Cost of Capital

Kinshuk Saurabh
 Cost of Capital
• Rate of return required by suppliers of capital
o for financing the firm’s investment projects by buying
securities
• Cost of Capital paid by firms who demand capital

• Expressed by an overall rate of return — a weighted

average cost of capital (WACC)

• In an all-equity firm,
o the cost of capital is equal to the opportunity cost of
equity capital, which depends only on the business
risk of the firm.
• What is the OCC of retained earnings?
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 Weighted Average
Cost of Capital

• WACC is the weighted marginal cost of capital;

i.e., the weighted average cost of new capital
given the firm’s target capital structure

𝐄 𝑫
𝐫wacc = 𝐫 + 𝐫 (𝟏−τ𝐂 )
E+D 𝐄 E+D 𝐃

• Because interest expense is tax-deductible, we multiply

the last term by (1 – TC).
 After tax cost of debt
• Interest paid on debt is tax deductible.
• The higher the interest charges the lower will be the
amount of tax payable by the firm
• This implies that the government indirectly pays a part of
the lender’s required rate of return.
• As a result of this interest tax shield the after tax cost of
debt to the firm will be substantially less than the lender’s
required rate of return. Govt indirectly pays a part of the
lender’s RRR. But this benefit is only available if the firm is
profitable and pays taxes.
• In the calculation of WACC the after tax cost of debt
should be used.
 Debt Yield as Cost of Debt

The before tax cost of debt is the rate of return required by

lenders. The higher the discount the higher before tax cost
of debt. Hence successful companies sell bond at premium
which reduces cost of debt. Absent default, the YTM is
taken as the cost of debt 𝒌𝒅 .

• Debt Issued at Discount or Premium

𝑡=1
𝑛 INT𝑡 𝐵𝑛
𝐵0 = ∑ +
(1 + 𝑘𝐷 )𝑡 (1 + 𝑘𝐷 )𝑛

• Tax adjustment

After_tax cost of debt = 𝑘𝐷 (1 − 𝑇)

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 Example

Now,

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 Problem -1
• Calculating Cost of Debt Advance, Inc., is trying to
determine its cost of debt. The firm has a debt issue
outstanding with 13 years to maturity that is quoted
at 95 percent of face value. The issue makes
semiannual payments and has a coupon rate of 7
percent.
o What is the company’s pretax cost of debt? If
the tax rate is 35 percent, what is the after-tax
cost of debt?
 Problem -2
Shanken Corp. issued a 30-year, 5.9 percent semi-annual
bond 6 years ago. The bond currently sells for 108 percent
of its face value. The company’s tax rate is 35 percent.
a. What is the pretax cost of debt?
b. What is the after-tax cost of debt?
c. Which is more relevant, the pretax or the after-tax
cost of debt? Why?
• Now, suppose the book value of the debt issue is $35 million. In
addition, the company has a second debt issue on the
market, a zero coupon bond with 12 years left to maturity; the
book value of this issue is $80 million and the bonds sell for 61
percent of par. What is the company’s total book value of
debt? The total market value? What is your best estimate of
the aftertax cost of debt now?
 Cost of Preference Capital
• Irredeemable Preference Share
PDIV
kp =
P0
• Redeemable Preference Share

n PDIVt Pn
P0 =  +
t =1 (1 + k p ) t (1 + k p ) n

• Unlike that for interest on debt, the cost of capital for

preference share is not adjusted for taxes

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Example

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 Determining Cost of Equity
• Capital Asset Pricing Model
𝑬 𝑹𝒊 = 𝒌𝒆 = 𝒓𝒊 = 𝒓𝒇 + 𝜷𝑴
𝒊 × (𝑬[𝑹𝑴 ] − 𝒓𝒇 )

• The cost of capital of any investment opportunity ri

equals the expected return 𝑬 𝑹𝒊 of available
investments with the same beta.
• The estimate derives from the Security Market Line

• The Dividend Growth Model

𝐃𝐈𝐕𝟏
𝒌𝒆 = +𝒈
𝑷𝟎

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 Example
• Suppose in the year 2002 the risk-free rate is 6 per
cent, the market risk premium is 9 per cent and
beta of L&T’s share is 1.54. What is the cost of equity
for L&T?

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Example
 Problem -3
• Calculating Cost of Equity The Dybvig Corporation’s
common stock has a beta of 1.17. If the risk-free
rate is 3.8 percent and the expected return on the
market is 11 percent, what is Dybvig’s cost of equity
capital?
 Problem
• Given the following information for Huntington
Power Co., find the WACC. Assume tax rate is 35%.

• Debt: 10,000 5.6 percent coupon bonds outstanding,

$1,000 par value, 25 years to maturity, selling for 97
percent of par; the bonds make semiannual payments
• Common stock: 425,000 shares outstanding, selling for
$61 per share; the beta is .95.
• Market: 7 percent market risk premium and 3.8 percent
risk-free rate.
 Limitations:
Dividend –Growth Model

• The dividend -growth model has limited use

o Assumes:

o dividend per share will grow at g, forever.

o g, should be less than ke, to arrive at the formula.
o Fails to deal with risk directly.

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Problem-4

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 Cost of Equity: CAPM

• CAPM has a wider application although it is based

on restrictive assumptions.
o The only condition for its use is that the company’s
share is quoted on the stock exchange.
o All variables are market determined (common to all
firms) except the company specific share price
o The value of beta is determined in an objective
manner by using sound statistical methods.
• One practical problem with the use of beta
o Beta does not remain stable over time .

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 The Market Risk Premium
• Determining the Risk-Free Rate
o The yield on U.S. Treasury securities
o Surveys suggest most practitioners use 10 to 30 year
treasury Bonds
• The Historical Risk Premium
o Estimate the risk premium (E[RM]-rf) using the historical
average excess return of the market over the risk-free
interest rate
 Beta Estimation
• Estimating Beta from Historical Returns
o Beta is the expected % change in the excess return of the
security for a 1% change in excess return of the market portfolio

• Two Methods
o Direct method
• Covariance between market return and the security’s stock
return over the market return variance
Cov(Ri ,RM )
=
Var(RM )

o Regression

 Direct Method: Problem

Returns on Sensex and Jaya Infotech

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 Example
Beta Calculation for Jaya Infotech Limited

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 Betas for the Sensex Companies
• The BSE’s sensitivity index includes 30 highly traded shares.
• The estimates are based on daily returns for one year.

Note that Jaiprakash Associates has the

highest beta of 2.28 and Gujarat Ambuja
Cement the lowest beta of 0.37.
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 Beta Estimation

• Regression: Estimating Beta from Historical Returns

o As the scatterplot on the previous slide shows, Cisco tends
to be up when the market is up, and vice versa.
o We can see that a 10% change in the market’s return
corresponds to about a 16% change in Cisco’s return.
• Thus, Cisco’s return moves about two for one with the
overall market, so Cisco’s beta is about 1.6.
o Beta corresponds to the slope of the best-fitting line in the
plot of the security’s excess returns versus the market
excess return.
Monthly Returns for Cisco Stock and
for the S&P 500, 2000-2012
 Scatterplot of Monthly Excess
Returns for Cisco Vs S&P 500, 2000-2012
 Using Linear Regression
• Linear Regression
o The statistical technique that identifies the best-fitting line through a set of
points. Given data for rf , Ri , and RM , linear regression can estimate βi.

(𝑅𝑖 − 𝑟𝑓 ) = 𝛼𝑖 + 𝛽𝑖 (𝑅𝑀 − 𝑟𝑓 ) + 𝜀𝑖

𝐸[𝑅𝑖 ] = 𝑟𝑓 + 𝛽𝑖 (𝐸[𝑅𝑀 ] − 𝑟𝑓 ) + 𝛼ณ𝑖

Expected return for 𝑖 from the SML Distance above / below the SML

o αi is the intercept term of the regression. αi represents a risk-adjusted performance

measure for the historical returns.
• If αi is positive, the stock has performed better than predicted by the CAPM.
• If αi is negative, the stock’s historical return is below the SML.
o βi(RM – rf) represents the sensitivity of the stock to market risk. When the market’s
return increases by 1%, the security’s return increases by βi%.
o εi is the error term and represents the deviation from the best-fitting line and is zero
on average. E[εi] = 0:
o A regression for Cisco using the monthly returns for 2000–2012 indicates the
estimated beta is 1.60.
o The estimate of Cisco’s alpha from the regression is -0.22%.
 Stability of Beta
• Most analysts argue that betas are generally stable for
firms remaining in the same industry.

• However, beta can change with:

o Change in Business Risk
• Changes in product line
• Changes in technology
• Deregulation
o Changes in Financial Risk
• Financial leverage
 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.
 Using Industry Beta
• One can better estimate a firm’s beta by involving
the whole industry
• If the firm’s operations are similar to the operations
of the rest of the industry
o may use the industry beta
• If the firm’s operations fundamentally different to the
operations of the rest of the industry
o may use the firm’s beta.
• Make adjustments for financial leverage.
 Determinants of Beta

• Business Risk
o Cyclicality of Revenues
• Do well in good times and badly in recession
o Operating Leverage
• Fixed costs/ total costs
• Financial Risk
o Financial Leverage
• Debt/ total capital
 Cyclicality of Revenues
• Highly cyclical stocks have higher betas.
o Empirical evidence suggests that retailers and automotive firms
fluctuate with the business cycle.
• Cement, Steel, Chemicals, Raw-materials
• Construction, capital goods, Exploration
• Restaurants, Hotels, Consumer discretionary items, Luxury
• Airlines
o Transportation firms and utilities are less dependent on the
business cycle.
• Food, power, water, gas
• Cyclicality is not the same as variability— stocks with high
standard deviations need not have high betas.
o 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.
 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:

o % change in operating income over % change in sales or
contribution margin over operating income

D EBIT Sales
DOL = ×
EBIT D Sales
 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:

Asset = Debt × Debt+ Equity × Equity

Debt + Equity Debt + Equity

• Financial leverage always increases the equity

beta relative to the asset beta.
 Levered Beta
• Levered (equity) beta:
o includes the impact of a company’s leverage
• The higher a company’s debt or leverage, the more
earnings from the company that is committed to
servicing that debt
• As a company adds more and more debt, the
company’s uncertainty of future earnings increases
• This increases the risk associated with the
company’s stock, but, it is not a result of the market
or industry risk
 Levered Beta
• For a levered firm, the proportion of equity will be
less than 1. Therefore, the beta of asset will be less
than the beta of equity. The beta of equity for a
levered firm is given as follows:

 Debt 
 E =  A 1 + 
 Equity 
 Asset (Unlevered) beta
• Since each firm’s capital structure is different, an analyst will
often want to look at how “risky” the assets of the firm are,
regardless of what % of debt or equity funding it has.
• Beta of a company without the impact of debt i.e.
o Without accounting for financial leverage
• It compares the risk of an unlevered company to the risk of the
market.
• The volatility of returns of a company is only the result of its
assets.
• For an unlevered (all-equity) firm, the asset beta and the
equity beta would be the same.
E D
βU = βE + βD
E+D E+D
 Industry Asset Betas
• We can combine estimates of asset betas for
multiple firms in the same industry
• Doing this will reduce the estimation error of the
estimated beta for the project.
Industry Asset Betas, US (2012)
 Example
• Stock of Stansfield Enterprises, a publisher of Power
Point presentations, has a beta of 1.5. The firm is 100%
equity financed. Assume a risk-free rate of 3% and a
market risk premium of 7%.
o What is the appropriate discount rate for an
expansion of this firm?
 Default Risk and the
Cost of Debt
• If there is significant risk of default, then promised YTM
will overstate investor’s expected rate of return.
• The 𝐤 𝐃 under default probability p will be less than
YTM promised in the case of default risk

kD = (1-p)YTM + p(YTM-L) = YTM - pL

• Under Default risk:

o 𝑘𝐷 = YTM – (Default Probability * Expected Loss Rate)
Annual Default Rates by Debt
Rating (1983–2011)
 Debt Cost of Capital under default
risk
• The average loss rate for unsecured debt is 60%.
• During average times the annual default rate for B-
rated bonds is 5.5%.
• As per the default rate the security will be rated B
• So, expected return to B-rated bondholders during
average times is
o 0.055 X 0.60 = 3.3% below the bond’s quoted yield.
Debt Cost of Capital and Debt Beta
• Debt Betas
o We can estimate the debt cost of capital using the
CAPM
o Debt betas are difficult to estimate because
corporate bonds are traded infrequently
o We can use option valuation method for estimating
debt betas
o We may also use estimates of betas of bond indices
by rating category
Average Debt Betas by Rating
and Maturity
Example
Example Solved
 Unlevered Cost of Capital
• Asset (unlevered) cost of capital
o Expected return on equity required by investors to hold
the firm’s underlying assets (i.e., D+E), if they were
entirely financed by equity without any debt
o Weighted average of equity and debt costs of capital
o Assumes, no debt in the capital structure => ignores T%
o It is a hypothetical cost of capital
E D D
rU = k A = rE + rD rwacc =rU - τ C rD
E+D E+D E+D
Typically,
(rU = k A ) > 𝑊𝐴𝐶𝐶
rD < 𝑊𝐴𝐶𝐶 < r𝑈 < r𝐸
 Cost of Capital of a Project

• All-equity comparables
o Find an all-equity financed firm in a single line of business
that is comparable to the project.
o Use the comparable firm’s equity beta and cost of capital
as estimates for the project
• Levered firms as comparables
 Example
Stansfield Enterprises is evaluating the following
independent projects. Each costs $100 and lasts one year.

Project Project  Project’s IRR NPV at

Estimated Cash 13.5%
Flows Next
Year
A 1.5 $125 25% $10.13

B 1.5 $113.5 13.5% $0

C 1.5 $105 5% -$7.49

 Using the CAPM
SML
IRR
Project
Good A
project

30% B

C Bad project
5%
Firm’s risk (beta)
2.5
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.
Example
Example
Example
 Cash and Net Debt
• Some firms maintain high cash balances
• Cash is a risk-free asset that reduces the average risk of
the firm’s assets
• Since the risk of the firm’s enterprise value is what we’re
concerned with, leverage should be measured in terms
of net debt.

Net Debt = Debt – Excess Cash and short-term investments

Example
Example
 Project Risk Characteristics
and Financing
• Differences in project risk
o Firm asset betas reflect market risk of the average project
in a firm.
o Individual projects may be more or less sensitive to market
risk.
• For example, 3M has both healthcare and computer
display and graphics divisions
o 3M’s own asset beta represents an average of the risk of
these and 3M’s other divisions
• Financial managers in multi-divisional firms should evaluate
projects based on asset betas of other firms in a similar line
of business as close as possible
Example
Example
 The WACC vs OCC
• How does rwacc compare with rU?
o Unlevered cost of capital (or pretax WACC):
• Expected return investors will earn by holding the
firm’s assets
• In a world with taxes, it can be used to evaluate an
all-equity project with the same risk as the firm.
o In a world with taxes, WACC is less than the expected
return of the firm’s assets.
• With taxes, WACC can be used to evaluate a
project with the same financing and the same risk as
the firm.
D
rwacc =rU - τ C rD
E+D
Example
Example
 Book Value Vs Market Value
Weights
• Market-value weights are theoretically superior to book-
value weights:
o They reflect economic values and are not influenced
by accounting policies
o They are also consistent with the market-determined
component costs

• The difficulty in using market-value weights:

o A market value based target capital structure means
that the amounts of debt and equity are
continuously adjusted as the value of the firm
changes

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 Cost of Capital of a
Division or Project
• A most commonly suggested method for
calculating the required rate of return for a division
(or project) is the pure-play technique.
• The basic idea is to use the beta of the
comparable firms, called pure-play firms, in the
same industry or line of business as a proxy for the
beta of the division or the project

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 Cost of Capital of a
Division or Project
• The pure-play approach for calculating the divisional
cost of capital involves the following steps:
o Identify comparable firms
o Estimate equity betas for comparable firms:
o Estimate asset betas for comparable firms:
o Calculate the division’s beta:
o Calculate the division’s all-equity cost of capital
o Calculate the division’s equity cost of capital:
o Calculate the division’s cost of capital

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Example

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 Final Thoughts on the CAPM
• There are a large number of assumptions made in the
estimation of cost of capital using the CAPM.
• How reliable are the results?
o Approximation are made throughout the capital budgeting
process. Approximation of cost of capital using CAPM are
no different. The errors in estimation of cost of capital are
not likely to make large different in NPV estimates.
• CAPM is practical, easy to implement, and robust.
• CAPM imposes a disciplined approach to cost of capital
estimation that is difficult to manipulate.
• CAPM requires managers to think about risk in the correct
way.