FINE 3010-02 Financial Management

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Nov 10, 2013 (3 years and 9 months ago)

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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

Risk-free 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