UNSW Business School
School of Banking and Finance
FINS1613: Business Finance
2021 Term 2
Section IV:
Cost of Capital
n
Robert Tumarki
r.tumarkin@unsw.edu.au
UNSW Business School
School of Banking and Finance
FINS1613: Business Finance
2021 Term 2
Week 8:
Risk, Return, and the Capital Asset
Pricing Model
The historical record: A rst look
The growth in value of $10, 000 invested three major Australian asset classes over the
past 30 years (1988 through 2017
Source: www.vanguard.com.au
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)
3
Risk and return concepts
4
Realised returns
De nition
The realised return on a security is the percent return change in the security’s value over a
particular time period.
V aluet+1 V aluet
V aluet
V aluet+1
=
1
V aluet
Return =
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5
Realised returns
Example: Return on a stock over 1 perio
You purchased a stock for P0. One period later you
received a dividend of Div1 and the stock price was P1
P1 + Div1
P0
1
6
d
Return =
Realised returns
To determine the cumulative return on a security over a multiple
time periods, compound the returns for each individual period
Assume a stock returns R1 from t=0 to t=1, R2 from t=1 to t=2,
and so on. Then the realised return on the stock from t=0 to t=4
is:
Return = (1 + R1 ) ⇥ (1 + R2 ) ⇥ (1 + R3 ) ⇥ (1 + R4 )
1
For stocks, we assume that all dividends are used to purchase new
shares in the stock. That is, dividends are reinvested in the stock.
(This is identical to the interest reinvestment assumption when compounding.)
.
7
Describing realised returns
A security’s arithmetic average return for a given timeperiod length (e.g. month, year, etc) is simply the average of the
realised returns over several such time-period
R̄ =
1
(R1 + R2 + · · · + RT )
T
It serves as an estimate of the expected return for a single
time-period in the future, assuming that the distribution of
returns does not change.
s
8
Describing realised returns
A security’s geometric average return for a given timeperiod length (e.g. month, year, etc) is simply the geometric
average of the realised returns over several such time-period
R̄G = ((1 + R1 ) ⇥ (1 + R2 ) ⇥ · · · ⇥ (1 + RT ))
1/T
1
It provides the constant periodic return required to achieve
the security’s total realised returns from time-0 to time-T. It is
not an estimate of the expected return for a single time-period
in the future due to a reinvestment and compounding
assumption.
s
9
Describing realised returns
A stock returned 10% one year and 50% the next. Assume that these two
returns are the only possibilities in the future and are equally likely
•
What is your total return in the stock expressed as a two-year rate and as a one-year
rate that assumes reinvestment and compounding
•
What is the stock’s expected one-year return
:
?
?
10
Describing the realised risk in returns
A security’s variance and standard deviation both measure
the variability in realised returns.
Variance is the average squared deviation of realised returns
from the average:
V ar(R) =
1
T
1
h
R1
R̄
2
+ R2
R̄
2
+ · · · + RT
R̄
Standard deviation is the square root of the variance:
R
11
SD(R) =
p
= V ar(R)
2
i
Using average and standard deviation
If we assume that returns are normally distributed…
95% of the time
Likelihood
68% of the time
-3
-2
-1
0
1
2
3
Standard Deviations
… then one can estimate the an interval in which the
realised return will fall a given percent of the time.
12
Sample problem
A stock has had annual returns of 15%, 30%, and -8%. What is your best
estimate of the 95% prediction interval for next year’s return assuming
the underlying distribution is normal?
13
Risk and return
Don’t forget that risk measures uncertainty after
normalising for the expected return
•
•
An investment that will always lose all your
money (e.g. the return is always -100%) has no
uncertainty
An investment that always makes money (e.g. the
return will be 150% or 300%) can have a large
amount of uncertainty.
.
.
14
Historical risk and return
15
The historical record: A rst look
The growth in value of $10, 000 invested three major Australian asset classes over the
past 30 years (1988 through 2017
Source: www.vanguard.com.au
fi
)
16
The historical record: A second look
In the U.S., a similar pattern emerges from 1926 - 2005
Asset class
Average annual return
Standard deviation
Small company stocks
17.4%
32.9%
Large company stocks
12.3%
20.2%
Long-term corporate bonds
6.2%
8.5%
Long-term government
bonds
5.5%
5.7%
U.S. Treasury bills
3.8%
3.1%
17
Risk premium
De nition
The reward for bearing risk. Measured as the excess return on a risky asset over the risk-free
rate, which is the rate of return on a risk-less investment.
Risk premium = Return on risky asset
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Risk f ree rate
Historical risk premiums
Investment
Average return
Risk premium
Australian shares
9.8%
3.6%
Australian bonds
8.3%
2.1%
Cash
6.2%
0.0
Observation: Stocks, which are relatively risky, have higher returns
than bonds, which are relatively safe.
19
Portfolios and individual stocks
= Portfolio
Observation: Portfolios, which are relatively low risk, can perform as
well as individual securities, which have relatively high risk.
Source: Fundamentals of Corporate Finance, Pearson
Objective
We would like a model that is compatible with two
observations about historical returns
•
•
Asset class returns increase with risk over the
long-term (stocks outperform bonds, which
outperform cash)
Portfolios can provide similar performance to
individual securities, despite having lower risk.
It is not obvious how these two observations can co-exist as they
seem to imply different relationships between risk and returns.
:
.
21
Thought exercise
22
A simple stock
Imagine there is a stock that once you invest immediately is worth either $2 or
$0. What is this stock worth
?
23
A LOT of stocks
Imagine there are an in nite number of stocks. Each is worth either $2 or $0
immediately after you have implemented your entire investment strategy.
Knowing the nal value of one stock does not tell you anything about the nal
value of another stock
What are these stocks worth? Assume you are very wealthy and can buy as many
stocks as you like
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fi
.
.
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A LOT of stocks?
Imagine there are an in nite number of stocks. Each is worth either $2 or $0
immediately after you have implemented your entire investment strategy.
Knowing the value of one stock tells you the value of every other stock. For
example, if one stock is worth $2, then all stocks are worth $2.
What are these stocks worth? Assume you are very wealthy and can buy as many
stocks as you like
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Observation
Recall the return equation
Return =
V aluet+1
V aluet
1
It shows that if you x the nal value of an asset, then …
A factor that alters the initial value in uences returns
A factor that does not change the initial value has no impact on returns
.
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•
•
Observation
Recall the return equation
Return =
P ricet+1
P ricet
1
It shows that if you x the nal price of an asset, then …
A factor that alters the initial price in uences returns
A factor that does not change the initial price has no impact on returns
.
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•
•
Lessons
•
Investors generally do not like uncertainty. This is often stated as investors are riskaverse
•
There are two types of risk
•
•
-
Risk that is unique to a security can be eliminated by buying many securities
Risk that is common to all securities can not be eliminated
Risk-averse investors will ignore risk that can be eliminated in securities. This risk
does not affect prices or returns.
Risk-averse investors will price securities with risk that can not be eliminated less
than the expected payoff.
Risk-averse investors will demand that securities containing risk
that can not be eliminated provide a positive return
(relative to the expected payoff ).
.
.
.
.
28
Portfolios, risk, and diversi cation
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Types of risk
There are two types of risk..
• Systematic risk: Risk that is linked across outcomes. Also
called common risk.
• Unsystematic risk: Risks that bear no relationship to each
other. Also called independent, diversi able, or idiosyncratic risk.
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Historical risk premiums
Investment
Average return
Risk premium
Australian shares
9.8%
3.6%
Australian bonds
8.3%
2.1%
Cash
6.2%
0.0
Do both systematic and unsystematic risks earn risk-premiums?
Source: www.vanguard.com.au
31
Portfolio
De nition
A portfolio is a collection of securities. It is de ned by:
(i) the securities that are in the portfolio and
(ii) the amount invested in each security.
It is possible to have negative amounts invested in a security.
Examples include borrowing cash and shorting stocks.
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Portfolio sample problem
One year ago, you invested $30,000 in stock A and $20,000 in stock B.
Today stock A is worth $45,000 and stock B is worth $15,000. What is
the return on your portfolio
?
33
Analysing portfolio return calculations
The key equation for computing portfolio returns follows from basic
properties of arithmetic
(A1 + B1 ) (A0 + B0 )
A0 + B 0
(A1 A0 ) + (B1 B0 )
=
A0 + B 0
RP =
=
=
A0 (A1A0A0 ) + B0 (B1B0B0 )
A0 + B 0
A0
B0
RA +
RB
A0 + B 0
A0 + B 0
Retur
The return on a security in the
portfolio.
Weight
The percent of the initial
investment in a security.
:
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34
Portfolio return
De nition
The return of a portfolio is a weighted average of the returns of the individual securities,
where the portfolio weight (wj) is the value of the investment in asset j as a percent of the total
portfolio value
RP = w A ⇥ RA + w B ⇥ RB + . . .
.
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Portfolio sample problem
One year ago, you invested $30,000 in stock A and $20,000 in stock B.
Over that year, stock A returned 50% and stock B lost 25%. What was
the return on your portfolio
?
36
Portfolio risk example
Returns
Stock A
Stock B
Portfolio
January
1.00%
-0.93%
0.04%
February
-14.00%
-7.16%
-10.58%
March
-18.00%
0.23%
-8.88%
April
-1.00%
3.07%
1.04%
May
-10.00%
-3.27%
-6.63%
June
-13.00%
-11.26%
-12.13%
July
-4.00%
10.70%
3.35%
August
12.00%
-8.27%
1.87%
September
19.00%
5.56%
12.28%
October
-20.00%
20.12%
0.06%
November
0.00%
9.86%
4.93%
December
-11.00%
5.70%
-2.65%
Average
-4.92%
2.03%
-1.44%
St Dev
11.34%
8.65%
6.80%
Correlation
-9.40%
Portfolio risk
A portfolio containing two assets has a variance given
by
2
p
= !a2
2
a
+ !b2
2
b
+ 2⇢a,b !a !b
a b
8
>
!a = Porfolio weight of asset a
>
>
>
>
>
<!b = Porfolio weight of asset b
where
b = Standard deviation of asset b
>
>
>
>
b = Standard deviation of asset b
>
>
:⇢ = Correlation of assets a and b
a,b
:
38
Computing portfolio risk
What is the standard deviation of a portfolio with 40% allocated
to Stock A and 60% allocated to Stock B? Stock A has a standard
deviation of 25%, Stock B has a standard deviation of 50%, and the
correlation coef cient for the two stocks is 0.3.
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Principle of diversi cation
Total unsystematic risk decreases as assets
are added to a portfolio
40
20
Unsystematic Risk
10
Systematic Risk
0
0
250
500
Number of Securities
40
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Standard Deviation (%)
30
750
1,000
Principle of diversi cation
De nition
As (i) different types of securities are added to a portfolio and (ii) the average
size of each position shrinks, the amount of unsystematic risk in the portfolio
declines to zero and only systematic risk remains
Unsystematic risk is essentially eliminated by diversi cation, so a
relatively large portfolio only has systematic risk.
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Systematic return principle
42
Risk and return
There are two types of risk..
• Systematic risk: Risk that is linked across outcomes. Also
called common risk.
• Unsystematic risk: Risks that bear no relationship to each
other. Also called independent, idiosyncratic, or diversi able
risk
... but only one type earns a risk-premium.
•
Investors must be rewarded for bearing systematic risk,
otherwise no one would own risky assets
•
As systematic risk increases, expected returns increase.
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.
.
43
The systematic risk principle
De nition
The risk premium of a security is determined by its systematic risk and does not depend on its
diversi able (unsystematic) risk.
Only systematic risk has earns a risk premium. The risk premium
for diversi able risk is zero; investors are not compensated for
holding unsystematic risk.
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The Capital Asset Pricing Model
(CAPM)
45
Risk premium
De nition
The reward for bearing risk. Measured as the excess return on a risky asset over the risk-free
rate, which is the rate of return on a riskless investment (for example, treasury bills).
Risk premium = Return on risky asset
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Risk f ree rate
Historical risk premiums
Historical
averages
Investment
Systema c Risk
Unsystema c
Risk
Expected
Return
Risk Premium
Stock A
3x equity risk
Medium
?
?
Australian equities
Equity risk
None
9.8%
3.6%
Stock B
0.5x equity risk
High
?
?
Risk-free
None
None
6.2%
0.0%
(All Ordinaries)
ti
ti
47
Capital Asset Pricing Model (CAPM)
Expected return of a security is linear in its ‘beta
Expected return
The expected rate of return on security i. It is
the expected return in the market on
investments with equivalent risk to the risk
associated with the security.
E[ri,t ] = rf +
i
Beta
Measures the sensitivity of security i to
market movements. Captures relative
systematic risk.
⇥ M arket Risk P remium
Market Risk Premiu
The average return market participants demand for
bearing the market’s systematic risk. It re ects the
average risk aversion of all market participants.
Risk-free retur
The return on a riskless
security.
M arket Risk P remium = E(rm )
rf
where E(rm) is the expected return on the market.
’
fl
m
n
48
Capital Asset Pricing Model (CAPM)
Key implications of the CAPM
•
Investors are compensated for holding systematic risk in form
of higher returns.
•
The size of the compensation depends on the market risk
premium
•
The market risk premium is increasing in
•
•
the volatility of the market portfoli
the risk aversion of average investor
:
o
:
.
49
Beta
De nition
The level of systematic risk in any asset relative to that of the “market”. By de nition, the
market has a beta of 1 and the risk-free asset has a beta of 0
In principle, the “market” contains every asset in the
economy (every stock, bond, property, etc).
In practice, the “market” is often chosen to be a stock
market index (e.g. Australian All Ordinaries, S&P 500).
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Implications of the CAPM
The excess return on a security is its return over the risk free
rate. The CAPM implies that the excess return of security i is
proportional to its systematic risk (beta):
E[ri,t ]
rf =
i
⇥ M arket Risk P remium
This implies that all security’s (e.g. security i and security j) have
the same excess return-to-risk ratio:
E[ri,t ]
rf
= M arket Risk P remium =
i
E[rj,t ]
j
51
rf
Estimating beta
The CAPM implies a relationship that can be used to estimate
beta. Using the relationship between security and market excess
returns (from the previous slides):
E[ri,t ]
rf =
i
=
i
⇥ M arket Risk P remium
⇥ (E [rm,t ]
rf )
This implies that one can use observed data to estimate beta:
ri,t
rf =
i
⇥ (rm,t
52
rf )
Estimating beta
Beta is generally found as the slope of the best tting linear
regression line between security excess returns (vertical axis) and
the market excess returns (horizontal axis). An example for Apple is
shown below
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) –
9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1st edition
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CAPM example
Assume the risk-free rate is 3.5% and the market-risk premium is 5%.
•
What is the expected return for a stock with β=1.07
Assume the expected return on a stock with β=0.69 is 12% and the risk-free
rate is 2.0%
•
What is the expected market return? From the Capital Asset Pricing Model (CAPM)
:
?
.
54
Betas for selected industries
Low betas suggest an asset’s returns
are relatively insensitive to market movements…
Industry
Beta
Industry
Beta
Apparel
0.82
Computer
1.19
Banks
0.57
Cable TV
1.15
Business & Consumer Services
0.94
Drugs (Biotech)
1.28
Education
0.87
Homebuilding
1.07
Food Wholesalers
0.69
Internet
1.15
Hospitals
0.74
Precious Metals
1.19
Power
0.81
Retail
1.11
Restaurant/Dining
0.78
Semiconductor
1.36
Tobacco
0.71
Telecom Equipment
1.16
…Assets with high betas have returns
that are relatively sensitive to market movements.
Source: Aswath Damodaran (http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datacurrent.html)
s
55
Security Market Line (SML)
De nition
The SML plots the expected return on a security as a function of its beta. It implies that a
security’s expected return linearly depends on systematic risk (beta).
Expected Return
Expected Return
E[ri,t ] = rf +
i
⇥ M arket Risk P remium
E[rm ]
rf
0
1
Beta(
Beta (β) )
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Security Market Line (SML)
De nition
The SML plots the expected return on a security as a function of its beta.
Expected Return
Expected Return
E[ri,t ] = rf +
i
⇥ M arket Risk P remium
E[rm ]
Securities (portfolios) with
Betas less than 1 are expected
to return less than the market.
rf
0
1
Beta(
Beta (β) )
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Security Market Line (SML)
De nition
The SML plots the expected return on a security as a function of its beta.
Expected Return
Expected Return
E[ri,t ] = rf +
i
⇥ M arket Risk P remium
E[rm ]
rf
0
1
Beta(
Beta (β) )
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Securities (portfolios) with
Betas greater than 1 are
expected to return more than
the market.
Portfolios and individual stocks
= Portfolio
Observation: Portfolios, which are relatively low risk, can perform as
well as individual securities, which have relatively high risk.
Source: Fundamentals of Corporate Finance, Pearson
CAPM and Portfolios
A portfolio’s expected return is
RP = w A ⇥ RA + w B ⇥ RB + . . .
… and must also satisfy the CAPM
P
⇥ M arket Risk P remium
60
…
E[rP,t ] = rf +
CAPM and Portfolios
The derivation of a portfolio’s beta follows from
substitution
RP = w A ⇥ RA + w B ⇥ RB + . . .
E[rP,t ] = rf +
P
⇥ M arket Risk P remium
:
61
CAPM and Portfolios
The CAPM can be applied to portfolios by setting beta equal
to the weighted average of the individual securities’ betas
E[rP,t ] = rf +
P
⇥ M arket Risk P remium
wher
P
= wA ⇥
A
+ wB ⇥
B
+ ...
:
e
62
Portfolio example
What is the expected return on the following portfolio assuming a risk-free rate
of 5% and a 7% risk-premium.
Asset
Shares
Price
Value
2,300
0.392
901.6
ANZ Banking
43
26.940
1.40
BHP Billiton
85
31.010
1.04
“The Market”
1
5986.10
3,500
1
Myer
Risk-free
asset
Portfolio
63
Weight
Beta
1.67
Expected
Return
Objective
The CAPM is compatible with two observations about
historical returns:
•
Stocks outperform bonds, which outperform cash.
Stocks have higher systematic risk than
bonds.
•
Portfolios can provide similar performance to
individual securities, despite having lower risk.
Portfolios can have lower total risk, but the
same systematic risk as individual securities.
64
UNSW Business School
School of Banking and Finance
FINS1613: Business Finance
2021 Term 2
Week 9:
Capital Structure and the Cost of
Capital
Cost of capital
66
Expected returns and discount rates
The analysis of risk and return shows that
•
The expected return premium on any asset is proportional to its systematic risk
As a consequence, a rm trying to attract investors must
•
Offer investments that meet the return expectations of the markets. That is, a project
must have a positive NPV when discounted at the appropriate expected return
•
Providing returns is a necessary cost to the company for accessing investor capital.
.
.
:
:
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Cost of capital
De nition
The required rate of return a company must offer investors for a project to compensate them
for risk. Consequently, it is the discount rate a company should use when valuing projects.
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Preliminaries
69
Valuation: Parts and their whole
Consider a nancial source (e.g. rm or project) that distributes the cash ows
generated across different nancial securitie
Source
Asset A
Asset B
There are two possible methods to value the entire nancial source
•
Value assets A and B individual at their respective discount rates and then add the
values
•
Value the source at an appropriate discount rate.
This distinction is relevant. Only the securities of a rm (e.g. debt and
equity) are directly valued in nancial market.s
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Valuing the parts to value the whole
Total cash ow
Source
Cash ows to
each security
Asset A
Asset B
Discount rates
rA
rB
Values
VA
+
fl
fl
71
VB
= ValueSource
Valuing the whole
Total cash ow
Source
Cash ows to
each security
Discount rates
Values
rSource
ValueSource
fl
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72
Valuing the parts to value the whole
Total cash ow
Source
Source
Cash ows to
each security
Asset A
Asset B
Discount rates
rA
rB
rSource
Values
VA
VB
ValueSource
+
Is there a relationship between the individual discount rates
and the source discount rate?
fl
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Example
Imagine an asset that yields cash ows in 1 period and never again.
•
•
Security A receives $6.25, and has a cost of capital of 25%.
Security B receives $11, and has a cost of capital of 10%
What is the value of each security when valued independently? What is the
asset’s total value?
.
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Example
Imagine an asset that yields cash ows in 1 period and never again.
•
•
Security A receives $6.25, and has a cost of capital of 25%.
Security B receives $11, and has a cost of capital of 10%
If you built a portfolio of securities a and b, what is the weighted average cost of
capital (WACC)
What is the value of the total cash ow at the WACC?
.
fl
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?
75
Weighted average cost of capital
(WACC)
76
The analysis of risk and return shows that
•
The return on a portfolio is a weighted average of the returns of the securities in the
portfolio
As a consequence, an investor that purchased all the securities receiving cash
ows from an asset could
•
Value this asset using the weighted average of the expected returns of the rm’s
securities, where the weights are based on the purchase price (market value).
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.
fl
Portfolios and discount rates
Portfolios and discount rates
The analysis of risk and return shows that
•
The return on a portfolio is a weighted average of the returns of the securities in the
portfolio
As a consequence, a rm trying to attract investors must
•
Offer a return equal to the weighted average of the expected returns of the asset’s
securities
•
The weights must be based on market values, as these are the value used by
investors.
:
:
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.
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Weighted Average Cost of Capital (WACC)
De nition
The weighted average of an asset’s costs of capital for each security used in nancing.
Weights are the fractional amounts of each security’s total market value.
Example:
rW ACC
✓
◆
✓
◆
✓
◆
Cost of
Cost of
Cost of
=wE ⇥
+ wP ⇥
+ wD ⇥
Ordinary Shares
P ref erence Shares
Debt
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Levered and unlevered rms
De nition
A rm without debt is called an unlevered rm, while a rm with debt outstanding is called
a levered rm. The weighted average cost of capital for an unlevered rm is just the cost of
equity.
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The WACC method values assets by discounting cash ows at the weighted
average cost of capital
•
This gives the total market value of all the rm’s securities when applied to the total
rm cash ow.
•
This gives an NPV when applied to project
The WACC method implicitly assumes that the relative market
values of the underlying securities do not change over time.
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Applications
Project discount rates
82
Weighted average cost of capital provides an important insight on discount rates
•
Cash ows should be discounted using an cost of capital that re ects the appropriate
risk in the cash ows
•
Securities are discounted using the cost of capital for the risk in the security’s cash
ows
•
Assets are discounted using the “average” cost of capital of the underlying securities;
this represents the average risk in the total asset cash ow
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83
.
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Insight from WACC
Project-speci c discount rates
Imagine two rms, each with a single project
Firm A: Has a low-systematic risk project with a discount rate of 5%. It requires $15 million
up front and generates $1 million per year in perpetuity.
Firm B: Has a high-systematic risk project with a discount rate of 15%. It requires $25 million
up front and generates $3 million per year in perpetuity
Should the rms invest in these projects?
.
.
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84
Project-speci c discount rates
Imagine a single rm with two projects
Project A: This is identical to that from Firm A. It has low-systematic risk, requires $15
million up front, and generates $1 million per year in perpetuity.
Project B: This is identical to that from Firm B. It has high-systematic risk project, requires
$25 million up front, and generates $3 million per year in perpetuity
The rm has on-average moderate systematic risk, with a discount rate of 10%.
•
•
Should the rm invest in these projects?
Would the rms invest in these projects if it uses a single 10% discount rate?
.
.
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85
Project-speci c Discount Rates
Firms should use a discount rate that is appropriate for each project
A rm that uses an “average” discount rate instead of project-speci c discount
rates
•
May not invest in positive NPV low-risk projects and may invest in negative NPV highrisk projects
•
As a consequence of these investment decisions, rms using a single, “average”
discount rates for all projects may become riskier over time.
.
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Implementation:
Costs of Debt and Equity
87
CAPM limitations
In principle, the CAPM can be used to nd the cost of capital for any asset or
security
•
This implies the CAPM can be used to value both equity and debt.
In practice, asset and security values must be current, with reliable market values,
to estimate the CAPM
•
Many debt securities and preference shares do not trade frequently and listed prices
may be outdated or stale. Estimated CAPM betas may be unreliable
•
Ordinary shares, which trade frequently, are generally valued using the CAPM.
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88
Cost of debt
Debt payments are tax deductible. As a result, rms that makes a debt
payment do not bear the “full” cost of the debt.
Example: A rm that borrows $10,000 at 10% interest per year with
a tax rate of 30%:
Item
Equa on
Value
Interest expense
-rD × $10,000
-$1,000
Tax savings
rD × Tax Rate ×$10,000
$300
Effective after-tax
interest expense
rD × (1-Tax Rate) ×$10,000
-$700
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There are two possible ways to ensure the tax-deductibility of interest payments
enters into the valuation
•
Compute “levered” cash ows by adjusting for tax savings. Discount “levered” cash
ows using the observed, pre-tax cost of deb
•
Ignore the impact of interest tax savings. Instead, adjust the cost of debt for the tax
savings. Discount the “unlevered” cash ows at the after-tax cost of debt.
In nance, we use the second option as this separates the analysis of the
project from the analysis of the choice of nancing.
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Cost of debt
Cost of debt
Debt payments are tax deductible. As a result, rms that makes a debt
payment do not bear the “full” cost of the debt.
Example: A rm that borrows $10,000 at 10% interest per year with
a tax rate of 30%:
Item
Equa on
Value
Interest expense
-rD × $10,000
-$1,000
Tax savings
rD × Tax Rate ×$10,000
$300
Effective after-tax
interest expense
rD × (1-Tax Rate) ×$10,000
-$700
The after tax cost of debt should re ect the tax bene ts:
rD × (1-Tax Rate)
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91
Cost of debt
De nition
The cost of debt used in WACC computations re ects the tax bene ts of debt. The debt’s yield
to maturity is the expected return on debt required by investors. Thus, the after tax cost of
debt to a rm is
Cost of Debt = rD (1
TC )
where rD is the yield to maturity and TC is the rm’s tax rate.
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92
Cost of preference shares
Preference shareholders typically have a xed dividend.
The price of a preference share can, therefore, be reliably estimated using a constant
growth dividend discount model
P0 =
Rearranging this equation provides that the cost of a preference share
rP =
Div1
+g
P0
.
93
.
•
Div1
rP g
fi
•
Cost of preference shares
De nition
The cost of preference shares used in WACC computations re ects the expected return
demanded by investors. As preference shares often have speci ed dividends, the cost of
preference shares is typically found using a constant growth dividend discount model
rP =
Div1
+g
P0
where P0 is the current price, Div1 is the expected dividend, and g is the dividend growth rate.
:
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94
Cost of ordinary shares
The Capital Asset Pricing Model (CAPM) is most often used to determine the
cost of ordinary shares
Expected return
The expected rate of return on security i. It is
the expected return in the market on
investments with equivalent risk to the risk
associated with the security.
rE,i = rf +
i
Beta
Measures the sensitivity of security i to
market movements. Captures relative
systematic risk.
⇥ M arket Risk P remium
Market Risk Premiu
The average return market participants demand for
bearing the market’s systematic risk. It re ects the
average risk aversion of all market participants.
Risk-free retur
The return on a riskless
security.
M arket Risk P remium = E(rm )
rf
where E(rm) is the expected return on the market.
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95
Cost of ordinary shares
Applying the CAPM requires several estimates
1. A risk-free rate
2. A market risk premium
3. An appropriate Beta, re ecting the risk in the project.
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96
Cost of ordinary shares
1. What is the risk-free rate
•
The risk-free rate needs to match the investment horizon for investors and for the
project.
•
•
As most projects have long-term horizons, a cash rate is not valid.
Most rms use yields on long-term government bonds (10- to 30-years) as a risk-free
rate
2. What is the market risk premium
•
Estimating the market risk premium requires a large amount of historic data. Historic
market risk premiums may not be valid going forward
•
Most rms use a market risk premium between 5.5% and 7%.
.
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97
Estimating beta
Beta is generally found as the slope of the best tting linear regression line
between security excess returns (vertical axis) and the market excess returns
(horizontal axis). An example for Apple is shown below
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) –
9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1st edition
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Cost of ordinary shares
3. What is the appropriate Beta
•
•
•
Beta re ects the systematic risk in the project
The historic beta on a rm’s stock may be inappropriate due t
-
estimation error (noise)
average rm risk not being re ective of project risk
average rm risk not being re ective of future rm or project risk, and/o
other factors
Firms generally use Betas based on the average of single-industry (“pure-play”) rms
in the same industry as the projec
-
Averaging many rms minimises estimation error for a single rm and
emphasises project risk
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99
Cost of ordinary shares
De nition
The cost of ordinary shares used in WACC computations re ects the expected return
demanded by investors. It is most often computed using the CAPM
rE,i = rf +
i
⇥ M arket Risk P remium
where rf is a long-term risk-free rate matching the project horizon, the market risk premium is
based on historical analysis, and Beta re ects the typical Beta of pure-plays rms in the project’s
industry.
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100
Weighted Average Cost of Capital (WACC)
De nition
The weighted average of a project’s costs of capital for each security used in nancing.
Weights are the fractional amounts of each security’s total project market value.
Typically:
rW ACC = wE ⇥ rE + wP ⇥ rP + wD ⇥ rD ⇥ (1
TC )
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101
Sample problem
102
Sample problem
You have the following information about an energy company (solar power) that is
evaluating an energy drink project
•
The rm has debt outstanding with a book value of $4 billion and a market value of $7
billion. The debt has an average yield-to-maturity of 6% and an average coupon rate of 10%
•
The rm’s preference shares just paid a dividend of $1.50 per share. Dividends are paid
annual and are growing at 2% annually. The preference shares have a price of $17. There are
200 million preference shares outstanding
•
The rm’s ordinary equity has a market capitalisation of $12 billion and a book value of $1
billion. The beta on this equity is 1.2
•
Energy company’s have an average beta of 1.14. Beverage company’s have an average beta of
0.91
•
•
•
The risk-free rate is 6.0% and the market risk-premium is 7.0%.
The rm’s marginal tax rate is 30%
The rm expects to nance the project using securities in proportion to its existing capital
structure
What is the correct discount rate to use on this project?
.
.
:
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103
Flotation Costs
104
Flotation cost
De nition
A cost incurred by a company when issuing securities. Common expenses include underwriting,
legal, and registration fees.
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Dealing with otation costs
There are two commonly used methods to dealing with otation
costs
•
•
Include the costs as an initial (t=0) expense for the project
Adjust the cost of capital to account for otation costs.
Which method is correct?
.
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106
Adjusting the cost of capital for otation costs
Imagine a rm that pays total otation cost, F, as a proportion to the capital
raised.
•
Instead of receiving P0 for a series of cash ows, the rm receives P0×(1-F). This
affects the cost of capital
•
Example:
-
The constant growth dividend discount model implies
P0 (1
-
F) =
Div1
rE g
The resulting cost of capital is:
rE =
Div1
+g
P0 (1 F )
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107
Example
Imagine a rm that is raising capital for a project that needs to consider the
impact of otation costs.
•
A “pure-play” rm for the project type has a preference share that trades for $30
based on a dividend in one year of $6 that will grow by 5% annually
•
The project requires an initial capital expenditure of $150 million. Positive cash ows
begin in 1 year with $10 million and grow at 20% in perpetuity. All cash ows will be
paid to investors
•
The rm expects to pay 10% in otation costs
What is the project NPV
•
•
When the otation costs are treated as an initial expense?
When the cost of capital is adjusted for otation costs?
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108
Example
Imagine a rm that is raising capital for a project that needs to consider the impact of otation costs.
•
A “pure-play” rm for the project type has a preference share that trades for $30 based on a dividend
in one year of $6 that will grow by 5% annually
•
The project requires an initial capital expenditure of $150 million. Positive cash ows begin in 1 year
with $10 million and grow at 20% in perpetuity. All cash ows will be paid to investors
•
The rm expects to pay 10% in otation costs
Project NPV when otation costs are treated as an initial expense
•
To answer, consider
-
How much money can the rm raise from investors
What are the cash ows of the project for the rm?
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109
Example
Imagine a rm that is raising capital for a project that needs to consider the impact of otation costs.
•
A “pure-play” rm for the project type has a preference share that trades for $30 based on a dividend
in one year of $6 that will grow by 5% annually
•
The project requires an initial capital expenditure of $150 million. Positive cash ows begin in 1 year
with $10 million and grow at 20% in perpetuity. All cash ows will be paid to investors
•
The rm expects to pay 10% in otation costs
Project NPV when the cost of capital is adjusted for otation costs.
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110
Dealing with otation costs
There are two commonly used methods to dealing with otation
costs
•
•
Include the costs as an initial (t=0) expense for the project
Adjust the cost of capital to account for otation costs.
Adding otation costs as an initial expenses is more accurate; adjusting
the cost of capital assumes that the issuance costs are recurrent
(ongoing) expenses.
.
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111
Capital structure determinants
112
Remaining question
How do rms choose among the types of nancing when raising capital for
projects
•
Part II implicitly focused on a rm's existing capital structure, when the cost of debt is
observed
•
It is not clear why rm’s decide whether to issue debt or equity.
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113
Debt-value ratios by industry
Debt-value =
D
D+E
Brokerage & Investment Banking
Power
Auto & Truck
Real Estate (General/Diversi ed)
Steel
Engineering/Construction
Food Wholesalers
Retail (General)
Homebuilding
Transportation
Electronics (Consumer & Of ce)
Why does debt’s percentage of total rm value vary by industry?
Chemical (Basic)
Entertainment
Computers/Peripherals
Information Services
Computer Services
Electronics (General)
Healthcare Products
Drugs
Semiconductor
Retail (Online)
Software (Internet)
0%
17.5%
35%
Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/data.html
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114
52.5%
70%
Raising capital
115
Raising equity
Firms typically initially raise capital by selling equity to private investors
•
Venture capitalists: Professional investors who focus almost exclusively on
purchasing shares in young rms
•
Institutional investors: Invest in nearly all types of assets. May invest in higher
risk new rms as a way to get higher returns
•
Corporate investors: May invest in rms in related industries as part of strategic
initiative.
.
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116
Raising equity
An initial public offering (IPO) provides a way for a successful young rm
to raise additional capital
•
•
•
Allows venture capitalists and other seed investors to realise pro ts
Founders and other members of the rm can sell shares to extract cash
The rm’s founders control of the rm will decrease as other investors now have
shares and, consequently, can vote for members of the rm’s board of directors
A seasoned equity offering (SEO) occurs when a publicly traded rm sells
additional shares.
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117
Raising equity
Several unresolved issues around IPOs remain
•
•
Pricing does not appear to serve either the rm or investors:
-
IPOs are generally underpriced, leading to a increase in price on the rst day
Shares generally underperform the market 3 to 5 years from the IPO
An IPO’s success does not exclusively depend on the rm’s outlook
-
IPOs are cyclical. Investors prefer IPOs at some times and prefer other source of
capital at others.
Even good rms may not have a successful IPO if the market is unreceptive.
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118
Raising debt
Debt may be either private or public
Private debt is nancing that is not publicly traded.
•
Avoids registration costs with regulators (e.g. Australian Securities and Investment
Commission (ASIC)
•
•
It is hard for the purchaser to sell the debt if necessary
Examples include bank loans and private placements
Public debt is publicly traded
Debt securities differ among many dimensions including
•
Seniority: Determines if the bond is paid before or after other creditors in
administration (bankruptcy).
•
Collateral: Secured debt may be backed by speci c rm assets. Unsecured debt has
no such guarantee
•
Covenants: Restrictions on the rm. May limit the rm’s ability to issue other
securities, execute acquisitions, sell assets, or pay dividends.
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119
Australian bond market: Bonds outstanding
Source: Deloitte “The Corporate Bond Report 2018”
Australian bond market: Ownership
Source: Deloitte “The Corporate Bond Report 2018”
Raising equity & debt
Underwriters (investment banks) usually manage the process of selling securities
to the public
•
•
•
•
Design securities and the method of sale
Market the rm to investors and institutions on a road show
Sets the initial price and may provide a guarantee on the amount of capital raised
Total fees are materia
-
Typically range between 5% and 10% of total raised with equity
Typically range between 3% and 5% of debt raised with debt.
Underwriting fees do not decrease (as a percentage) as the amount of capital
raised increases (i.e. there are not signi cant “size” discounts).
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122
Pros and cons of security issuance
Equity
Pro
Debt
Dividends are not mandatory
No administration (bankruptcy)
Low issuance costs
No change in control
Interest is tax deductible
High issuance costs
Con
Interest payments are required
Loss of control
Dividends are not tax deductible
123
Administration (bankruptcy) costs
Pros and cons of security issuance
Equity
Debt
Taxes
Dividends are not tax deductible
Interest is tax deductible
Administration
No administration (bankruptcy)
Administration (bankruptcy) costs
Dividends are not mandatory
Interest payments are required
Costs
High issuance costs
Low issuance costs
Other
Loss of control
No change in control
Payouts
124
Real capital markets
Capital markets have many “frictions:”
•
•
Taxes create a cash ow bene t for rms that have debt outstanding.
•
•
•
Security prices may deviate from the present value of future cash ows
Administration is costly for the rm. Bond holders can force the rm to alter
strategy, affecting project and values
There are many costs affecting the issuance of new securities, securities trading, etc
Financing decisions may affect project investment decisions and cash ows.
Financing decisions may reveal information about cash ows.
.
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125
The capital structure problem
The rm must decide which combination of debt and equity maximises the value
of either a project or the overall rm
V alue =P V (Cash f lows) + P V (Interest tax shield)
P V (F inancial distress costs)
P V (Issuance costs) + P V (Other f actors)
This is a complicated problem. We initially simplify the analysis and then add
complexity.
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Perfect capital markets:
A starting point
127
Perfect capital markets
Perfect capital markets do not have friction
•
•
Taxes do not exist.
•
•
•
Security prices are fair, re ecting the present value of future cash ows
Administration is not costly for the rm. It can negotiate with bond holders and
recapitalise without affecting either projects or rm values
There are no costs affecting the issuance of new securities, securities trading, etc
Financing decisions are independent of project cash ows.
We analyse perfect capital markets as a basic
framework and starting point.
.
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128
Starting business example
Imagine you are starting a business that will last for only 1 year
•
•
It requires $20,000 upfront to set up operations
After salary and expenses, you expect total free cash ows available to investors to be $30,000, but
may range between $25,000 and $35,000
You are considering two possible ways to raise the money to fund operations
•
•
Option 1 is to nance entirely by equity
Option II is to nance with both debt and equity.
:
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129
An investor may purchase all the securities issued by a rm to nance a project.
In perfect capital markets
•
•
Cash ows are independent of the capital structure.
-
Taxes do not help overall cash ow through tax savings.
The rm’s investment decisions are the same irrespective of nancing
Security prices re ect the discounted value of the rm cash ows
This implies that in perfect capital market
•
•
Project and rm value does not depend on the choice of nancing
Weighted average cost of capital (WACC) does not depend on the choice of
nancing.
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130
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Portfolios and rm values in perfect capital markets
Leverage
De nition
An unlevered rm is one that does not have any debt outstanding. A rm with debt
outstanding is considered levered
In perfect capital markets, the weighted average cost of capital does not depend on capital
structure
rW ACC,L = rW ACC,U
This means that
E
D
rE,L +
rD = rE,U
E+D
E+D
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Leverage
De nition
An unlevered rm is one that does not have any debt outstanding. A rm with debt
outstanding is considered levered
In perfect capital markets, the weighted average cost of capital does not depend on capital
structure
rW ACC,U = rW ACC,L
This means that:
Cost of levered equity
Cost of unlevered equity
rE,L = rE,U +
D
(rE,U
E
rD )
Cost of debt
Market values o
equity and debt
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Modigliani and Miller (MM) Propositions
Modigliani and Miller (MM) provided two important observations (propositions)
that are direct consequences of the perfect capital markets assumptions
MM Proposition I
In perfect capital markets, the total value of a r
-
is equal to the market value of the free cash ows generated by its assets an
is not affected by its choice of capital structure
MM Proposition II
The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a
premium that is proportional to the debt-equity ratio (measured using market values)
rE,L = rE,U +
D
(rE,U
E
rD )
.
d
m
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133
Leverage and WACC
50
45
40
Cost of capital (%)
35
Equity cost
of capital
30
25
20
15
WACC
10
5
0
0
Debt cost of capital
10
20
30
40
50
60
Debt-value ratio (%)
134
70
80
90
100
Starting business example problem
Imagine you are starting a business that will last for only 1 year
•
•
It requires $20,000 upfront to set up operations.
After salary and expenses, you expect total free cash ows available to investors to be $30,000, but
may range between $25,000 and $35,000
You are considering two possible ways to raise the money to fund operations in perfect
capital markets
•
•
Option 1 is to nance entirely by equity.
Option II is to nance with both debt and equity
What is the NPV of the project if it is nanced entirely by equity? What is the initial price of
equity
•
The correct cost of capital is 15%. The appropriate risk free rate is 5%
:
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135
Starting business example problem
Imagine you are starting a business that will last for only 1 year
•
•
It requires $20,000 upfront to set up operations
After salary and expenses, you expect total free cash ows available to investors to be $30,000, but
may range between $25,000 and $35,000
You are considering two possible ways to raise the money to fund operations in perfect
capital markets
•
•
Option 1 is to nance entirely by equity
Option II is to nance with both debt and equity
What is the NPV of the project if it is nanced by debt and equity? What is the initial price of
equity
•
•
The correct cost of capital is 15%. The appropriate risk free rate is 5%
You will borrow $10,000 debt in present value terms
:
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136
Starting business example problem
How will the realised return on equity vary with the cash ows under both possible capital
structures? You are operating in perfect capital markets.
Security cash flows
FCF
Bad
$25000
Expected
$30000
Good
$35000
Unlevered
Equity
Levered
Equity
Debt
Unlevered
Equity
Debt
137
fl
Scenario
Security returns
Levered
Equity
The costs of equity capital and debt capital may change with the
rm’s choice of leverage
However, in perfect capital markets, any such changes
balance such that WACC is constant regardless of leverage.
138
.
fi
Lessons from perfect capital markets
Tax bene ts of debt
A next step
:
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Nearly perfect capital markets
“Nearly perfect” capital markets have one friction — taxes
•
•
Taxes create a cash ow bene t for rms that have debt outstanding.
•
•
•
Security prices are fair, re ecting the present value of future cash ows
Administration is not costly for the rm. It can negotiate with bond holders and
recapitalise without affecting either projects or rm values
There are no costs affecting the issuance of new securities, securities trading, etc
Financing decisions are independent of project cash ows.
.
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140
Woolworths’ 2012 ($ milllions)
Interest payments to bond holders reduce the rm’s tax burden
Actual
(levered)
Hypothetical
(unlevered)
EBIT
3919.60
3919.60
Interest expense
-318.30
0.00
Income before tax
3601.30
3919.60
-1080.39
-1175.88
2520.91
2743.72
Taxes
Net profit
… resulting in greater total cash ows available to investors
Actual
(levered)
Interest paid to debt holders
Hypothetical
(unlevered)
318.30
0.00
Income available to equity holders
2520.91
2743.72
Total available to investors
2839.21
2743.72
…
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Aside: WACC with debt and taxes
Recall from earlier that the weighted average cost of capital uses the after tax cost of debt
rW ACC =
E
D
rE +
rD (1
E+D
E+D
TC )
Rearranging suggests tha
rW ACC =
E
D
rE +
rD
E+D
E+D
|
{z
}
P re tax W ACC
D
rD ⇥ T C
E+D
|
{z
}
Reduction f rom
tax shield
This “reduction” is valid for a given capital structure.
It is not particularly helpful for a rm determining its capital
structure as the costs of debt and equity may change with leverage.
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142
Debt, taxes, and rm value
The total value of a levered rm is greater than that of a rm without leverage
due to the tax savings (shield) of debt payments
VL = VU + P V (Interest tax shield)
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143
Estimating the present value of the tax shield
Valuing the tax shield would require projecting all the interest payments made to bond holders
for the life of the rm. This is complicated because of
•
•
•
•
Changing debt levels in a rm over tim
Changing interest rates over tim
A marginal tax rate that varies over tim
Default risk leading to unpaid interes
A crude simpli cation is that the market value of current debt outstanding re ects the
present value of perpetual interest payments
D = P V (Interest payments)
As the tax shield is just the tax rate multiplied by the interest payments, the present value of
the tax shield with a constant tax rate TC is
P V (Interest tax shield) = P V (TC ⇥ Interest payments) = TC ⇥ D
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144
The costs of equity capital and debt capital may change with the
rm’s choice of leverage
The tax shield bene ts of debt increase with leverage
Without any material disadvantages of debt, all rms and
project should be nanced exclusively (or nearly exclusively) with
debt.
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.
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145
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Lessons from tax bene ts of debt
Trade-off Theory
A nal step
:
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146
Real capital markets
Capital markets have many “frictions:”
•
•
Taxes create a cash ow bene t for rms that have debt outstanding.
•
•
•
Security prices may deviate from the present value of future cash ows
Administration is costly for the rm. Bond holders can force the rm to alter
strategy, affecting project and values
There are many costs affecting the issuance of new securities, securities trading, etc
Financing decisions may affect project investment decisions and cash ows.
Financing decisions may reveal information about cash ows.
.
.
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147
Administration and nancial distress
A rm that has trouble meeting its debt obligations is in nancial distress. This may lead
to administration (bankruptcy).
Administration (bankruptcy) has signi cant direct costs
•
•
•
Professional services (accounting, legal, investment banking, appraisal, auction, etc…
•
Average direct costs are 3-4% of rm value.
Costs are greater in rms with complicated businesse
Costs can be greater for rms with a large number of creditors as it may be dif cult to
reach an agreement suitable to all partie
Financial distress and administration have indirect costs that affect the ability of the
business to operate:
•
•
•
•
•
Loss of revenues as customers fear a company may not be able to ful l its promise
Loss of suppliers who worry they may never get pai
Dif culty hiring and retaining employee
Sale of assets to meet debt payments impairs the rm’s future operation
Costs can be 10-20% of rm value
)
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148
Trade-off theory
De nition
The total value of a levered rm equals the value of the rm without leverage plus the present
value of the tax savings from debt, less the present value of nancial distress costs:
VL = VU + P V (Interest tax shield)
P V (F inancial distress costs)
Trade-off theory implies that rms choose an optimal
capital structure to maximise the value of the rms.
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149
Trade-off theory: Optimal leverage and firm value
No financial
distress costs
Low distress costs
V
Firm value
Low
V
High
High distress costs
V
U
D
High
Value of debt
D
Low
Estimating nancial distress costs
An all-equity nanced rm has a current share price of $17 and 15 million shares outstanding.
The rm announces it will lower its corporate taxes by borrowing $160 million of perpetual
debt and repurchasing shares. The rm pays taxes at 30%. If the price per share rises to $19
after the announcement, what is the present value of nancial distress costs
?
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151
The costs of equity capital and debt capital may change with the
rm’s choice of leverage
The tax shield bene ts of debt and the costs of nancial distress
both increase with leverage
Firms should balance the bene ts and costs of debt to nd an
optimal amount of leverage
The approach can be adapted to account for other costs of debt,
equity, and other securities.
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152
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Lessons from trade-off theory
A practical method
153
A practical method
One common approach to estimate a WACC for any prospective amount of
leverage
•
•
Estimate a cost of debt based on the rm’s ability to make interest payments
Determine a “levered” beta for the ordinary equity that accounts for leverage and the
“unlevered” risk of the project/ r
This approach ignores many factors (e.g. distress costs), but provides guidance for rms that
wish to change their capital structure.
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154
Estimating a cost of debt
•
A simple method is to estimate the interest coverage ratio (EBIT/Interest expense)
Interest coverage ratio
≥
8.5
6.5
5.5
4.25
3
2.5
2.25
2
1.75
1.5
1.25
0.8
0.65
0.2
Rating
Credit spread
8.50
6.50
5.50
4.25
3.00
2.50
2.25
2.00
1.75
1.50
1.25
0.80
0.65
0.20
Aaa/AAA
Aa2/AA
A1/A+
A2/A
A3/ABaa2/BBB
Ba1/BB+
Ba2/BB
B1/B+
B2/B
B3/BCaa/CCC
Ca2/CC
C2/C
D2/D
0.60%
0.80%
1.00%
1.10%
1.25%
1.60%
2.50%
3.00%
3.75%
4.50%
5.50%
6.50%
8.00%
10.50%
14.00%
More sophisticated approaches exist.
155
:
•
≤
Leveraging beta
A value with leverage follows from the de nition of the tax shield
VL = EL + D = VU + P V (Interest tax shield)
= VU + TC ⇥ D
Portfolio beta is a weighted average. Treating each side as separate portfolios
D
VL
D
=
+D
D
= VU
+
E,L
E,L
E,L
E,L
VU
VL
E,U
E,U
+
TC ⇥ D
VL
+ TC ⇥ D
D
D
VU
D
(1 TC ) ⇥
E,U
D
EL
EL
EL + D T C D
D
=
(1 TC ) ⇥
E,U
D
EL
EL
✓
◆
D
D
= 1+
(1 TC ) E,U (1 TC ) ⇥
EL
EL
=
D
156
:
EL
E,L
fi
EL
VL
Leveraging beta
Beta with leverage depends on the beta of unlevered equity, the beta of debt, and
the marginal tax rate
E,L
=
✓
D
1+
(1
EL
TC )
◆
E,U
(1
TC ) ⇥
D
EL
D
In the special case where the beta of debt is zero (βD=0)
E,L
=
✓
D
1+
(1
EL
TC )
◆
E,U
D/E is called the debt-to-equity ratio.
:
:
157
Estimating a cost of equity
Estimating a levered cost of equity for a project or rm is a multiple step
process
1. Find a set of single industry (pure play) rms
2. Estimate the beta for these rms. This is a levered beta
3. Compute the unlevered cost of equity for each rm based on each rm’s debt-toequity ratio and tax rate
4. Average the unlevered cost of equity to estimate the project/ rm cost of unlevered
equity
5. Compute the levered cost of equity for the project or rm using the estimate from
step 4 and the appropriate tax rate.
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158
Leverage and the cost of capital with taxes
One common approach to estimate a WACC for any prospective amount of
leverage
•
•
Estimate a cost of debt based on the rm’s ability to make interest payments
Determine a “levered” beta for the ordinary equity that accounts for leverage and the
“unlevered” risk of the project/ r
Note that this approach has a few internal inconsistencies
•
Debt provides yields above the risk-free rate, but is generally considered risk-less
when leveraging beta
•
The nal rm valuation may deviate from the leverage assumptions (i.e. assuming
$100m in debt with 20% a debt-value ratio yields a WACC that gives a rm value
above $500 million). One should verify that the nal valuation supports the leverage
assumptions.
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159
Example
A rm is considering recapitalising by issuing debt to repurchase equity
•
•
•
It currently has $5 billion of debt and $8 billion of equity outstanding
Its pre-tax cost of debt is 8%, its current beta is 0.5, and it pays taxes at 30%
The risk-free rate is 4% and the market risk premium is 6%
What will be the cost of common equity if it issues $4 billion of debt and the issue does not
change the total rm market capitalisation?
.
:
.
.
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160
UNSW Business School
School of Banking and Finance
FINS1613: Business Finance
2021 Term 2
Week 10:
Payout Policy and Course Summary
Payout Policy
162
A rm with positive free cash ows must decided whether to retain the cash
ows or distribute them to investors
Free cash ow
Retain
Invest in new
projects
Distribute
Increase cash
reserves
Pay dividends
Repurchase shares
Investors ultimately would like the rm to make the decision that
best increases the value of their investment.
:
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163
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Cash distributions
Reinvestment
164
The ef cient markets hypothesis suggests that competition eliminates positive
NPV trading opportunities until all information is in security prices
•
Expectations about cash ows and discount rates are determined by information
known to investors
•
Security trading and the forces of supply and demand ensures that information is
re ected in security prices
•
Security prices are the best estimate of the discounted value of expected future cash
ows.
.
.
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165
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Ef cient capital markets
Ef cient capital markets
Public, easily interpretable information
•
Known to all investors who can determine how the information affects cash ows
and discount rate
•
Should be re ected in security prices due to security trading and the forces of supply
and deman
•
Examples include news reports, nancial statements, press reports, etc
Private or dif cult to interpret information
•
Investors may be able to use private information to trade pro tably. However, trading
will cause prices to shift until the information is re ected in security prices
•
Dif cult to interpret information may slowly enter security prices allowing temporary
pro table trading opportunities.
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166
Reinvestment example problem
Consider two rms that are trying to decide if they should pay cash to investors or reinvest in new
projects. Assume all positive cash ows begin at t=1 and have a 10% cost of capital
Firm A
•
•
•
Cash balance of $1 billion
Current projects generates $250 million in perpetuity
Has a new project that requires $1 billion today and generates cash ows of $150 million in perpetuity. This
project has not been announced and is not yet priced to market participants
Firm B
•
•
•
Cash balance of $1 billion
Current projects generate $1 billion in perpetuity
Has a project that requires $1 billion today and generates cash ows of $500 million in perpetuity. This project has
not been announced and is not yet priced to market participants
.
.
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.
fl
.
.
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167
Reinvestment
When a rm reinvests cash in a positive NPV project
•
•
Investors recognise the effect of the decision on cash ow
•
•
The NPV accrues to the rm’s current owner
Supply and demand ensure that the security prices adjust to re ect the fair value of
the cash ows (assuming capital markets are ef cient)
The rm’s current owners bene t in the form of abnormal security returns
above the risk-adjusted cost of capital
Firms should always reinvest cash ows in positive NPV projects;
this is the best option to increase the value of ownership.
:
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168
Reinvestment
A rm should always use available free cash ows to invest in positive NPV
projects. Afterwards, it may choose to either
•
Retain cash ows and purchase nancial assets so as to have money when positiveNPV investments arise
•
Payout cash ows to investors
:
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169
Cash reserves
170
Perfect capital markets
Perfect capital markets do not have friction
•
•
Taxes do not exist.
•
•
•
Security prices are fair, re ecting the present value of future cash ows
Administration is not costly for the rm. It can negotiate with bond holders and
recapitalise without affecting either projects or rm values
There are no costs affecting the issuance of new securities, securities trading, etc
Financing decisions are independent of project cash ows.
.
.
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.
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171
Cash reserves and payout in perfect capital markets
After reinvesting in all positive NPV projects, a rm is trying to decide if it should
(i) distribute the remaining cash reserve to investors or (ii) invest on behalf of
investors and then distribute. In perfect capital markets, how are investors
best served
Retain:
Firm
Cash
Invest in nancial
asset
Realise returns
Investors
Distribute
Distribute:
Firm
Cash
Investors
Distribute
Invest in nancial
asset
Realise returns
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?
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172
Retention and payout in perfect capital markets
Modigliani and Miller (MM) provide yet an important observation that is a direct
consequences of the perfect capital markets assumption
MM payout irrelevance
In perfect capital markets, if a rm invests excess cash ows in nancial securities, the choice of
payout versus retention is irrelevant and does not affect the initial value of the rm
In perfect capital, all investments have zero NPV and payouts are untaxed.
It does not matter whether a rm or its owners purchase securities.
.
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173
Cash reserves and payout with taxes
After reinvesting in all positive NPV projects, a rm is trying to decide if it should (i) distribute
the remaining cash reserve to investors or (ii) invest on behalf of investors and then distribute.
For simplicity, assume that both dividends and capital gains are taxed at Ti for investors and Tc
for corporations. Are investors better off if the rm retains or distributes cash?
Retain:
Firm
$1 + r(1
$1
Invest in nancial
asset
Cash
($1 + r(1
Distribute:
$1
Firm
Cash
Investors
Distribute and pay
taxes
$1 ⇥ (1
Invest in nancial
asset
fi
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s
TC )) ⇥ (1
TI )
Realise returns and
pay taxes
$1 ⇥ (1
TI )
174
fi
Realise return
and pay taxes
Distribute and pay
taxes
Investors
fi
TC )
TI ) ⇥ (1 + r(1
TI ))
After reinvesting in all positive NPV projects, a rm is trying to decide if it should
distribute the remaining cash reserve to investors. The rm
•
•
Cash reserves are $100 million
•
If it retains cash, the will invest in the a risk-free asset yielding 3%. Investors that
receive distributed cash are expected to invest in the risk-free asset
•
In one year, there is a 50% chance that a research and development will yield a
project that requires $103 million upfront and generates $25 million per year starting
at t=2 in perpetuity at a 10% discount rate.
•
Issuance costs are 10% of capital raised
Current projects generates $250 million starting at t=1 in perpetuity at a cost of
capital of 5%
Ignoring taxes and assuming that we can use the 50% probability to determine
rm value, are investors better off if the rm retains or distributes cash?
:
.
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.
.
175
.
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Cash reserves for future projects example problem
Cash reserves for future projects example problem
Today
One Year
Firm’s existing
projects
Firm’s existing
projects
Retain:
Firm Cash
Firm Cash
50% probability
Use cash to fund
project
50% probability
Risk free investment
Distribute:
Firm’s existing
projects
Firm’s existing
projects
Raise capital to
fund project
Distribution
Investor Cash
Risk free investment
176
Investor Cash
50% probability
Imperfect capital markets
Firms may choose to retain cash for several factors
•
Taxes: Firm should invest on behalf of shareholders if the rm pays a lower marginal
tax rate than shareholders
•
Future shortfalls: Firms may retain cash to fund future projects, avoiding issuance
costs. Extra cash also provides a cushion against nancial distress
However, there are costs of having excess cash
Agency costs: Firms may use excess cash inef ciently (e.g. money-losing pet
projects, executive perks, or overpaying for acquisitions)
.
…
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177
.
•
Cash reserves
When a rm retains cash to build cash reserves
•
•
Investors recognise the effect of the decision on cash ow
•
The rm’s current owners bene t may bene t from a reduction in expected
future issuance and distress costs, but can suffer from increased agency costs
Supply and demand ensure that the security prices adjust to re ect the fair value of
the cash ows (assuming capital markets are ef cient)
Firms may build cash reserves in real capital markets, but should
consider the costs and bene ts of doing so.
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178
Payouts: Dividends and repurchases
in perfect capital markets
179
Distribution
If a rm distributes cash to investors
•
Investors receive cash through either a dividend or share repurchase and must pay
taxe
•
•
Investors must nd new investment
•
The rm’s current owners do not earn abnormal returns
New investments return on average the risk-adjusted cost of capital (assuming capital
markets are ef cient
Distributions are the only way for rms to return cash to investors. Investors
must then determine what to do with the money received.
:
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180
Taxes on dividends and capital gains
Distributions
Pay dividends
Repurchase shares
181
Dividend timeline
} Dividend “value”
Price
Time
Declaration
Ex-dividend
Record
Payment
Important dates for dividend payments
-
Declaration date: Board authorises dividend and rm is obligated to pay
Ex-dividend and record date: To receive a dividend, the share must be
purchased before the ex-dividend date and still owned on the record date. Stock
price adjusts when investors are eligible to receive the dividend — the exdividend date
Payable (distribution) date: Date payment is received by shareholders.
.
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182
Dividends and repurchases
Example problem
A rm has $20 million in cash available for payouts and projects that have a present value of
$48 million. There are 10 million shares outstanding
Option 1: If the rm pays announces it pay the cash as a dividend, what is the value of the
investment before the ex-dividend date? After the ex-dividend date
?
.
:
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183
Repurchase timeline
Price
Time
Repurchase
Announcement
Repurchase
Important dates for share repurchases
-
Announcement: Company announces it will conduct repurchases, but is not
obligated to do so
Repurchases: Generally occur over a period of time. These should not the
affect stock price.
:
.
184
Dividends and repurchases
Example problem
A rm has $20 million in cash available for payouts and projects that have a present value of
$48 million. There are 10 million shares outstanding
Option 2: If the rm uses the cash to repurchase shares, how many shares does it purchase?
What is the price of a share after the repurchase? Does it make a difference if you sell the
shares in perfect capital markets?
.
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185
Dividends and repurchases
Example problem
A rm has $20 million in cash available for payouts and projects that have a present value of
$48 million. There are 10 million shares outstanding
Pay dividends
Repurchase shares
7.0588 million current shareholders
10 million shareholders
-
-
Stock worth $4.80
Stock worth $6.8
2.9412 million former shareholders
Cash worth $2.00
-
Cash worth $6.80
.
:
:
:
:
0
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186
Dividends and repurchases
In perfect capital markets
•
The share price drops by the amount of the dividend when the share begins to trade
ex-dividend
•
A share repurchase through a stock exchange that is available to all shareholders
(open market repurchase) has no effect on the share price.
:
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187
Payout policy in perfect capital markets
Modigliani and Miller (MM) provided an important observation that is a direct
consequences of the perfect capital markets assumption
MM dividend irrelevance
In perfect capital markets, holding xed the investment policy of a rm, the rm’s choice of
dividend policy is irrelevant and does not affect the share price
Firm value ultimately derives from free cash ows. In perfect
capital markets, it does not matter whether payouts are through
dividends or share repurchases.
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188
Payouts: Dividends and repurchases
with personal taxes
189
Taxes on dividends and capital gains
Distributions
Pay dividends
Repurchase shares
Dividends
Repurchases
•
Treated as income, taxed at
marginal tax rat
•
Selling shareholders pay taxes at
the capital gain rat
•
May have franking credit in
imputation tax system. “Double
taxation” in classical tax system.
•
No difference between imputation
and classical tax systems
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190
Franking credit
De nition
A tax credit transfer to shareholders for the amount of tax the company has paid in an
imputation tax system. The franking credit is used by shareholders to reduce his or her own tax
liability, with any excess paid back as a refund. Only available to resident tax payers in Australia.
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191
Dividend taxation and tax systems
Dividend taxation depends on the tax system
Classical: Personal tax based on after-tax dividends to a shareholder
Imputation: Personal tax based on pre-tax net pro t with a credit for corporate tax.
Tax system
Classic
Imputation
Classic
Imputation
Classic
Imputation
Company tax rate
30%
30%
30%
Marginal personal tax rate
45%
30%
15%
Company
Net profit before tax
1.000
1.000
1.000
1.000
1.000
1.000
Corporate tax
-0.300
-0.300
-0.300
-0.300
-0.300
-0.300
Net profit after tax
0.700
0.700
0.700
0.700
0.700
0.700
Shareholder
Dividend before tax
0.700
0.700
0.700
0.700
0.700
0.700
Taxable income
0.700
1.000
0.700
1.000
0.700
1.000
Personal tax
-0.315
-0.450
-0.210
-0.300
-0.105
-0.150
Franking credit
0.300
0.300
0.300
Tax payable
-0.315
-0.150
-0.210
0.000
-0.105
0.150
Income after tax
0.385
0.550
0.490
0.700
0.595
0.850
.
:
192
fi
•
•
Capital gain taxation and share holding period
Capital gain taxation depends on the length of time a share is held
Less than one year: Taxes based on marginal tax rate (Australia)
More than one year: Taxes based on half marginal rate (Australia).
Holding period
< 1 year
Capital gain rate
> 1 year
< 1 year
45%
> 1 year
< 1 year
30%
> 1 year
15%
Shareholder
Gain on sale of share
0.700
0.700
⨉½ 0.700
0.700
0.700
0.700
Taxable component
0.700
0.350
0.700
0.350
0.700
0.350
Capital gain tax
-0.315
-0.158
-0.210
-0.105
-0.105
-0.053
Income after tax
0.385
0.543
0.490
0.595
0.595
0.648
Note: Tax regimes vary worldwide. In the U.S., short-term gains (<1 year)
taxed as income, most long-term gains (>1 year) taxed at about 20%.
:
193
.
•
•
Dividends versus capital gains
The income for the investor after taxes depends on
•
•
•
Method of distribution: Dividends vs. repurchase
Tax system: Imputation vs. classica
Length of time the shares are hel
Comparing the systems — capital gain equal to marginal personal tax rates:
Tax system
Classic
Imputation
Classic
Imputation
Classic
Imputation
Company tax rate
30%
30%
30%
Marginal personal tax rate
45%
30%
15%
Capital gain rate
45%
30%
15%
Amount received by investor on $0.70 distribution
Dividends
0.385
0.550
0.490
0.700
0.595
0.850
Repurchase (> 1yr)
0.543
0.543
0.595
0.595
0.648
0.648
Note: This comparison assumes the marginal personal tax rate and the capital gain
rate are equal. This is just for illustrative purposes. Rates vary globally.
:
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194
Dividends versus capital gains
Optimal payout policy suggests rms should maximise the money received by
investors. This suggests payment by
•
Dividends: When the personal tax payable on dividends is less than the personal tax
payable on capital gains
•
Repurchases: When the personal tax payable on dividends is more than the personal tax
payable on capital gains
Payout policies appear to re ect investor preferences
•
Relatively low taxes on dividends induced by Australia’s switch to the imputation
system in 1987 led to increased dividend payments
•
Relatively low capital gain rates in the U.S. have led to increased share repurchases.
:
.
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.
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195
Payouts: Dividend and
repurchase signalling
196
Imperfect capital markets
Payout policy will also be in uenced by investor perceptions. Firm “smooth”
dividends, setting them at a level they expect to maintain, because
•
•
Investors may prefer stable dividend
Management may prefer to set dividends as a target fraction of earning
Dividend signalling suggests changes to dividend policy provide information
to investors
•
•
Dividend cuts suggests earnings will be lower in the future
Dividend increases suggest the rm can afford greater future payout
Share repurchases are not as credible a signal as dividends
•
Repurchases are less informative about future earnings as repurchases are set
infrequently and rms do not maintain regular repurchases schedule
•
Repurchases suggest the rm is under-valued as management will not buy overpriced
shares
:
s
s
:
s
s
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:
197
Note: Dividend imputation and
the cost of equity
198
Imputation and the cost of equity capital
Dividend franking credits create a tax bene t for shareholders
•
This is similar to how rm’s realise cash ow bene ts from the tax deductibility of
interest payments
•
The imputation adjusted cost of equity is the standard cost of equity multiplied by a
scaling factor:
rE,I = rE ⇥
✓
1
1
TC
TC (1 F ⇥ ✓)
◆
where:
TC is the corporate tax rate,
F is the percent of available franking credits rms distribute, and
is the market value of a franking credit
:
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fi
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.
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199
Imputation and WACC
The imputation adjusted WACC
◆
TC
=wE ⇥ rE ⇥
1 TC (1 F ⇥ ✓)
✓
◆
1 TC
+ w P ⇥ rP ⇥
1 TC (1 F ⇥ ✓)
+ wD ⇥ rD ⇥ (1
200
:
rW ACC
✓
1
TC )
Imputation and the cost of equity capital
Studies estimate that in Australia
•
Firms pay approximately 70% of available franking credits (F=0.70)
(Hathaway and Of cer (2004) for ATO)
•
Estimates of the market value of a franking credit differ widely. Available studies
provide estimates of between 0 and 0.81
•
Using F=0.7, =0.55, andTC=0.3 suggests that the imputation corrected cost of
equity is about 86% of the standard cost of equity.
.
:
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201
Imputation and the cost of equity capital
Market practice does not adjust for the value of franking credits
•
85% of those surveyed in Australia by Truong, Partington, and Peat (2008) do no
adjust the cost of equity for franking credits1
•
•
•
Leads to incorrectly high discount rates being used when valuing project and rms
Suggests rms may attach negative values to positive NPV project
Firms may not invest in positive NPV projects as a result
1 Truong, G., Partington, G., and
Peat, M, Cost-of-capital estimation and capital-budgeting
practice in Australia, Australian Journal of Management, 2008, 33 (1), 95 -121.
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202
Putting it all together: Free
cash ow models
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203
Discounted free cash ow model (Project)
Discounted free cash ow models are the workhorse models in project
valuation
1. Determine pro forma incremental earnings, capital expenditures, depreciation, working
capital needs, and salvage for a project (Cash Flows: Topic 6)
2. Compute free cash ows (Cash ows: Topic 6)
3. Determine the debt-equity mix and corresponding weighted average cost of capital
that captures the appropriate risk of the project cash ows (Cost of capital: Topic 8)
- Debt:Yield to maturity (Loans and Bonds: Topic 3)
- Equity: Use CAPM with levered beta appropriate for project risk (Equity: Topic 4,
Risk & Return/CAPM: Topic 7
- Preference shares: Implied discount rate from dividend growth model (Equity:
Topic 4
4. Compute a net present value and decide if the project is worth pursuing (Financial
Mathematics: Topic 2, Investment decision rules: Topic 5
5. Determine cash retention and payout policy (Payout policy: Topic 9)
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)
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)
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:
)
204
Discounted free cash ow model (Firm)
Discounted free cash ow models are also the workhorse models in rm
valuation
1. Determine pro forma incremental earnings, capital expenditures, depreciation, working
capital, and salvage for the rm (Cash Flows: Topic 6)
2. Compute free cash ows (Cash ows: Topic 6)
3. Determine the debt-equity mix and corresponding weighted average cost of capital
that captures the appropriate risk of the total rm cash ows (Cost of capital: Topic
8)
- Debt:Yield to maturity (Loans and Bonds: Topic 3
- Equity: Use CAPM with levered beta appropriate for rm risk (Equity: Topic 4,
Risk & Return/CAPM: Topic 7)
- Preference shares: Implied discount rate from dividend growth model (Equity:
Topic 4)
4. Compute a net present value, which is the enterprise value of the rm (Financial
Mathematics: Topic 2, Investment decision rules: Topic 5)
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)
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:
205
Free cash ow model (Firm)
Once the enterprise value has been obtained the total market value of the rm’s
securities can be calculated
M arket V alue Equity + M arket V alue Debt = Enterprise V alue + Cash
This is often used to “price” shares, where an investor determines their own
value of the shares:
P rice per share =
Enterprise V alue + Cash M arket V alue Debt
N umber of Shares Outstanding
:
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206