Managerial Finance
FINA 6335
The CAPM and Cost of Capital
Lecture 9
Simplifying Assumptions
• Individuals can trade securities without
regard to fees, taxes, and other frictions.
• Individuals get any relevant information
about the firms they are interested in
costlessly.
• Individual investors can borrow or save at
the same riskless rate equal the the
“riskfree rate”
return
Market Equilibrium
Optimal
Risky
Porfolio
rf

All investors have the same CML because
they all have the same optimal risky
portfolio given the risk-free rate.
return
Market Equilibrium
Optimal
Risky
Porfolio
rf

The CML:
Rp = Rf + (p /M )(RM- Rf )
Definition of Risk When Investors
Hold the Market Portfolio
• Researchers have shown that the best
measure of the risk of a security in a large
portfolio is the beta (b)of the security.
• Beta measures the responsiveness of a
security to movements in the market
portfolio.
bi 
Cov( Ri , RM )
 ( RM )
2
Estimates of b for Selected
Stocks
Stock
Beta
Bank of America
Borland International
1.55
2.35
Travelers, Inc.
Du Pont
Kimberly-Clark Corp.
1.65
1.00
0.90
Microsoft
1.05
The Formula for Beta
bi 
Cov( Ri , RM )
 ( RM )
2
 ( Ri , RM ) ( Ri )
bi 
 ( RM )
Relationship between Risk and
Expected Return (CAPM)
• Expected Return on the Market:
R M  RF  Market Risk Premium
• Expected return on an individual security:
Ri  RF  βi  ( R M  RF )
Market Risk Premium
This applies to individual securities held within welldiversified portfolios.
Expected Return on an Individual
Security
• This formula is called the Capital
Asset Pricing Model (CAPM)
Ri  RF  βi  ( R M  RF )
Expected
return on
a security
RiskBeta of the
=
+
×
free rate
security
Market risk
premium
• Assume bi = 0, then the expected return is RF.
• Assume bi = 1, then Ri  R M
Expected return
Relationship Between Risk &
Expected Return
Ri  RF  βi  ( R M  RF )
RM
RF
1.0
Ri  RF  βi  ( R M  RF )
b
Expected
return
Relationship Between Risk &
Expected Return
13.5%
3%
βi  1.5
RF  3%
1.5
b
R M  10%
R i  3%  1.5  (10%  3%)  13.5%
Summary and Conclusions
• This chapter sets forth the principles of
modern portfolio theory.
• The expected return and variance on a
portfolio of two securities A and B are
given by
E(rP )  wA E(rA )  wB E(rB )
σ P2  (wAσ A )2  (wB σ B )2  2(wB σ B )(wAσ A )ρAB
Summary and Conclusions
• The efficient set of risky assets can be
combined with riskless borrowing and
lending. In this case, a rational investor will
always choose to hold the portfolio of risky
securities represented by the market
portfolio.
P
Summary and Conclusions
• The contribution of a security to the risk of
a well-diversified portfolio is proportional to
the covariance of the security's return with
the market’s return. This contribution is
called the beta.
• The CAPM states that the expected return on a security is
positively related to the security’s beta:
Ri  RF  βi  ( R M  RF )
Security Returns
Estimating b with regression
Slope = bi
Return on
market %
Ri = a i + biRm + ei
Security Returns
Security Market Line
Slope =
R(m)-R(f)
Beta
Ri = Rf + bi(Rm – Rf )
Practical Issues in CAPM
• Forecasting Beta
– The problem is that you assume your
estimate of Beta is the true value of Beta
– “regression toward one”
– Allow for extremes
– What Time Horizon
• 2 years of weekly, or 5 years of monthly
The Security Market Line
• Risk free interest rate?
• The Market Risk Premium
5.7%
Firm valuation
• See Chapter 18, Section 1 and 2.
• We will want to value the firm using the
Discounted Cash Flow (DCF) method.
• Three issues:
– What do you want to discount?
– How do you project this over time?
– How do you discount it?
Be Heroic!!!
Basic Valuation
• What do you want to Discount?
• How do you project these?
• How do you discount these?
Basic Valuation
• What do you want to Discount?
– Free Cash Flow
• How do you project these?
• How do you discount these?
Basic Valuation
• What do you want to Discount?
– Free Cash Flow
• How do you project these?
– From Historical Data
• How do you discount these?
Basic Valuation
• What do you want to Discount?
– Free Cash Flow
• How do you project these?
– From Historical Data
• How do you discount these?
– The Cost of Capital or (Weighted Average)
Free Cash Flow
• Start with EBIT
• Subtract Taxes
• Leaves EBIT(1-t) = Unlevered (Operating)
Net Income
• Plus Depreciation
• Less Capital Expenditures
• Less Increases in Working Capital
• Bottom Line: = Free Cash Flow
Example:
Current Sales =
Cost of Goods Sold
Gross Profit
Less Operating Expenses
Less Depreciation
EBIT
Less Income Tax Rate (@ 35%)
Operating (Unlevered) NI
Plus Depreciation
Less Capital Expenditures
Less Increases in Working Capital
Free Cash Flow
$60
25
35
9
6
20
7
13
6
2
1
16
How do we make estimates?
• 1. Income tax should be the statutory rate.
• Depreciation: You need to project
depreciation into the future. Will increase
as Capital Expenditures increase. How do
you estimate?
• Capital Expenditures: Note, to propel
growth, you need to invest: How do you
determine Cap Ex =???
• Finally, Changes in Working Capital?
Projections of Growth:
• Recall: growth depends on 2 variables:
Retention rate = (1 – Payout ratio)
Return on Investments = Operating Income as a
percentage of Book Value of Assets
• Consider Historical Rates as well:
Discount Rate
• Conceptually:
V = Present Value of the firm’s Cash flows,
discounted by a number called the “cost of
capital”
Basically it is the IRR of the Firm.
Conceptually, you want to discount by a rate
that reflects the risk of the firm’s operating
Cash Flow.
How do you estimate this
• Weighted Average Cost of Capital
Once you have the stream of operating Cash Flows generated by the
firm, the next problem is to determine how to discount it.
The discount rate that makes the Value of the firm equal the firm’s cash
flow is what we call the Cost of Capital.
As a practical matter this can be approximated by the Weighted
Average Cost of Capital (WACC)
WACC
• The WACC is defined as:
rWACC = rE X (E/(E+D)) + rD(1-t) X (D/(E+D))
The weighted average of the (after tax) cost of the component
securities issued by the firm, weighted by the proportion of those
securities issued by the firm.
rE is the required return to the equity of the firm
rD is the required return to the debt of the firm
D is the (market value) of the debt issued by the firm
E is the market value of the equity.
t is the firms tax rate.
WACC Estimation
• Some of these variables are not easily
estimated so we make some assumptions:
To estimate D use the Book value of the
debt.
To estimate rD use the ratio of Total Interest
payments to the total book value of the
debt
To estimate rE use the Capital Asset Pricing
Model