Download Introduction to Financial Management

Valuation and levered
Betas
Some interesting questions
to consider in applications
FIN 819: lecture 5
Today’s plan
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Review what we have learned in the last lecture
An example of a cash-flow calculation
Examine the impact of financing on the cost of
equity (levered Betas)
Two approaches to calculate NPV
•
•
WACC ( weighted average cost of capital approach)
APV (adjusted present value approach)
What have we learned
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Risk, returns and WACC
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Your view of risk in finance
measure investment performance
measure risk
portfolio diversification and two types of risk
systematic risk and its measurement
three portfolio rules
CAPM and the security market line
Cost of capital and WACC
The things you have to pay attention to in calculating WACC
Example 1
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Based on the CAPM, ABC Company has a
cost of capital of 17%. (4 + 1.3(10)). A
breakdown of the company’s investment
projects is listed below.
• 1/3 Nuclear Parts: β=2.0
• 1/3 Computer Hard Drive:
• 1/3 Dog Food Production:

β =1.3
β =0.6
When evaluating a new dog food production
investment, which cost of capital should be
used and how much?
Solution
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Since dog food projects may have
similar systematic risk to the dog food
division, we use a beta of 0.6 to measure
the risk of the projects to be taken.
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Thus the expected return on the project
or the cost of capital is
0.04+0.6*(0.1)=0.l or 10%
Example 2
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Stock A has a beta of .5 and investors
expect it to return 5%. Stock B has a
beta of 1.5 and investors expect it to
return 13%. What is the market risk
premium and the expected rate of return
on the market portfolio?
Solution
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According to the CAPM
5  r f  0.5 * ( Rm  r f )
13  r f  1.5 * ( Rm  r f )
r f  1%
Rm  9%
Example 3
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You have $1 million of your own money
and borrow another $1 million at a riskfree rate of 4% to invest in the market
portfolio. The expected return for the
market portfolio is 12%, what is the
expected return on your portfolio?
Solution
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We can use two approaches to solve it:
• First, the expected rate of return of a portfolio
•
is the weighed average of the expected rates
of return of the securities in the portfolio.
Second , the beta of a portfolio is the weighed
average of the betas of the securities in the
portfolio. Then use the CAPM to get the
expected rate of return.
Solution (continue)
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First approach

Second approach
W  $1; W f  1; Wm  2
1
2
xf 
 1; xm   2
1
1
R p  1* 4  2 *12  20%
W  $1; W f  1; Wm  2
1
2
xf 
 1; xm   2
1
1
 p  1* 0  2 *1  2
R p  4  2 * 8  20%
The cost of capital
Cost of Capital
• The expected return the firm’s investors
require if they invest in securities or projects
with comparable degrees of risk.
Cost of capital with tax benefit

When tax benefit of debt financing is
considered, the company cost of capital
is as
D
E
WACC 
rdebt (1  Tc ) 
requity
DE
DE
The cost of capital for the bond
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The cost of capital for the bond
• It is the YTM, the expected return required
•
the investors.
That is
Pbond 
cpn
cpn
cpn  principal


1  rd 1  rd 2
1  rd t
• The expected return on a bond can also be
calculated by using CAPM
rd  r f   d ( Rm  r f )
by
Example 2
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A bond with a face value of $2000
matures in 5 years. The coupon rate is
8%. If the market price for this bond is
$1900.
(a) What is the expected return on this bond or
what is the cost of debt for this bond?
(b) Suppose that the YTM is 9%, what is the
market value of this bond?
Solution
(a)
 1

1
2000

1900  160


5 
5
 YTM YTM (1  YTM )  (1  YTM )
YTM  9.3%
(b)
 1
 2000
1
Pbond  160

 $1,922
 
5
5
 0.09 0.09 *1.09  1.09
The cost of capital for a stock
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The cost of capital for a stock is
calculated by using
• CAPM
re = rf + i (R m - rf )
• Dividend growth model
DIV1
DIV1
P0 
 re 
g
re  g
P0
Example 3
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Sock A now pays a dividend of $1.5 per
share annually, It is expected that
dividend is going to grow at a constant
rate of 2%. The current price for stock A
is $25 per share. What is the expected
return or the cost of capital by investing
in this stock?
Another cash flow problem!
Company A has a very old packaging machine which can be used
for another two years. It has no book and market values. The
maintenance cost for this old machine is $20,000 every year. Now
a new packaging machine is available at the price of $ 300,000,
which is depreciated in three years. If the new packaging machine
is used, the maintenance cost is $10,000 every year. If there is no
inflation, the cost capital is 10%, and the tax rate is 40% for
company A.
Questions:
a. What is the valuation horizon used in this problem?
b. Should company A invest in the new packaging machine now or
waiting two years later?
How does debt financing affect
investment?
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When firms issue debt, tax-shield and
thus introduced financial risk impact the
valuation of the projects and thus
investments.
To understand how financing affects
investments or real project valuations,
we will introduce several variables.
Some terminology
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D: the market value of debt
E: the market value of equity
UA: the value of the unlevered asset of the
firm ( the value of the asset when D=0)
A: the value of the levered asset of the firm,
i.e., D is positive; sometimes, V is used to
refer to the same thing.
TX: the present value of the tax shield
Some terminology (continues)
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 D : the beta of debt
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 E : the beta of equity
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UA
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: The beta of the unlevered asset
 A : the beta of the levered asset
TX : the beta of the tax-shield
Some terminology (continues)
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rD : the cost of debt
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rE : the cost of equity
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rUA
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: the cost of the unlevered asset
rA : the cost of the levered asset
rTX : the cost of the tax-shield
The balance sheet
Assets
Debt Tax shield (TX)
Unlevered asset (UA)
Liabilities and Equity
Debt
D
Equity
E
The relationship among all kinds
of values
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From the balance sheet, we can have
the following relationships
A  UA  TX
A DE
The present value of tax-shield
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If the tax-shield is as risky as debt, and
the firm issues risk-free perpetual debt,
then the present value of the tax-shield
can be regarded as a simple perpetuity
with the amount of level cash flow as
Dr f Tc
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Clearly,
TX  Dr f Tc / r f  DTc
The beta of equity
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Using portfolio, we have
D

 E  1  1  Tc  UA
E

In this text book, we can assume that
UA is not affected by firms’ capital
structure, but decided by firms’ business
risk.
The betas of equity and asset
(continues)
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Thus, for firms with the same business
line, UA should be the same
theoretically.
Two questions?
• Is this making sense?
• Why are we interested in the betas of
unlevered assets?
An example
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Firm D has the same business as firms
A, B and C, whose betas and market
values of debt and equity are given in
the table in the next slide. Suppose all
the firms have the risk-free debt and the
risk free rate is 4%, the risk premium on
the market portfolio is 8.4% annually and
the corporate tax rate is 34%, what is the
WACC for firm D?
Information for example
Firms
A
B
Beta
Debt
0.75
4.0
1.00
230
Equity
96
770
790
1.08
210
C
150
D
800
The two approaches for
calculating NPV
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WACC approach:
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Basic idea: calculate free cash flows, as if the
project is all-equity financed
Lower the cost of the capital to incorporate
tax-shield; this is taken care of by WACC
Discount free cash flows by WACC to get
NPV
APV approach
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In contrast to the WACC approach, the APV
approach is strongly recommended in
academics.
Basic idea:
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Calculate free cash flows
Use the cost of unlevered asset to discount the free
cash flows
In addition, calculate the NPV of the tax shield
The sum of the two NPVs is the NPV of the project
What are the pros and cons of
the two approaches
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Which approach would you like ? Why or
why not?
Can you predict which approach will be
used more in the future?
An example
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Firm D wants to expand its business. Currently
the firm has D/V of 40%. The cost of the firm’s
equity is 14.6%, the risk free rate is 8% and the
debt is risk-free. Suppose that the firm wants to
finance the expansion project by issuing $20
million of risk-free perpetual debt and $80
millions of equity. The expansion project will
generate a perpetual free cash flow of $5
million at every year, starting next year. The
tax rate is 35%. Please use two approaches to
calculate the present value of the expansion
project?
Solution
First approach:
Suppose that the tax-shield is as risky as
debt.
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