Description
company and project costs of capital, measuring the Cost of Equity, capital structure and Cost of capital, discount Rates for International Projects, estimating discount rates, Risk and discounted cashflow method.
? Company and Project Costs of Capital
? Measuring the Cost of Equity
? Capital Structure and COC
? Discount Rates for Intl. Projects
? Estimating Discount Rates
? Risk and DCF
? Maximize the wealth of the
Shareholders
? Pursue strategies, goals and policies
to maximize market cap or wealth
? Increase the value of the firm
? Almost everything we do in Corp. Fin.
relies on valuation in some form or
the other
? Analyzing an investment or project or
any decision
? Decisions
? how to finance investments
? whether Debt or Equity
? Whether to return the money to
shareholders or reinvest in business
? It is the variability of actual return from
expected returns associated with that
Security.
? Project risk
? Competitive Risk
? Sector/ Industry Risk
? Exchange rate risk
? Political risk
? Interest rate risk
? Inflation risk
? Cyclical industry – economic risks
? Treasury bills - as safe an investment as you can
make. No risk of default. Their short maturity
means that the prices of Treasury bills are
relatively stable.
? Long term G-Bonds – investor acquires an asset
whose price fluctuates as interest rates vary.
Bond prices fall when interest rates increase and
vice versa
? Corporate Bonds – accept additional default risk
? Common Stocks – direct share in the risk of the
enterprise
Variance - Average value of squared
deviations from mean. A measure of
volatility.
Standard Deviation - Average value of
squared deviations from mean. A
measure of volatility.
? Are Std. Dev. And rate of return in same
unit?
? What is the std. for certain outcome?
? What is the SD, if we don’t know the
what will happen?
? Are portfolios with histories of high
variability predictable?
? If you hold the security/ portfolio longer
what would happen?
? Std. deviation is in the same unit as the rate of
return.
? Std. deviation for certain outcome is?
? It is positive when we don’t know what will
happen.
? Reasonable to assume that portfolio with
histories of high variability also have the least
predictability.
? The longer the security/ portfolio you hold the
more risk you have taken.
? Variance is approximately proportional to the
length of time interval over which a security or
portfolio is measured.
? Std. deviation is proportional to the square root
of the interval.
What should be the strategy to reduce
risk?
What is Unique Risk?
What is Market Risk?
2
2
2
2
2 1 12 2 1
12 2 1
2 1 12 2 1
12 2 1 2
1
2
1
? x
? ? ? x x
? x x
2 Stock
? ? ? x x
? x x
? x 1 Stock
2 Stock 1 Stock
=
=
The variance of a two stock portfolio is the sum of these four boxes
) r x ( ) r (x Return Portfolio Expected
2 2 1 1
+ =
) ? ? ? x x ( 2 ? x ? x Variance Portfolio
2 1 12 2 1
2
2
2
2
2
1
2
1
+ + =
Example
Suppose you invest 65% of your portfolio in
Coca-Cola and 35% in Reebok. The expected
dollar return on your CC is 10% and on
Reebok it is 20%. Calculate the expected
return on your portfolio. Assume a correlation
coefficient of 1 and calculate the portfolio risk,
if ? for Coca Cola is 31.5% and ? for Reebok
is 58.5%.
2 2 2
2
2
2
2 1 12 2 1
2 1 12 2 1 2 2 2
1
2
1
) 5 . 58 ( ) 35 (. ? x
5 . 58 5 . 31 1
35 . 65 . ? ? ? x x
Reebok
5 . 58 5 . 31 1
35 . 65 . ? ? ? x x
) 5 . 31 ( ) 65 (. ? x Cola - Coca
Reebok Cola - Coca
× =
× × ×
× =
× × ×
× =
× =
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in
Reebok. The expected dollar return on your CC is 10% x 65% = 6.5%
and on Reebok it is 20% x 35% = 7.0%. The expected return on your
portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in
Reebok. The expected dollar return on your CC is 10% x 65% = 6.5%
and on Reebok it is 20% x 35% = 7.0%. The expected return on your
portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
% 31.7 1,006.1 Deviation Standard
1 . 006 , 1 5) 1x31.5x58. 2(.65x.35x
] x(58.5) [(.35)
] x(31.5) [(.65) Valriance Portfolio
2 2
2 2
= =
= +
+
=
What is Market Portfolio?
What is Beta?
beta
Expected
return
Expected
market
return
10% 10% - +
+10%
stock
-10%
1. Total risk =
diversifiable risk +
market risk
2. Market risk is
measured by beta,
the sensitivity to
market changes
2
m
im
i
B
o
o
=
Covariance with the
market
Variance of the market
It turns out that this covariance to variance ratio measures a stock’s contribution to
portfolio risk.
? Stock’s contribution to portfolio risk
will depend on its relative importance
in the portfolio and the average
covariance with the stocks in the
portfolio.
? The proportion depends on the size of
the holding and a measure of the effect
of that holding on portfolio risk. The
latter values are ?s of individual stocks
relative to that portfolio.
0
5 10 15
Number of Securities
P
o
r
t
f
o
l
i
o
s
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
Market risk
Unique
risk
? No. Rational investors will minimize risk
by holding portfolios.
? They bear only market risk, so prices and
returns reflect this lower risk.
? The one-stock investor bears higher
(stand-alone) risk, so the return is less
than that required by the risk.
Can an investor holding one stock earn
a return commensurate with its risk?
? Market risk, which is relevant for stocks
held in well-diversified portfolios, is
defined as the contribution of a security to
the overall riskiness of the portfolio.
? It is measured by a stock’s beta coefficient,
which measures the stock’s volatility
relative to the market.
? What is the relevant risk for a stock held in
isolation?
How is market risk measured for
individual securities?
? Valuing firms/ assets, discount rate
should reflect risk in the investment
? A good model provided us with tools to
measure the risk in any investment &
uses that risk measure to come up with
the appropriate expected return on that
investment.
? Returns & Std. Deviations
Particular Return Std.
Dev.
T-Bills 6% 0%
ABC 10 14
DEF 14.5 28
GHI 21 26
Calculate the portfolio of the following portfolio:
? 50% T-bills 50% ABC
? 50% DEF 50% GHI assuming the shares have
? Perfect +ve correlation
? Perfect –ve correlation
? No correlation
? 7%
? 27%
? 1%
? 19.1%
? A game offers the following odds and pay
offs. Each game costs Rs. 100.
Probability Payoff
10% 500
50% 100
40% 0
What are the expected cash payoffs and
expected rate of return?
Calculate the variance and standard deviation
of this rate of return.
27
? Expected cash payoffs – 100
? Expected rate of return – 0
? Variance – 20,000
? Standard deviation – 141%
28
? Ritesh Modi, Head of Aum Mutual Fund, has
produced the following rates of return from 2003 to
2007. Rates of return of BSE 100 have been given
for comparison
Year Modi(%) BSE 100(%)
2003 16.1 23.1
2004 28.4 33.4
2005 25.1 28.6
2006 14.3 21.0
2007 -6.0 -9.1
? Calculate Modi’s average return and standard
deviation.
? Did he do better or worse than BSE 100 by these
measures?
29
? Result Modi BSE
100
Average return 15.6 19.4
Standard deviation 12.0 14.9
30
? State whether True or False
1. Investors prefer diversified companies because they
are less risky
2. If stocks were perfectly positively correlated,
diversification would not reduce risk
3. The contribution of a stock to the risk of a well
diversified portfolio depends in its market risk
4. A well diversified portfolio with a beta 2 is twice as
risky as the market portfolio
5. An undiversified portfolio with a beta of 2 is less
than twice as risky as the market portfolio
31
? F
? T
? T
? T
? F
32
? Suppose stand deviation of the market
return is 20%.
1. What is the standard deviation of returns
of a well diversified portfolio with beta
1.3 another with beta 0.
2. A well diversified portfolio having
standard deviation of 15%, what is its
beta.
33
1. Beta 1.3 - 26%
Beta 0 – 0%
2. Standard deviation 15% Beta – 0.75
34
? Combining stocks into portfolios can
reduce standard deviation, below the level
obtained from a simple weighted average
calculation.
? Correlation coefficients make this
possible.
? The various weighted combinations of
stocks that create this standard deviations
constitute the set of efficient portfolios.
Coca Cola
Reebok
Standard Deviation
Expected Return (%)
35% in Reebok
? Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks
Standard Deviation
Expected Return (%)
Each half egg shell represents the possible weighted combinations for two
stocks.
The composite of all stock sets constitutes the efficient frontier
? Expected return is simply a weighted average of the
expected return in the holding.
? The risk of the portfolio is less than the average risk of
the separate stocks.
? Markowitz – efficient portfolio – along solid enveloping
line
? Problem of rationing – to deploy a limited amount of
capital to capital investment in a mixture of projects to
give the highest NPV. Here we deploy investors funds to
give the highest expected return for a given std. dev.
Solution using quadratic programming
? Given the expected return & std. dev of each stock, as
well as correlation between each pair of stocks, we can
calculate a set of efficient portfolios using quadratic
program
? If stocks are highly correlated they offer less
diversification benefits
Limitations of this theory
? Requires very large number of inputs –
co-variances
? Ignores riskfree T-bills in coming up
with optimum portfolio
Standard Deviation
Expected Return (%)
•Lending or Borrowing at the risk free rate (r
f
) allows us to exist outside the
efficient frontier.
r
f
T
S
? Start with the vertical axis at Rf and draw the steepest
line or tangent to the curved heavy line of efficient
portfolios. The efficient portfolio at the tangency point
is better than all others. It offers the highest ratio of
risk premium to std. dev.
? Best portfolio of common stock must be selected S.
? This portfolio must be blended with borrowing or lending
to obtain an exposure to risk that suits the particular
investors’ taste.
? Each investor must therefore put money in 2
benchmark investments – risky portfolio S and risk free
loan (lending or borrowing) T-bills
? Portfolio S is the point of tangency to the set of
efficient portfolios. It offers the highest expected risk
premium (r – Rf) per unit of std. dev.
Return
BETA
r
f
1.0
SML
SML Equation = r
f
+ B ( r
m
- r
f
)
R = r
f
+ B ( r
m
- r
f
)
CAPM
? It is defined as the expected return on
a portfolio of all company’s existing
assets/ securities.
? It is used to discount cash flows on
projects that have similar risk to that
firm as a whole
? A firm’s value can be stated as the sum
of the value of its various assets
? Is it the correct discounting rate if the new projects are
more or less risky than the firm’s existing business?
? No
? Each project should in principle be evaluated at its own
opportunity cost of capital.
? How is a firm’s value can be stated as the sum of the
value of its various assets?
? True cost of capital depends on the use to which the
capital is put.
PV(B) PV(A) PV(AB) value Firm + = =
10% nology known tech t, improvemen Cost
COC) (Company 15% business existing of Expansion
20% products New
30% ventures e Speculativ
Rate Discount Category
? A company’s cost of capital can be
compared to the CAPM required return
Required
return
Project Beta
1.26
Company Cost of
Capital
13
5.5
0
SML
? Company’s cost of capital rule: Accept any project
regardless of its risk as long as it offers a higher
returns than the company’s cost of capital –
comment on it
Required
return
Project Beta
1.26
Company Cost of
Capital
13
5.5
0
SML
? Firms raise money both from equity
investors and lenders to fund
investments
? Both require returns
? Why is company’s cost of capital
estimated?
? For projects that are of average risk –the
average of company’s other assets.
? The company cost of capital is a useful
starting point for setting discount rates
for unusual risky or safe projects.
? It is easier to add up or subtract from the
company cost of capital than the estimate
project capital from scratch.
? Businessmen have good intuition about
relative risks.
? As long as firms are growing rapidly,
they do not need to know their costs of
equity or capital. Is this statement true?
Why or why not?
? It is the rate of return investors require
on an equity investment in a firm
? This expected return of equity includes
compensation for market risk in the
investment and its cost of equity.
? Expected Return = Riskfree rate + Beta X
Risk Premium
? What are the conditions for risk-free
rate?
? No default risk
? No uncertainty of reinvestment rate
? Should we use short term or long term
Government Bond rate as risk free rate?
? It depends on when the cash flows
come due – for a 5 year project we
require 5 year riskfree rate and not 6
month riskfree rate
? The riskfree rate is the rate on zero
coupon Govt. bonds that matches
being analyzed.
? What is the Risk Premium suppose to
measure?
? It measures return that would be
demanded by investors for shifting their
money from a riskfree investment to an
average risk investment
? It should be a function of how risk
averse investors are & how risky they
perceive stocks to be relative to riskfree
investment
? Look at past & estimate the premium
earned by stocks over riskfree investors
(historic premiums)
? Use the premium extracted by looking at
how markets price risky assets today
(implied premium)
? Should we use Arithmetic or Geometric
averages while estimating?
? CAPM is based average returns
? Variance is estimated around arithmetic
average
? Assumption – overall market prices
stocks correctly
? Using P
0
= D
1
/(r-g),
where P
0
is known
D
1
– estimated by market
g – estimated by analysts
? Advantages
? Market Driven
? Current
? Does not require historical data
? Bounded
? Whether valuation model is appropriate
? Whether inputs are available
? Whether market has correctly priced the
stock currently
? Assume that the implied premium is 3%
and that you are using a historical
premium of 7.5%. If you value a stock
using historical premium, are you likely
to find more under- or over-valued
stock? Why?
? The SML shows the relationship between
return and risk
? CAPM uses Beta as a proxy for risk
R = R
f
+ B(R
m
– R
f
)
? Other methods can be employed to
determine the slope of the SML and thus
Beta
? Regression analysis can be used to find
Beta
? Run a regression with returns on the
stock in question plotted on the Y axis
and returns on the market portfolio
plotted on the X axis.
? The slope of the regression line, which
measures relative volatility, is defined
as the stock’s beta coefficient, or b.
Dell Computer
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
D
e
l
l
r
e
t
u
r
n
(
%
)
R
2
= .11
B = 1.62
Dell Computer
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
D
e
l
l
r
e
t
u
r
n
(
%
)
R
2
= .27
B = 2.02
General Motors
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
G
M
r
e
t
u
r
n
(
%
)
R
2
= .13
B = 0.80
General Motors
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
G
M
r
e
t
u
r
n
(
%
)
R
2
= .25
B = 1.00
Exxon Mobil
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
E
x
x
o
n
M
o
b
i
l
r
e
t
u
r
n
(
%
)
R
2
= .28
B = 0.52
Exxon Mobil
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
E
x
x
o
n
M
o
b
i
l
r
e
t
u
r
n
(
%
)
R
2
= .16
B = 0.42
? What does R squared measure?
– measures the proportions of the total variance in the
stock’s return that can be explained by market
movements.
? What does then (1 – R squared) measure?
- measures the proportions of the total variance in the
stock’s return that can be explained by unique risk.
? What is Standard error?
– shows the extent of possible mis-measurement
? What is Confidence interval?
- estimated values plus or minus 2 standard errors
? A firm that has a beta = 1 has average
market risk. The stock is no more or less
volatile than the market.
? A firm with a beta > 1 is more volatile than
the market.
? (ex: technology firms)
? A firm with a beta < 1 is less volatile than the
market.
? (ex: utilities)
? Assume that both Tata Steel and Biocon
have beta of 0.96. Tata Steel has R
square of 30% and Biocon has only 10%.
If you were a well diversified investor,
which of the 2 stocks will you prefer in
your portfolio? If you were not well
diversified, which one of these would you
prefer?
? Company Cost of Capital (COC) is based
on the average beta of the assets
? The average Beta of the assets is based
on the % of funds in each asset
Example
1/3 New Ventures B=2.0
1/3 Expand existing business B=1.3
1/3 Plant efficiency B=0.6
AVG B of assets = 1.3
What is Capital Structure?
- the mix of debt & equity within a company
Expand CAPM to include Capital Structure
R = r
f
+ B ( r
m
- r
f
)
becomes
R
equity
= r
f
+ B ( r
m
- r
f
)
COC
=
r
portfolio
= r
assets
r
assets
= WACC = r
debt
(D) + r
equity
(E)
(V) (V)
B
assets
= B
debt
(D) + B
equity
(E)
(V) (V)
r
equity
= r
f
+ B
equity
( r
m
- r
f
)
IMPORTANT
E, D, and V are all
market values
0
20
0 0.2 0.8 1.2
Expected
return (%)
B
debt
B
assets
B
equity
R
rdebt
=8
R
assets
=12.2
R
equity
=15
Expected Returns and Betas prior to refinancing
R
equity
= Return on Stock
= 15%
R
debt
= YTM on bonds
= 7.5 %
.17 .50 Portfolio Industry
.21 .40 Pacific Union
.26 .52 Southern Norfolk
.24 .46 tion Transporta CSX
.20 .64 Northern Burlington
Error Standard. Beta
? The estimated industry beta is more
reliable.
? It shows lower standard error.
? R
f
= 3.5%
? R
m
= 8%
? B (Union) = 0.4
? B (Industry) = 0.5
? Expected Return = ?
? E(r) = R
f
+ B (Industry) x (R
m
– R
f
)
? = 7.75%
Example
100 value Firm Assets Total
70 ue Equity val
30 Debt value 100 Assets
% 75 . 12 % 15
70 30
70
% 5 . 7
70 30
30
=
+
+
+
=
+
+
+
=
assets
equity debt assets
R
r
equity debt
equity
r
equity debt
debt
R
The following table summarizes the unlevered betas for
publicly traded software firms.
Grouping Number of Beta D/E Ratio
Unlevered Firms
Beta
All Software 264 1.45 3.70% 1.42
Small-cap Software 125 1.54 10.12% 1.45
Entertainment Software 31 1.50 7.09%
1.43
? We will use the beta of entertainment software firms as
the unlevered beta for InfoSoft.
? We will also assume that InfoSoft’s D/E ratio will be
similar to that of these publicly traded firms (D/E =
7.09%)
? Beta for InfoSoft = 1.43 (1 + (1-.42) (.0709)) = 1.49
(Assumption: tax rate of 42%)
? Adjust the beta to reflect total risk rather than market
risk. This adjustment is a relatively simple one, since
the R squared of the regression measures the
proportion of the risk that is market risk.
Total Beta = Market Beta / ?R squared
? In the InfoSoft example, where the market beta is 1.10
and the average R-squared of the comparable publicly
traded firms is 16%,
? Total Beta = 1.49/?0.16 = 3.725
? Total Cost of Equity = 5% + 3.725 (5.5%)= 25.49%
? This cost of equity is much higher than the cost of
equity based upon the market beta because the owners
of the firm are not diversified.
0.77 .30 2.58 Venezuela
1.39 .48 2.91 Thailand
0.81 .42 1.93 Poland
0.55 .18 3.11 Egypt
Beta
t coefficien
n Correlatio
Ratio o
Source: The Brattle Group, Inc.
s Ratio - Ratio of standard deviations, country index vs. S&P composite
index
? Much of cyclical industries risk reflects
unique or diversifiable risk.
? Measure it by accounting betas or cash
flow betas – changes in book earnings or
cash flows instead of rates of returns on
securities
? Tend to have high betas
? Cash flow = revenue – fixed costs –
variable cost
? PV (assets) = PV (revenue) – PV (fixed
costs) – PV (variable cost)
? PV (revenue) = PV (fixed costs) + PV
(variable cost) + PV (assets)
? To find asset beta, we use the previous
equation with their betas.
) PV(revenue
PV(asset)
B
) PV(revenue
cost) e PV(variabl
B
) PV(revenue
cost) PV(fixed
B B
asset cost variable
cost fixed revenue
+ +
+ =
(
¸
(
¸
÷ =
=
PV(asset)
cost) PV(fixed
1 B
PV(asset)
cost) e PV(variabl - ) PV(revenue
B B
revenue
revenue asset
Higher the ratio of fixed cost to project value – higher the project Beta
? Operating Leverage
? function of a firm’s cost structure
? defined in terms of the relationships between fixed
costs and total costs
? High fixed costs relative total costs – high
operating leverage
? A firm with high operating leverage will also
have higher variability in operating income –
will lead to higher beta
? Alternative calculations
? Degree of Operating Leverage = % change in
operating profit/ % change in sales
? Can a firm change their operating leverage?
? Suppose a firm uses its company’s cost
of capital for all project, what would be
the effect on the value of projects having
higher risk than the firm’s average risk?
? A company is financed 40% by risk-free
debt. Interest rate is 10%, expected
market return is 18% and the stock’s
beta is 0.5, what is the cost of capital?
? Market value of ORC is Rs. 60 crores and value
of debt is Rs. 40 crores, which is riskfree. B of
the stock is 1.5 expected market premium is
9%.
a) What is the expected return?
b) What is the B of the existing assets?
c) Estimate cost of capital?
d) Estimate disc. Rate for existing business
e) If it wants to diversify, the unleveraged B of
similar companies is 1.2, estimate the
required return for new business?
? A firm has the following cap str:
Security Beta Mkt. Val.
Debt 0 100
Pref. Share 0.2 40
Ordinary Eq 1.2 200
a) What is the firm’s beta
b) How would the Basset change if firm issued
additional equity of 140 to repurchase Debt &
Pref shares?
c) What should the disc rate be if firm
expands its scale of operation without
changing its asset beta? Assume rf = 5% rm =
6%
Std. Dev. R
2
B Std. err.
BP 25 .25 .90 .17
BA 38 .25 1.37 .22
a) What proportion of each was market risk & unique risk?
b) What is the variance of BP? What is the unique variance?
c) What is the confidence level on BA’s Beta?
d) If CAPM is correct, what is the expected return of BA? Rf
= 5% & Rm = 12%
e) Suppose next year the market provides a 0% return.
What return would you expect from BA?
a) Both BP and BA had R
2
values of 0.25, which
means that, for both stocks 25% of total risk
comes from movements in the market (i.e.,
market risk). Therefore, 75% of total risk is
unique risk.
b) The variance of BP is: (25)^2 = 625
Unique variance for BP is: (0.75 × 625) = 468.75
c) The t-statistic for |BA is: (0.90/0.17) = 5.29
This is significant at the 1% level, so that the
confidence level is 99%.
d) rBP = rf + |BP ×(rm - rf) = 0.05 + (1.37)×(0.12 –
0.05) = 0.1459 = 14.59%
e) rBP = rf + |BP ×(rm - rf) = 0.05 + (1.37)×(0 –
0.05) = -0.0185 = -1.85%
? Convert cash-flows to certain equivalents
(CEQ).
? Then discount it at risk-free rate.
t
f
t
t
t
r
CEQ
r
C
PV
) 1 ( ) 1 ( +
=
+
=
Example
Project A is expected to produce CF =
$100 mil for each of three years. Given
a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is
the PV of the project?
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Now assume that the
cash flows change, but
are RISK FREE. What is
the new PV?
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
240.2 PV Total
71.2 84.8 3
79.7 89.6 2
89.3 94.6 1
6% @ PV Flow Cash Year
Project B
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
240.2 PV Total
71.2 84.8 3
79.7 89.6 2
89.3 94.6 1
6% @ PV Flow Cash Year
Project B
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project? DEDUCTION FOR RISK
15.2 84.8 100 3
10.4 89.6 100 2
5.4 94.6 100 1
risk for
Deduction
CEQ Flow Cash Year
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
The difference between the 100 and the certainty equivalent (94.6)
is 5.4%…this % can be considered the annual premium on a risky
cash flow
flow cash equivalent certainty
054 . 1
flow cash Risky
=
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
8 . 84
054 . 1
100
3 Year
6 . 89
054 . 1
100
2 Year
6 . 94
054 . 1
100
1 Year
3
2
= =
= =
= =
doc_798630521.pptx
company and project costs of capital, measuring the Cost of Equity, capital structure and Cost of capital, discount Rates for International Projects, estimating discount rates, Risk and discounted cashflow method.
? Company and Project Costs of Capital
? Measuring the Cost of Equity
? Capital Structure and COC
? Discount Rates for Intl. Projects
? Estimating Discount Rates
? Risk and DCF
? Maximize the wealth of the
Shareholders
? Pursue strategies, goals and policies
to maximize market cap or wealth
? Increase the value of the firm
? Almost everything we do in Corp. Fin.
relies on valuation in some form or
the other
? Analyzing an investment or project or
any decision
? Decisions
? how to finance investments
? whether Debt or Equity
? Whether to return the money to
shareholders or reinvest in business
? It is the variability of actual return from
expected returns associated with that
Security.
? Project risk
? Competitive Risk
? Sector/ Industry Risk
? Exchange rate risk
? Political risk
? Interest rate risk
? Inflation risk
? Cyclical industry – economic risks
? Treasury bills - as safe an investment as you can
make. No risk of default. Their short maturity
means that the prices of Treasury bills are
relatively stable.
? Long term G-Bonds – investor acquires an asset
whose price fluctuates as interest rates vary.
Bond prices fall when interest rates increase and
vice versa
? Corporate Bonds – accept additional default risk
? Common Stocks – direct share in the risk of the
enterprise
Variance - Average value of squared
deviations from mean. A measure of
volatility.
Standard Deviation - Average value of
squared deviations from mean. A
measure of volatility.
? Are Std. Dev. And rate of return in same
unit?
? What is the std. for certain outcome?
? What is the SD, if we don’t know the
what will happen?
? Are portfolios with histories of high
variability predictable?
? If you hold the security/ portfolio longer
what would happen?
? Std. deviation is in the same unit as the rate of
return.
? Std. deviation for certain outcome is?
? It is positive when we don’t know what will
happen.
? Reasonable to assume that portfolio with
histories of high variability also have the least
predictability.
? The longer the security/ portfolio you hold the
more risk you have taken.
? Variance is approximately proportional to the
length of time interval over which a security or
portfolio is measured.
? Std. deviation is proportional to the square root
of the interval.
What should be the strategy to reduce
risk?
What is Unique Risk?
What is Market Risk?
2
2
2
2
2 1 12 2 1
12 2 1
2 1 12 2 1
12 2 1 2
1
2
1
? x
? ? ? x x
? x x
2 Stock
? ? ? x x
? x x
? x 1 Stock
2 Stock 1 Stock
=
=
The variance of a two stock portfolio is the sum of these four boxes
) r x ( ) r (x Return Portfolio Expected
2 2 1 1
+ =
) ? ? ? x x ( 2 ? x ? x Variance Portfolio
2 1 12 2 1
2
2
2
2
2
1
2
1
+ + =
Example
Suppose you invest 65% of your portfolio in
Coca-Cola and 35% in Reebok. The expected
dollar return on your CC is 10% and on
Reebok it is 20%. Calculate the expected
return on your portfolio. Assume a correlation
coefficient of 1 and calculate the portfolio risk,
if ? for Coca Cola is 31.5% and ? for Reebok
is 58.5%.
2 2 2
2
2
2
2 1 12 2 1
2 1 12 2 1 2 2 2
1
2
1
) 5 . 58 ( ) 35 (. ? x
5 . 58 5 . 31 1
35 . 65 . ? ? ? x x
Reebok
5 . 58 5 . 31 1
35 . 65 . ? ? ? x x
) 5 . 31 ( ) 65 (. ? x Cola - Coca
Reebok Cola - Coca
× =
× × ×
× =
× × ×
× =
× =
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in
Reebok. The expected dollar return on your CC is 10% x 65% = 6.5%
and on Reebok it is 20% x 35% = 7.0%. The expected return on your
portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
Example
Suppose you invest 65% of your portfolio in Coca-Cola and 35% in
Reebok. The expected dollar return on your CC is 10% x 65% = 6.5%
and on Reebok it is 20% x 35% = 7.0%. The expected return on your
portfolio is 6.5 + 7.0 = 13.50%. Assume a correlation coefficient of 1.
% 31.7 1,006.1 Deviation Standard
1 . 006 , 1 5) 1x31.5x58. 2(.65x.35x
] x(58.5) [(.35)
] x(31.5) [(.65) Valriance Portfolio
2 2
2 2
= =
= +
+
=
What is Market Portfolio?
What is Beta?
beta
Expected
return
Expected
market
return
10% 10% - +
+10%
stock
-10%
1. Total risk =
diversifiable risk +
market risk
2. Market risk is
measured by beta,
the sensitivity to
market changes
2
m
im
i
B
o
o
=
Covariance with the
market
Variance of the market
It turns out that this covariance to variance ratio measures a stock’s contribution to
portfolio risk.
? Stock’s contribution to portfolio risk
will depend on its relative importance
in the portfolio and the average
covariance with the stocks in the
portfolio.
? The proportion depends on the size of
the holding and a measure of the effect
of that holding on portfolio risk. The
latter values are ?s of individual stocks
relative to that portfolio.
0
5 10 15
Number of Securities
P
o
r
t
f
o
l
i
o
s
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
Market risk
Unique
risk
? No. Rational investors will minimize risk
by holding portfolios.
? They bear only market risk, so prices and
returns reflect this lower risk.
? The one-stock investor bears higher
(stand-alone) risk, so the return is less
than that required by the risk.
Can an investor holding one stock earn
a return commensurate with its risk?
? Market risk, which is relevant for stocks
held in well-diversified portfolios, is
defined as the contribution of a security to
the overall riskiness of the portfolio.
? It is measured by a stock’s beta coefficient,
which measures the stock’s volatility
relative to the market.
? What is the relevant risk for a stock held in
isolation?
How is market risk measured for
individual securities?
? Valuing firms/ assets, discount rate
should reflect risk in the investment
? A good model provided us with tools to
measure the risk in any investment &
uses that risk measure to come up with
the appropriate expected return on that
investment.
? Returns & Std. Deviations
Particular Return Std.
Dev.
T-Bills 6% 0%
ABC 10 14
DEF 14.5 28
GHI 21 26
Calculate the portfolio of the following portfolio:
? 50% T-bills 50% ABC
? 50% DEF 50% GHI assuming the shares have
? Perfect +ve correlation
? Perfect –ve correlation
? No correlation
? 7%
? 27%
? 1%
? 19.1%
? A game offers the following odds and pay
offs. Each game costs Rs. 100.
Probability Payoff
10% 500
50% 100
40% 0
What are the expected cash payoffs and
expected rate of return?
Calculate the variance and standard deviation
of this rate of return.
27
? Expected cash payoffs – 100
? Expected rate of return – 0
? Variance – 20,000
? Standard deviation – 141%
28
? Ritesh Modi, Head of Aum Mutual Fund, has
produced the following rates of return from 2003 to
2007. Rates of return of BSE 100 have been given
for comparison
Year Modi(%) BSE 100(%)
2003 16.1 23.1
2004 28.4 33.4
2005 25.1 28.6
2006 14.3 21.0
2007 -6.0 -9.1
? Calculate Modi’s average return and standard
deviation.
? Did he do better or worse than BSE 100 by these
measures?
29
? Result Modi BSE
100
Average return 15.6 19.4
Standard deviation 12.0 14.9
30
? State whether True or False
1. Investors prefer diversified companies because they
are less risky
2. If stocks were perfectly positively correlated,
diversification would not reduce risk
3. The contribution of a stock to the risk of a well
diversified portfolio depends in its market risk
4. A well diversified portfolio with a beta 2 is twice as
risky as the market portfolio
5. An undiversified portfolio with a beta of 2 is less
than twice as risky as the market portfolio
31
? F
? T
? T
? T
? F
32
? Suppose stand deviation of the market
return is 20%.
1. What is the standard deviation of returns
of a well diversified portfolio with beta
1.3 another with beta 0.
2. A well diversified portfolio having
standard deviation of 15%, what is its
beta.
33
1. Beta 1.3 - 26%
Beta 0 – 0%
2. Standard deviation 15% Beta – 0.75
34
? Combining stocks into portfolios can
reduce standard deviation, below the level
obtained from a simple weighted average
calculation.
? Correlation coefficients make this
possible.
? The various weighted combinations of
stocks that create this standard deviations
constitute the set of efficient portfolios.
Coca Cola
Reebok
Standard Deviation
Expected Return (%)
35% in Reebok
? Expected Returns and Standard Deviations vary given
different weighted combinations of the stocks
Standard Deviation
Expected Return (%)
Each half egg shell represents the possible weighted combinations for two
stocks.
The composite of all stock sets constitutes the efficient frontier
? Expected return is simply a weighted average of the
expected return in the holding.
? The risk of the portfolio is less than the average risk of
the separate stocks.
? Markowitz – efficient portfolio – along solid enveloping
line
? Problem of rationing – to deploy a limited amount of
capital to capital investment in a mixture of projects to
give the highest NPV. Here we deploy investors funds to
give the highest expected return for a given std. dev.
Solution using quadratic programming
? Given the expected return & std. dev of each stock, as
well as correlation between each pair of stocks, we can
calculate a set of efficient portfolios using quadratic
program
? If stocks are highly correlated they offer less
diversification benefits
Limitations of this theory
? Requires very large number of inputs –
co-variances
? Ignores riskfree T-bills in coming up
with optimum portfolio
Standard Deviation
Expected Return (%)
•Lending or Borrowing at the risk free rate (r
f
) allows us to exist outside the
efficient frontier.
r
f
T
S
? Start with the vertical axis at Rf and draw the steepest
line or tangent to the curved heavy line of efficient
portfolios. The efficient portfolio at the tangency point
is better than all others. It offers the highest ratio of
risk premium to std. dev.
? Best portfolio of common stock must be selected S.
? This portfolio must be blended with borrowing or lending
to obtain an exposure to risk that suits the particular
investors’ taste.
? Each investor must therefore put money in 2
benchmark investments – risky portfolio S and risk free
loan (lending or borrowing) T-bills
? Portfolio S is the point of tangency to the set of
efficient portfolios. It offers the highest expected risk
premium (r – Rf) per unit of std. dev.
Return
BETA
r
f
1.0
SML
SML Equation = r
f
+ B ( r
m
- r
f
)
R = r
f
+ B ( r
m
- r
f
)
CAPM
? It is defined as the expected return on
a portfolio of all company’s existing
assets/ securities.
? It is used to discount cash flows on
projects that have similar risk to that
firm as a whole
? A firm’s value can be stated as the sum
of the value of its various assets
? Is it the correct discounting rate if the new projects are
more or less risky than the firm’s existing business?
? No
? Each project should in principle be evaluated at its own
opportunity cost of capital.
? How is a firm’s value can be stated as the sum of the
value of its various assets?
? True cost of capital depends on the use to which the
capital is put.
PV(B) PV(A) PV(AB) value Firm + = =
10% nology known tech t, improvemen Cost
COC) (Company 15% business existing of Expansion
20% products New
30% ventures e Speculativ
Rate Discount Category
? A company’s cost of capital can be
compared to the CAPM required return
Required
return
Project Beta
1.26
Company Cost of
Capital
13
5.5
0
SML
? Company’s cost of capital rule: Accept any project
regardless of its risk as long as it offers a higher
returns than the company’s cost of capital –
comment on it
Required
return
Project Beta
1.26
Company Cost of
Capital
13
5.5
0
SML
? Firms raise money both from equity
investors and lenders to fund
investments
? Both require returns
? Why is company’s cost of capital
estimated?
? For projects that are of average risk –the
average of company’s other assets.
? The company cost of capital is a useful
starting point for setting discount rates
for unusual risky or safe projects.
? It is easier to add up or subtract from the
company cost of capital than the estimate
project capital from scratch.
? Businessmen have good intuition about
relative risks.
? As long as firms are growing rapidly,
they do not need to know their costs of
equity or capital. Is this statement true?
Why or why not?
? It is the rate of return investors require
on an equity investment in a firm
? This expected return of equity includes
compensation for market risk in the
investment and its cost of equity.
? Expected Return = Riskfree rate + Beta X
Risk Premium
? What are the conditions for risk-free
rate?
? No default risk
? No uncertainty of reinvestment rate
? Should we use short term or long term
Government Bond rate as risk free rate?
? It depends on when the cash flows
come due – for a 5 year project we
require 5 year riskfree rate and not 6
month riskfree rate
? The riskfree rate is the rate on zero
coupon Govt. bonds that matches
being analyzed.
? What is the Risk Premium suppose to
measure?
? It measures return that would be
demanded by investors for shifting their
money from a riskfree investment to an
average risk investment
? It should be a function of how risk
averse investors are & how risky they
perceive stocks to be relative to riskfree
investment
? Look at past & estimate the premium
earned by stocks over riskfree investors
(historic premiums)
? Use the premium extracted by looking at
how markets price risky assets today
(implied premium)
? Should we use Arithmetic or Geometric
averages while estimating?
? CAPM is based average returns
? Variance is estimated around arithmetic
average
? Assumption – overall market prices
stocks correctly
? Using P
0
= D
1
/(r-g),
where P
0
is known
D
1
– estimated by market
g – estimated by analysts
? Advantages
? Market Driven
? Current
? Does not require historical data
? Bounded
? Whether valuation model is appropriate
? Whether inputs are available
? Whether market has correctly priced the
stock currently
? Assume that the implied premium is 3%
and that you are using a historical
premium of 7.5%. If you value a stock
using historical premium, are you likely
to find more under- or over-valued
stock? Why?
? The SML shows the relationship between
return and risk
? CAPM uses Beta as a proxy for risk
R = R
f
+ B(R
m
– R
f
)
? Other methods can be employed to
determine the slope of the SML and thus
Beta
? Regression analysis can be used to find
Beta
? Run a regression with returns on the
stock in question plotted on the Y axis
and returns on the market portfolio
plotted on the X axis.
? The slope of the regression line, which
measures relative volatility, is defined
as the stock’s beta coefficient, or b.
Dell Computer
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
D
e
l
l
r
e
t
u
r
n
(
%
)
R
2
= .11
B = 1.62
Dell Computer
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
D
e
l
l
r
e
t
u
r
n
(
%
)
R
2
= .27
B = 2.02
General Motors
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
G
M
r
e
t
u
r
n
(
%
)
R
2
= .13
B = 0.80
General Motors
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
G
M
r
e
t
u
r
n
(
%
)
R
2
= .25
B = 1.00
Exxon Mobil
Slope determined from plotting the
line of best fit.
Price data – Aug 88- Jan 95
Market return (%)
E
x
x
o
n
M
o
b
i
l
r
e
t
u
r
n
(
%
)
R
2
= .28
B = 0.52
Exxon Mobil
Slope determined from plotting the
line of best fit.
Price data – Feb 95 – Jul 01
Market return (%)
E
x
x
o
n
M
o
b
i
l
r
e
t
u
r
n
(
%
)
R
2
= .16
B = 0.42
? What does R squared measure?
– measures the proportions of the total variance in the
stock’s return that can be explained by market
movements.
? What does then (1 – R squared) measure?
- measures the proportions of the total variance in the
stock’s return that can be explained by unique risk.
? What is Standard error?
– shows the extent of possible mis-measurement
? What is Confidence interval?
- estimated values plus or minus 2 standard errors
? A firm that has a beta = 1 has average
market risk. The stock is no more or less
volatile than the market.
? A firm with a beta > 1 is more volatile than
the market.
? (ex: technology firms)
? A firm with a beta < 1 is less volatile than the
market.
? (ex: utilities)
? Assume that both Tata Steel and Biocon
have beta of 0.96. Tata Steel has R
square of 30% and Biocon has only 10%.
If you were a well diversified investor,
which of the 2 stocks will you prefer in
your portfolio? If you were not well
diversified, which one of these would you
prefer?
? Company Cost of Capital (COC) is based
on the average beta of the assets
? The average Beta of the assets is based
on the % of funds in each asset
Example
1/3 New Ventures B=2.0
1/3 Expand existing business B=1.3
1/3 Plant efficiency B=0.6
AVG B of assets = 1.3
What is Capital Structure?
- the mix of debt & equity within a company
Expand CAPM to include Capital Structure
R = r
f
+ B ( r
m
- r
f
)
becomes
R
equity
= r
f
+ B ( r
m
- r
f
)
COC
=
r
portfolio
= r
assets
r
assets
= WACC = r
debt
(D) + r
equity
(E)
(V) (V)
B
assets
= B
debt
(D) + B
equity
(E)
(V) (V)
r
equity
= r
f
+ B
equity
( r
m
- r
f
)
IMPORTANT
E, D, and V are all
market values
0
20
0 0.2 0.8 1.2
Expected
return (%)
B
debt
B
assets
B
equity
R
rdebt
=8
R
assets
=12.2
R
equity
=15
Expected Returns and Betas prior to refinancing
R
equity
= Return on Stock
= 15%
R
debt
= YTM on bonds
= 7.5 %
.17 .50 Portfolio Industry
.21 .40 Pacific Union
.26 .52 Southern Norfolk
.24 .46 tion Transporta CSX
.20 .64 Northern Burlington
Error Standard. Beta
? The estimated industry beta is more
reliable.
? It shows lower standard error.
? R
f
= 3.5%
? R
m
= 8%
? B (Union) = 0.4
? B (Industry) = 0.5
? Expected Return = ?
? E(r) = R
f
+ B (Industry) x (R
m
– R
f
)
? = 7.75%
Example
100 value Firm Assets Total
70 ue Equity val
30 Debt value 100 Assets
% 75 . 12 % 15
70 30
70
% 5 . 7
70 30
30
=
+
+
+
=
+
+
+
=
assets
equity debt assets
R
r
equity debt
equity
r
equity debt
debt
R
The following table summarizes the unlevered betas for
publicly traded software firms.
Grouping Number of Beta D/E Ratio
Unlevered Firms
Beta
All Software 264 1.45 3.70% 1.42
Small-cap Software 125 1.54 10.12% 1.45
Entertainment Software 31 1.50 7.09%
1.43
? We will use the beta of entertainment software firms as
the unlevered beta for InfoSoft.
? We will also assume that InfoSoft’s D/E ratio will be
similar to that of these publicly traded firms (D/E =
7.09%)
? Beta for InfoSoft = 1.43 (1 + (1-.42) (.0709)) = 1.49
(Assumption: tax rate of 42%)
? Adjust the beta to reflect total risk rather than market
risk. This adjustment is a relatively simple one, since
the R squared of the regression measures the
proportion of the risk that is market risk.
Total Beta = Market Beta / ?R squared
? In the InfoSoft example, where the market beta is 1.10
and the average R-squared of the comparable publicly
traded firms is 16%,
? Total Beta = 1.49/?0.16 = 3.725
? Total Cost of Equity = 5% + 3.725 (5.5%)= 25.49%
? This cost of equity is much higher than the cost of
equity based upon the market beta because the owners
of the firm are not diversified.
0.77 .30 2.58 Venezuela
1.39 .48 2.91 Thailand
0.81 .42 1.93 Poland
0.55 .18 3.11 Egypt
Beta
t coefficien
n Correlatio
Ratio o
Source: The Brattle Group, Inc.
s Ratio - Ratio of standard deviations, country index vs. S&P composite
index
? Much of cyclical industries risk reflects
unique or diversifiable risk.
? Measure it by accounting betas or cash
flow betas – changes in book earnings or
cash flows instead of rates of returns on
securities
? Tend to have high betas
? Cash flow = revenue – fixed costs –
variable cost
? PV (assets) = PV (revenue) – PV (fixed
costs) – PV (variable cost)
? PV (revenue) = PV (fixed costs) + PV
(variable cost) + PV (assets)
? To find asset beta, we use the previous
equation with their betas.
) PV(revenue
PV(asset)
B
) PV(revenue
cost) e PV(variabl
B
) PV(revenue
cost) PV(fixed
B B
asset cost variable
cost fixed revenue
+ +
+ =
(
¸
(
¸
÷ =
=
PV(asset)
cost) PV(fixed
1 B
PV(asset)
cost) e PV(variabl - ) PV(revenue
B B
revenue
revenue asset
Higher the ratio of fixed cost to project value – higher the project Beta
? Operating Leverage
? function of a firm’s cost structure
? defined in terms of the relationships between fixed
costs and total costs
? High fixed costs relative total costs – high
operating leverage
? A firm with high operating leverage will also
have higher variability in operating income –
will lead to higher beta
? Alternative calculations
? Degree of Operating Leverage = % change in
operating profit/ % change in sales
? Can a firm change their operating leverage?
? Suppose a firm uses its company’s cost
of capital for all project, what would be
the effect on the value of projects having
higher risk than the firm’s average risk?
? A company is financed 40% by risk-free
debt. Interest rate is 10%, expected
market return is 18% and the stock’s
beta is 0.5, what is the cost of capital?
? Market value of ORC is Rs. 60 crores and value
of debt is Rs. 40 crores, which is riskfree. B of
the stock is 1.5 expected market premium is
9%.
a) What is the expected return?
b) What is the B of the existing assets?
c) Estimate cost of capital?
d) Estimate disc. Rate for existing business
e) If it wants to diversify, the unleveraged B of
similar companies is 1.2, estimate the
required return for new business?
? A firm has the following cap str:
Security Beta Mkt. Val.
Debt 0 100
Pref. Share 0.2 40
Ordinary Eq 1.2 200
a) What is the firm’s beta
b) How would the Basset change if firm issued
additional equity of 140 to repurchase Debt &
Pref shares?
c) What should the disc rate be if firm
expands its scale of operation without
changing its asset beta? Assume rf = 5% rm =
6%
Std. Dev. R
2
B Std. err.
BP 25 .25 .90 .17
BA 38 .25 1.37 .22
a) What proportion of each was market risk & unique risk?
b) What is the variance of BP? What is the unique variance?
c) What is the confidence level on BA’s Beta?
d) If CAPM is correct, what is the expected return of BA? Rf
= 5% & Rm = 12%
e) Suppose next year the market provides a 0% return.
What return would you expect from BA?
a) Both BP and BA had R
2
values of 0.25, which
means that, for both stocks 25% of total risk
comes from movements in the market (i.e.,
market risk). Therefore, 75% of total risk is
unique risk.
b) The variance of BP is: (25)^2 = 625
Unique variance for BP is: (0.75 × 625) = 468.75
c) The t-statistic for |BA is: (0.90/0.17) = 5.29
This is significant at the 1% level, so that the
confidence level is 99%.
d) rBP = rf + |BP ×(rm - rf) = 0.05 + (1.37)×(0.12 –
0.05) = 0.1459 = 14.59%
e) rBP = rf + |BP ×(rm - rf) = 0.05 + (1.37)×(0 –
0.05) = -0.0185 = -1.85%
? Convert cash-flows to certain equivalents
(CEQ).
? Then discount it at risk-free rate.
t
f
t
t
t
r
CEQ
r
C
PV
) 1 ( ) 1 ( +
=
+
=
Example
Project A is expected to produce CF =
$100 mil for each of three years. Given
a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is
the PV of the project?
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?
% 12
) 8 ( 75 . 6
) (
=
+ =
÷ + =
f m f
r r B r r
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Now assume that the
cash flows change, but
are RISK FREE. What is
the new PV?
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
240.2 PV Total
71.2 84.8 3
79.7 89.6 2
89.3 94.6 1
6% @ PV Flow Cash Year
Project B
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
240.2 PV Total
71.2 84.8 3
79.7 89.6 2
89.3 94.6 1
6% @ PV Flow Cash Year
Project B
240.2 PV Total
71.2 100 3
79.7 100 2
89.3 100 1
12% @ PV Flow Cash Year
A Project
Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project? DEDUCTION FOR RISK
15.2 84.8 100 3
10.4 89.6 100 2
5.4 94.6 100 1
risk for
Deduction
CEQ Flow Cash Year
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
The difference between the 100 and the certainty equivalent (94.6)
is 5.4%…this % can be considered the annual premium on a risky
cash flow
flow cash equivalent certainty
054 . 1
flow cash Risky
=
Example
Project A is expected to produce CF = $100 mil for each
of three years. Given a risk free rate of 6%, a market
premium of 8%, and beta of .75, what is the PV of the
project?.. Now assume that the cash flows change, but are
RISK FREE. What is the new PV?
8 . 84
054 . 1
100
3 Year
6 . 89
054 . 1
100
2 Year
6 . 94
054 . 1
100
1 Year
3
2
= =
= =
= =
doc_798630521.pptx