.04910.06890.02790.03420060.1579
0.00280.04970.025420070.05490.10850.04520.04082008-
0.370.41780.01240.000920090.2646-
0.25610.00150.027220100.15060.07730.00140.01520110.02110.
35750.00060.029620120.160.0180.00080.017420130.3239-
0.14690.00050.01520140.13690.24740.00030.007520150.0141-
0.00640.00040.007420160.11980.01760.00210.02110.1176280.0
575090.0375890.030752
Sheet2
Sheet3
Large

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COST OF CAPITALCHAPTER 14Copyright © 2019 McGraw-Hill Educat