INTRODUCTION TO
CORPORATE FINANCE
SECOND EDITION
Lawrence Booth & W. Sean Cleary
Prepared by Ken Hartviksen & Jared Laneus
Chapter 20
Cost of Capital
20.1 Financing Sources
20.2 The Cost of Capital
20.3 Estimating the Non-Equity Component Costs
20.4 The Effects of Operating and Financial Leverage
20.5 Growth Models and the Cost of Common Equity
20.6 Risk-Based Models and the Cost of Common Equity
20.7 The Cost of Capital and Investment
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Learning Objectives
20.1 Explain how the three major problem areas in finance:
valuation, cost of capital, and determining cash flows are related.
20.2 Calculate the weighted average cost of capital and explain its
significance.
20.3 Estimate the cost of capital and its non-equity components.
20. 4 Explain how operating and financial leverage affect a firm’s
risk.
20. 5 Apply the discounted cash flow model to estimate the equity
cost and describe its advantages and disadvantages.
20.6 Estimate the cost of equity using risk-based models and
describe the advantages and limitations of these models.
20.7 Explain how the WACC interacts with the investment decision
framework introduced in chapters 13 to 17.
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Financing Sources
•
•
•
•
•
Table 20-1 illustrates the basic structure of a firm’s balance sheet
This is a snapshot of a firm’s financial position at a point in time
Assets are things the firm owns
Liabilities are sources of financing obtained from lenders
Equity is the shareholders’ investment in the business plus any retained
earnings
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Financing Sources
• Table 20-2 shows an example of a balance sheet
• Financial structure is the whole right-hand side of the balance sheet, and
includes both short and long term sources of financing
• Capital structure is how the firm finances its invested capital, such as bank
loans, long-term debt, common stock and retained earnings. It excludes
accruals and accounts payable (i.e., short term liabilities that are not
strictly debt contracts which spontaneously change in response to the
operations of the business).
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Interpreting Balance Sheets
• Balance sheets are prepared in accordance with GAAP and most often
represent historical costs which may not be relevant for current decision
making purposes.
• An analysis of reported data should include ratios such as the debt-toequity ratio. In the example provided in Table 20-2, the firm has $50 of
short term debt, $650 of long term debt and $1,000 of shareholders’
equity. This gives a debt-to-equity ratio of ($50 + $650) / $1,000 = 0.7.
• Book values can be converted into market values by multiplying the
market-to-book (M/B) ratio by the book value
• Suppose that the market value of the shareholders’ equity of the firm in
the example provided in Table 20-2 was $2,500 instead of the historical
cost $1,000. Suppose also that the market values of the total debt is still
$700. This makes the debt-to-equity ratio $700 / $2,500 = 0.28 which is
much lower than the ratio when using the historical cost measure of the
shareholders’ equity.
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Valuation for a Perpetuity
• Equation 20-1 reprises what you learned in Chapter 5 about how to
determine the present value of an infinite stream of equal, periodic
cash flows (i.e., a perpetuity). Equation 20-2 rearranges to solve
for the required return and is also known as the earnings yield;
Equation 20-3 rearranges to solve for the forecast earnings
• The earnings yield is not normally used as the investor’s required
return because it simply measures the forecast earnings as a
proportion of the current market price ignoring growth
opportunities
X
X
S
 Ke 
 X  Ke  S
Ke
S
where:
• S = the present value of the perpetuity
• X = the forecast annual earnings
• Ke = the investor’s required return
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Setting Performance Targets
• Given market values and required rates of return, it is possible to establish
performance targets for management to sustain market values
• For a firm financed by both debt and equity, the firm must plan to earn
sufficient returns to cover the interest cost on debt plus the required return for
shareholders
• Working back from these requirements, we can forecast the level of sales the
firm must earn in order to achieve these operating results which sets a
performance target for management
• Suppose that the required return is 6%
on debt and 12% on equity; Table 20-3
shows the forecast income statement
that establishes a performance target
for management
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Setting Performance Targets
• Once sales performance targets are established, other targets can be
determined through the application of ratios
• Since equity, in this case, is a perpetuity, we can express the price per share
using Equation 20-4:
P
EPS ROE  BVPS

Ke
Ke
• Dividing both sides of Equation 20-4 by book value per share (BVPS) derives
the market-to-book (M/B) ratio given in Equation 20-5:
P
ROE

BVPS
Ke
• Notice that if the return on equity exceeds the investor’s required return,
then the price of the stock will rise above book value.
• This is how a financial manager can add value
Booth/Cleary Introduction to Corporate Finance, Second Edition
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The Cost of Capital
• The overall market value of the firm is the market value of its debt,
preferred equity and common equity sources of financing:
V=D+P+S
• In our example, V = $3,200, EBIT = $542 and the tax rate is 40%.
Therefore, after tax EBIT is $325.20.
• We can represent EBIT as ROI × IC, and this allows us to use Equation
20-6 to determine the value of the firm and Equation 20-7 to find the
capital cost of an all equity firm:
V 
ROI  IC
ROI  IC $325.20
 Ka 

 10.16%
Ka
V
$3,200
Booth/Cleary Introduction to Corporate Finance, Second Edition
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The Cost of Capital
• We can now substitute the component costs for both debt and equity
to develop a general equation for (WACC) as the weighted average of
the component costs, as in Equations 20-8 and 20-9
ROI  IC K e S  K d D(1  T )  K P P
Ka 

Ka
V
S
P
D
WACC  K e  K P  K d (1  T )
V
V
V
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating Market Values
• The total market value of equity (the market capitalization) is the price
per share multiplied by the number of shares outstanding, as in
Equation 20-10:
S  P0  n
• The market price for a preferred share is the annual preferred dividend
divided by the preferred shareholder’s required return (as in Equation
20-11), and the market capitalization of both common and preferred
stock is determined using Equation 20-10.
DP
P0 
kP
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating Market Values
• The market value of bonds differs from book value only if the
required rates of return in the market have changed since the
bond’s original issue and do not currently equal the coupon rate.
• Knowing the term to maturity, the coupon rate and the
bondholder’s required return, we can determine the market value
of the bonds with Equation 20-12:
I
B
kb


1
F

1 
n 
n
(
1

k
)
(
1

k
)
b
b


• Determine the total market value of debt by multiplying the
market value of an individual bond by the number of bonds
outstanding
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Market Values Weights
• In order to calculate the market value weights required to calculate
WACC (D/V, P/V and S/V), you will need to know the total market
value of debt, preferred stock and common stock
Example: Suppose a firm has 1 million common shares outstanding
trading for $21.50 each and 4,000 long term bonds trading for $950
each. The firm has no preferred stock. Calculate the market value
weights of each source of financing.
• These weights, D/V = 15.02% and S/V = 84.98%, can be used to
calculate the weighted average cost of capital (WACC)
Type
Bonds
Common stock
Market Price
Number
Outstanding
Total Market
Value
Market Value
Weight
$950.00
4,000
$3,800,000
15.02%
$21.50
1,000,000
$21,500,000
84.98%
$25,300,000
100.00%
Total
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating the Non-Equity Component Costs
• Table 20-4 illustrates average issuing costs for
different forms of capital
• Issuing or floatation costs are incurred by a firm
when it raises new capital through the sale of
securities in the primary market, and include:
• Underwriting discounts paid to the investment
dealer
• Direct costs associated with the issue including
legal and accounting costs
• The net proceeds of the sale of each security is
therefore less than the price paid by each
investor (this is called a financing wedge)
• Therefore, the component cost of capital
exceeds the investor’s required return
Booth/Cleary Introduction to Corporate Finance, Second Edition
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WACC Versus Marginal Cost of Capital
• The marginal cost of capital (MCC) is the weighted average cost
of the next dollar of financing to be raised
• At low levels of financing, WACC = MCC
• But, as a firm raises more and more capital in a given year, it will
exhaust the supply of lower cost sources of capital and then
have to access marginally higher cost sources of capital
• Therefore, MCC increases with the amount of capital to be
raised
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating the Non-Equity Component
Costs: The Cost of Debt
• The cost of debt is a function of:
• The investor’s required rate of return
• The tax-deductibility of interest expenses
• The floatation costs incurred to issue new debt
• If you know the debt investor’s required rate of return, the corporate tax
rate and the floatation cost percentage for debt, you can estimate the cost
of debt as:
K d (1  T )
Cost of Debt 
1 fd
Example: If the investor requires a 10% return, 40% is the corporate tax rate
and there is a 3% floatation cost, then the firm’s cost of debt is:
K d (1  T ) 0.1(1  0.4)
Cost of Debt 

 6.19%
1 fd
1  0.03
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating the Non-Equity Component
Costs: The Cost of Debt
• The bond valuation formula can also be adjusted, as in Equation 2013, for the tax deductibility of interest expenses and the net proceeds
the firm would receive on the sale of one bond after floatation costs.
Then, solve for the rate that causes the formula to equal the market
price.

I (1  T ) 
1
F
Net proceeds 

1 
n 
K i  (1  K i )  (1  K i ) n
Where Ki = the after-tax and after-floatation cost of debt
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating the Non-Equity Component
Costs: The Cost of Preferred Shares
• If you know the preferred share investor’s required rate of return and the
floatation cost percentage for preferred share financing, you can
estimate the cost of preferred shares as:
Investor' s Required Return
Cost of Preferred Equity 
1 fP
Example: If an investor requires a 14% return and floatation costs are 5%,
then the preferred shares cost is:
0.14
Cost of Preferred Equity 
 14.74%
1  0.05
• Note that preferred share dividends are paid out of after-tax earnings, so
there are no taxation effects on the preferred share component cost of
capital
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Estimating the Non-Equity Component
Costs: The Cost of Preferred Shares
• Alternatively, as in Equation 20-14, the component cost of preferred
shares can be found by dividing the preferred share dividend by the
net proceeds or the selling price of each preferred share less the
floatation costs per share:
DP
KP
NP
Booth/Cleary Introduction to Corporate Finance, Second Edition
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The Effects of Operating and Financial
Leverage
• Leverage is the increased volatility in operating income over time,
created by the use of fixed costs in lieu of variable costs
• Leverage multiplies both profits and losses
• There are two types: operating leverage and financial leverage
• Both types of leverage have the same effect on shareholders, but
are accomplished in very different ways and for different strategic
purposes
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The Effects of Operating and Financial
Leverage
• Operating leverage is the increased volatility in operating income
caused by fixed operating costs. This is commonly accomplished by a
firm choosing to become more capital intensive and less labor intensive,
thereby increasing operating leverage.
• Financial leverage is the increased volatility in operating income caused
by fixed financial costs and can be increased by taking on financial
obligations with fixed annual claims on cash flow (e.g., bonds or
preferred stock), or using the proceeds from the debt to retire equity
• Shareholders bear the added risks associated with the use of leverage
• The higher the use of leverage, the higher the risk to the shareholder
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The Effects of Operating and Financial
Leverage
Operating Leverage
Advantages
Disadvantages
• Magnification of profits to shareholders
• Operating efficiencies, such as faster
production, fewer errors and higher
quality, usually result in increasing
productivity
•
•
•
•
Magnification of losses to shareholders
Higher break even point
High capital cost of equipment
Equipment can be illiquid
Financial Leverage
Advantages
Disadvantages
• Magnification of profits to shareholders
• Lower cost of capital at low to
moderate levels of financial leverage
because interest expense is tax
deductible
• Magnification of losses to shareholders
• Higher break even point
• At higher levels of financial leverage,
the low after-tax cost of debt is offset by
other effects such as bankruptcy and
agency costs
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common
Equity
• To this point we have been valuing stock as a no-growth perpetuity,
which means we are assuming that the current dividend will be the
same in each future year
• Table 20-8 illustrates the importance of growth: on average, 62.22% of
the market value of this sample of firms could be attributed to growth
opportunities
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• The Gordon, or constant growth, model assumes constant growth in the
stream of dividends, as in Equation 20-15
• The price per share today equals the next expected dividend divided by
the shareholder’s required return less the long-run constant growth
rate
• Equation 20-15 can be rearranged into Equation 20-16 to solve for the
investor’s required rate of return
D1
D1
P0 
 Ke 
g
Ke  g
P0
• This shows that the investor’s required rate of return consists of two
components: expected dividend yield and the long-run growth rate
• This is known as the cost of internal equity, or the cost of retained
earnings where the firm does not need to incur floatation costs
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Growth Models and the Cost of Common Equity
• The Gordon, or constant growth, model can be modified to solve for the
cost of new equity by using the net proceeds (NP) the firm receives for
each new share sold after floatation costs, as in Equation 20-17:
D1
Ke 
g
NP
• The constant growth model can only be used in cases where it is
reasonable to assume that the growth rate can be sustained in the very
long term, which usually means for large, mature companies that
already pay a significant dividend
• But, the constant growth model should not be used for smaller, more
rapidly growth firms where higher current growth rates are experienced
which are not expected to be sustained in the long term
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Growth Models and the Cost of Common Equity
• Equation 20-18 shows one way to estimate the constant growth rate is
the sustainable growth method: multiplying the firm’s retention ratio
by the forecast return on equity:
g  ROE  b
• Substituting the sustainable growth rate into the Gordon model gives
Equation 20-19:
D
P0 
1
K e  b  ROE
• We can rewrite this as Equation 20-20 by recognizing that the expected
dividend is the expected earnings per share (X) multiplied by the
dividend payout ratio (which is one minus the retention ratio):
P0 
Booth/Cleary Introduction to Corporate Finance, Second Edition
X 1 (1  b)
K e  b  ROE
27
Growth Models and the Cost of Common Equity
Conclusion:
• A firm’s share price is determined by:
•
•
•
•
Forecast earnings per share
Dividend payout
Return on equity
Shareholders’ required return
• The higher the growth rate, the higher the share price because larger
future dividends and earnings are forecast
• We can rearrange Equation 20-20 into Equation 20-21 by substituting in
alternative expressions for the dividend and growth rate:
D1
X 1 (1  b)
Ke 
g
 b  ROE
P0
P0
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• Table 20-9 shows the use of Equation 20-21 to estimate the cost of
internal equity for three different growth scenarios
• Notice that sustainable growth rate increases with return on equity, but
that expected dividend yield falls
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• Table 20-10 demonstrates that
the cost of capital is a hurdle
rate, or the return on an
investment required to create
value; below this value an
investment will destroy value
• When a firm retains earnings and
reinvests them at lower rates
than what shareholders require,
the value of the firm falls
• The key to share price growth is
the reinvest earnings at rates
greater than the cost of capital
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• Growing firms reinvest in projects that offer rates equal to its cost of
capital (ROE = Ke)
• Growth firms reinvest earnings at rates higher than the cost of capital
(ROE > Ke)
• This is the reason that earnings yield is not an appropriate estimate of
the firm’s cost of capital
• What is relevant is not whether dividends or earnings are growing, but
rather whether the firm is investing at rates of return greater than the
cost of capital
• This means the firm should be investing in projects with positive NPVs
(IRRs > cost of capital)
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Growth Models and the Cost of Common Equity
• Multi-stage growth models, such as the multi-stage dividend discount
model, account for different levels of growth in earnings and dividends
over time
• Since there is no limit to the number of growth stages one can forecast
for a given company, this is a very flexible model
• Equation 20-22 shows a two-stage growth model that breaks price into
two components:
• Present value of existing opportunities (PVEO)
• Present value of growth opportunities (PVGO)
ROE  BVPS
Inv  ROE 2  K e 
P0 



Ke
1 Ke 
Ke

P0  PVEO  PVGO
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Growth Models and the Cost of Common Equity
• PVGO is discounted to the present by one year because it represents an
incremental investment decision today that will not result in the first
cash flow until one year from now
• PVGO adds a perpetual amount represented by the difference between
the ROE2 and the cost of equity
• If ROE2 = Ke then the future investment adds nothing to the value of the
firm
• If ROE2 > Ke then the future investment adds value to the firm
ROE  BVPS
Inv  ROE 2  K e 



Ke
1 Ke 
Ke

P0  PVEO  PVGO
P0 
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
Figure 20-1 shows four
scenarios:
1. Star – high PVEO and
high PVGO
2. Cash Cow – high
PVEO and low PVGO
3. Turnaround – low
PVEO and high PVGO
4. Dog – low PVEO and
low PVGO
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• The Fed Model is used by the U.S. Federal Reserve to estimate whether
the stock market is over or under valued and is given in Equation 20-23:
Vactual
Vactual

VFed
Exp( EPS ) /( K TBond  1.0%)
• Aggregate valuation across the entire market is easier because
unsystematic risk attached to individual stocks is eliminated as a factor
• The Fed’s estimate of the market value is the expected EPS on the S&P
500 index divided by the yield on long-term U.S. Treasury bonds less 1%
• We can rearrange Equation 20-23 into Equation 20-24:
V Fed
Booth/Cleary Introduction to Corporate Finance, Second Edition
Exp( EPS )

K TBond  1.0%
35
Growth Models and the Cost of Common Equity
• All of the data required for this model is readily available, so this estimate
of value is easy to produce and track over time, as shown in Figure 20-2:
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Growth Models and the Cost of Common Equity
• Equation 20-25 is a variation of the Fed model that can be used to
determine if the market is fairly valued: X
PS & P 500
 K TBond  1.0%
• When the earnings yield on the S&P 500 (the market proxy) is equal to
the long-term Treasury bond yield less 1% the market is fairly valued
• The earnings yield is the appropriate discount rate for the no-growth
(perpetual) case, whereas we would expect the market as a whole to
grow at the nominal GDP growth rate
• The required return on the market as a whole is, then, the long-term
Treasury yield plus an approximately 4% risk premium (5% nominal GDP
less 1%), and can serve as a useful benchmark for financial managers as
they attempt to estimate their own firm’s cost of capital
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• The capital asset pricing model (CAPM) can be used to estimate the
return required by common shareholders, particularly in situations
where discounted cash flow methods will perform poorly (i.e., growth
firms)
• CAPM estimates a market determined estimate, because the risk-free
rate (RF) is the benchmark return and is measured directly, and the
market risk premium (MRP) is taken from current market estimates
• Equation 20-26 shows the CAPM is a single-factor model, so we
estimate the required return on equity based on an estimate of the
systematic risk of the firm as measured by the firm’s beta coefficient:
K e  RF  MRP   e
• The yield on 91-day Treasury bills is often used for RF
• But MRP is harder to forecast: one common approach is to use an
estimate of the current expected MRP based on a long-run average
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Table 20-11
shows the returns
on the S&P/TSX
Composite Index
annually between
2003 and 2008
• Table 20-12 gives long-term return statistics for
several types of asset classes
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Table 20-13 shows TD Economics’ long-run forecasts for the returns on
different asset classes
• Note that the Scotia Universe Bond Index is a long-term bond index that
contains Canadian government and corporate bonds
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Figure 20-3 shows that the estimated betas for the major sub-indices of
the S&P/TSX have varied significantly over time
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Table 20-14 shows the data charted in Figure 20-3
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Risk-Based Models and the Cost of Common
Equity
Figure 20-3 and Table 20-14 show the following:
• The IT sub index shows rapidly increasing betas while other subindices show relatively constant betas
• The weighted average of all betas is, by definition, the market beta
of 1.0
• If one sub index is changing, that change alone affects all others in
the opposite direction
• During the internet bubble of the late 1990s, rapid growth in the IT
sector caused its beta to change
• When betas are measured over the period of a sector bubble or
crash, it is necessary to adjust the beta estimates of firms in other
sectors by taking the industry grouping as a major input to develop
estimates of equity capital cost using the range of company betas
prior to the bubble or crash
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Figure 20-4 shows Nortel’s stock price, and illustrates the IT bubble
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Figure 20-5 shows both Tim Horton’s stock price and the S&P/TSX
Composite Index during the 2008 financial crisis. Notice how the value
of the index crashes while Tim Horton’s stock holds its value. How
would this affect Tim Horton’s beta?
Booth/Cleary Introduction to Corporate Finance, Second Edition
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Risk-Based Models and the Cost of Common
Equity
• Equation 20-27 shows we can scale our estimate of the equity
holder’s required return when accessing new equity and
incurring floatation costs:
K ne
Booth/Cleary Introduction to Corporate Finance, Second Edition
K e P0

NP
46
The Cost of Capital and Investment
• The investment opportunity schedule (IOS) is the ranking of a firm’s
investment opportunities from highest to lowest profitability according to
expected internal rate of return (IRR)
• When superimposed on a marginal cost of capital (MCC) curve, the firm can
identify projects that will increase the value of the firm by looking at the
portion of the IOS that lies above the WACC line. Projects represented by the
portion of the IOS below WACC should be rejected.
Booth/Cleary Introduction to Corporate Finance, Second Edition
47
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