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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”
Market Equilibrium
All investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate.
rf
retu
rn
Optimal Risky Porfolio
CML
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 ()of the security.
• Beta measures the responsiveness of a security to movements in the market portfolio.
)(
)(2
,
M
Mii R
RRCov
Estimates of for Selected Stocks
Stock BetaBank of America 1.55
Borland International 2.35
Travelers, Inc. 1.65
Du Pont 1.00
Kimberly-Clark Corp. 0.90
Microsoft 1.05
Relationship between Risk and Expected Return (CAPM)
• Expected Return on the Market:
• Expected return on an individual security:
PremiumRisk Market FM RR
)(β FMiFi RRRR
Market Risk Premium
This applies to individual securities held within well-diversified portfolios.
Expected Return on an Individual Security
• This formula is called the Capital Asset Pricing Model (CAPM)
)(β FMiFi RRRR
• Assume i = 0, then the expected return is RF.• Assume i = 1, then Mi RR
Expected return on a security
=Risk-
free rate+
Beta of the security
×Market risk
premium
Relationship Between Risk & Expected Return
Exp
ecte
d re
turn
)(β FMiFi RRRR
FR
1.0
MR
)(β FMiFi RRRR
Relationship Between Risk & Expected Return
Exp
ecte
d re
turn
%3FR
%3
1.5
%5.13
5.1β i %10MR
%5.13%)3%10(5.1%3 iR
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
ABAABB2
BB2
AA2P )ρσ)(wσ2(w)σ(w)σ(wσ
)()()( BBAAP rEwrEwrE
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:
)(β FMiFi RRRR
Estimating with regression
Sec
uri
ty R
etu
rns
Sec
uri
ty R
etu
rns
Return on Return on market %market %
RRii = = ii + + iiRRmm + + eeii
Slope = Slope = iiCharacte
ristic
Line
Characteris
tic Line
Security Market Line
Sec
uri
ty R
etu
rns
Sec
uri
ty R
etu
rns
BetaBeta
RRii = = RRff + + ii(R(Rmm – R – Rff ) )
Slope = Slope = R(m)-R(f)R(m)-R(f)
Securit
y Mark
et
Securit
y Mark
et
LineLine
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
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?
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 = $60 Cost of Goods Sold 25
Gross Profit 35Less Operating Expenses 9Less Depreciation 6
EBIT 20Less Income Tax Rate (@ 35%) 7
Operating (Unlevered) NI 13Plus Depreciation 6Less Capital Expenditures 2Less Increases in Working Capital 1Free Cash Flow 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.