CHAPTER
12 Risk, Cost of Capital, and Capital Budgeting
Slide 2
Key Concepts and Skills
• Know how to determine a firm’s cost of
equity capital
• Understand the impact of beta in
determining the firm’s cost of equity capital
• Know how to determine the firm’s overall
cost of capital
• Understand how the liquidity of a firm’s
stock affects its cost of capital
Slide 3
Chapter Outline
The Cost of Equity Capital
Estimation of Beta
Determinants of Beta
Extensions of the Basic Model
Estimating Eastman Chemical’s Cost of
Capital
Reducing the Cost of Capital
Slide 4
Where Do We Stand?
• Earlier chapters on capital budgeting
focused on the appropriate size and
timing of cash flows.
• This chapter discusses the
appropriate discount rate when cash
flows are risky.
Slide 5
Invest in project
The Cost of Equity Capital
Firm with
excess cash
Shareholder’s
Terminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets,
the expected return on a capital-budgeting project should be at least as
great as the expected return on a financial asset of comparable risk.
A firm with excess cash can either pay a
dividend or make a capital investment
Slide 6
The Cost of Equity Capital
• From the firm’s perspective, the
expected return is the Cost of Equity
Capital:
• To estimate a firm’s cost of equity capital, we
need to know three things:
1. The risk-free rate, RF
2. The market risk premium,
3. The company beta,
Slide 7
Example
• Suppose the stock of Stansfield Enterprises, a
publisher of PowerPoint presentations, has a
beta of . The firm is 100% equity financed.
• Assume a risk-free rate of 5% and a market
risk premium of 10%.
• What is the appropriate discount rate for an
expansion of this firm?
Slide 8
Example
Suppose Stansfield Enterprises is evaluating the
following independent projects. Each costs $100 and
lasts one year.
Project Project b Project’s
Estimated Cash
Flows Next
Year
IRR NPV at
30%
A $150 50% $
B $130 30% $0
C $110 10% -$
Slide 9
Using the SML
An all-equity firm should accept projects whose IRRs
exceed the cost of equity capital and reject projects
whose IRRs fall short of the cost of capital.
Pr
oj
ec
t
IR
R
Firm’s risk (beta)
5%
Good
project
Bad project
30%
A
B
C
Slide 10
Estimation of Beta
Market Portfolio - Portfolio of all assets in
the economy. In practice, a broad stock
market index, such as the S&P
Composite, is used to represent the
market.
Beta - Sensitivity of a stock’s return to the
return on the market portfolio.
Slide 11
Estimation of Beta
• Problems
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.
• Solutions
– Problems 1 and 2 can be moderated by more sophisticated statistical
techniques.
– Problem 3 can be lessened by adjusting for changes in business and
financial risk.
– Look at average beta estimates of comparable firms in the industry.
Slide 12
Stability of Beta
• Most analysts argue that betas are
generally stable for firms remaining in the
same industry.
• That is not to say that a firm’s beta cannot
change.
– Changes in product line
– Changes in technology
– Deregulation
– Changes in financial leverage
Slide 13
Using an Industry Beta
• It is frequently argued that one can better
estimate a firm’s beta by involving the whole
industry.
• If you believe that the operations of the firm are
similar to the operations of the rest of the
industry, you should use the industry beta.
• If you believe that the operations of the firm are
fundamentally different from the operations of
the rest of the industry, you should use the firm’s
beta.
• Do not forget about adjustments for financial
leverage.
Slide 14
Determinants of Beta
• Business Risk
–Cyclicality of Revenues
–Operating Leverage
• Financial Risk
–Financial Leverage
Slide 15
Cyclicality of Revenues
• Highly cyclical stocks have higher betas.
– Empirical evidence suggests that retailers and
automotive firms fluctuate with the business cycle.
– Transportation firms and utilities are less dependent
upon the business cycle.
• Note that cyclicality is not the same as
variability—stocks with high standard
deviations need not have high betas.
– Movie studios have revenues that are variable,
depending upon whether they produce “hits” or
“flops,” but their revenues may not be especially
dependent upon the business cycle.
Slide 16
Operating Leverage
• The degree of operating leverage measures
how sensitive a firm (or project) is to its fixed
costs.
• Operating leverage increases as fixed costs
rise and variable costs fall.
• Operating leverage magnifies the effect of
cyclicality on beta.
• The degree of operating leverage is given by:
DOL =
EBIT Sales
Sales EBIT
×
Slide 17
Operating Leverage
Sales
$
Fixed costs
Total
costs
EBIT
Sales
Operating leverage increases as fixed costs rise
and variable costs fall.
Fixed costs
Total
costs
Slide 18
Financial Leverage and Beta
• Operating leverage refers to the sensitivity to
the firm’s fixed costs of production.
• Financial leverage is the sensitivity to a firm’s
fixed costs of financing.
• The relationship between the betas of the
firm’s debt, equity, and assets is given by:
• Financial leverage always increases the equity beta
relative to the asset beta.
bAsset = Debt + Equity
Debt × bDebt + Debt + Equity
Equity × bEquity
Slide 19
Example
Consider Grand Sport, Inc., which is currently all-
equity financed and has a beta of .
The firm has decided to lever up to a capital
structure of 1 part debt to 1 part equity.
Since the firm will remain in the same industry, its
asset beta should remain .
However, assuming a zero beta for its debt, its
equity beta would become twice as large:
bAsset = =
1 + 1
1 × bEquity
bEquity = 2 × =
Slide 20
Extensions of the Basic
Model
• The Firm versus the Project
• The Cost of Capital with Debt
Slide 21
The Firm versus the Project
• Any project’s cost of capital depends
on the use to which the capital is
being put—not the source.
• Therefore, it depends on the risk of
the project and not the risk of the
company.
Slide 22
Capital Budgeting & Project
Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value.
Pr
oj
ec
t I
R
R
Firm’s risk (beta)
rf
bFIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate
The SML can tell us why:
Slide 23
Suppose the Conglomerate Company has a cost of capital,
based on the CAPM, of 17%. The risk-free rate is 4%, the
market risk premium is 10%, and the firm’s beta is .
17% = 4% + × 10%
This is a breakdown of the company’s investment projects:
1/3 Automotive Retailer b =
1/3 Computer Hard Drive Manufacturer b =
1/3 Electric Utility b =
average b of assets =
When evaluating a new electrical generation investment,
which cost of capital should be used?
Capital Budgeting & Project Risk
Slide 24
Capital Budgeting & Project
Risk
Pr
oj
ec
t I
R
R
Project’s risk (b)
17%
r = 4% + ×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investment
in electrical generation, given the unique risk of the project.
10%
24% Investments in hard
drives or auto retailing
should have higher
discount rates.
SML
Slide 25
The Cost of Capital with Debt
• The Weighted Average Cost of Capital is given
by:
• Because interest expense is tax-deductible, we
multiply the last term by (1 – TC).
rWACC =
Equity + Debt
Equity × rEquity +
Equity + Debt
Debt × rDebt ×(1 – TC)
rWACC = S + B
S
× rS + S + B
B
× rB ×(1 – TC)
Slide 26
Example: International Paper
• First, we estimate the cost of equity
and the cost of debt.
–We estimate an equity beta to estimate
the cost of equity.
–We can often estimate the cost of debt
by observing the YTM of the firm’s debt.
• Second, we determine the WACC by
weighting these two costs
appropriately.
Slide 27
Example: International Paper
• The industry average beta is , the
risk free rate is 3%, and the market
risk premium is %.
• Thus, the cost of equity capital is:
rS = RF + bi × ( RM – RF)
= 3% + .82×%
= %
Slide 28
Example: International Paper
• The yield on the company’s debt is 8%,
and the firm has a 37% marginal tax rate.
• The debt to value ratio is 32%
% is International’s cost of capital. It should be used to
discount any project where one believes that the project’s risk
is equal to the risk of the firm as a whole and the project has
the same leverage as the firm as a whole.
= × % + × 8% × (1 – )
= %
rWACC = S + B
S
× rS + S + B
B
× rB ×(1 – TC)
Slide 29
Reducing the Cost of
Capital
• What is Liquidity?
• Liquidity, Expected Returns and the
Cost of Capital
• Liquidity and Adverse Selection
• What the Corporation Can Do
Slide 30
What is Liquidity?
• The idea that the expected return on a stock and
the firm’s cost of capital are positively related to
risk is fundamental.
• Recently, a number of academics have argued
that the expected return on a stock and the
firm’s cost of capital are negatively related to the
liquidity of the firm’s shares as well.
• The trading costs of holding a firm’s shares
include brokerage fees, the bid-ask spread and
market impact costs.
Slide 31
Liquidity, Expected Returns
and the Cost of Capital
• The cost of trading an illiquid stock
reduces the total return that an
investor receives.
• Investors will thus demand a high
expected return when investing in
stocks with high trading costs.
• This high expected return implies a
high cost of capital to the firm.
Slide 32
Liquidity and the Cost of
Capital
C
os
t o
f C
ap
ita
l
Liquidity
An increase in liquidity (., a reduction in trading costs)
lowers a firm’s cost of capital.
Slide 33
Liquidity and Adverse Selection
• There are a number of factors that determine the
liquidity of a stock.
• One of these factors is adverse selection.
• This refers to the notion that traders with better
information can take advantage of specialists
and other traders who have less information.
• The greater the heterogeneity of information, the
wider the bid-ask spreads, and the higher the
required return on equity.
Slide 34
What the Corporation Can Do
• The corporation has an incentive to lower
trading costs since this would result in a lower
cost of capital.
• A stock split would increase the liquidity of the
shares.
• A stock split would also reduce the adverse
selection costs, thereby lowering bid-ask
spreads.
• This idea is a new one, and empirical evidence
is not yet available.
Slide 35
What the Corporation Can Do
• Companies can also facilitate stock purchases
through the Internet.
• Direct stock purchase plans and dividend
reinvestment plans handled on-line allow small
investors the opportunity to buy securities
cheaply.
• Companies can also disclose more information,
especially to security analysts to narrow the gap
between informed and uninformed traders. This
should reduce spreads.
Slide 36
Quick Quiz
• How do we determine the cost of equity
capital?
• How can we estimate a firm or project
beta?
• How does leverage affect beta?
• How do we determine the cost of capital
with debt?
• How does the liquidity of a firm’s stock
affect the cost of capital?
Slide 37
• 1. With the information given, we can find
the cost of equity using the CAPM. The
cost of equity is:
• RE = .045 + (.13 – .045) = .1555 or
%
Slide 38
• 3. a. The pretax cost of debt is the YTM of
the company’s bonds, so:
• P0= $1,080 = $50(PVIFAR%,46) +
$1,000(PVIFR%,46)
• R = %
• YTM = 2 × % = %
• b. The aftertax cost of debt is:
• RD= .0916(1 – .35) = .0595 or %
• c. The aftertax rate is more relevant
because that is the actual cost to the
company.
Slide 39
• 5. Using the equation to calculate the
WACC, we find:
• WACC = .55(.16) + .45(.09)(1 – .35) =
.1143 or %
Slide 40
• 8. a. The book value of equity is the book value
per share times the number of shares, and the
book value of debt is the face value of the
company’s debt, so:
• BVE = ($5) = $
• BVD = $75M + 60M = $135M
• So, the total value of the company is:
• V = $ + 135M = $
• And the book value weights of equity and debt
are:
• E / V = $ = .2603
• D / V = 1 – E/V = .7397
Slide 41
• b. The market value of equity is the share price
times the number of shares, so:
• MVE = ($53) = $
• Using the relationship that the total market value
of debt is the price quote times the par value of
the bond, we find the market value of debt is:
• MVD = .93($75M) + .965($60M) = $
• This makes the total market value of the
company:
• V = $ + = $
• And the market value weights of equity and debt
are:
• E/V = $ = .7978
• D/V = 1 – E/V = .2022
• c. The market value weights are more relevant.
Slide 42
• 11. We will begin by finding the market
value of each type of financing. We find:
• MVD = 4,000($1,000)() = $4,120,000
• MVE = 90,000($57) = $5,130,000
• And the total market value of the firm is:
• V = $4,120,000 + 5,130,000 = $9,250,000
Slide 43
• Now, we can find the cost of equity using the
CAPM. The cost of equity is:
• RE = .06 + (.08) = .1480 or %
• The cost of debt is the YTM of the bonds, so:
• P0 = $1,030 = $35(PVIFAR%,40) +
$1,000(PVIFR%,40)
• R = %
• YTM = % × 2 = %
• And the aftertax cost of debt is:
• RD = (1 – .35)(.0672) = .0437 or %
• Now we have all of the components to calculate
the WACC. The WACC is:
• WACC = .0437( + .1480( =
.1015 or %
Slide 44
• 13. a. Projects X, Y and Z.
• b. Using the CAPM to consider the projects, we need to
calculate the expected return of each project given its
level of risk. This expected return should then be
compared to the expected return of the project. If the
return calculated using the CAPM is higher than the
project expected return, we should accept the project; if
not, we reject the project. After considering risk via the
CAPM:
• E[W] = .05 + .60(.12 – .05) = .0920 < .11, so accept W
• E[X] = .05 + .90(.12 – .05) = .1130 < .13, so accept X
• E[Y] = .05 + (.12 – .05) = .1340 < .14, so accept Y
• E[Z] = .05 + (.12 – .05) = .1690 > .16, so reject Z
Slide 45
• 15. We will begin by finding the market value of
each type of financing. We will use D1 to
represent the coupon bond, and D2 to represent
the zero coupon bond. So, the market value of
the firm’s financing is:
• MVD1 = 50,000($1,000)() = $59,900,000
• MVD2 = 150,000($1,000)(.1385) = $20,775,000
• MVP = 120,000($112) = $13,440,000
• MVE = 2,000,000($65) = $130,000,000
• And the total market value of the firm is:
• V = $59,900,000 + 20,775,000 + 13,440,000 +
130,000,000 = $224,115,000
Slide 46
• Now, we can find the cost of equity using
the CAPM. The cost of equity is:
• RE = .04 + (.09) = .1390 or %
• The cost of debt is the YTM of the bonds,
so:
• P0 = $1,198 = $40(PVIFAR%,50) +
$1,000(PVIFR%,50)
• R = %
• YTM = % × 2 = %
• And the aftertax cost of debt is:
• RD1 = (1 – .40)(.0640) = .0384 or %
Slide 47
• And the aftertax cost of the zero coupon
bonds is:
• P0 = $ = $1,000(PVIFR%,60)
• R = %
• YTM = % × 2 = %
• RD2 = (1 – .40)(.0670) = .0402 or %
Slide 48
• To find the required return on preferred
stock, we can use the preferred stock
pricing equation, which is the level
perpetuity equation, so the required return
on the company’s preferred stock is:
• RP = D1 / P0
• RP = $ / $112
• RP = .0580 or %
Slide 49
• Now we have all of the components to
calculate the WACC. The WACC is:
• WACC = .0384( +
.0402( +
.1390(130/)
+ .0580(
• WACC = .0981 or %
