Why do the bond rating and cost of debt
depend upon the amount of debt borrowed?
• As the firm borrows more money, the firm
increases its financial risk causing the firm’s bond
rating to decrease, and its cost of debt to
increase.
• Levered beta and unlevered beta
Cost of Debt at Different Debt Ratios
Amount
Borrowed
$ 0
D/Cap.
Ratio
0
D/E
Ratio
0
Bond
Rating
--
250
0.125
0.143
AA
8.0%
500
0.250
0.333
A
9.0%
750
0.375
0.600
BBB
11.5%
1,000
0.500
1.000
BB
14.0%
rd
--
What effect does more debt have on a firm’s
cost of equity?
• If the level of debt increases, the firm’s risk
increases.
• We have already observed the increase in the
cost of debt.
• However, the risk of the firm’s equity also
increases, resulting in a higher rs.
The Hamada Equation (Levered Beta)
• Because the increased use of debt causes both
the costs of debt and equity to increase, we need
to estimate the new cost of equity.
• The Hamada equation attempts to quantify the
increased cost of equity due to financial leverage.
• Uses the firm’s unlevered beta, which represents
the firm’s business risk as if it had no debt.
The Hamada Equation (Levered Beta)
bL = bU[1 + (1 – T)(D/E)]
Bu = bL/[1 + (1 – T)(D/E)]
• Suppose, the risk-free rate is 6%, as is the market
risk premium. The unlevered beta (bu) of the
firm is 1.0. We were previously told that invested
capital was $2,000,000. T (tax rate), D (debts) E
(equities)
Calculating Levered Betas and Costs of Equity
If D = $250,
bL
= 1.0[1 + (0.6)($250/$1,750)]
= 1.0857
re
= rRF + (rM – rRF)bL
= 6.0% + (6.0%)1.0857
= 12.51%
Table for Calculating Levered Betas and Costs
of Equity
Amount
Borrowed
$ 0
D/Cap.
Ratio
0%
D/E
Ratio
0%
Levered
Beta
1.00
250
12.50
14.29
1.09
12.51
500
25.00
33.33
1.20
13.20
750
37.50
60.00
1.36
14.16
1,000
50.00
100.00
1.60
15.60
rs
12.00%
The Boeing 7E7
Adv. Corporate Finance
Questions to answer
• What is an appropriate required rate of return against
which to evaluate the prospective IRRs from the Boeing
7E7?
•
•
•
•
Estimate the cost of equity using the CAPM.
Which risk-premium, beta and risk-free rate did you use? Why?
which capital-structure weights did you use? Why?
What does sensitivity analysis reveal about the nature of
Boeing’s gamble on the 7E7?
Cost of Equity
• Beta, Risk Premium, and Risk-Free Rate?
• Beta? Exhibit 10
• Currently Boeing traded at NYSE
• Beta for Boeing =X.XX (Entire Firm)
• However, Boeing consists of two major divisions: commercial and defense
Unlevered Beta
• The unlevered beta is the beta of a company without any debt.
• Unlevering a beta removes the financial effects from leverage.
• Beta measures a firm’s total risk = Business risk + Financial
risk
• Basically, we want to measure a Boeing's business risk arising from the
7E7 project
• In this case, unlevered β measure a Boeing’s pure business risk
Boeing's commercial beta
• Boeing’s asset beta can be split into Boeing’s commercial beta and Boeing’s
defense beta
• Boeing’s beta = (% defense)(βdefense)+ (% commercial) (βcommercial)
• Boeing’s defense beta=?
• You must use peers’ unlevered beta
• You also need Boeing’s unlevered beta
• Once you calculate the commercial department’s unlevered beta, and must re-lever to get
levered beta
Boeing's commercial beta-levered
• βL for commercial= ?
• Cost of Equity = ?
• WACC= ?
• Should the board approve the 7E7?
Requirement: Your case report must include 1) a page-long executive summary that identify the
questions you are addressing in your report, 2) all calculation steps for the cost of capital
(weights, cost of debts, cost of equity, weighted average cost of capital) with proper
explanations, 3) especially calculations related to levered beta and unlevered beta, 4) source of
your data, 5) your recommendation to the board of directors whether they should or should
not approve the 7E7
Chapter 9
The Cost of
Capital
Learning Goals
LG1
Understand the basic concept and sources of
capital associated with the cost of capital.
LG2
Explain what is meant by the marginal cost of
capital.
LG3
Determine the cost of long-term debt, and
explain why the after-tax cost of debt is the
relevant cost of debt.
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9-2
Learning Goals (cont.)
LG4
Determine the cost of preferred stock.
LG5
Calculate the cost of common stock equity, and
convert it into the cost of retained earnings and
the cost of new issues of common stock.
LG6
Calculate the weighted average cost of capital
(WACC) and discuss alternative weighting
schemes.
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9-3
Overview of the Cost of Capital
• The cost of capital represents the firm’s cost of
financing, and is the minimum rate of return that a
project must earn to increase firm value.
– Financial managers are ethically bound to only invest in
projects that they expect to exceed the cost of capital.
– The cost of capital reflects the entirety of the firm’s
financing activities.
• Most firms attempt to maintain an optimal mix of
debt and equity financing.
– To capture all of the relevant financing costs, assuming
some desired mix of financing, we need to look at the
overall cost of capital rather than just the cost of any single
source of financing.
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9-4
Overview of the Cost of Capital (cont.)
A firm is currently faced with two investment
opportunities. Assume the following:
– Investment A
• Cost = $100,000
• Life = 20 years
• Expected Return = 7%
– Least costly financing source available
• Debt (bonds) = 6%
– Because the firm can earn 7% on the investment
of funds costing only 6%, the analyst
recommends that the firm undertake this
investment.
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9-5
Overview of the Cost of Capital (cont.)
– Investment B
• Cost = $100,000
• Life = 20 years
• Expected Return = 12%
– Least costly financing source available
• Equity = 14%
– In this instance, the analyst recommends that
the firm reject the opportunity, because the 14%
financing cost is greater than the 12% expected
return.
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9-6
Overview of the Cost of Capital (cont.)
What if instead the firm used a combined cost of
financing?
– Assuming that a 50–50 mix of debt and equity is targeted,
the weighted average cost here would be:
(0.50 6% debt) + (0.50 14% equity) = 10%
– With this average cost of financing, the first opportunity
would have been rejected (7% expected return < 10%
weighted average cost), and the second would have been
accepted
(12% expected return > 10% weighted average cost).
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9-7
Focus on Ethics
The Ethics of Profit
– Introduced in 1999, Vioxx was an immediate success,
quickly reaching $2.5 billion in annual sales.
– However, a Merck study launched in 1999 eventually found
that patients who took Vioxx suffered from an increased
risk of heart attacks and strokes.
– Despite the risks, Merck continued to market and sell
Vioxx.
– Vioxx was withdrawn from the market in 2006, dealing a
severe blow to the firm’s reputation, profits, and stock
price.
The Vioxx recall increased Merck’s cost of capital. What effect
would an increased cost of capital have on a firm’s future
investments?
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9-8
Overview of the Cost of Capital:
Sources of Long-Term Capital
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9-9
Cost of Long-Term Debt
• The pretax cost of debt is the financing cost
associated with new funds through long-term
borrowing.
–
Typically, the funds are raised through the sale of
corporate bonds.
• Net proceeds are the funds actually received by
the firm from the sale of a security.
• Flotation costs are the total costs of issuing and
selling a security. They include two components:
1. Underwriting costs—compensation earned by investment
bankers for selling the security.
2. Administrative costs—issuer expenses such as legal,
accounting, and printing.
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9-10
Cost of Long-Term Debt (cont.)
Duchess Corporation, a major hardware
manufacturer, is contemplating selling $10 million
worth of 20-year, 9% coupon bonds with a par value
of $1,000. Because current market interest rates are
greater than 9%, the firm must sell the bonds at
$980. Flotation costs are 2% or $20. The net
proceeds to the firm for each bond is therefore $960
($980 – $20).
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9-11
Cost of Long-Term Debt (cont.)
• The before-tax cost of debt, rd, is simply the rate of
return the firm must pay on new borrowing.
• The before-tax cost of debt can be calculated in any
one of three ways:
1. Using market quotations: observe the yield to maturity
(YTM) on the firm’s existing bonds or bonds of similar
risk issued by other companies
2. Calculating the cost: find the before-tax cost of debt by
calculating the YTM generated by the bond cash flows
3. Approximating the cost
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9-12
Cost of Long-Term Debt (cont.)
The cash flows associated with the sale of Duchess
Corporation’s bond issue are as follows:
We can determine the cost of debt by finding the
YTM, which is the discount rate that equates the
present value of the bond outflows to the initial
outflow.
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9-13
Cost of Long-Term Debt (cont.)
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9-14
Cost of Long-Term Debt (cont.)
Approximating the cost
where
I = annual interest in dollars
Nd = net proceeds from the sale of debt (bond)
n = number of years to the bond’s maturity
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9-15
Cost of Long-Term Debt (cont.)
Approximating the cost
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9-16
Cost of Long-Term Debt:
After-Tax Cost of Debt
• The interest payments paid to bondholders are tax
deductable for the firm, so the interest expense on
debt reduces the firm’s taxable income and,
therefore, the firm’s tax liability.
• The after-tax cost of debt, ri, can be found by
multiplying the before-tax cost, rd, by 1 minus the
tax rate, T, as stated in the following equation:
ri = rd (1 – T)
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9-17
Cost of Long-Term Debt:
After-Tax Cost of Debt (cont.)
Duchess Corporation has a 40% tax rate. Using the
9.452% before-tax debt cost calculated using Excel or
a financial calculator, we find an after-tax cost of debt
of 5.67% [9.452% (1 – 0.40)].
Typically, the cost of long-term debt for a given firm
is less than the cost of preferred or common stock,
partly because of the tax deductibility of interest.
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9-18
Personal Finance Example
Kait and Kasim Sullivan, a married couple in the 28%
federal income-tax bracket, wish to borrow $60,000
for a new car.
– They can either borrow the $60,000 through the auto
dealer at an annual interest rate of 6.0%, or they can take
a $60,000 second mortgage on their home at an annual
interest rate of 7.2%.
– If they borrow from the auto dealer, the interest on this
“consumer loan” will not be deductible for federal tax
purposes. However, the interest on the second mortgage
would be tax-deductible because the tax law allows
individuals to deduct interest paid on a home mortgage.
– Because interest on the auto loan is not tax-deductible, its
after-tax cost equals its stated cost of 6.0%.
– Because interest on the auto loan is tax-deductible, its
after-tax cost equals its stated cost of 7.2% (1 – 0.28) =
5.2%.
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9-19
Cost of Preferred Stock
• Preferred stock gives preferred stockholders the
right to receive their stated dividends before the
firm can distribute any earnings to common
stockholders.
– Preferred stock dividends may be stated as a dollar
amount.
– Sometimes preferred stock dividends are stated as an
annual percentage rate, which represents the percentage
of the stock’s par, or face, value that equals the annual
dividend.
• The cost of preferred stock, rp, is the ratio of the
preferred stock dividend to the firm’s net proceeds
from the sale of preferred stock.
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9-20
Cost of Preferred Stock (cont.)
Duchess Corporation is contemplating the issuance of
a 10% preferred stock that they expect to sell for $87
per share. The cost of issuing and selling the stock is
expected to be $5 per share. The dividend is $8.70
(10% $87). The net proceeds (Np) equal $82 ($87 –
$5), the share price less the flotation costs. The cost
of Duchess’ preferred stock is:
rP = DP/Np = $8.70/$82 = 10.6%
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9-21
Cost of Common Stock
• The cost of common stock is the return required on
the stock by investors in the marketplace.
• There are two forms of common stock financing:
1. retained earnings
2. new issues of common stock
• The cost of common stock equity, rs, is the rate
at which investors discount the expected dividends
of the firm to determine its share value.
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9-22
Cost of Common Stock (cont.)
The constant-growth valuation (Gordon) model assumes
that the value of a share of stock equals the present value of all
future dividends (assumed to grow at a constant rate) that it is
expected to provide over an infinite time horizon.
where
P0 = value of common stock
D1 = per-share dividend expected at the end of year 1
rs = required return on common stock
g = constant rate of growth in dividends
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9-23
Cost of Common Stock (cont.)
Solving for rs results in the following expression for
the cost of common stock equity:
The equation indicates that the cost of common stock
equity can be found by dividing the dividend expected
at the end of year 1 by the current market price of
the stock (the “dividend yield”) and adding the
expected growth rate (the “capital gains yield”).
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9-24
Cost of Common Stock (cont.)
Duchess Corporation wishes to
determine its cost of common stock
equity, rs. The market price, P0, of
its common stock is $50 per share.
The firm expects to pay a dividend,
D1, of $4 at the end of the coming
year, 2016. The dividends paid on
the outstanding stock over the past
6 years (2010–2015) were as
follows:
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9-25
Cost of Common Stock (cont.)
We can calculate the annual rate at which dividends
have grown, g, from 2007 to 2012. It turns out to be
approximately 5% (more precisely, it is 5.05%).
Substituting D1 = $4, P0 = $50, and g = 5% into the
previous equation yields the cost of common stock
equity:
rs = ($4/$50) + 0.05 = 0.08 + 0.05 = 0.130, or 13.0%
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9-26
Cost of Common Stock (cont.)
The capital asset pricing model (CAPM) describes
the relationship between the required return, rs, and
the nondiversifiable risk of the firm as measured by
the beta coefficient, b.
rs = RF + [b (rm – RF)]
where
RF = risk-free rate of return
rm = market return; return on the market portfolio of
assets
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9-27
Cost of Common Stock (cont.)
Duchess Corporation now wishes to calculate its cost
of common stock equity, rs, by using the capital asset
pricing model. The firm’s investment advisors and its
own analysts indicate that the risk-free rate, RF,
equals 7%; the firm’s beta, b, equals 1.5; and the
market return, rm, equals 11%.
Substituting these values into the CAPM, the company
estimates the cost of common stock equity, rs, to be:
rs = 7.0% + [1.5 (11.0% – 7.0%)] = 7.0% + 6.0% = 13.0%
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9-28
Cost of Common Stock (cont.)
• The CAPM technique differs from the constantgrowth valuation model in that it directly considers
the firm’s risk, as reflected by beta, in determining
the required return or cost of common stock equity.
• The constant-growth model does not look at risk; it
uses the market price, P0, as a reflection of the
expected risk–return preference of investors in the
marketplace.
• The constant-growth valuation and CAPM
techniques for finding rs are theoretically
equivalent, though in practice estimates from the
two methods do not always agree.
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9-29
Cost of Common Stock (cont.)
• Another difference is that when the constantgrowth valuation model is used to find the cost of
common stock equity, it can easily be adjusted for
flotation costs to find the cost of new common
stock; the CAPM does not provide a simple
adjustment mechanism.
• The difficulty in adjusting the cost of common stock
equity calculated by using CAPM occurs because in
its common form the model does not include the
market price, P0, a variable needed to make such
an adjustment.
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9-30
Cost of Common Stock:
Cost of Retained Earnings
The cost of retained earnings, rr, is the same as
the cost of an equivalent fully subscribed issue of
additional common stock, which is equal to the cost of
common stock equity, rs.
rr = rs
The cost of retained earnings for Duchess Corporation
was actually calculated in the preceding examples: It
is equal to the cost of common stock equity. Thus rr
equals 13.0%.
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9-31
Matter of Fact
Retained Earnings, the Preferred Source of Financing
– In the United States and most other countries,
firms rely more heavily on retained earnings than
any other source of financing.
– For example, a 2013 survey of Chinese firms
found that 64% of the companies surveyed listed
retained earnings as one of their primary sources
of funds.
– Bank loans were a distant second choice,
mentioned as a primary source of funds by just
44% of companies.
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9-32
Cost of Common Stock: Cost of New
Issues of Common Stock
• The cost of a new issue of common stock, rn, is
the cost of common stock, net of underpricing and
associated flotation costs.
• New shares are underpriced if the stock is sold at
a price below its current market price, P0.
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9-33
Cost of Common Stock: Cost of New
Issues of Common Stock (cont.)
We can use the constant-growth valuation model
expression for the cost of existing common stock, rs,
as a starting point. If we let Nn represent the net
proceeds from the sale of new common stock after
subtracting underpricing and flotation costs, the cost
of the new issue, rn, can be expressed as follows:
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9-34
Cost of Common Stock: Cost of New
Issues of Common Stock (cont.)
• The net proceeds from sale of new common stock,
Nn, will be less than the current market price, P0.
• Therefore, the cost of new issues, rn, will always be
greater than the cost of existing issues, rs, which is
equal to the cost of retained earnings, rr.
• The cost of new common stock is normally greater
than any other long-term financing cost.
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9-35
Cost of Common Stock: Cost of New
Issues of Common Stock (cont.)
Duchess Corporation common stock is currently
selling at $50 per share. To determine its cost of new
common stock, rn, Duchess Corporation has
estimated that on average, new shares can be sold
for $47. The $3-per-share underpricing is due to the
competitive nature of the market. A second cost
associated with a new issue is flotation costs of $2.50
per share that would be paid to issue and sell the new
shares. The total underpricing and flotation costs per
share are therefore $5.50.
rn = ($4.00/$44.50) + 0.05 = 0.09 + 0.05 = 0.140,
or 14.0%
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9-36
Weighted Average Cost of Capital
The weighted average cost of capital (WACC), ra,
reflects the expected average future cost of capital
over the long run; found by weighting the cost of
each specific type of capital by its proportion in the
firm’s capital structure.
ra = (wi ri) + (wp rp) + (ws rr or n)
where
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9-37
Weighted Average Cost of Capital (cont.)
Three important points should be noted in the
equation for ra:
1. For computational convenience, it is best to convert the
weights into decimal form and leave the individual costs in
percentage terms.
2. The weights must be non-negative and sum to 1.0. Simply
stated, WACC must account for all financing costs within
the firm’s capital structure.
3. The firm’s common stock equity weight, ws, is multiplied
by either the cost of retained earnings, rr, or the cost of
new common stock, rn. Which cost is used depends on
whether the firm’s common stock equity will be financed
using retained earnings, rr, or new common stock, rn.
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9-38
Weighted Average Cost of Capital (cont.)
In earlier examples, we found the costs of the various
types of capital for Duchess Corporation to be as
follows:
–
–
–
–
Cost
Cost
Cost
Cost
of
of
of
of
debt, ri = 5.6%
preferred stock, rp = 10.6%
retained earnings, rr = 13.0%
new common stock, rn = 14.0%
The company uses the following weights in calculating
its weighted average cost of capital:
– Long-term debt = 40%
– Preferred stock = 10%
– Common stock equity = 50%
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9-39
Calculation of the Weighted Average Cost
of Capital for Duchess Corporation
Table 9.1 Calculation of the Weighted Average Cost
of Capital for Duchess Corporation
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9-40
Focus on Practice
Uncertain Times Make for an Uncertain Weighted Average Cost of
Capital
– As U.S. financial markets experienced and recovered from
the 2008 financial crisis and 2009 “great recession,” firms
struggled to keep track of their weighted average cost of
capital since the individual component costs were moving
rapidly in response to the financial market turmoil.
– The financial crisis pushed credit costs to a point where
long-term debt was largely inaccessible, and the great
recession saw Treasury bond yields fall to historic lows
making cost of equity projections appear unreasonably low.
– Ron Domanico is the CFO at Caraustar Industries, Inc. and
he reported that his company dealt with the cost-of-capital
uncertainty by abandoning the one-size-fits-all approach.
Why don’t firms generally use both a short and long-run
weighted average cost of capital?
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9-41
Weighted Average Cost of Capital:
Weighting Schemes
• Book Value versus Market Value:
– Book value weights are weights that use accounting
values to measure the proportion of each type of capital in
the firm’s financial structure.
– Market value weights are weights that use market
values to measure the proportion of each type of capital in
the firm’s financial structure.
• Historical versus Target:
– Historical weights are either book or market value
weights based on actual capital structure proportions.
– Target weights are either book or market value weights
based on desired capital structure proportions.
• From a strictly theoretical point of view, the
preferred weighting scheme is target market value
proportions.
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9-42
Personal Finance Example
Chuck Solis currently has three loans outstanding, all
of which mature in exactly 6 years and can be repaid
without penalty any time prior to maturity. The
outstanding balances and annual interest rates on
these loans are noted below.
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9-43
Personal Finance Example (cont.)
Chuck found a lender who would loan him $80,000 for
6 years at an annual interest rate 9.2% on the
condition that the loan proceeds be used to fully
repay the three outstanding loans, which combined
have an outstanding balance of $80,000 ($26,000 +
$9,000 + $45,000).
Chuck wishes to choose the least costly alternative:
(1) do nothing or (2) borrow the $80,000 and pay off
all three loans.
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9-44
Personal Finance Example (cont.)
Chuck calculates the weighted average cost of his current debt
by weighting each debt’s annual interest cost by the proportion
of the $80,000 total it represents and then summing the three
weighted values as follows:
= [($26,000/$80,000) 9.6%] + [($9,000/$80,000) 10.6%]
+ [($45,000/$80,000) 7.4%]
= (.3250 9.6%) + (.1125 10.6%) + (.5625 7.4%)
= 3.12% + 1.19% + 4.16% = 8.47% ≈ 8.5%
Given that the weighted average cost of the $80,000 of current
debt of 8.5% is below the 9.2% cost of the new $80,000 loan,
Chuck should do nothing and just continue to pay off the three
loans as originally scheduled.
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9-45
Review of Learning Goals
LG1
Understand the basic concept and sources of
capital associated with the cost of capital.
The cost of capital is the minimum rate of return that a
firm must earn on its investments to grow firm value.
A weighted average cost of capital should be used to
find the expected average future cost of funds over
the long run. The individual costs of the basic sources
of capital (long-term debt, preferred stock, retained
earnings, and common stock) can be calculated
separately.
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9-46
Review of Learning Goals (cont.)
LG2
Explain what is meant by the marginal cost of
capital.
The relevant cost of capital for a firm is the marginal
cost of capital necessary to raise the next marginal
dollar of financing the firm’s future investment
opportunities. A firm’s future investment opportunities
in expectation will be required to exceed the firm’s
cost of capital.
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9-47
Review of Learning Goals (cont.)
LG3
Determine the cost of long-term debt, and
explain why the after-tax cost of debt is the
relevant cost of debt.
The before-tax cost of long-term debt can be found by
using cost quotations, calculations, or an
approximation. The after-tax cost of debt is calculated
by multiplying the before-tax cost of debt by 1 minus
the tax rate. The after-tax cost of debt is the relevant
cost of debt because it is the lowest possible cost of
debt for the firm due to the deductibility of interest
expenses.
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9-48
Review of Learning Goals (cont.)
LG4
Determine the cost of preferred stock.
The cost of preferred stock is the ratio of the preferred
stock dividend to the firm’s net proceeds from the sale
of preferred stock.
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9-49
Review of Learning Goals (cont.)
LG5
Calculate the cost of common stock equity, and
convert it into the cost of retained earnings and
the cost of new issues of common stock.
The cost of common stock equity can be calculated by
using the constant-growth valuation (Gordon) model
or the CAPM. The cost of retained earnings is equal to
the cost of common stock equity. An adjustment in the
cost of common stock equity to reflect underpricing
and flotation costs is necessary to find the cost of new
issues of common stock.
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9-50
Review of Learning Goals (cont.)
LG6
Calculate the weighted average cost of capital
(WACC) and discuss alternative weighting
schemes.
The firm’s WACC reflects the expected average future
cost of funds over the long run. It combines the costs
of specific types of capital after weighting each of
them by its proportion. The theoretically preferred
approach uses target weights based on market values.
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9-51
Chapter Resources on MyFinanceLab
• Chapter Cases
• Group Exercises
• Critical Thinking Problems
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9-52
Integrative Case: Eco Plastics Company
The target capital structure for ECO is given
by the weights in the following table:
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9-53
Integrative Case: Eco Plastics Company
• Eco can raise debt by selling 20-year bonds with a
$1,000 par value and a 10.5% annual coupon
interest rate.
• Eco’s corporate tax rate is 40% and its bonds
generally require an average discount of $45 per
bond and flotation costs of $32 per bond when
being sold.
• Eco’s outstanding preferred stock pays a 9%
dividend and has a $95-per-share par value. The
cost of issuing and selling additional preferred stock
is expected to be $7 per share.
• Eco does not currently pay a dividend to common
stockholders.
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9-54
Integrative Case: Eco Plastics Company
• In order to track the cost of common stock the CFO uses the
capital asset pricing model (CAPM). The CFO and the firm’s
investment advisors believe that the appropriate risk-free rate
is 4% and that the market’s expected return equals 13%.
Using data from 2012 through 2015, Eco’s CFO estimates the
firm’s beta to be 1.3.
• Although Eco’s current target capital structure includes 20%
preferred stock, the company is considering using debt
financing to retire the outstanding preferred stock, thus
shifting their target capital structure to 50% long-term debt
and 50% common stock.
• If Eco shifts its capital mix from preferred stock to debt, its
financial advisors expect its beta to increase to 1.5.
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9-55
Integrative Case: Eco Plastics Company
(cont.)
a.
b.
c.
d.
e.
Calculate Eco’s current after-tax cost of long-term debt.
Calculate Eco’s current cost of preferred stock.
Calculate Eco’s current cost of common stock.
Calculate Eco’s current weighted average cost capital.
(1) Assuming that the debt financing costs do not change,
what effect would a shift to a more highly leveraged
capital structure consisting of 50% long-term debt, 0%
preferred stock, and 50% common stock have on the risk
premium for Eco’s common stock? What would be Eco’s
new cost of common equity?
(2) What would be Eco’s new weighted average cost of
capital?
(3) Which capital structure—the original one or this one—
seems better? Why?
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9-56
The Cost of Capital
What sources of capital do firms use?
Capital
Debt
Notes
Payable
Preferred
Stock
Long-Term
Debt
Common
Equity
Retained
Earnings
New Common
Stock
Calculating the Weighted Average Cost
of Capital
WACC = wdrd(1 – T) + wprp + wcrs
•The w’s refer to the firm’s capital structure
weights.
•The r’s refer to the cost of each component.
Overview of Coleman Technologies Inc.
• Firm calculating cost of capital for major
expansion program.
– Tax rate = 40%.
– 15-year, 12% coupon, semiannual payment
noncallable bonds sell for $1,153.72. New bonds
will be privately placed with no flotation cost.
– 10%, $100 par value, quarterly dividend,
perpetual preferred stock sells for $111.10.
– Common stock sells for $50. D0 = $4.19 and g =
5%.
– b = 1.2; rRF = 7%; RPM = 6%.
– Bond-Yield Risk Premium = 4%.
– Target capital structure: 30% debt, 10% preferred,
60% common equity.
Review of Coleman’s Capital Structure
Book
Value
Market
Value
Target
%
48%
25%
30%
Preferred stock
2
5
10
Common equity
50
70
60
Debt (includes notes payable)
Number of shares not given in problem, so
actual calculations cannot be done.
How are the weights determined?
WACC = wdrd(1 – T) + wprp + wsrs
•
•
Use accounting numbers or market value (book vs.
market weights)?
Use actual numbers or target capital structure?
➢ Use the market value or target capital structure
Component Cost of Debt
WACC = wdrd(1 – T) + wprp + wcrs
•
•
rd is the marginal cost of debt capital.
•
Why tax-adjust; i.e., why rd(1 – T)?
The yield to maturity on outstanding L-T debt is
often used as a measure of rd.
A 15-year, 12% semiannual coupon bond sells
for $1,153.72. What is the cost of debt (rd)?
• Remember, the bond pays a semiannual
coupon, so rd = 5.0% x 2 = 10%.
INPUTS
30
N
OUTPUT
I/YR
5
-1153.72
60
1000
PV
PMT
FV
Component Cost of Debt
• Interest is tax deductible, so
A-T rd = B-T rd(1 – T)
= 10%(1 – 0.40) = 6%
• Flotation costs are small, so ignore them.
Component Cost of Preferred Stock
WACC = wdrd(1 – T) + wprp + wcrs
• rp is the marginal cost of preferred stock,
which is the return investors require on a
firm’s preferred stock.
• Preferred dividends are not tax-deductible,
so no tax adjustments necessary. Just use
nominal rp.
• Our calculation ignores possible flotation
costs.
What is the cost of preferred stock?
• The cost of preferred stock can be solved
by using this formula:
rp
= Dp/Pp
= $10/$111.10
= 9%
Component Cost of Equity
WACC = wdrd(1 – T) + wprp + wcrs
•
•
rs is the marginal cost of common equity using
retained earnings.
The rate of return investors require on the firm’s
common equity using new equity is re.
Why is there a cost for retained
earnings?
• Earnings can be reinvested or paid out as
dividends.
• Investors could buy other securities, earn a
return.
• If earnings are retained, there is an
opportunity cost (the return that
stockholders could earn on alternative
investments of equal risk).
– Investors could buy similar stocks and earn rs.
– Firm could repurchase its own stock and earn rs.
Three Ways to Determine the Cost of Common
Equity, rs
• CAPM: rs = rRF + (rM – rRF)b
• DDM:
rs = (D1/P0) + g
• Bond-Yield-Plus-Risk-Premium:
rs = rd + RP
Find the Cost of Common Equity Using the
CAPM Approach
The rRF = 7%, RPM = 6%, and the firm’s beta is
1.2.
rs = rRF + (rM – rRF)b
= 7.0% + (6.0%)1.2 = 14.2%
Find the Cost of Common Equity Using the
DCF Approach
D0 = $4.19, P0 = $50, and g = 5.
D1 = D0(1 + g)
= $4.19(1 + 0.05)
= $4.3995
rs = (D1/P0) + g
= ($4.3995/$50) + 0.05
= 13.8%
Find rs Using the Bond-Yield-Plus-RiskPremium Approach
rd = 10% and RP = 4%.
• This RP is not the same as the CAPM RPM.
• This method produces a ballpark estimate
of rs, and can serve as a useful check.
rs = rd + RP
rs = 10.0% + 4.0% = 14.0%
What is a reasonable final estimate of rs?
Method Estimate
CAPM
14.2%
DCF
13.8
rd + RP
14.0
Range = 13.8%-14.2%, might use
midpoint of range, 14%.
Why is the cost of retained earnings cheaper
than the cost of issuing new common stock?
• When a company issues new common
stock they also have to pay flotation costs
to the underwriter.
• Issuing new common stock may send a
negative signal to the capital markets,
which may depress the stock price.
If new common stock issue incurs a flotation
cost of 15% of the proceeds, what is re?
D0 (1 + g)
re =
+g
P0 (1 − F)
$4.19(1.05)
=
+ 5.0%
$50(1 − 0.15)
$4.3995
=
+ 5.0%
$42.50
= 15.4%
Flotation Costs
• Flotation costs depend on the firm’s risk
and the type of capital being raised.
• Flotation costs are highest for common
equity. However, since most firms issue
equity infrequently, the per-project cost is
fairly small.
• We will frequently ignore flotation costs
when calculating the WACC.
Ignoring flotation costs, what is the
firm’s WACC?
WACC = wdrd(1 – T) + wprp + wcrs
= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
= 1.8% + 0.9% + 8.4%
= 11.1%
What factors influence a company’s composite
WACC?
• Market conditions.
• The firm’s capital structure and dividend
policy.
• The firm’s investment policy. Firms with
riskier projects generally have a higher
WACC.
Should the company use the composite WACC
as the hurdle rate for each of its projects?
• NO! The composite WACC reflects the risk of
an average project undertaken by the firm.
Therefore, the WACC only represents the
“hurdle rate” for a typical project with
average risk.
• Different projects have different risks. The
project’s WACC should be adjusted to reflect
the project’s risk.
• Next slide illustrates importance of riskadjusting cost of capital.
Estimating the Cost of Capital
General Survey Results
14-26
General Survey Results
14-27
General Survey Results
14-28
General Survey Results
14-29
General Survey Results
14-30
General Survey Results
14-31
General Survey Results
14-32
General Survey Results
14-33
Overview of Coleman Technologies Inc.
Firm calculating cost of capital (financing costs) for major expansion program.
--tax rate = 40%
--5 year, 12% coupon, seminannual payment noncallable bonds sell for $1,153.72. New bonds will be privately placed w
no floation costs
--10%, $100 par value, quarterly dividend, perpetual preferred stock sells for $111.10
-- Common stock sells for $50. D0= $4.19 and g =5%
-- b (beta) =1.2, Rf (risk free rate)=7%, Rp (returns on the market)=6% , Rp (risk premium= Rm - Rf)
--bond-yield risk premium = 4%
--target capital structure: 30% debt, 10% preferred, 60% common equity
WACC = Wd x Kd (1-T) + Wps x Kps + Wcs x Kcs
Wd
N
CR
Bp
FV
Kd
I/Y (YTM)
I/Y (YTM)
0.3
5
10%
1153
1000
Wps
Dp/s
Pp/s
Kps
10
50 PMT
3.19% 6 month
6.38% 12 month
0.1
10
111.1
9.00%
will be privately placed with
ST debts
LT debts
10,000
50,000
ST debts
LT debts
C/S (BV)
50,000
C/S (MV)
Wd
Wcs
Wcs
0.6
0.545455
0.454545
1
This is wrong
Kc/s
1) CAPM
Rf
Rp
b
Kc/s (1)
Wd
Wcs
10,000
50,000
2000000 Price
20
Shares Outs 100000
0.029126
0.970874
This is right
Expected returns = Rf + b x (Rm - Rf)
0.07
0.06
1.12
0.1372
g: growth rate, D1: dividend payment next year
P: stock price today, Rcs: returns on stock investment
2) Discounted divided model (DDM)
P = (D1)/(Rcs -g)
Kcs=Rcs = (D1/P) + g
D1
= D0 x (1+g)
4.3995
P
50
g
0.05
Kcs (2)
0.13799
Kcs
0.128397
WACC
0.097519
Kcs(3)
Kcs(3)
payment next year
s on stock investment
=Rf + Bp
0.11

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