Calm

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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