Cost of Capital
^
CF1
^
CF2
^
CFn
Asset
+…+
+
=
Value
(1 + r)1 (1 + r)2
(1 + r)n
r = firm’s required rate of return, which represents
the return investors receive for providing funds
to the firm
1
Chapter Essentials—The Questions





What types of capital do firms use to finance
investments?
What is the cost of capital?
How is the cost of capital used to make
financial decisions?
Why do funds generated through retained
earnings have a cost?
Who determines a firm’s cost of capital?
2
Cost of Capital
 Introduction
 Cost of Debt, rdT
 Cost of Equity, rps and (rs or re)
 Marginal Cost of Capital (MCC)
 MCC and Investment Opportunity (IOS)
Schedules
3
Basic Definitions
 Capital—refers to the long-term funds used by a firm to finance
its assets.
 Capital components—the types of capital used by a firm—longterm debt and equity
 Cost of capital—the cost associated with the various types of
capital used by the firm, which is based on the rate of return
required by the investors who provide the funds to the firm.
 Weighted average cost of capital, WACC—the average
percentage cost, based on the proportion of each type of capital,
of all the funds used by the firm to finance its assets.
 Capital structure—the mix of the types of capital used by the firm
to finance its assets.
 Optimal capital structure—the mix of capital that minimizes the
firm’s WACC, thus maximizes its value.
4
Weighted Average Cost of Capital
(WACC)—Logic
 A firm generally uses different types of funds to finance its
assets—that is, debt and equity.
 Costs associated with different types of capital (funds) usually
are not the same—e.g., debt generally is cheaper than equity.
 The overall cost, or average, should be weighted based on the
proportion of each type of funds used by the firm.
 Example: A firm is financed with debt and equity with the
following characteristics:
Cost
Proportion
Debt
rdebt = 8%
10%
Equity rstock =12%
90%
The average cost of each dollar of financing is:
Weighted average = 8%(0.1) + 12%(0.9) = 11.6%
5
Cost of Capital
 Investors who are the participants in the
financial markets determine the firm’s costs
of funds.
 The firm’s costs of funds change when



conditions in the financial markets change
investors’ general risk aversion changes
firm’s risk changes
6
Cost of Debt, rdT
 rd—the before-tax cost of debt is simply the
yield to maturity (YTM) of the debt
 YTM—bondholders’ required rate of return =
rd
 rdT—the after-tax cost of debt
rdT
Tax sav ings
 Bondholders' required 

  

 
rate of return

  associated with debt

rd

rd  T
 rd (1  T)
T = marginal tax rate
7
Cost of Debt, rdT—Example
A firm has debt with the following characteristics:
Maturity value, M
$1,000.00
Coupon rate, C
8.0% (paid semiannually)
Years to maturity
6 yrs
Market price
$1,099.50
Marginal tax rate
40.0%
Based on this information, we know that the following
relationship exists:
Vd  $1,099.50 
$40
(1  rd )1

$40
(1  rd )2

$1,040
(1  rd )12
Solving for rd gives us the YTM for this bond
8
Cost of Debt, rdT—Example
Solve using:
 Trial-and-error process (numerical
solution)
 approximation equation
 Financial calculator
 Spreadsheet
9
Cost of Debt, rdT—Example
rd approximation
Approximate yield

to maturity

INT 


M  Vd
N
2(Vd )  M
3
$40 




$1,000  $1,099.50
12
2($1,099.50)  $1,000
3


$31.71
 0.0297  2.97%
$1,066.33
rd/2 = 2.97% per six-month period (interest payment)
rd = 2.97% x 2 = 5.94% ≈ 6%
10
Cost of Debt, rdT—Example
Financial calculator
N
=
12
PV = -1,099.50
PMT =
40
FV =
1,000
I/Y =
?
rd
solution:
= 6 years x 2
= (0.08 x 1,000)/2
= 3.0% per six-month period
= 3.0% x 2 = 6.0% per year = YTM
11
Cost of Debt, rdT—Example
 Bondholders/investors demand a 6 percent rate of
return to invest in this firm’s long-term debt.
 rd = YTM = 6% is the rate of return paid to
bondholders.
 The firm pays $80 interest per year, which is a tax
deductible expense.
 rd is a before-tax amount that needs to be
adjusted so as to represent the actual after-tax
cost to the firm—that is, the cost of the bond to
the firm isn’t really 6 percent.
12
Cost of Debt, rT
Tax Deductibility of Interest
Example: The firm issues a new $1,000 face value bond with a 6
percent coupon rate, thus interest equal to $60 is paid each year.
If the firm’s taxable income before considering the interest
payment is $500 and its marginal tax rate is 40 percent, then the
tax liability with and without the interest expense is:
Tax without interest = $500(0.40)
= $200
Tax with interest = ($500 - $60)( 0.40) = $176
Savings = $24
= $60(0.4)
Net interest after tax savings = $60 - $24 = $36
After-tax cost of the new bond = $36/$1,000 = 3.6%
rdT = rd x (1 – T) = 6% x (1 – 0.4) = 3.6%
13
Cost of Debt, rdT
rdT = rd x (1 – T)
= YTM x (1 – T)
rd = before-tax cost of debt
T = marginal tax rate
14
Cost of Equity
The cost of equity is based on the rate of return
required by the firm’s stockholders.
 Cost of preferred stock—dividends received by preferred
stockholders represent an annuity
 Cost of retained earnings (internal equity)—return that
common stockholders require the firm to earn on the
funds that have been retained, thus reinvested in the
firm, rather than paid out as dividends
 Cost of new (external) equity—rate of return required by
common stockholders after considering the cost
associated with issuing new stock (flotation costs)
15
Cost of Equity—Preferred Stock
 Most preferred stocks pay constant dividends, thus the
dividend stream represents a perpetuity.
 Valuing preferred stock as a perpetuity gives:
P0 
Dps
rps
 Solving for the required rate of return, rps, gives:
rps 
Dps
P0
 Because flotation (issuing) costs have to be paid when
preferred stock is issued, the cost of preferred stock is:
Dps
Dps
NP0 = net proceeds from issue
rps 

NP0 P0 (1 - F)
F = flotation costs (percent)
16
Cost of Preferred Stock, rps—Example
 A firm has preferred stock with the following
characteristics:
Market price, P0
Dividend, Dps
Flotation cost, F
rps 
$75.00
$5.76
4.0%
$5.76
$5.76

= 0.08 = 8.0%
$75.00(1 - 0.04) $72.00
 No tax adjustment, because dividends are not a tax-
deductible expense.
17
Cost of Equity—Retained Earnings, rs
 The firm must earn a return on reinvested earnings
that is sufficient to satisfy existing common
stockholders’ investment demands.
 If the firm does not earn a sufficient return using
retained earnings, then the earnings should be paid
out as dividends so that stockholders can invest the
funds outside the firm to earn an appropriate rate.
18
Cost of Equity—Retained Earnings, rs
Assuming the stock market is at or near equilibrium,
we know that the following relationship exists:
Required rate
of return
rs  rRF  (rM  rRF )β s
rRF = risk-free rate
rM = market return
bs = stock’s beta coefficient

Expected rate
of return
Dˆ 1

 g  rˆs
P0
ˆ = next expected dividend
D
1
g = constant growth rate
19
Cost of Retained Earnings, rs
CAPM Approach
rs  rRF  (rM  rRF )β s
If rRF = 4%, rM = 9%, and bs = 1.4
rs = 4% + (9% - 4%)1.4 = 11.0%
 Assumes the firm’s stockholders are very well diversified;
if not, then beta probably is not the appropriate measure
of risk for determining the firm’s cost of retained earnings.
 rRF generally is associated with with Treasury securities;
there are many different rates for Treasuries that have
different terms to maturity.
20
Cost of Retained Earnings, rs
Bond-Yield-Plus-Risk-Premium Approach
 Studies have shown that the return on equity for a
particular firm is approximately 3 to 5 percentage points
higher than the return on its debt.
 As a general rule of thumb, firms often compute the
YTM, or rd, for their bonds and then add 3 to 5 percent.
 In the current example, rd = 6.0%. As a rough estimate,
then, we might say the cost of retained earnings is
rs ≈ rd + 4% = 6% + 4% = 10.0%
21
Cost of Retained Earnings, rs
Discounted Cash Flow (DCF) Approach
 If the firm is expected to grow at a constant rate, then
we have the following relationship:
ˆ
 Div idend  Capital
D
1
ˆ
  

rs  rs 
 g  
P0
 y ield   gain 
 Example: The firm, which is growing at a constant rate of
5 percent, just paid a dividend equal to $1.20; its stock
currently sells for $18.
rs 
$1.26 )
$1.20(1.05
0.05 = 0.07 + 0.05 = 0.12 = 12.0%
 0.05
$18.00
$18.00
22
Cost of Retained Earnings, rs
 The three approaches we used to determine the cost of
retained earnings give three different results.
 The three approaches are based on different
assumptions:
 CAPM approach assumes investors are extremely well
diversified
 DCF approach assumes the firms grows at a constant rate
 Bond-yield-plus-risk-premium approach assumes that the return
on equity is related to the return on the firm’s debt
 Ideally all three approaches should give the same
result; if not, however, we might average the results:
rs = (11% + 10% + 12%)/3 = 11%
23
Cost of Equity
Newly Issued Common Stock, re
 Rate of return required by common stockholders after
considering the costs associated with issuing new
stock, which are called flotation costs.
 Because the firm has to provide the same gross return
to new stockholders as existing stockholders, when the
flotation costs associated with a common stock issue
are considered, the cost of new common stock always
must be greater than the cost of existing stock—that
is, the cost of retained earnings.
 Modify the DCF approach for computing the cost of
retained earnings to include flotation costs
24
Cost of Newly Issued Common Stock
(External Equity), re
Dˆ 1
Dˆ 1
re 
g
g
P0 (1  F)
NP0
NP0 = net proceeds from the sale of the stock
If flotation costs equal 6 percent, then re in our example
is
$1.26
$1.26
re 
 0.05 
 0.05
$18(1  0.06)
$16.92
 0.1245  12.45%
25
Cost of Newly Issued Common Stock, re
Rationale
Assume a firm (different than in our example) has:
 total assets equal to $50,000
 is financed with common stock only (5,000 shares)
 pays all earnings as dividends, thus g = 0
 cost of retained earnings, rs = 10% = ROE
Current
 $50,000(0.10)  $5,000
income
$5,000
Current
 D0 
 $1.00
dividend
5,000
Current stock $1.00

 $10.00
price, P0
0.10
26
Cost of Newly Issued Common Stock, re
Rationale
 The firm sells new common stock:
 800 shares, so that 5,800 shares are outstanding after the




sale
market price, P0 = $10.00
net proceeds received by the firm, NP0 = $9.50
total amount received by the firm = $9.50 x 800 = $7,600
total assets after stock sale = $50,000 + $7,600 = $57,600
 Cost of new equity, re
$1.00
re 
 0  0.1053  10.53%
$9.50
27
Cost of Newly Issued Common Stock, re
Rationale
 Total assets after stock sale = $57,600
 If the firm earns rs = 10% on all investments
New
 $57,600(0.10)  $5,760
income
$5,760
New
D 
 $0.9931
dividend
5,800
New stock $0.9931

 $9.93
price, P0
0.10
28
Cost of Newly Issued Common Stock, re
Rationale
 Total assets after stock sale = $57,600
 If the firm earns re = 10.53% on new investments
Income from

  Income from 
  

Income  
 existing inv estments   new inv esmtents 
 $50,000(0. 10)  $7,600(0.1053)  $5,800
$5,800
New
D
 $1.00
dividend
5,800
 Stock price would remain at $10, because investors
require a 10 percent return; but, the firm must earn 10.53
on new investments to generate 10 percent to investor
(due to flotation costs)
29
Weighted Average Cost of Capital, WACC


To make decisions about capital budgeting projects,
we need to combine the various costs of capital—
debt, preferred stock, and common stock—into a
single required rate of return.
Weighted average cost of capital, or WACC—the
weighted average of the component costs of capital
using as the weights the proportion each type of
financing makes up of the total financing of the firm.
 %   After - tax   % preferred  Cost of
  % common  

Cost of
  
  
  
  
  

WA C C 
cost
of
debt
preferred
stock
equity
common
equity
stock
 
 
 

 
 debt  

w r
d dT

w
r
ps ps

w (r or r )
s s
e
30
Weighted Average Cost of Capital, WACC
Suppose our illustrative firm has the following capital structure:
Type of Financing
Debt, d
Preferred stock, ps
Common equity, s

Percent
of total
40.0
10.0
50.0
100.0
After-Tax
Cost, r
3.6%
8.0
11.0 or 12.45
If the firm can use retained earnings to finance new projects
WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(11.0%) = 7.74%

If the firm has to issue new common stock to finance new
projects
WACC = 0.4(3.6%) + 0.1(8.0%) + 0.5(12.45%) = 8.47%
31
Marginal Cost of Capital, MCC
 Weighted average cost of raising additional funds.
 Generally, MCC often is greater than the existing
WACC—that is, the cost of new funding increases—
because the
 firm’s risk increases, which causes investors to require a
higher rate of return
 costs of issuing new funds increase
 MCC schedule—a graph that shows the average cost
of funds at various levels of new financing
32
MCC Schedule
 If the firm expects to retain $200,000 this year
New WACC =
MCC (%)
WACC2
8.5
7.7
0
WACC1
Break
Point
Total of New
Funds Raised ($)
400,000
CE = 400,000 x 0.5 = 200,000
33
MCC Schedule—Break Points
 Break points occur when WACC increases, which is caused
by an increase in any of the component costs of capital
 debt—when rd1 < rd2 < … < rdn
 preferred stock—when rps1 < rps2 < … < rpsn
 common equity—retained earnings or new common stock
 There is a break point when retained earnings generated in the
current period is exhausted.
 Once the current addition to retained earnings is exhausted, then
the firm must issue new common stock to satisfy additional
common equity financing requirements.
 Costs of funds often increase as the firm uses significantly
higher amounts—risk increases.
34
MCC Schedule—Break Points
Break Total amount of a given type of capital at the lower cost

point
Proportion of this type of capital in the capital structure

Retained earnings
$200,000

 $400,000
Proportion of common equity
0.50
35
MCC Schedule Break Points—Example
 Assume the firm faces the following situation this year:
 Debt (40%):
Amount
$0
100,001
200,001
of Funds
Cost of Debt, rdT
- $100,000
6.0%
- 200,000
6.5
7.0
 Preferred Stock (10%): rps = 8.0%, no matter the amount needed
 Common Equity (50%):
 Retained earnings generated during the year = $200,000
 Cost of retained earnings (internal equity), rs = 11.0%
 Cost of new common stock (external equity), re = 12.4%, no matter
how much is needed
36
MCC Schedule Break Points—Example
 Debt (40%):
Amount of Funds
$ 0 - $100,000
100,001 - 200,000
200,001 -
Cost of Debt, rdT
6.0%
7.0
7.5
If the firm needs total funds equal to
$100,000
Break

 $250,000 $250,000, 40%, or $100,000 would be debt.
Point debt1
0.40
$200,000
Break
If the firm needs total funds equal to

 $500,000 $500,000, 40%, or $200,000 would be debt.
Point debt2
0.40
37
MCC Schedule Break Points—Example
 Preferred Stock (10%): rps = 8.0%, no matter the amount
needed
Constant cost—no break due to preferred stock
 Common Equity (50%):

Retained earnings generated during the year = $200,000

Cost of retained earnings (internal equity), rs = 11.0%

Cost of new common stock (external equity), re = 12.4%, no
matter how much is needed
Break $200,000

 $400,000
Point RE
0.50
If the firm needs total funds equal to
$400,000, 50%, or $200,000 would be RE.
38
MCC Schedule—Example
Funds = $0 - $250,000
Debt
Preferred Stock
Common Equity
Amount at
$250,000
$100,000
25,000
125,000
250,000
Weight
0.4
0.1
0.5
1.0
Funds = $250,001 - $400,000
Debt
Preferred Stock
Common Equity
Amount at
$400,000
$160,000
40,000
200,000
400,000
Weight
0.4
0.1
0.5
1.0
After-Tax
After-Tax
x Cost, rk
6.0
8.0
11.0
After-Tax
x Cost, r
7.0
8.0
11.0
=
WACC
2.4
0.8
5.5
8.7% = WACC1
=
WACC
2.8
0.8
5.5
9.1% = WACC2
39
MCC Schedule—Example
Funds = $400,001 - $500,000
Debt
Preferred Stock
Common Equity
Amount at
$500,000
$200,000
50,000
250,000
500,000
Weight
0.4
0.1
0.5
1.0
Funds = above $500,000
Debt
Preferred Stock
Common Equity
Amount at
$600,000
$240,000
60,000
300,000
600,000
Weight
0.4
0.1
0.5
1.0
After-Tax
After-Tax
x Cost, rk
7.0
8.0
12.4
After-Tax
x Cost, r
7.5
8.0
12.4
=
WACC
2.8
0.8
6.2
9.8% = WACC3
=
WACC
3.0
0.8
6.2
10.0% = WACC4
40
MCC Schedule
MCC (%)
11.0
10.0
WACC3 = 9.8
WACC4 = 10.0
WACC2 = 9.1
9.0
WACC1 = 8.7
8.0
0
100
200
300
BP1 = 250
400
BP2
500
Total Funds
Raised ($000)
BP3
41
MCC Schedule and Investment
Opportunity (IOS) Schedule
The firm’s capital budgeting analysis results are:
Project
A
B
C
D
Cost
$150,000
200,000
200,000
100,000
IRR
11.0%
10.5
10.1
9.5
42
IOS Schedule
IRR (%)
IRRA = 11.0
11.0
IRRB = 10.5
IRRC = 10.1
10.0
IRRD = 9.5
9.0
8.0
0
100
200
300
400
500
600
700
Total Funds Raised ($000)
43
MCC Schedule
MCC (%)
11.0
10.0
WACC3 = 9.8
WACC4 = 10.0
WACC2 = 9.1
9.0
WACC1 = 8.7
8.0
0
100
200
300
400
500
Total Funds
Raised ($000)
44
MCC & IOS Schedules
IRRA = 11.0
11.0
IRRB = 10.5
IRRC = 10.1
10.0
WACC3 = 9.8
WACC2 = 9.1
9.0
WACC1 = 8.7
100
200
IRRD = 9.5
Optimal Capital
Budget = 550
8.0
0
WACC4 = 10.0
300
400
500
600
700
Total Funds Raised ($000)
45
Chapter Essentials—The Answers
 What types of capital do firms use to finance
investments?
 Either debt (bond issues) or equity (preferred
stock and common equity)
 What is the cost of capital?
 The average price a firm pays for the funds it
uses to purchase assets
 How is the cost of capital used to make
financial decisions?
 A firm should invest in projects that are expected
to provide returns greater than its WACC
46
Chapter Essentials—The Answers
 Why do funds generated through retained
earnings have a cost?
 Firms may retain earnings only as long as it can
reinvest the earnings at a higher rate than
stockholders can earn elsewhere
 Who determines a firm’s cost of capital?
 Investors
47