Download Lecture 4: Cost of capital and CAPM. First lecture

Economics of Competition and
Regulation
Lecture 4
The cost of capital and CAPM
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Overview
•
•
•
•
The cost of capital
Risk
Risk and return
Cost of equity: CAPM
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Cost of capital
• Terms on which privatised companies can
raise funds for regulated businesses
• Two main types of capital:
– Debt
– Equity
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Debt or bond finance
• “Guaranteed” interest payments (before equity
holders)
• Tax deductible
• Normally lower cost than equity
• Cost of debt =
risk free rate plus risk premium
• Risk free rate measured by gov’t stocks
• Risk premium depends on rating assessed by
rating agencies
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Equity finance
• Gives shareholders rights to residual incomes
– higher risk than debt
• Shareholders can spread risk by holding balanced
portfolio of equities
• But even a completely balanced equity portfolio
has a risk = market risk –cannot be diversified
• This market risk has a risk premium
= market risk premium (topic for another day)
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Calculating the cost of capital
Weighted average cost of capital =
cost of debt  proportion of debt in financing +
cost of equity  proportion of equity in financing
cost of finance =risk free rate +risk premium
• Equity risk premium =
market risk premium  equity “beta”
• Beta measures the relative risk of the company’s
equity with that of the market as a whole
• Based on Capital Asset Pricing Model
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CAPM
• Focus on the equilibrium relationship between the
risk and expected return on risky assets
• Builds on Markowitz portfolio theory
• Each investor is assumed to diversify his or her
portfolio according to the Markowitz model
• Only compensate investors for bearing nondiversifiable risk
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A. Market Portfolio
• From the Markowitz Portfolio Selection model
– Separation Theorem
– All investors hold the same portfolio of risky assets
•
CAPM: extension of the Markowitz model
– In equilibrium: this risky portfolio consists of all risky
securities in the market
– Hence, the name - market portfolio
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Characteristics of the
Market Portfolio
• All risky assets must be in the market portfolio, so
it is completely diversified
– Contains only systematic risk
• All securities included in proportion to their
market value
• In theory, should contain all risky assets
worldwide
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B. Capital Market Line
L
M
E(RM)

x
RF
 Line from RF to L is

y
M
Risk


the capital market
line (CML)
x = risk premium
= E(RM) - RF
y = risk = M
Slope = x/y
= [E(RM) - RF]/M
y-intercept = RF
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CML (cont’d)
• Relationship between risk and expected return for
portfolio P (Equation for CML):
E(RM )  RF
E(R C )  RF 
C
M
• Slope of the CML is the market price of risk for
efficient portfolios, or the equilibrium price of risk
in the market (Risk premium per unit of risk)
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C. Security Market Line
• The CML applies to markets in equilibrium and to the
selection of efficient portfolios
• The Security Market Line depicts the trade-off between
risk and expected return for individual securities in
equilibrium
• Under CAPM, all investors hold the market portfolio
– How does an individual security contribute to the risk of the
market portfolio? Focus: covariance between security and
market
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SML (cont’d)
• Equation for the expected return for an
individual stock, E(Ri), is similar to the CML
equation:
E(R M )  RF i,M
E(R i )  RF 
M
M
 RF  E(R M )  RF i
 All securities should lie on the SML
The expected return on the security should be
only that return needed to compensate for
systematic risk (CAPM is a one-factor model) 13
SML (cont’d)
 Beta = 1.0 implies:
SML
as risky as market
 Securities A and B
are riskier than the
market
E(R)
A
E(RM)
B
 Beta > 1.0
C
RF
 Security C is less
risky relative to the
market
0
0.5
1.0 1.5
BetaM
2.0
 Beta < 1.0
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SML: Application
• to calculate the required rate of return on an
asset (ki):
ki = RF +i [ E(RM) - RF ]
–
–
Risk-free rate (RF)
Risk premium (i [ E(RM) - RF ])
•
Market risk premium adjusted for security i
The greater the systematic risk, the greater the
required return
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Finding Beta
Plot stock returns against
market:
Return to
Equity
Beta = 1 CoC = risk
free rate + equity
risk premium
High Beta and
equity cost
Low Beta =>low
cost of equity
Return to
market
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Company “Beta”
• Ideally should relate to regulated company
rather than plc
• Based on degree to which company returns
vary with those of market.
• Estimated from regression equation:
company return = alpha + beta  market
return
• For regulated companies Beta should be <1
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Using data
• Returns to stock
– price increase: log(pt)-log(pt-1) plus
– dividend: added in at day goes ex-dividend
• Regressed on stock market return:
– price change plus dividends
• Rough measure, data easily found:
– just look at price changes - see today's lab
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Recent examples of the cost of capital
Regulator
Ofgem
Ofwat
CC
CC
CC
Postcomm
Ofgem
CAA
Ofgem
Oftel
MMC
ORR
Ofgem
Case
Basis
Electricity distribution (2004) Gross, real
net of tax
Water (2004)
Post tax, real
Mobile phone inquiry (2003) Pre-tax, real
Manchester Airport (2002) Pre-tax, real
BAA (2002)
Pre-tax, real
Consignia (2002)
Pre-tax, real
Independent gas transporters (02)
NATS (2001)
Pre-tax, real
Transco (2001)
Pre-tax, real
Eff comp review:mobiles(01) Pre-tax, noml
Mid Kent Water (2000)
Pre-tax, real
Railtrack (2000)
Pre-tax, real
NGC (2000)
Pre-tax, real
WACC
6.9%
4.8%
5.1%
11%a
7.25%a
7.21%a
9.4-11.6%
Pre-tax, real
7.0-8.8%
6.0-6.25%
13.01-16.95%
7.4%b
6.9-8.2%
5.5-6.25%
Gearing
57.5%
55% (assumed)
10% (estimate of actual level)
30-35% (estimate of actual)
25% (estimate of actual level)
20% (actual)
6.4-8.5%
37.5%
40-50% (optimal)
62.5%
10-30% (optimal)
35%
50% (assumed)
60-70%
Source: Cepa: Report to the London Underground PPP Arbiter: Cost Of Capital Annex 3 ( July 2003), plus author's update.
Notes: a including 0.5% uncertainty premium b including 1% small size premium and 0.3% embedded debt premium
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Further reading
A study into certain aspects of the cost of
capital for regulated utilities in the UK
February 2003
Paper 08/03 from Ofgem or
www.ofcom.org.uk/static/archive/
oftel/publications/pricing/2003/cofk0203.htm
Authors are academics and core paradigm is
non-diversifiable risk, as above.
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