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Chapter 13 - Risk, Cost of Capital, and Valuation
Chapter 13
RISK, COST OF CAPITAL, AND VALUATION
SLIDES
CHAPTER WEB SITES
Section Web Address
13.10 finance.yahoo.com
www.reuters.com
13-1
Copyright © 2016 McGraw-Hill Education. All rights reserved. No reproduction or
distribution without the prior written consent of McGraw-Hill Education.
13.1 Key Concepts and Skills
13.2 Chapter Outline
13.3 Where Do We Stand?
13.4 The Cost of Equity Capital
13.5 The Cost of Equity Capital
13.6 Example
13.7 Example
13.8 Using the SML
13.9 The Risk-Free Rate
13.10 Market Risk Premium
13.11 Estimation of Beta
13.12 Estimation of Beta
13.13 Stability of Beta
13.14 Using an Industry Beta
13.15 Determinants of Beta
13.16 Cyclicality of Revenues
13.17 Operating Leverage
13.18 Operating Leverage
13.19 Financial Leverage and Beta
13.20 Example
13.21 Dividend Discount Model
13.22 Capital Budgeting & Project Risk
13.23 Capital Budgeting & Project Risk
13.24 Capital Budgeting & Project Risk
13.25 Cost of Debt
13.26 Cost of Preferred Stock
13.27 The Weighted Average Cost of Capital
13.28 Firm Valuation
13.29 Example: International Paper
13.30 Example: International Paper
13.31 Example: International Paper
13.32 Flotation Costs
13.33 Quick Quiz
Chapter 13 - Risk, Cost of Capital, and Valuation
finra-markets.morningstar.com/BondCenter
CHAPTER ORGANIZATION
13.1 The Cost of Capital
13.2 Estimating the Cost of Equity Capital with the CAPM
The Risk-Free Rate
Market Risk Premium
13.3 Estimation of Beta
Real-World Betas
Stability of Beta
Using an Industry Beta
13.4 Determinants of Beta
Cyclicality of Revenues
Operating Leverage
Financial Leverage and Beta
13.5 The Dividend Discount Model Approach
Comparison of DDM and CAPM
13.6 Cost of Capital for Divisions and Projects
13.7 Cost of Fixed Income Securities
Cost of Debt
Cost of Preferred Stock
13.8 The Weighted Average Cost of Capital
13.9 Valuation with RWACC
Project Evaluation and the RWACC
Firm Valuation with the RWACC
13.10 Estimating Eastman Chemical’s Cost of Capital
13.11 Flotation Costs and the Weighted Average Cost of Capital
The Basic Approach
Flotation Costs and NPV
Internal Equity and Flotation Costs
ANNOTATED CHAPTER OUTLINE
13-2
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
Slide 13.0 Chapter 13 Title Slide
Slide 13.1 Key Concepts and Skills
Slide 13.2 Chapter Outline
13.1. The Cost of Capital
Creating shareholder wealth depends on the magnitude, timing,
and risk of cash flows. Prior chapters have dealt with magnitude
and timing. In this chapter, we concentrate on the risk of the cash
flows.
Slide 13.3 Where Do We Stand?
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:
1. Good capital budgeting decisions – neither the NPV rule nor
the IRR rule can be implemented without knowledge of the
appropriate discount rate
2. Financing decisions – the optimal/target capital structure minimizes the
cost of capital
3. Operating decisions – cost of capital is used by regulatory agencies in
order to determine the “fair” return in some regulated
industries (e.g. utilities)
Cost of capital, required return, and discount (hurdle) rate are different phrases
that all refer to the opportunity cost of using capital in one way as
opposed to alternative financial market investments of the same
systematic risk.
-required return is from an investor’s point of view
-cost of capital is the same return from the firm’s point of view
-discount rate is the same as used in a PV calculation
13.2. Estimating the Cost of Equity Capital with the CAPM
Slide 13.4 -
Slide 13.5 The Cost of Equity Capital
CAPM, RS = RF + (RM – RF)
Implementing the Approach
13-3
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
Betas are widely available, and T-bill rates or the rate on long-term
Treasury securities are often used for RF. The expected market
risk premium is the more difficult number to come up with –
make sure that the market risk premium used is consistent with
the risk-free rate chosen.
One of the problems is that we really do need an expectation, but we only
have past information, and market risk premiums do vary
through time. Early in 2000, Federal Reserve Chairman Alan
Greenspan indicated that part of his concern with the state of
the U.S. stock markets at that time was the reduction in the
market risk premium. He felt that investors were either
becoming less risk averse, or they did not truly understand the
risk they were taking by investing in stock.
Nonetheless, the historical average is often used as an estimate of the
market risk premium.
Advantages and Disadvantages of the Approach
-This approach explicitly adjusts for risk in a fashion that is consistent
with capital market history.
-It is applicable to virtually all publicly traded stocks.
-The main disadvantage is that the past is not a perfect predictor of the
future, and both beta and the market risk premium vary through
time.
A recent study finds that almost ¾ of U.S. companies use the
CAPM in capital budgeting, indicating that industry has largely
approved this approach for estimating the cost of equity.
Slide 13.6 –
Slide 13.7 Example
Slide 13.8 Using the SML
Lecture Tip: Some students may question how you value the stock
for a firm that does not 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
13-4
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
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, with an even
larger one-time dividend being paid in late 2004.Even Apple, with
its massive cash pile, began paying dividends in 2012.
.A The Risk-Free Rate
Slide 13.9 The Risk-Free Rate
No bond is completely risk free; however, Treasury securities
come as close as possible to this description. Nonetheless, even
these still have interest rate risk, so the question of maturity is a
relevant one.
Since the CAPM is a period model, most agree that a short-term
(such as T-bill) rate should be chosen. However, since projects are
generally long-lived, we need to use an average anticipated one-
year rate, which can be estimated using implied forward rates built
into the yield curve.
Historically, longer-term (20-year) government bonds have had a
term premium of approximately 1-2% over T-bills. So, if, at the
time of the project, 20-year notes are yielding 4.5% and the term
premium is 2%, then the implied risk-free rate for the average one-
year rate is 2.5% = 4.5% - 2.0%.
Another approach is to select a Treasury security whose maturity
matches the project under consideration.
.B Market Risk Premium
Slide 13.10 Market Risk Premium
The MRP can be estimated using two methods.
Method 1: We could use historical data. In chapter 10, we
estimated that 7% might be a good approximation.
Method 2: We could use the dividend discount model (DDM).
Rearranging the DDM provides the following:
13-5
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
g
P
RD
s 1
Whereas we previously applied this to an individual stock,
we could also relate this to the market as a whole. The
dividend yield on the S&P500 is readily available, and
analysts’ forecasted dividend growth (say, over the next
five years) can be used as an estimate for g.
13.3. Estimation of Beta
Measuring Company Betas: Prior chapters define beta as a
measure of systematic risk, i.e., how an asset moves relative to an
index. Although in theory we would like an index that measures all
assets, practically we use a broad stock market index such as the
S&P500.
Slide 13.11 Estimation of Beta
Beta is defined in the prior chapter as: S = i,M / M2;
Financial publications, such as ValueLine, provide beta estimates.
Slide 13.12 Estimation of Beta
In practice, there are some problems in estimating beta:
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Changing financial leverage and business risk influences
betas.
Solutions
1. Problems 1 and 2 (above) can be moderated by more
sophisticated statistical techniques.
Problems 1 and 2 relate to the selection of the measurement period.
Beta is conventionally measured with either (a) 60 monthly
observations over a five-year period or (b) weekly observations
over two to five-year periods. For example, ValueLine uses five
years of weekly observations.
Daily returns often have too much measurement error, especially in
thinly traded stocks. The choice of the measurement interval is a
trade-off between statistical accuracy and timeliness. A long
measurement period provides more observations and gives a higher
13-6
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
statistical confidence in the beta estimate. On the other hand, a
long measurement period may include outdated information, and
the beta estimate will be incorrect. Most of the statistical
techniques mentioned in solution 1 are beyond the scope of most
financial management courses. One example, that could be used is
the adjustment for regression towards the mean (beta of an average
stock = 1) by Value Line.
2. Problem 3 can be lessened by adjusting for changes in
business and financial risk.
3. Look at average beta estimates of several comparable firms
in the industry. (see below)
.A Real-World Betas
.B Stability of Beta
Although a firm’s beta is relatively stable over time, it will be
impacted by changes in product line, technology, regulations, and
leverage, among other things.
Slide 13.13 Stability of Beta
.C Using an Industry Beta
Industry versus Company Beta:
An industry is a portfolio of individual companies. Therefore, the
beta estimate for an industry is more accurate than the beta
estimate for a single company. However, using an industry beta in
place of the company beta will be incorrect if:
1. the company has a significant amount of business in more
than one industry
2. the financial leverage of the company is very different
from the industry average.
The second problem of using industry beta can be solved by
adjusting the industry beta for the company’s financial leverage,
which we discuss below.
Slide 13.14 Using an Industry Beta
13.4. Determinants of Beta
Slide 13.15 Determinants of Beta
13-7
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
.A Cyclicality of Revenues
Highly cyclical firms generally have higher betas. However, this is
not the same as revenue variability.
Slide 13.16 Cyclicality of Revenues
.B Operating Leverage
There is almost always some flexibility in production to decide
between fixed and variable costs. Fixed costs generally magnify
forecasting errors, as well as reduce the firm’s flexibility in the
production process.
The Basic Idea: Operating leverage is the degree to which a project
or firm uses fixed costs in production. Plant and equipment and
non-cancelable rentals are typical fixed cost items.
Implications of Operating Leverage: Since fixed costs do not
change with sales, they make good situations better and bad
situations worse, i.e., they “lever” results.
Measuring Operating Leverage: Degree of Operating Leverage
(DOL) is the percentage change in EBIT relative to a percentage
change in sales.
Operating leverage magnifies the effect of cyclicality on beta.
Slide 13.17 –
Slide 13.18 Operating Leverage
.C Financial Leverage and Beta
Financial leverage is determined by the extent of fixed financing
costs, which is determined by the level of debt in a firm’s capital
structure.
Portfolio betas are weighted averages of the betas of the underlying
securities. Since a firm is essentially a portfolio, its asset beta, in a
similar fashion, is a weighted average of debt and equity betas.
Debt does not vary, at least dramatically, with changes in market
indexes. So, debt betas are typically assumed to be 0. In addition,
the separation theorem suggests asset betas do not change with
financing decisions. Thus, there is a strict relation between
leverage and equity beta.
13-8
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
ASSET = EQUITY × S/(S+B) + DEBT × B/(S+B)
where S is Equity and B is Debt.
If debt beta = 0, then:
ASSET = EQUITY × S/(S+B)
EQUITY = ASSET × (1 +
S
B
)
Lecture Tip: Adjusting for taxes would provide:
EQUITY = ASSET × (1 + (1-
c
T
)
S
B
)
Slide 13.19 Financial Leverage and Beta
Slide 13.20 Example
13.5. The Dividend Discount Model Approach
Slide 13.21 Dividend Discount Model
The Dividend Growth Model is an alternative for estimating the
cost of equity capital. According to the dividend growth model,
P0 = D1 / (Rs – g)
Rearranging and solving for the cost of equity gives:
Rs = (D1 / P0) + g
which is equal to the dividend yield plus the growth rate (capital gains yield).
Implementing the Approach
Price and latest dividend are observed; g must be estimated.
Estimating g – typically use historical growth rates or analysts’
forecasts.
Advantages and Disadvantages of the Approach
-Approach only works for dividend paying firms
-Rs is very sensitive to the estimate of g
-Historical growth rates may not reliably predict future growth
-Risk is only indirectly accounted for by the use of the price
13-9
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
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.
.A Comparison of DDM and CAPM
The DDM and CAPM are internally consistent, but academics generally favor
the CAPM and companies seem to use the CAPM more
consistently.
The CAM has two primary advantages:
1. It explicitly adjusts for risk
2. It is applicable to companies that pay no dividends
Lecture Tip: Students are often surprised when they find that the
two approaches (DDM and CAPM) 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.
13.6. Cost of Capital for Divisions and Projects
13-10
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
When a firm has different operating divisions with different risks,
its WACC is an average of the divisional required returns. In such
cases, the cost of capital for projects of average risk in each
division needs to be established. If you do use the firm’s WACC
across divisions, then riskier divisions will receive the bulk of the
funding, and less risky divisions will have to forgo what would be
good projects if the appropriate discount rate were used. This will
lead to an increase in risk for the overall firm.
Slide 13.22 –
Slide 13.24 Capital Budgeting & Project Risk
To estimate the cost of capital for a division, a “pure play”
approach could be used, although finding exactly similar firms
may be difficult, particularly considering underlying financial and
operational structure.
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.
13.7. Cost of Fixed Income Securities
.A Cost of Debt
Slide 13.25 Cost of Debt
13-11
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
Cost of debt (RD) – the interest rate on new debt can easily be estimated using
the yield-to-maturity on outstanding debt or by knowing the bond
rating and looking up rates on new issues with the same rating.
The only adjustment is to reduce the cost to account for the tax
deductibility of the interest expense. Thus, the after-tax cost of
debt should be used:
after-tax debt cost = (1-T)*borrowing rate
Lecture Tip: It is beneficial to reemphasize the distinction between the
coupon rate, the current yield, and the yield-to-maturity. The cost
of debt is equal to the yield-to-maturity because it is the market
rate of interest that would be required on new debt issues. The
coupon rate, on the other hand, is the firm’s promised interest
payments on existing debt, and the current yield is the income
portion of total return. If you do not emphasize this point, some
students want to just use the coupon rate on current debt.
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. Market values should be used since these represent the
current opportunity cost of investment.
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.
.B Cost of Preferred Stock
Slide 13.26 Cost of Preferred Stock
13-12
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
Preferred stock is a perpetuity, so its price is equal to the coupon
paid divided by the current required return.
Rearranging this formula, the cost of preferred stock is:
RP = C / PV
There is no tax adjustment because dividends are not tax
deductible.
13.8. The Weighted Average Cost of Capital
Slide 13.27 The Weighted Average Cost of Capital
After-tax cash flows require an after-tax discount rate. Let TC denote the
firm’s marginal tax rate. Then, the weighted average cost of capital
is:
WACC = (S/(B+S))RS + (B/(B+S))RD(1-TC)
With preferred stock:
WACC = (S/(B+P+S))RS + (P/(B+P+S))RP + (B/(B+P+S))RD(1-TC)
WACC – overall return the firm must earn on its assets to maintain the value
of its stock. It is a market rate that is based on the market’s
perception of the risk of the firm’s assets.
13.9. Valuation with RWACC
.A Project Evaluation and the RWACC
The discussion of NPV in prior chapters relied on a discount rate to
be applied to the estimated cash flows. We now know how this
discount rate (i.e., the RWACC) is calculated.
.B Firm Valuation with the RWACC
Slide 13.28 Firm Valuation
Remember from our discussion of NPV, that a firm’s value is just
the sum of the NPV of all its projects. Thus, as with any asset, the
firm’s value is the PV of all its future cash flow.
13-13
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distribution without the prior written consent of McGraw-Hill Education.
Chapter 13 - Risk, Cost of Capital, and Valuation
With the WACC, we can discount our estimate of future cash flow,
which should represent all cash flow (free cash flow, or
distributable cash flow). As usual, we would need to apply a
terminal valuation at some point.
Once firm value is obtained, we would subtract the market value of
the debt to find the equity value. We could then divide by the
number of shares outstanding to find a per share price.
13.10. Estimating Eastman Chemical’s Cost of Capital
Several web sites are utilized to find the information required to compute the
WACC.
1. Go to a site such as finance.yahoo.com; type in EMN and choose key
statistics. Get the market value of equity (price*shares outstanding)
and beta. This can also be found at www.reuters.com.
2. Find the yield on 20-year Treasuries and subtract the historical
yield difference. Next, decide on an estimate of the market risk
premium, such as 7%. Estimate Rs using the CAPM.
3. Go to https://finra-markets.morningstar.com/BondCenter to find
the weighted average of the yield-to-maturity for bond issues.
Book value and market value of debt is often similar, so you may
want to use the book value for simplicity.
4. Use market value weights to compute the WACC.
Slide 13.29 –
Slide 13.31 Example: International Paper
13.11. Flotation Costs and the Weighted Average Cost of Capital
Flotation costs represent the expenses incurred upon the issue, or float, of
new bonds or stocks. If a firm lacks sufficient available funds to support a
new project, it may incur incremental flotation costs
The WACC is unchanged as a result of the flotation costs, as it represents
the risk of the project, not the source of funds. The NPV, however, is
impacted (typically negatively) since the flotation costs represent a
relevant incremental cash flow.
.A The Basic Approach
13-14
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Chapter 13 - Risk, Cost of Capital, and Valuation
The net proceeds in an offering are equal to the total amount raised
less flotation costs. Thus, to finance a given amount for a project,
additional funds must be raised in the offering. The net effect is
that the total funds raised are:
Amount Raised = Necessary Proceeds / (1- % flotation cost)
The flotation cost percentage (f) is a weighted average measure
based on the average cost of issuance for each funding source and
the firm’s target capital structure.
fA = (E/V)* fE + (D/V)* fD
where E is equity; D is debt; and V is total firm value.
Slide 13.32 Flotation Costs
.A Flotation Costs and NPV
When flotation costs are positive, which is generally the case, the
NPV is lower when these costs are accounted for.
.B Internal Equity and Flotation Costs
Firms rarely issue external equity, focusing rather on generating
internal funds to cover the costs of projects. When this is the case,
the best approach is to assign a flotation cost of zero to the equity
portion of the average flotation cost.
Slide 13.33 Quick Quiz
To access Appendix 13A (Economic Value Added and the Measurement of Financial
Performance) go to www.mhhe.com/rwj.
13-15
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distribution without the prior written consent of McGraw-Hill Education.
