The document provides an introduction to the Capital Asset Pricing Model (CAPM) for calculating the cost of equity for publicly traded companies. It discusses key concepts such as the value of a company being equal to the value of its debt plus the value of its equity. It also covers the equity return rate being a function of the risk-free rate plus a risk premium related to the market return rate. The CAPM model sets the expected return on equity equal to the risk-free rate plus the product of the market risk premium and the stock's beta coefficient.

1. Capital Asset Pricing
Model: Introduction
D Keck
October 3, 2016

2. CAPM
The most common model for the rate cost of
equity, , for a publicly traded companykE
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3. Value of Company
The fair value for a company is the fair value of
company's debt plus the fair value of the equity
capital
DCF for the value of a company
FCF is the cash flow to the debt and
equity capital providers
is the (weighted average) cost of capital
But what is ?
V = D + E
V = ∑n
i=1
FCFi
(1+k)i
k
k = ⋅ (1 − τ) ⋅ + ⋅kD
D
V kE
E
V
kE
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4. Free Cash Flow
Operating cash flow minus capital expenditures
More later
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5. Equity Value of Company
Dividend discount method
FCFE is the cash flow available to the equity
capital providers
FCFE Method
But what is ?
E = ∑n
i=1
DIVi
(1+kE)i
p = ∑n
i=1
di
(1+kE)i
=di
DIVi
ns
E = ∑n
i=1
FCFEi
(1+kE)i
kE
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6. Equity Return Rates
Return rate on a firm's book value of equity, EB
Expected total return rate on a firm's market
value of equity, E
roe = NP
EB
=rE
E[NP]
E
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7. Equity Return Rates
The total return rate on an asset, E, is a function
of the risk free and risky (excess) rates of return
One simple and very typical model is as follows
= f( , , . . . )rE rrisk free rrisky
= f( , , . . . )rE rF rexcess
= +rE rF rexcess
= −rexcess rE rF
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8. Equity Return Rates
excess mean rate of return
= ⋅ ( − )rexcess
1
n
∑n
i=1 rEi
rFi
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9. Market Risk Premium
The market or equity risk premium is the excess
return rate on the total stock market, denoted M
(the "market")
Sampling frequency (per year), m ?
Number of samples, n ?
is equity or market risk premium (ERP or
MRP)
= ⋅ ( − )rMexcess
1
n
∑n
i=1 rMi
rFi
rMexcess
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10. Expected Return on Equity
Simple linear regression
( − ) = α + β ⋅ ( − ) +rEi
rFi
rMi
rFi
ϵi
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11. Expected Return on Equity
Simple linear regression
is a measure of risk for pubicly traded equity
is the excess or risky return rate for taking
market risk
( − ) = α + β ⋅ ( − ) +rEi
rFi
rMi
rFi
ϵi
β
α
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12. CAPM Model
E[ ] = + β ⋅ ( − )rE rF rM rF
= + β ⋅ ( − )rE rF rM rF
= + β ⋅ MRPrE rF
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13. CAPM Model
Model calibration
Levered
Historical data:
Current data:
·
MRP
- β
-
·
- rF
β
= ⋅ (1 + (1 − τ)) ⋅βL βU
D
E
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14. More on regression
First column of are 1's, second column is
excess market rates
simple: has 2 columns and has 2 rows
linear: is linear
regression: is numeric
ordinary: linear
least squares: scalar measure of
( − ) = α + β ⋅ ( − ) +rEi
rFi
rMi
rFi
ϵi
y = X ⋅ β + ϵ
y = ( − )rE rF
β = (β0 β1 )T
X
X β
β
y
ϵ
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15. Regression Fit
Linear regresssion hypothesis
p-value =
Reject with 95% confidence if p-value < .05
coefficient of determination
is the fraction of variance in explained by the
fitted line
: β = 0H0
: β ≠ 0HA
P( | data)H0
H0
R2
y
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16. Cost of Equity
CAPM Model
To this point assume that the sampling frequency
is one year so that the expected rate of return
and the cost of capital are annual
≡ E[ ]kE rE
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17. INTC
Intel Corp data
INTC (http://finance.yahoo.com/quote/INTC?
p=INTC)
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18. Rates of Return
Simple rates of return
Natural log rates of return
= ⋅ (1 + )Pi Pi−1 ri
=ri
−Pi Pi−1
Pi−1
ln( ) = ln( ) +Pi Pi−1 ui
= ln( ) − ln( )ui Pi Pi−1
= ln( )ui
Pi
Pi−1
= ⋅Pi Pi−1 eui
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19. Mean Rates of Return
Mean over n periods, e.g., n months
Arithmetic mean of simple rates
Arithmetic mean of natural log rates
Geometric mean of simple rates
r = ⋅1
n
∑n
i=1
−Pi P1−1
Pi−1
u = ⋅ ln( )1
n
∑n
i=1
Pi
Pi−1
g = [ (1 + ) − 1∏n
i=1 ri ]
1
n
g = [ − 1Pn
P0
]
1
n
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20. Converting Mean Rates of
Return
Future value factors, f, over m periods, e.g., 12
months
Exact only if is normally distributed
Mean
Median
ui
= ⋅ (1 + rPm P0 )m
= ⋅Pm P0 e(u+ )⋅mσ2
2
= (1 + r =fmean )m
e(u+ )⋅mσ2
2
r = − 1e(u+ )σ2
2
= ⋅ (1 + gPm P0 )m
= ⋅Pm P0 eu⋅m
= (1 + g =fmedian )m
eu⋅m
g = − 1eu
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21. Homework 6A, 6B
by RWJ
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22. Homework 6C
by RWJ
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23. Homework 6D
by RWJ
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24. Homework 6D Solution
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25. Homework 6D Solution
In the previous image, the expression for F
should have $15M subtracted off so that F equals
$1,639,610
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26. Homework 6D Solution Code
d = 1 / ( 1 + 1/.4)
psp('debt / value',d,2)
## [1] "debt / value 28.57 %"
e = 1 / 1.4
psp('equity / value',e,2)
## [1] "equity / value 71.43 %"
kD = .1
psp('cost of debt capital',kD,2)
## [1] "cost of debt capital 10 %"
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27. Homework 6D Solution Code
t = .34
kE = .2
psp('cost of capital',kE,2)
## [1] "cost of capital 20 %"
k = d * (1-t) * kD + e * kE
psp("cost of capital",k,2)
## [1] "cost of capital 16.17 %"
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28. Homework 6D Solution Code
V = 15000000 * ( e / .88 + d / .96 )
psr('funds raised $',V,0)
## [1] "funds raised $ 16639610"
F = V - 15000000
psr('flotation cost $',F,0)
## [1] "flotation cost $ 1639610"
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29. Homework 6D Solution Code
PV = 3000000 / k
psr('present value of future cash flows $',PV,0)
## [1] "present value of future cash flows $ 18551237"
NPV = PV - V
psr('net present value $',NPV,0)
## [1] "net present value $ 1911626"
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30. Homework 6E
by RWJ
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