2. Corporate Finance
• Sources of funding and the capital structure.
• Capital expenditure for future growth.
• Tools & analytics used for allocation of funds.
14. On Leverage
"Over the years, a number of very smart people
have learned the hard way that a long stream of
impressive numbers multiplied by a single zero
always equals zero.“ –Warren E Buffett
15. Tools used in corporate Finance
• NPV-Net Present Value
• IRR-Internal rate of return
• Payback period
• Leverage
16. Price and Value
Price is analogues to reputation and value is
analogues to character.
17.
18.
19. Price and Return
• By paying higher for a business or any
investment opportunity, you diminish your
potential return.
32. Corporate Goals of Indian Companies
• Empire building once the sale cross certain value.
• Ensuring family members are involved in
business.
• Starting new venture to employee a new family.
• Keeping unutilized funds within the business
instead of giving dividends.
• Renting personal property for corporate purpose.
• Borrowing money from the business.
38. FCFF
• FCFF=Operating cash flow-Capex
• Operating cash flow=Profit before tax+ non
cash expenses-gain/loss from sale of fixed
assets-change in working capital-tax paid
• IAS gives the freedom to either subtract
Interest from operations or financing.
39. FCFE
• FCFE = Operating cash flow - Net Capital
Expenditure-Net Change in debt
• Net Change in Debt=Debt Repayment- New
Debt
45. Valuation of Bond
• Coupon bond with a coupon of Rs.100,
maturity 5 years and principal Rs.1000.You are
asked to value the bond at the beginning of
the issuance. Assume that it is a government
bond and hence risk free rate would apply and
assume the risk free rate to be 10%.
46. • Zero Coupon bond with maturity 5 years from
now and principal Rs.1000.You are asked to
value the bond at the beginning of the
issuance. Assume that it is a government bond
and hence risk free rate would apply and
assume the risk free rate to be 10%.
48. Using FCF
We use the NPV method and come up with an
“estimate” of Intrinsic Value.
49. Assumptions
• Cost of debt is 12%
• Beta of Small Cap companies is 1.8 and of Large Cap it
is 1.2.
• For Small Cap companies the growth period is assumed
to be 20 years and for Large Cap it is assumed to be 10
years.
• Considering the growth potential of Indian Economy
we assume the perpetual growth rate to be 5%.
56. Modern Portfolio Theory
– Modern portfolio theory (MPT)—or portfolio theory—
was introduced by Harry Markowitz with his paper
"Portfolio Selection," which appeared in the 1952
Journal of Finance. 38 years later, he shared a Nobel
Prize with Merton Miller and William Sharpe for what
has become a broad theory for portfolio selection.
– MPT has had most influence in the practice of portfolio
management
– MPT commonly referred to as Mean – Variance Analysis
– MPT is a normative theory
– In its simplest form, MPT provides a framework to
construct and select portfolios based on the expected
performance of the investments and the risk appetite of
the investors.
57. Applications of MPT
• Asset Allocation
• Asset-liability management
• Optimal Manager Selection
• Index funds/Mutual funds
• Fund of Funds
58. Modern Portfolio Theory - In Nut Shell
• Due to scarcity of resources, all economic decisions are made in the
face of trade-offs
• Markowitz identified the trade-off facing the investor : risk versus
return
• The investment decision is not merely which securities to own, but
how to divide investor’s wealth amongst securities – the problem of
portfolio selection
• Markowitz extends the techniques of linear programming to
develop the critical line algorithm
• The critical line algorithm identifies portfolios that minimize risk for
a given level of expected return
• MPT quantified the age old wisdom of diversification by
introducing the statistical notion of covariance or correlation.
MPT and CAPM
59. Assumptions of
Markowitz Portfolio Theory
• Investors consider each investment alternative as
being presented by a probability distribution of
expected returns over some holding period.
• For a given risk level, investors prefer higher
returns to lower returns. Similarly, for a given
level of expected returns, investors prefer less
risk to more risk.
• Your portfolio includes all of your assets and
liabilities
60. Markowitz Portfolio Theory
• Quantifies risk
• Derives the expected rate of return for a portfolio of
assets and an expected risk measure
• Shows that the variance of the rate of return is a
meaningful measure of portfolio risk
• Derives the formula for computing the variance of a
portfolio, showing how to effectively diversify a
portfolio
61. Covariance of Returns
• A measure of the degree to which two variables “move
together” relative to their individual mean values over time
• For two assets, i and j, the covariance of rates of return is
defined as:
• Covij = E{[Ri - E(Ri)][Rj - E(Rj)]}
62. Covariance and Correlation
• The correlation coefficient is obtained by
standardizing (dividing) the covariance by the
product of the individual standard deviations
• Correlation coefficient varies from -1 to +1
jt
iti
ij
Rofdeviationstandardthe
Rofdeviationstandardthe
returnsoftcoefficienncorrelatiother
:where
Cov
r
j
ji
ij
ij
63. Correlation Coefficient
• It can vary only in the range +1 to -1.
• A value of +1 would indicate perfect positive correlation. This
means that returns for the two assets move together in a
completely linear manner.
• A value of –1 would indicate perfect correlation. This means
that the returns for two assets have the same percentage
movement, but in opposite directions
64. Portfolio Standard Deviation
Calculation
• Any asset of a portfolio may be described by
two characteristics:
– The expected rate of return
– The expected standard deviations of returns
• The correlation, measured by covariance,
affects the portfolio standard deviation
• Low correlation reduces portfolio risk while
not affecting the expected return
65. Portfolio Standard Deviation Formula
ji
ijij
ij
2
i
i
port
n
1i
n
1i
ijj
n
1i
i
2
i
2
iport
rCovwhere
j,andiassetsforreturnofratesebetween thcovariancetheCov
iassetforreturnofratesofvariancethe
portfolioin thevalueofproportionby thedeterminedareweights
whereportfolio,in theassetsindividualtheofweightstheW
portfoliotheofdeviationstandardthe
:where
Covwww
66. Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
Rij = +1.00
1
2
With two perfectly
correlated assets, it is only
possible to create a two
asset portfolio with risk-
return along a line between
either single asset
67. Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
Rij = 0.00
Rij = +1.00
f
g
h
i
j
k
1
2
With uncorrelated assets it is
possible to create a two
asset portfolio with lower
risk than either single asset
68. Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
Rij = 0.00
Rij = +1.00
Rij = +0.50
f
g
h
i
j
k
1
2
With correlated assets it is
possible to create a two
asset portfolio between the
first two curves
69. Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
Rij = 0.00
Rij = +1.00
Rij = -0.50
Rij = +0.50
f
g
h
i
j
k
1
2
With
negatively
correlated assets it
is possible to
create a two asset
portfolio with
much lower risk
than either single
asset
70. Portfolio Risk-Return Plots for
Different Weights
-
0.05
0.10
0.15
0.20
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
Rij = 0.00
Rij = +1.00
Rij = -1.00
Rij = +0.50
f
g
h
i
j
k
1
2
With perfectly negatively correlated assets it is possible to
create a two asset portfolio with almost no risk
Rij = -0.50
71. • Suppose two securities have perfect negative
Correlation. Would it make sense to invest in
these two securities only?
73. The Efficient Frontier
• The efficient frontier represents that set of
portfolios with the maximum rate of return for
every given level of risk, or the minimum risk
for every level of return
• Frontier will be portfolios of investments
rather than individual securities
– Exceptions being the asset with the highest return
74. Implementation of MPT
• Though the theory is straight forward ….
Implementation is a complication process.
75. Estimation Issues
• Results of portfolio allocation depend on
accurate statistical inputs
• Estimates of
– Expected returns
– Standard deviation
– Correlation coefficient
• Among entire set of assets
• With 100 assets, 4,950 correlation estimates
• Estimation risk refers to potential errors
76. The Proof Is In the Pudding
• The MPT has been around for 40 years and is
still going strong
– But, it has flaws
• There are alternatives, but none has yet to
prove itself better
76
78. Risk-Free Asset
• An asset with zero standard deviation
• Zero correlation with all other risky assets
• Provides the risk-free rate of return (RFR)
• Will lie on the vertical axis of a portfolio graph
79. Risk-Free Asset
• Covariance between two sets of returns is
n
1i
jjiiij )]/nE(R-)][RE(R-[RCov
Because the returns for the risk free asset are certain,
0RF Thus Ri = E(Ri), and Ri - E(Ri) = 0
Consequently, the covariance of the risk-free asset with any risky asset or portfolio will
always equal zero. Similarly the correlation between any risky asset and the risk-free asset
would be zero.
80. Combining a Risk-Free Asset
with a Risky Portfolio
• Expected return
• the weighted average of the two returns
))E(RW-(1(RFR)W)E(R iRFRFport
This is a linear relationship
81. Combining a Risk-Free Asset
with a Risky Portfolio
• The expected variance for a two-asset
portfolio is
211,221
2
2
2
2
2
1
2
1
2
port rww2ww)E(
Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this
formula would become
iRFiRF iRF,RFRF
22
RF
22
RF
2
port )rw-(1w2)w1(w)E(
Since we know that the variance of the risk-free asset is zero and the correlation
between the risk-free asset and any risky asset i is zero we can adjust the formula
22
RF
2
port )w1()E( i
82. Combining a Risk-Free Asset
with a Risky Portfolio
• Given the variance formula 22
RF
2
port )w1()E( i
22
RFport )w1()E( i The standard deviation is
i)w1( RF
Therefore, the standard deviation of a portfolio that combines the risk-free asset
with risky assets is the linear proportion of the standard deviation of the risky
asset portfolio.
83. Combining a Risk-Free Asset
with a Risky Portfolio
Since both the expected return and the standard deviation of
return for such a portfolio are linear combinations, a graph of
possible portfolio returns and risks looks like a straight line
between the two assets
84. Combining a Risk-Free Asset
with a Risky Portfolio
)E( port
)E(Rport
RFR
M
C
A
B
D
Since both the expected return and the standard deviation of
return for such a portfolio are linear combinations, a graph of
possible portfolio returns and risks looks like a straight line
between the two assets
85. Combining a Risk-Free Asset
with a Risky Portfolio
)E( port
)E(R port
RFR
M
C
A
B
D
Since both the expected return and the standard deviation of
return for such a portfolio are linear combinations, a graph of
possible portfolio returns and risks looks like a straight line
between the two assets To attain a higher
expected return than is
available at point M (in
exchange for accepting
higher risk) either invest
along the efficient
frontier beyond point M,
such as point D or, add
leverage to the portfolio
by borrowing money at
the risk-free rate and
investing in the risky
portfolio at point M
87. The Market Portfolio
• Because portfolio M lies at the point of tangency, it has
the highest portfolio possibility line
• Everybody will want to invest in Portfolio M and
borrow or lend to be somewhere on the CML
• Therefore this portfolio must include ALL RISKY ASSETS
• Because the market is in equilibrium, all assets are
included in this portfolio in proportion to their market
value
• Because it contains all risky assets, it is a completely
diversified portfolio, which means that all the unique
risk of individual assets (unsystematic risk) is diversified
away
88. Systematic Risk
• Only systematic risk remains in the market
portfolio
• Systematic risk is the variability in all risky
assets caused by macroeconomic variables
• Systematic risk can be measured by the
standard deviation of returns of the market
portfolio and can change over time
89. Unsystematic Risk
• The firm specific risks that can be diversified
away using diversification.
90. Number of Stocks in a Portfolio and the
Standard Deviation of Portfolio Return
Standard Deviation of Return
Number of Stocks in the Portfolio
Standard Deviation of the Market
Portfolio (systematic risk)
Systematic Risk
Total Risk
Unsystematic
(diversifiable) Risk
91. SML
Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an
individual security as a function of systematic, non-diversifiable risk
An investor with a low risk profile would choose an investment at the beginning of the security market line. An investor with a higher risk
profile would thus choose an investment higher along the security market line.
92. Slope of SML
• Given the SML reflects the return on a given
investment in relation to risk, a change in the slope of
the SML could be caused by the risk premium of the
investments. Recall that the risk premium of an
investment is the excess return required by an investor
to help ensure a required rate of return is met. If the
risk premium required by investors was to change, the
slope of the SML would change as well.
• Risk premium=Rm-Rf
93. Properties of any asset on , above or
below the SML
• On the line assets are fairly valued.
• Above the line they are undervalued.
• Below the line they are overvalued.
94. Assumptions of CAPM
• Aim to maximize economic utilities (Asset quantities are given and
fixed).
• Are rational and risk-averse.
• Are broadly diversified across a range of investments.
• Are price takers, i.e., they cannot influence prices.
• Can lend and borrow unlimited amounts under the risk free rate of
interest.
• Trade without transaction or taxation costs.
• Deal with securities that are all highly divisible into small parcels (All
assets are perfectly divisible and liquid).
• Have homogeneous expectations.
• Assume all information is available at the same time to all investors.
95. Statement of CAPM
A model that describes the relationship between
risk and expected return and that is used in the
pricing of risky securities.
96. Shabby pillars of modern finance
Efficient markets
Rational &
uniform
expectations
Risk & return
directly
proportional
108. Cost of Capital
• It is the opportunity cost of capital.
• It is the minimum required return on the
funds committed to a project and depends on
the riskiness of its cash flows.
• Cost of capital is defined by risk, rather than
the characteristics of the firm.
• It is the benchmark or the required rate of
return.
110. Importance of Cost of Capital
• Evaluating Investment decisions
• Designing a firm’s debt policy
• Apprising the financial performance of top
management.
111. Cost of Capital from whose
Perspective?
• Management
• Majority Shareholder
• Minority Shareholder
• Debt holder
113. We are still studying Modern Finance
What is the relation between risk & return?
114. Arrange them in order of Cost of
Capital
• Ordinary Shareholder
• Preference Shareholder
• Debt Holder
115. Component Cost of Capital
• Debt = 6%
• Equity = 11%
• Project A (totally financed with debt) expected
return 10%
• Project B (totally financed with equity)
expected rate of return 10%
Which project will be selected?
118. Cost of Debt
• Before tax cost of debt is the rate of return
required by the lender.
• Cost of Debt for securities issued at:
1. Par
2. Discount
3. Premium
119. After-Tax Cost of Debt
• Interest paid is a tax deductible expense.
• Higher the interest paid, lower will be the tax
paid.
• This means government pays a portion of the
lender’s interest.
• So, only a portion of lender’s interest is paid
by the firm.
• After tax cost of debt= Kd*(1-t)
