Instructor:
Rogério
Mazali
Lecture 14: 12/05/2011
1
FINE 3010

04
Instructor:
Rogério
Mazali
Fundamentals of
Corporate
Finance
Sixth Edition
Richard A.
Brealey
Stewart C. Myers
Alan J. Marcus
McGraw Hill/Irwin
2
Chapter 13:
The Weighted

Average
Cost of Capital and
Company Valuation
Agenda
Cost of Capital of an All

Equity Firms
Cost of Capital of Leveraged Firms: the Weighted

Average
Cost of Capital (WACC)
Use Market Weights, not Book Weights
Taxes and the WACC
Three (or more) Sources of Funding
Measuring Capital Structure
Expected Rates of Return on Bonds
Expected Return on Common Stock
Expected Return on Preferred Stock
Valuing Entire Businesses
3
Cost of Capital of All

Equity Firms
According to the CAPM, the expected return of any
security
i
is given by:
E(
R
i
) =
r
f
+
β
i
* [E(R
M
)
–
r
f
]
where
β
i
=
Cov
(
R
i
, R
M
) /
Var
(R
M
).
That is, if the firm is 100% equity financed, we can
discount the cash flows of security
i
at this rate!
4
Cost of Capital of All

Equity Firms
An all

equity firm is considering an investment opportunity
with these features:
Initial Investment:
350,000
Cash Flows (5 years):
100,000
Risk

free Rate:
3%
E(R
M
):
9%
Beta of our firm is
1.2
AND the project
has the
same risk as the firm
5
Cost of Capital of All

Equity Firms
Step 1:
Calculate the Cost of Equity Capital
E(R) =
r
f
+
β
[E(R
M
)
–
r
f
]= 0.03 + 1.2 * [0.09
–
0.03] =
0.102
Step 2:
Calculate the NPV of the project
6
Cost of Capital of All

Equity Firms
7
0
1
2
3
4
5
Cash Flows
350,000
100,000
100,000
100,000
100,000
100,000
PV(0)
90,744
82,345
74,723
67,807
61,531
Sum PV(0)
377,150
NPV
27,150
100,000 / 1.102
Cost of Capital of Leveraged Firms: the
Weighted

Average Cost of Capital (WACC)
Consider now a firm that has been financed by both
debt and equity:
Bondholders expect return
r
debt
on their investment
Shareholders expect return
r
equity
on their investment
Q: How much return should a project give in order to
be considered viable?
A: Enough money to pay both shareholders and
bondholders
Q: And how much is that, exactly?
8
Cost of Capital of Leveraged Firms: the
Weighted

Average Cost of Capital (WACC)
Consider the following example: Geothermal Corp.
Company debt pays return
r
debt
= 8%.
Company stock pays return
r
equity
= 14%.
Therefore, shareholders require extra
r
equity
×
E
= 0.14
×
$453
mi = $63.42 mi.
Also, bondholders require extra
r
debt
×
D
= 0.08
×
$194 mi =
$15.52 mi.
Newly created assets would be then = $63.42 mi + $15.52 mi
= $78.94 mi, and ROA = $78.94/$647 = .122 = 12.2%.
9
Cost of Capital of Leveraged Firms: the
Weighted

Average Cost of Capital (WACC)
This procedure is known as the
Weighted Average
Cost of Capital (WACC).
10
V
)
r
x
(E
+
)
r
x
(D
assets
equity
debt
r
equity
V
E
debt
V
D
assets
r
x
r
x
r
s
investment
of
value
income
total
assets
=
r
Taxes and the WACC
So far we have not considered the effect of taxes on the
cost of capital.
Why are taxes important?
Note that interest payments are tax

deductible:
For each $1 paid in interest, taxable income is reduced by
$1, and the firm’s tax bill is reduced by $0.35 (if the firm
is in the 35% tax rate bracket).
11
)
T
(
r
c
debt
1
=
rate)
tax

(1
cost x
pretax
=
debt
of
cost
tax

After
Taxes and the WACC
We can now state our tax

included WACC formula:
In our Geothermal Example, we have:
12
equity
debt
c
r
V
E
)r
T
(
V
D
WACC
1
%
4
.
11
114
.
0
14
.
0
70
.
0
052
.
0
30
.
0
14
.
0
647
$
453
$
08
.
0
35
.
0
1
647
$
194
$
)
(
WACC
Valuing an Entire Business
Example:
I
0
= 50 m
Cash Flows (for 6 years) = 12 m each year
Debt/Equity ratio:
0.6
Cost of Debt:
15.15%
Cost of Equity:
20%
Tax Rate:
34%
Is this a good project?
13
Valuing an Entire Business
Step 1: Calculate the Cost of Equity Capital
Step 2: Calculate the Cost of Debt
Step 3: Calculate the WACC
Step 4: Calculate the PV & the NPV of the project
14
Valuing an Entire Business
Step 1:
Calculate the Cost of Equity Capital
E(R
E
) = 0.20
Step 2:
Calculate the Cost of Debt
E(R
D
) = 0.1515
Step 3:
Calculate WACC
Additional input:
Debt/Value = 0.6 /(0.6 + 1) = 0.375
Equity/Value = 1

0.375 = 0.625
WACC = 0.375 * 0.1515 * (1
–
0.34) + 0.625 * 0.2 = 0.1625
Step 4:
Calculate the NPV of the project
15
Valuing an Entire Business
0
1
2
3
4
5
6
Cash Flows
50
12
12
12
12
12
12
PV(0)
10.323
8.8797
7.6385
6.5708
5.6523
4.8622
SUM PV(0)
43.93
NPV
(6.07)
16
Valuing an Entire Business
Another Example:
17
Debt
Equity
Book Value (millions)
60
# of Shares (millions)
5
Trading at
120%
Price per Share
20
YTM
0.12
Beta
1.4
Tax Rate
0.34
E(R(m))
0.1
Riskfree Rate
0.03
Cash Flows' Growth Rate
Initial Investment
25
Year 2 to 5
0.05
Cash Flows @ 1
2
Year 5 forever
0.03
Project's Cash Flows (millions)
Valuing an Entire Business
Market Value of Debt:
60 * 120 % = 72
Market Value of Equity:
5 * 20 = 100
Debt / (Debt + Equity)
= 72 / 172 = 41.9 %
Equity / (Debt + Equity)
= 100 / 172 = 58.1 %
Cost of Equity:
0.03 + 1.4 [0.1
–
0.03] = 0.128
Cost of Debt:
0.12 (equal to YTM)
WACC = 0.419 * 0.12 * 0.66 + 0.581 * 0.128 = 10.75%
18
Valuing an Entire Business
19
Cash Flows
25.00
2.00
2.10
2.21
2.32
2.43
2.50
Terminal Value
32.28
Total Cash Flows
25.00
2.00
2.10
2.21
2.32
34.71
Discount Factor
1.108
1.227
1.359
1.505
1.667
PV(0)
1.806
1.712
1.623
1.539
20.825
SUM PV(0)
27.505
NPV
2.50
TV
5
= 2.5 / (0.1075
–
0.03)
Three (or more) Sources of Funding
Consider the case in which the firm is funded by:
Debt
Common stock
Preferred stock
WACC formula can be adapted to include all 3 sources
of funding:
In general, if
V
n
is the amount of the firm’s assets
financed by means
n
, then:
20
preferred
equity
debt
c
r
V
P
r
V
E
)r
T
(
V
D
WACC
1
N
n
tax
fter
a
n
n
r
V
V
WACC
1
Comments
When calculating capital structure,
use market
values
, not book values.
21
Market Value of Bonds

PV of all
coupons and par value discounted at the
current YTM.
Market Value of Equity

Market price
per share multiplied by the number of
outstanding shares.
Comments
Required Rates of Return:
Bonds:
r
debt
= YTM;
Common Stock:
CAPM:
DDM:
Preferred Stock:
Fixed dividend:
Bank Loans: Interest on Bank Loan
22
f
m
f
equity
r
r
E
r
r
g
P
d
r
equity
0
1
0
1
P
d
r
preferred
Comments
The WACC is an appropriate discount rate only for a project
that is a carbon copy of the firm's existing business
There are two costs of debt financing. The explicit cost of
debt is the rate of interest bondholders demand. The
implicit cost is the required increase in return from equity.
When evaluating a business, always use
Free Cash Flows
(FCF)
FCF = Op. CF
–
Inv. In PPE and working capital
23
H
H
H
H
WACC
PV
WACC
FCF
WACC
FCF
WACC
FCF
PV
)
1
(
)
1
(
...
)
1
(
)
1
(
2
2
1
1
Example:
Concatenator
Manufacturing
Capital Structure: 60% Equity, 40% Debt
Cost of debt: 5%
Cost of equity: 12%
Growth after horizon period: 5%
Cash Flows: See Next Table
24
Example:
Concatenator
Manufacturing
25
Comments
Example:
Concatenator
Manufactoring
26
40
.
271
,
2
05
.
085
.
5
.
79
Value
Horizon
40
.
290
,
1
085
.
1
40
.
271
,
2
085
.
1
2
.
40
085
.
1
1
.
34
085
.
1
9
.
102
085
.
1
1
.
87
085
.
1
73.6

PV(FCF)
5
5
4
3
2
%
5
.
8
085
.
0
12
.
0
60
.
0
05
.
0
40
.
0
WACC
Comments 0
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