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Chapter 14
Cost of Capital
Chapter 14 Outline
14.1 The Marginal
Cost of Capital
Schedule
• The Cost of Capital
• The WACC: The
Basics
• Steps in Calculating
the Weighted
Average Cost of
Capital
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14.2 Estimating
the Weights
• What is Capital?
• Financial Structure
vs. Capital Structure
• Which Weights
should be Used?
• Estimating Market
Values of Common
Shares
• Estimating Market
Values of Preferred
Shares
14.3 Estimating the Costs
of Capital
14.4 Assembling
the Pieces
• The Cost of Debt
• The Cost of Preferred
Equity
• The Cost of Common
Equity
• The Gordon Model
• Sustainable Growth,
Retention, and the
Return on Equity
• Step 1: Calculate
the proportions of
capital
• Step 2: Estimate the
costs of capital
• Step 3: Assemble
the pieces
• Chapter Summary
14.1 The Marginal Cost of Capital
Schedule
 The cost of capital is the return the investor
requires; hence, we refer to the cost of capital
as the required rate of return from the
perspective of the suppliers of funds (that is,
the creditor or owner).
 The cost of capital is often used in valuing a
company, a subsidiary, or any asset, whereby
future cash flows are discounted at the cost of
capital to estimate a value.
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The Cost of Capital
The cost of capital is a marginal cost, the cost of
raising an additional dollar of financing. We
calculate this marginal cost of capital as the
weighted average cost of capital, or WACC,
where:
 the weights are the proportions of capital the
company uses when it raises new capital
 the costs are the marginal cost for each source
of capital
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The WACC: The Basics
We can represent this in notation form as:
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The WACC: The Basics (continued)





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V represents the total value of the company’s capital,
D represents the value of debt,
P represents the value of preferred stock,
E represents the value of common equity, and
r*d, rp, and re represent the marginal costs of capital for
debt, preferred equity, and common equity, respectively.
The WACC: The Basics (continued)
We can simplify this using the notation for
the weights of the different sources of
capital, the wt, as:
𝑊𝐴𝐶𝐶 = 𝑤𝑑 𝑟𝑑 ∗ + 𝑤𝑝 𝑟𝑝 + 𝑤𝑒 𝑟𝑒
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The WACC: The Basics (continued)
 The reason we designate the cost of debt
differently than the costs of preferred and
common equity (that is, with an “*”) is that
the relevant cost of debt is the after-tax cost
because of the tax deductibility of interest.
 Therefore, for every dollar of interest paid, the
company only bears a portion of that dollar
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Calculating the Weighted Average
Cost of Capital
Step 1: Estimate
the weights
• Proportions in
target capital
structure
Step 2:
Estimate the
costs of capital
• Costs of each
of the
sources used
by the
company
Step 3:
Assemble the
pieces
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• Calculate
WACC as
weighted
average of
the costs
14.2 Estimating the Weights
 When
calculating the cost of capital, we
weight the component costs of capital by
the proportion of capital that each source
of capital represents when the company
raises additional capital.
 We must first determine what is “capital”,
and then we will deal with the appropriate
proportions.
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What is Capital?
 Capital
is that it is the sum of the interestbearing debt and the equity of a company.
 Debt capital consists of the interestbearing obligations of the company,
whereas equity capital is the sum of the
capital of preferred and common
shareholders.
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Financial Structure vs. Capital
Structure
 A company’s financial structure is the entire set of
liabilities and equity accounts, whereas the capital
structure of the company is how this invested
capital is financed by debt and equity capital.
 The distinction between a company’s financial and
capital structure is that the financial structure
includes all liability and equity, whereas the
capital structure includes only invested capital.
 Invested capital is the sum of the debt capital and
equity capital.
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Example of Financial Structure vs.
Capital Structure


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The financial structure is $2,000, consisting of $1,000 of liabilities and
$1,000 of equity.
The capital structure consists of invested capital and is $1,700: $1,000 in
shareholders’ equity, and $700 of interest-bearing debt (i.e., $50 1 $650).
This capital structure results in a debt-to-equity ratio of $700 4 $1,000 5
0.70 and a debt-to-invested-capital ratio of $700 4 $1,700 5 0.41.
Which Weights Should Be Used?

Theoretically, we would like to use the proportions that
represent the company’s target capital structure, that is,
the capital structure that the company aims for over time.


As a next-best alternative to the target capital structure,
absent other information that may indicate otherwise, we
use a company’s present capital structure as the best
estimate of the target capital structure.

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However, we cannot observe this target capital structure.
We generally use the market values of the capital that the
company uses because we assume that the financial decision
making of a company is based on market values of capital, rather
than on the book values.
Estimating Market Values of
Common Shares
 This is straightforward whenever
a company has
shares that are traded publicly.

We simply use the market capitalization, which is the
product of the company’s market price per common
share and the number of shares outstanding.
 If the equity is not publicly traded, we need to use
an approach such as the method of multiples to
estimate the value based on market multiples of
comparable, but publicly traded companies.
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Estimating Market Values of
Preferred Shares


Estimating the market value of a company’s preferred
shares is also quite straightforward if they are publicly
traded.
In the event that the company’s preferred shares are
not actively traded, we can estimate the market value
of the preferred shares by using the present value of a
perpetuity equation, where Pp is the price per share,
Dp is the dividend per share, and rp is the required rate
of return on preferred shares: 𝑃𝑝 =
16
𝐷𝑝
𝑟𝑝
Example: Microsoft FYR2013
in billions
June-30-2013
Book
value
Market
value
Long-term liabilities
15.600
15.665
Equity
78.944
290.163
Total
94.544
305.828
Debt
16.5%
5.1%
Equity
83.5%
94.9%
Proportions
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14.3 Estimating the Costs of
Capital
 Our objective is to estimate what it would cost
the company to raise additional capital—
specifically one more dollar of capital. This is
the marginal cost of capital.
 The marginal cost of capital is the cost of
raising one more dollar of capital. To this end,
we need to estimate the marginal costs of
each of the sources of capital the company
uses.
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First: The Cost of Debt
 The cost of debt
is the yield or interest on
debt if the company borrows one more dollar.

If the company has publicly traded debt, you can
look at sources such as FINRA for yields:
www.FINRA.org
 Although that may seem simple, it is more
complicated than that because most large
companies have many issues of debt
outstanding.
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Example: Apple Computer
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Source: www.FINRA.org
Example: Apple Computer
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Source: FINRA.org
Cost of debt after taxes
The cost of debt is adjusted for the tax
benefit of interest deductibility:
𝑟𝑑 ∗ = 𝑟𝑑 × 1 − 𝑡
where t is the marginal tax rate.
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Example
$2,000 debt @ 8%, t=40%
Without interest
deductibility
EBIT
With interest
deductibility
$1,000
Interest
0
EBIT
Interest
$1,000
160
EBT
$1,000
EBT
$840
Tax
400
Tax
336
Net income
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$600
Net income
$504
Benefit from deductibility=$400 − 336=$64 less in taxes
$160−64
Cost of debt =
= 0.048 or 4.8%
$2,000
Or, 0.08 × 1 −0.4 =0.048
Second: The Cost of Preferred Equity
We estimate the cost of preferred shares, rp,
at the ratio of the dividend to the current
value of a share.
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Third: The Cost of Common Equity
 The
value of a common share is the present value
of its future dividends.
 The dividend discount model (DDM) represents
the value of a share of stock today as the present
value of all future dividends, discounted at the
stock’s required rate of return.

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A special case of the DDM is the constant growth version
of the dividend discount model (DDM), which represents
the value of a share of stock as the present value of a
growing perpetuity.
The Gordon Model
 The
dividend discount model with constant growth
is commonly referred to as the Gordon model.
 The basic valuation equation with constant growth
is:
 The
price of a share, P0, equals the expected next
period’s dividend, D1, divided by the return
required by common share investors, re, minus the
forecast long-run growth rate, g, in dividends and
earnings.
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The Gordon Model (continued)
 We can rearrange this equation to estimate the
common equity investors’ discount rate or
required rate of return. This process is the
discounted cash flow method for estimating the
investors’ required rate of return:
 In this equation, the required
rate of return is
composed of the expected dividend yield, D1 ÷ P0,
plus the expected long-run growth rate, g.

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The long-run growth rate is then the estimate of the
increase in the share price and the investors’ capital gain.
Example: Cost of equity
Consider a company that has a current dividend
of $1 per share and a current share price of $20.
If the dividends are expected to grow at a rate of
5 percent per year, what is the required rate of
return for this stock?
We are given:
D0 = $1
P0 = $20
g = 5%
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Solution
1.
2.
The current dividend is $1, so next period’s
dividend, D1, is $1 x (1 + 0.05) = $1.05.
Calculate D1:
D1 = D0 (1 + g) = $1.00(1.05) = $1.05
3.
4.
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Calculate the dividend yield =
$1.05  $20 = 4.2%
Calculate the cost of equity:
re = 4.2% + 5% = 9.2%
Sustainable Growth, Retention, and
the Return on Equity

One of the issues we face in estimating the value of a
share of stock is how to estimate the growth rate.


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Although the actual growth rate of the value of a share of
stock may change from year to year, what we are most
concerned with in valuing a stock today is the long-term
growth of the stock’s value.
We can estimate this long-term growth using the
sustainable growth rate. Sustainable growth rate is the
growth we expect a company to be able to sustain in
the future. We estimate sustainable growth as the
product of the company’s retention rate, b, multiplied
by forecasted return on equity (ROE):
Example: PG sustainable growth
Dividend payout ratio
150%
100%
50%
0%
-50%
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
Return or payout
Return on equity
Fiscal year
Sustainable growth=0.17 ×0.55=9.35%
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Risk-based Models and the Cost of
Common Equity

The most important risk-based model is the
capital asset pricing model (CAPM), which
states that the expected return on a stock is the
sum of the expected risk-free rate of interest and
a premium for bearing market risk,


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Specifically the stock’s beta multiplied by the difference
between the expected return on the market and the
risk-free rate of interest.
We can represent the central equation of the
CAPM : 𝑟𝑖 = 𝑟𝑓 + 𝑟𝑀 − 𝑟𝑓 𝛽𝑖
Capital Asset Pricing Model (CAPM)
Formula
𝑟𝑖 = 𝑟𝑓 + 𝑟𝑀 − 𝑟𝑓 𝛽𝑖
 The
expected risk-free rate of return, rf, which
represents compensation for the time value of
money.
 The expected market risk premium [rM - rf], which is
compensation for assuming the risk of the market
portfolio; rM is the expected return on the market.
 The beta coefficient (or simply beta), bi, for the
company’s common shares, which measures the
company’s systematic or market risk.
Flotation Costs and the Marginal
Cost of Capital
 One complication that arises with respect to all
sources of capital, except for internally generated
funds, is that the company incurs issuing costs or
flotation costs when new securities are issued.
 These include any fees paid to the investment dealer
and/or any discounts provided to investors to entice
them to purchase the securities.
 As a result, the cost of issuing new securities will be
higher than the return required by investors because
the net proceeds to the company from any security
issue will be lower than that security’s market price.
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Approaches to adjust for
flotation costs
 Adjust
individual cost for the cost of
flotation
 Problem: timing (flotation costs are up-front,
costs of capital affect all flows of a project)
 Subtract
flotation costs from the
projects(s) net present value.
 Issue: not always possible
to associate financing
with a particular investment project
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14.4 Assembling the Pieces
Once we have the weights and the costs of
the different sources of capital, we calculate
the weighted average cost of capital:
𝑊𝐴𝐶𝐶 = 𝑤𝑑 𝑟𝑑 ∗ + 𝑤𝑝 𝑟𝑝 + 𝑤𝑒 𝑟𝑒
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Chapter Summary

The WACC is a market value weighted average of the
marginal costs of the different sources of capital.


The weights in the WACC are the proportions that each
source of capital represents when the company raises new
capital.

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If the company earns its WACC, then its present market values are
supported; if it is expected to earn less than its WACC, then its
market value will fall, and if it is expected to earn more than its
WACC, then its market value will increase.
If we assume that the company is at its target capital structure,
then we use the current capital structure as the target capital
structure. When calculating the proportions, it is important to use
the market value of the different sources of capital, not the book or
carrying values.
Chapter Summary (continued)



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A proxy for the before-tax cost of debt is the yield on the
company’s current debt. We can proxy the cost of preferred
equity in a similar manner, looking at how the market
currently prices the company’s preferred stock.
The most challenging estimate in the WACC is that for the
cost of common equity capital. In estimating this, the
financial decision maker can use the dividend discount
model (or variants) of this model, or the capital asset pricing
model.
We use the proportions and the costs of each source of
capital to estimate the weighted cost of capital. This
weighted cost of capital is a marginal cost because each of
the component costs is a marginal cost.