RISK AND RETURN RELATIONSHIP
AND
COST OF CAPITAL
Lesson 5
Corporate Finance
6th
Castellanza,
October, 2010
Executive Summary
 Risk and return relationship: the financial value of
time
 The cost of capital
 Capital Asset Pricing Model (CAPM)
 Markovitz Portfolio Theory
Corporate Finance
Key factors influencing financial decisions
Return
FINANCIAL
DECISIONS
(i.e. capital budgeting/
investment decisions)
Risk
Time
Corporate Finance
Key factors influencing financial decisions
1. RETURN
r = rf + Expected Risk Premium
Where:
“rf” = Free Risk Return
“Expected Risk Premium” = extra expected return required by
adverse risk investors for taking on risk
2. RISK
-
Risk in investment means that future returns are
UNPREDICTABLE
Risk states the possibility that Effective Return can
“deviates” from Expected Return
(the spread of possible returns is measured by standard
deviation)
Corporate Finance
Key factors influencing financial decisions
3. TIME
Financial value of time is connected to:

Risk (it is propotional to the probability that expected return
will be effectively realized)

Flexibility

Temporal distribution of value
Corporate Finance
The cost of capital
DEFINITION:
We define the company cost of capital as “the expected return on
portfolio of all the company’s existing securities”.
That portfolio usually includes DEBT as well as EQUITY.
ASSUMPTIONS:
 Every company’s financial fonts have a cost
 The returns to investors vary according to the risk the have borne
RISK
=
COST OF CAPITAL
Corporate Finance
The cost of Equity capital (Ke) 1/2
In general terms, in order to estimate “Ke” it is necessary to
consider the OPPORTUNITY COST, defined as “the expected
return on other securities with the same degree of risk”.
It means that:
A potential shareholder will invest in a company’s capital only if
the expected return is at least equal to the return that can be
earned in the capital market on securities of comparable risk.
Ke = rf + Risk Premium
Corporate Finance
The cost of Equity capital (Ke) 2/2
When it is possible to estimate the enterprise market
value, the correct ratio to calculate “Ke” is:
Ke = EPS / P*
Where:
EPS = Earning per Share
P*= Market Value
Corporate Finance
The cost of Debt (Kd)
Kd = i (1-t)
Where:
i = Interest Rate on Debt
(1-t) = Fiscal Effect due to interest tax deductibility
Corporate Finance
The Weighted-Average Cost of Capital (WACC)
The WACC is the average rate of return demanded by
investors in the company’s debt and equity securities:
WACC = [Ke E / (E + D)] + [Kd D / (E + D)]
Where:
E = Equity
D = Debt
Ke > WACC > Kd
Corporate Finance
The Risk/Return relationship 1/4
r = rf + Expected Risk Premium
Where:
“rf” = Free Risk Return
“Expected Risk Premium” = extra expected return
required by adverse risk investors for taking on risk
From which:
Expected Risk Premium = r – rf
Corporate Finance
The Risk/Return relationship 2/4
• HOW TO ESTIMATE RETURN FREE RISK (rf) AND
EXPECTED RISK PREMIUM?
 rf = the interest rate free risk is conventionally the return on
Treasury bills: it is fixed and unaffected by what happens to
the market.
 Expected Risk Premium = r – rf
=β·
(Market Risk)
(rm – rf)
(Market Risk Premium)
Corporate Finance
The Risk/Return relationship 3/4
• THE CAPITAL ASSET PRICING MODEL (CAPM)
It states that in a competitive market the expected risk
premium on each investment is proportional to its Beta.
Expected
Return on
Investment
Security market line
rm
Market portfolio (β = 1)
rf
Treasury Bills (β = 0)
0
1
β
…This means that each investment should lie on the sloping security market
line connecting Treasury Bills and the Market Portfolio.
Corporate Finance
The Risk/Return relationship 4/4
• THE CAPM CONCLUSION
An investor can always obtain an Expected Risk
Premium of β (rm –rf) by holding a mixture of the
Market Portfolio and a Risk Free loan
The most efficient way to decrease risk is
DIVERSIFICATION
Corporate Finance
The Markovitz Portfolio Theory
Markovitz
Theory
is
DIVERSIFICATION
based
REDUCES
on
the
concept
VARIABILITY
that
(standard
deviation = risk).
The market portfolio is made up of individual stocks, but its
variability doesn’t reflect the average variability of its
components.
Diversification works because prices of different stocks do not
move exactly together.
VARIABILITY =
RISK =
Corporate Finance
COST OF CAPITAL
Unique Risk and Market Risk 1/3
The risk that potentially can be eliminated by diversification is called UNIQUE
RISK (also called SPECIFIC RISK or UNSYSTEMATIC RISK). It stems from
the fact that many of the perils that surround an individual company are
peculiar to that company and perhaps its immediate competitors.
It is impossible to totally eliminate risk, because it is impossible to have stock
prices perfectly correlated.
…That is why…
… Diversification reduces risk rapidly at first, than more slowly, untill a point in
which the effect on standard deviation (risk) is null.
Corporate Finance
Unique Risk and Market Risk 2/3
There is also some risk that it is impossible to avoid, regardless of how
much a company diversify.This risk is generally known as MARKET
RISK (also called SYSTEMATIC RISK).
Market risk stems from the fact that there are other economywide
perils that treaten all businesses.
… That is why…
… Stocks have a tendency to move together, and investors are exposed
to market uncertainities, no matter how many stocks they hold.
Corporate Finance
Unique Risk and Market Risk 3/3
Portfolio
standard
deviation
Unique Risk
Market Risk
Corporate Finance
Number of
securities
How to estimate the Market Risk (β)
From CAPM:
 Expected Risk Premium = r – rf
= β
·
(rm – rf)
MARKET RISK: the Beta of an individual security measures its
SENSITIVITY to market movements.
ß = % re / % rm
Where:
“re” = Expected Return from security
“rm“ = Expected Return on Market
Corporate Finance
The meaning of “Beta”
MARKET RISK: the Beta of an individual security
measures its SENSITIVITY to market movements.
 Stocks with β > 1 = tend to amplify the overall movements of
the market;
 Stocks with 0< β <1 = tend to move in the same direction as the
market, but not as far.
Corporate Finance
The meaning of “Beta”
Return on Stock A
(%)
1.26
β
1.0
Return on Market
(%)
The Return on Stock A changes on
average by 1.26% for each additional
1% change in the Market Return.
Beta is therefore 1.26
- When the market rises an extra 1%, stock A price will rise by 1.26%
- When the market falls an extra 2%, stock A price falls an extra 2X1.26=
2.52%
Corporate Finance
How do individual securities affect portfolio risk?
The risk of a well-diversified portfolio depends on
the Market Risk of the securities included in the
portfolio
Corporate Finance