# FINE 3010-02 Financial Management

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

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

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

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

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

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

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

Another Example:

17

Debt
Equity
Book Value (millions)
60
# of Shares (millions)
5
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)

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

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

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.

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

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

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