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Lecture 11

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BU393

Bruce Everitt

Winter

Description

Chapter
11
The
Cost
of
Capital
LEARNING
OBJECTIVES
(Slide
11-‐2)
1. Understand the different kinds of financing available to a company: debt financing,
equity financing, and hybrid equity financing.
2. Understand the debt and equity components of the weighted average cost of capital
(WACC) and explain the tax implications on debt financing and the adjustment to the
WACC.
3. Calculate the weights of the components using book values or market values.
4. Explain how the capital budgeting models use WACC.
5. Determine a project's beta and its implications in capital budgeting problems.
6. Select optimal project combinations from a company’s portfolio of acceptable
projects.
IN
A
NUTSHELL…
This chapter clarifies the mystery of the hurdle rate or discount rate that was heretofore
assumed as a given. Companies can finance their capital requirements by issuing
different types of debt, preferred stock and common stock. After describing the salient
features of each type of capital component, the author explains the methodology that can
be used to determine a firm’s weighted average cost of capital (WACC). In particular, the
tax implications, weighting procedures, and methods to calculate component costs are
explained with examples. The use of the WACC as the hurdle rate when doing capital
budgeting problems, and the process by which a firm can use the WACC to form optimal
combinations of projects, are covered last.
LECTURE
OUTLINE
11.1
The
Cost
of
Capital:
A
Starting
Poin(Slides
11-‐3
to
11-‐6)
There are primarily 3 broad sources of financing that companies can avail of for raising
capital: debt, common stock (equity), and preferred stock (hybrid equity).
Figure 11.1 (shown below) displays the three sources and their main suppliers.
373
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Each capital component has its own risk and return profile and therefore its own rate of
return required by investors to provide funds to the firm.
Firms estimate their weighted average cost of capital (WACC) by multiplying each
component weight by the component cost and summing up the products.
The WACC is essentially the minimum acceptable rate of return that the firm should earn
on its investments of average risk, in order to be profitable.
In other words, the WACC should be used as the discount rate when computing NPV, or
as the criterion that must be exceeded when using IRR for making capital budgeting
decisions.
Example
1:
Measuring
weighted
average
cost
of
a
mortgage
Jim wants to refinance his home by taking out a single mortgage and paying off all the
other sub-prime and prime mortgages that he took on while the going was good. Listed
below are the balances and rates owed on each of his outstanding home-equity loans and
mortgages:
Lender Balance Rate
First Cut-Throat Bank $ 150,000 7.5%
Second Considerate Bank $ 35,000 8.5%
Third Pawn Mortgage Co. $ 15,000 9.5%
Below what rate would it make sense for Jim to consolidate all these loans and refinance
the whole amount?
Jim’s weighted average cost of borrowing = Proportion of each loan * Rate
è (150,000/200,000)*.075+(35,000/200,000)*.085+(15,000/200,000)*.095
è (.75*.075) + (.175*.085) (+.075*.095) = .07825 or 7.825%
Jim’s average cost of financing his home is 7.825%. Any rate below 7.825% would be
beneficial.
11.2
Components
of
the
Weighted
Average
Cost
of
Capital
(Slides
11-‐7
to
11-‐22)
In order to determine a firm’s WACC we need to know how to calculate the relative
weights and costs of the debt, preferred stock, and common stock of a firm.
11.2
(A)
Debt
ComponThe cost of debt (Rd) is the rate that firms have to pay when
they borrow money from banks, finance companies, and other lenders.
It is essentially measured by calculating the yield to maturity (YTM) on a firm’s
outstanding bonds, as covered in Chapter 6.
Although best solved for by using a financial calculator or spreadsheet, the YTM can also
be figured out as follows:
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The YTM on outstanding bonds, based on the bonds’ current selling price, tells us what
investors require for lending the firm their money in current market conditions.
However, if a firm were to go ahead and issue new debt, which is what typically happens
when firms expand or grow, it would also have to pay some transactions costs to the
investment bankers, and thereby receive lower net proceeds from each bond. The lower
the amount the firm gets to keep from the sale, the higher its costs are going to be.
Accordingly, to correctly estimate the cost of debt for inclusion in the WACC
calculation, we must adjust the market price by the amount of commissions that would
have to be paid when issuing new debt, and then calculate the YTM.
Example
2:
Calculating
the
cost
of
debt
Kellogg’s wants to raise an additional $3,000,000 of debt as part of the capital that would
be needed to expand their operations into the Morning Foods sector. They were informed
by their investment banking consultant that they would have to pay a commission of
3.5% of the selling price on new issues. Their CFO is in the process of estimating the
corporation’s cost of debt for inclusion into the WACC equation. The company currently
has an 8%, AA-rated, non-callable bond issue outstanding, which pays interest semi-
annually, will mature in 17 years, has a $1000 face value, and is currently trading at
$1075. Calculate the appropriate cost of debt for the firm.
First determine the net proceeds on each bond = Selling price –Commission
=$1075-(.035*1075) = $1037.38
Using a financial calculator we enter:
P/Y = C/Y = 2
Input 34 ? -1037.38 40 1000
Key N I/Y PV PMT FV
Output 7.60%
The appropriate cost of debt for Kellogg’s is 7.6%.
Note: It is important to stress the point that it is the net proceeds and not the market price
that determines the appropriate cost of new debt.
11.2
(B)
Preferred
Stock
CoSince preferred stock holders receive a constant
dividend with no maturity point, its cost (R )can be estimated by dividing the annual
p
dividend by the net proceeds (after floatation cost) per share of preferred stock
R p D /pet price
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Example
3:
Cost
of
Preferred
Stock
Kellogg’s will also be issuing new preferred stock worth $1 million. They will pay a
dividend of $4 per share which has a market price of $40. The floatation cost on preferred
will amount to $2 per share. What is their cost of preferred stock?
Net price on preferred stock = $38; Dividend on preferred = $4
Cost of preferred = Rp = $4/$38 = 10.53%
11.2
(C)
Equity
ComponentThe cost of equity (R )is essentially the rate of return that
e
investors are demanding or expecting to make on money invested in a company’s
common stock.
The cost of equity can be estimated by using either the SML approach (covered in
Chapter 8) or the Dividend Growth Model (covered in Chapter 7).
The Security Market Line Approach: calculates the cost of equity as a function of the
risk-free rate (r ) the market risk-premium [E(r )-r ],and beta (β). That is,
f m f i
Example
4:
Calculating
Cost
of
Equity
with
the
SML
equation
Remember Kellogg’s from the earlier 2 examples? Well, to reach their desired capital
structure their CEO has decided to utilize all of their expected retained earnings in the
coming quarter. Kellogg’s beta is estimated at 0.65 by Value Line. The risk-free rate is
currently 4%, and the expected return on the market is 15%. How much should the CEO
put down as one estimate of the company’s cost of equity?
R e r +f[E(r )-rm]β f i
R e4%+[15%-4%]0.65
R = 4%+7.15% = 11.15%
e
The Dividend Growth Approach to R The Gordone:odel, introduced in Chapter 7, is
used to calculate the price of a constant growth stock.
However, with some algebraic manipulation it can be transformed into Equation 11.6,
which calculates the cost of equity, as shown below:
where Div = 0ast paid dividend per share;
P o Current market price per share; and
g = constant growth rate of dividend.
For newly issued common stock, the price must be adjusted for floatation cost
(commission paid to investment banker) as shown in Equation 11.7 below:
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Where F is the floatation cost in percent.
Example
5:
Applying
the
Dividend
Growth
Model
to
calce
R
Kellogg’s common stock is trading at $45.57 and its dividends are expected to grow at a
constant rate of 6%. The company paid a dividend last year of $2.27. If the company
issues stock they will have to pay a floatation cost per share equal to 5% of selling price.
Calculate Kellogg’s cost of equity with and without floatation costs.
Cost of equity without floatation cost:
R e (Div *(0+g)/P ) + o è ($2.27*(1.06)/$45.57)+.06è11.28%
Cost of equity with floatation cost:
R e [$2.27*(1.06)/(45.57*(1-.05)]+.06 è11.56%
Depending on the availability of data, either of the two models, or both, can be used to
estimate R .e
With two values, the average can be used as the cost of equity. For example, in Kellogg’s
case we have (11.15%+11.28%)/2è11.22% (without floatation costs)
or (11.15% + 11.56%)/2 è 11.36%
11.2
(D)
Retained
Earningalthough, housed within a firm, does have a cost, i.e. the
opportunity cost for the shareholders not being able to invest the money themselves.
The cost of retained earnings can be calculated by using either of the above two
approaches, without including floatation cost.
11.2
(E)
The
Debt
Component
and
Since interest expenses are tax deductible, the
cost of debt, must be adjusted for taxes, as shown below, prior to including it in the
WACC calculation:
After-tax cost of debt = R *(1-T )
d c
So if the YTM (with floatation cost) = 7.6%, and the company’s marginal tax rate is 30%,
the after-tax cost of debtè7.6%*(1-0.3)è5.32%
11.3
Weighting
the
Components:
Book
Value
or
Market
Value?
(Slides
11-‐23
to
11-‐29)
As explained earlier, in order to calculate the WACC of a firm, each component’s cost is
multiplied by its proportion in the capital mix and then summed up.
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There are two ways to determine the proportion or weights of each capital component,
using book value, or using market values.
11.3
(A)
Book
weights can be determined by taking the balance sheet values for
debt, preferred stock, and common stock, adding them up, and dividing each by the total.
11.3
(B)
Adjusted
Weighted
Average
Cost Equation 11.9 can be used to
combine all the weights and component costs into a single average cost which can be
used as the firm’s discount or hurdle rate:
S EDP
WACC adj× + ×e+1× ×− ps Rd ( T c ) 11.9
V V V
11.3
(C)
Market
weights are determined by taking the current market prices of the
firm’s outstanding securities and multiplying them by the number outstanding, to get the
total value; and then dividing each by the total market value to get the proportion or
weight of each
If possible, market value weights should be used since they are a better representation of
a company’s current capital structure, which would be relevant for raising new capital.
Example
6:
Calculating
capital
component
weights
Kellogg’s CFO is in the process of determining the firm’s WACC and needs to figure out
the weights of the various types of capital sources. Accordingly, he starts by collecting
information from the balance sheet and the capital markets, and makes up the Table
shown below:
Current
Balance Sheet Number Market Market
Component Value outstanding Price Value
Debt $ 150,000,000 150,000 $1,075 $161,250,000
Preferred Stock $ 45,000,000 1,500,000 $40 $ 60,000,000
Common Stock $ 180,000,000 4,500,000 $45.57 $205,065,000
What should he do next?
1) Calculate the total book value and total market value of the capital
2) Divide each component’s book value and market value by their respective totals.
èTotal Book Value = $375,000,000; Total Market Value = $426,315,000
èBook Value Weights: èMarket Value Weights:
Debt = 150m/375m=40%; Debt = 161.25m/426.32m=38%
P/ S=$45m/$375m=12%; P/S = 60m/426.32=14%
C/S = 180m/375m=48%; C/S= 205.07m/$426.32m=48%
(Rounded to nearest whole number)
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He should use the market value weights as they represent a more current picture of the
firm’s capital structure.
Example
7:
Calculating
Adjusted
WACC
Using the market value weights and the component costs determined earlier, calculate
Kellogg’s adjusted WACC.
Capital Component Weight After-tax Cost%
Debt .38 7.6%*(1-.3) =5.32% èR (1-dc)
Preferred Stock .14 10.53% èR p
Common Stock .48 11.36% èR
e
*using average of SML and DGM (with floatation cost)
WACC = .38*5.32% + .14*10.53%+.48*11.36%
=2.02%+1.47%+5.45%=8.94%
11.4
Using
the
Weighted
Average
Cost
of
Capital
in
a
Budgeting
Decision (Slides
11-‐30
to
11-‐35)
Once a firm’s WACC has been determined, it can be used either as the discount rate to
calculate the NPV of the project’s expected cash flow or as the hurdle rate which must be
exceeded by the project’s IRR.
Table 11.1 presents the incremental cash flow of a $5 million project being considered by
a firm whose WACC is 12%.
Using a discount rate of 12%, the project’s NPV would be determined as follows:
Since the NPV > 0 this would be an acceptable project.
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Alternatively, the IRR could be determined using a financial calculatorè14.85%
Again, since IRR>12%, this would be an acceptable project.
11.4
(A)
Individual
Weighted
Average
Cost
of
Capital
for
Individual
Projects
Using the WACC for evaluating projects assumes that the project is of average risk. If
projects have varying risk levels, using the same discount rate could lead to incorrect
decisions.
Figure 11.3 illustrates such a situation with 4 projects, whose IRRs range from 8% to
11%, but the risk levels also go from lowàmoderateàhighàvery high.
With a WACC of 9.5%, only Projects 3 and 4, with IRRs of 10% and 11% respectively
would be accepted.
However, Projects 1 and 2 could have been profitable lower risk projects that are being
rejected in favor of higher risk projects, merely because the risk levels have not been
adequately adjusted for.
To adjust for risk, we would need to get individual project discount rates based on each
project’s beta.
Using a risk-free rate of 3%; a market risk premium of 9%; a before-tax cost of 10%, a
tax rate of 30%; equally-weighted debt and equity levels, and varying project betas we
can compute each project’s hurdle rate as follows:
Table 11.2 summarizes how the decisions made with and without adjusting for varying
project risk could lead to incorrect decisions.
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Note that under the risk-adjusted approach, Project 1 (IRR=8%>7.7%)and Project 2
(IRR=9%>8.6%) should be accepted, while Project 3 (IRR=10%< 10.4%) and Project 4
(IRR=11%<13.1%) should be rejected as shown in Figure 11.4.
11.5
Selecting
Appropriate
Betas
for
Projects
(Slide
11-‐36)
We have determined that it is important to adjust the discount rate used when evaluating
projects of varying risk, based on their individual betas.
However, since project betas are not easily available, it is more of an art than a science.
There are two approaches generally used:
1. Pure play betas: i.e. matching the project with a company that has a similar single
focus, and using that company’s beta.
2. Subjective modification of the company’s average beta: i.e. adjusting the beta up or
down to reflect different levels of risk.
11.6
Constraints
on
Borrowing
and
Selecting
Projects
for
the
Portfolio
(Slides
11-‐37
to
11-‐39)
Firms often have capital constraints that prevent them from funding all potentially
profitable projects that come their way.
Capital rationing is a process whereby the managers can select projects based on their
costs and expected profitability, while fulfilling capital constraints.
The process requires the rank ordering of projects based on either their NPV or IRRs
along with their costs and then choosing the combination which has the highest combined
return or NPV while using up as much of the limited capital budget.
Example
8:
Selecting
Projects
with
Capital
Constraints
The XYZ Company’s managers are reviewing various projects that are being presented
by unit managers for possible funding. They have an upper limit of $5,750,000 for this
forthcoming year. The cost and NPV of each project has been estimated and is presented
below. Which combination of projects would be best for them to invest in?
Project Cost NPV
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1 2,000,000 500,000
2 2,250,000 400,000
3 1,750,000 300,000
4 750,000 100,000
5 500,000 50,000
1) Form combinations of projects by adding the costs to sum up as close to the
$5,750,000 limit as possible. Sum up the NPVs as well.
Combinations Total Cost NPV
1,2,4,5 2m+2.25m+.75m + .5m=$5.5m 1.5m
1,3,4,5 2m+1.75m+.75m + .5m=$5m 0.95m
2,3,4,5 2.25m+1.75m + .75m + .5m=$5.25m 0.85m
All other combinations would either exceed the $5.75m limit or under utilize the
funds.
2) Select the combination which has the highest NPV i.e. Combination 1 including
projects 1,2,4, and 5 with a total NPV of $1.5m.
Questions
1. From what sources can a company raise capital? Do these different sources of
capital all charge the same rate? Why or why not?
A company can borrow from owners, preferred stockholders, banks, non-bank
lenders, suppliers, and the company itself. They all have different lending rates. These
lenders all charge different rates because they all have different risk exposures and
different supply and demand schedules for their lending funds.
2. Why is the yield to maturity on a bond the appropriate cost of debt financing?
The yield-to-maturity is the cost of the bond and implies the return the investor is
demanding based on his or her willingness to buy the bond at the current price. It is
also the price of the loan from the borrower’s perspective.
3. What are the two different ways to estimate the cost of equity for a firm?
The two ways to estimate the cost of equity are the dividend model and the security
market line. If you have sufficient information you can use the average of the two
models or pick the one that seems most appropriate. Usually the most appropriate
model is the security market line because it can handle the potential other investment
opportunities of the lender. Lender’s pick across a wide variety of stocks and the
security market line determines the appropriate rate for the level of risk of the
investment.
4. Should retained earnings reinvested in the company have a zero cost of capital
because it generates the funds internally and the company does not need to pay
itself for borrowing money? If not, why?
These funds should not have a zero cost. The funds have an opportunity cost (the
shareholders could be paid this money via dividends instead of reinvesting in the
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company). Therefore there is a cost associated with using these funds and thus a zero
cost of capital is inappropriate.
5. When calculating the cost of capital, why is it that the company only adjusts the
cost of debt for taxes?
Interest expense for debt loans is a deductible expense of the firm and is part of the
income statement used for determining the taxable income of a company. Payment of
dividends to owners is not a business expense but considered a return of permanent
capital to investors. Thus it does not appear on the income statement. So only debt has
a tax impact and thus only debt is adjusted for taxes in the cost of capital.
6. What are the two ways to estimate the percentage (weights) of funds that a
company has received from lenders and owners? Which is more appropriate?
The two methods are book value and market value for estimating the components
(weights) of the cost of capital. The preferred choice is market value.
7. Why not use a single WACC for all company projects?
If all projects are assigned the same discount rate we can make some poor decisions
on which projects to accept and which to reject. We will tend to pick high risk
projects and reject low risk projects.
8. What are the types of errors a manager can make if he or she does not assign
individual WACCs to each potential project?
By assigning the same discount rate to every project, a manager will tend to reject low
risk projects, despite their positive NPV if assigned the appropriate discount rate for
the level of risk, and accept high risk projects despite their negative NPV if assigned
the appropriate discount rate for the level of risk.
9. Why is selecting a beta for a project more of an art than a science?
It is more of an art than a science because we are trying to forecast future cash flow
and its relative riskiness. The future is full of uncertainty and therefore it is more
difficult of a model to accurately handle or forecast the uncertainty surrounding future
events.
10. If the capital budget is constrained by the amount of funds available for
potential projects, what mistake might a manager make if he or she just lists the
potential projects by highest to lowest NPV and picks the projects moving down
the list until the funds are exhausted?
By simply ranking projects by their NPVs and then going from top to bottom we are
not guaranteed the highest total NPV with constrained funding. Top to bottom
selecting may leave unused investment dollars that could be used by dropping a large
cost NPV project for two smaller NPV projects that together have a larger NPV than
the large cost project.
Prepping
for
Exams
1. d
2. a
3. d
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4. c
5. c
6. c
7. d
8. c
9. d
10. d
Problems
1. WACC. Eric has another get-rich-quick idea but needs funding to support it. He
chooses an all-debt funding scenario.Eric will borrow $2,000 from Wendy, who will
charge Eric 6% on the loan. He will also borrow $1,500 from Bebe, who will charge
8% on the loanand $800 from Shelly, who will charge 14% on the loan. What is the
weighted average cost of capital for Eric?
ANSWER
Total funds borrowed = $2,000 + $1,500 + $800 = $4,300
WACC = ($2,000 / $4,300) × 0.06 + ($1,500 / $4,300) × 0.08 + ($800 /
$4,300) × 0.14
WACC = 0.4651 × 0.06 + 0.3488 × 0.08 + 0.1860 × 0.14
WACC = 0.0279 + 0.0279 + 0.0260 = 0.0819 or 8.19%
2. WACC. Grey’s Pharmaceuticals has a new project that will require funding of $4
million. The company has decided to pursue an all-debt scenario. Grey’s has made an
agreement with four lenders for the needed financing. These lenders will advance the
following amounts and interest rates:
What is the weighted average cost of capital for the $4,000,000?
ANSWER
WACC = ($1.5 / $4) × 0.11 + ($1.2 / $4) × 0.09 + ($1 / $4) × 0.07 + ($0.3 / $4) × 0.08
WACC = 0.375 × 0.11 + 0.3 × 0.09 + 0.25 × 0.07 + 0.075 × 0.08
WACC = 0.04125 + 0.0270 + 0.0175 + 0.0060 = 0.09175 = 9.175%
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3. Cost of debt. Kenny Enterprises has just issued a bond with a par value of $1000,
twenty years to maturity, and an 8% coupon rate with semiannual payments. What is
the cost of debt for Kenny Enterprises if the bond sells at the following prices? What
do you notice about the price and the cost of debt?
a. $920
b. $1,000
c. $1,080
d. $1,173
ANSWER
a. If the bond sells for $920 we have:
$920 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -920 40 1000
Variables N I/Y PV PMT FV
OUTPUT 8.86%
b. If the bond sells for $1000 we have:
$1000 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -1000 40 1000
Variables N I/Y PV PMT FV
OUTPUT 8.00%
c. If the bond sells for $1080 we have:
40 40
$1080 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -1080 40 1000
Variables N I/Y PV PMT FV
OUTPUT 7.24%
d. If the bond sells for $1080 we have:
$1173 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -1173 40 1000
Variables N I/Y PV PMT FV
OUTPUT 6.45%
We note that as the price of the bond increases (proceeds from the sale) the lower is
the cost of debt. This inverse relationship exists between price and the cost of debt
since the future cash flows of the bond are fixed at issue; and thus buyers willing to
pay more for the fixed stream of cash flows are lending money at a lower rate to the
company.
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4. Cost of debt. Dunder-Mifflin, Inc. (DMI) is selling 600,000 bonds to raise money for
the publication of new magazines in the coming year. The bonds will pay a coupon
rate of 12% on semiannual payments. The bond's par value is $100, and the bond will
mature in thirty years. What is the cost of debt to DMI if the bonds raise
a. $45,000,000?
b. $54,000,000?
c. $66,000,000?
d. $75,000,000?
ANSWER
a. The price of a individual bond is $45,000,000 / 600,000 = $75 so,
60 60
$75 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -75 6 100
Variables N I/Y PV PMT FV
OUTPUT 16.05%
b. The price of a individual bond is $54,000,000 / 600,000 = $90 so,
60 60
$90 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -90 6 100
Variables N I/Y PV PMT FV
OUTPUT 13.36%
c. The price of a individual bond is $66,000,000 / 600,000 = $110 so,
$110 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -110 6 100
Variables N I/Y PV PMT FV
OUTPUT 10.87%
d. The price of a individual bond is $75,000,000 / 600,000 = $125 so,
$125 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -125 6 100
Variables N I/Y PV PMT FV
OUTPUT 9.47%
5. Cost of debt with fees. Kenny Enterprises will issue the same debt in Problem 3 but
now will use an investment banker that charges $25 per bond for their services. What
is the new cost of debt for Kenny Enterprises at a market price of
a. $920?
b. $1,000?
c. $1,080?
©2013
Pearson
Education,
Inc.
Publishing
as
Prentice
Hall
Chapter
11
n
The
Cost
of
Capital
387
d. $1,173?
ANSWER
a. If the bond sells for $920 and Kenny pays $25 per bond the net proceeds are $895
$895 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -895 40 1000
Variables N I/Y PV PMT FV
OUTPUT 9.15%
b. If the bond sells for $1000 and Kenny pays $25 per bond the net proceeds are $975
$975 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -975 40 1000
Variables N I/Y PV PMT FV
OUTPUT 8.26%
c. If the bond sells for $1080 and Kenny pays $25 per bond the net proceeds are $1055
40 40
$1055 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -1055 40 1000
Variables N I/Y PV PMT FV
OUTPUT 7.47%
d. If the bond sells for $1173 and Kenny pays $25 per bond the net proceeds are $1148
40 40
$1148 = $1,000 / (1+ (YTM/2)) + $40 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 40 ? -1148 40 1000
Variables N I/Y PV PMT FV
OUTPUT 6.65%
6. Cost of debt with fees. In Problem 4, Dunder-Mifflin, Inc. hires an investment banker
for the sale of the 600,000 bonds. The investment banker charges a fee of 2% on each
bond sold. What is the cost of debt to DMI if the proceeds below are before the
banker's fees are deducted?
a. $45,000,000?
b. $54,000,000?
c. $66,000,000 ?
d. $75,000,000?
ANSWER
a. The price of an individual bond is $45,000,000 / 600,000 = $75 and t2% soe is
the net proceeds are $75 × ( 1 - .02) = $73.50 and the cost of debt is
$73.50 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
©2013
Pearson
Education,
Inc.
Publishing
as
Prentice
Hall
388
Brooks
n
Financial
Management:
Core
Concepts ,
2e
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -73.50 6 100
Variables N I/Y PV PMT FV
OUTPUT 16.38%
b. The price of a individual bond is $54,000,000 / 600,000 = $90 and the fee is 2% so the
net proceeds are $90 × ( 1 - .02) = $88.20 and the cost of debt is
$88.20 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -88.20 6 100
Variables N I/Y PV PMT FV
OUTPUT 13.64%
c. The price of a individual bond is $66,000,000 / 600,000 = $110 and the fee is 2% so
the net proceeds are $110 × ( 1 - .02) = $107.80 and the cost of debt is
60 60
$107.80 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -107.80 6 100
Variables N I/Y PV PMT FV
OUTPUT 11.10%
d. The price of a individual bond is $75,000,000 / 600,000 = $125 and the fee is 2% so
the net proceeds are $125 × ( 1 - .02) = $122.50 and the cost of debt is
60 60
$122.50 = $100 / (1+ (YTM/2)) + $6 × (1 – 1/(1 + (YTM/2)) )/(YTM/2)
And solving via a calculator we have: set P/Y = 2; C/Y =2
INPUTS 60 ? -122.50 6 100
Variables N I/Y PV PMT FV
OUTPUT 9.69%
7. Cost of preferred stock. Kyle is raising funds for his company by selling preferred
stock. The preferred stock has a par value of $100 and a dividend rate of 6%. The
stock is selling for $80 in the market. What is the cost of preferred stock for Kyle?
ANSWER
The dividend is $100 × 0.06 = $6.00
And with a price of $80 the cost of preferred stock is $6/$80 = 0.075 or 7.5%
8. Cost of preferred stock. Kyle hires Wilson Investment Bankers to sell the preferred
stock from Problem 7. Wilson charges a fee of 3% on the sale of preferred stock.
What is the cost of preferred stock for Kyle using the investment banker?
©2013
Pearson
Education,
Inc.
Publishing
as
Prentice
Hall
Chapter
11
n
The
Cost
of
Capital
389
ANSWER
The dividend remains the same but the proceeds are $80 × (1 – 0.03) or $77.60 so the
cost of preferred stock is now, $6/$77.60 = 0.0773 or 7.73%
9. Cost of equity: SML. Stan is expanding his business and will sell common stock for
the needed funds. If the current risk-free rate is 4% and the expected market return is
12%, what is the cost of equity for Stan if the beta of the stock is
a. 0.75?
b. 0.90?
c. 1.05?
d. 1.20?
ANSWER
a. Using the security market line we have,
E(r)i= r + f (E(i ) – m ) f
Cost of Equity = E(r) = 0i04 + 0.75 (0.12 – 0.04)
Cost of Equity = 0.04 + 0.75 (0.08) = 0.04 + 0.06 = 0.10 or 10%
b. Using the security market line we have,
E(r)i= r + f (E(i ) – m ) f
Cost of Equity = E(r) = 0i04 + 0.90 (0.12 – 0.04)
Cost of Equity = 0.04 + 0.90 (0.08) = 0.04 + 0.072 = 0.112 or 11.2%
c. Using the security market line we have,
E(r)i= r + f (E(i ) – m ) f
Cost of Equity = E(r) = 0.04 + 1.05 (0.12 – 0.04)
i
Cost of Equity = 0.04 + 1.05 (0.08) = 0.04 + 0.084 = 0.124 or 12.4%
d. Using the security market line we have,
E(r)i= r + f (E(i ) – m ) f
Cost of Equity = E(r) = 0i04 + 1.20 (0.12 – 0.04)
Cost of Equity = 0.04 + 1.20 (0.08) = 0.04 + 0.096 = 0.136 or 13.6%
10. Cost of equity: SML. Stan had to delay the sale of the common stock as outlined in
Problem 9 for six months. When he finally did sell the stock, the risk-free rate had
fallen to 3%, but the expected return on the ma

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