Factor Model
1
From CAPM (single factor model) to
multi-factor model
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The CAPM has not been verified
completely.
Investors seem to be concerned with
both market risk and other risk factors.
Therefore, the it may not produce a
correct estimate of ri.
ri = rRF + βi (rM – rRF) + ???
2
Fama-French 3 factor model
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The required return is based on 3 factors.
In addition to the market factor, there are
also a size factor and book-to-market factor.
Rt  R f , t   *( Rm, t  R f , t )  s * SMBt  h * HMLt   t
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The Cost of Capital
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WACC
Component costs
Adjusting for risk
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As a financial manager in a firm
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You are often faced with the decision
whether to invest in some potential
projects.
For example, should a firm buy a new
production line?
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Discount rate = required return
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From the project, we need to earn at least the
required return to compensate our investors
for the financing they have provided.
The required return is the same as the
appropriate discount rate and is based on the
risk of the cash flows from the project.
How to decide the appropriate discount rate
(to discount future FCFs from the project)?
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Required rate of return
Also called:
 Cost of Capital
 Hurdle rate
 Discount rate
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Estimate discount rate in a project
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One simple approach is to ASSUME that the
new project has the same risk as the
existing business or assets in the firm.
We can estimate what is the required return
on the firm’s existing assets.
Then use this required return as the
discount rate for the new project.
Of course, if the new project has risk
very different from the existing
business, one CANNOT do this.
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Cost of Capital
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Company Cost of Capital (COC) is the
required return on the existing firm assets.
It is based on the risk of assets.
The risk of firm’s overall assets is equal to
the weighted average risks of firm’s debt,
preferred stock and common equity.
Thus the cost of capital of a firm equals the
weighted average of the cost of debt, the
cost of preferred stock, and the cost of
common equity.
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Example:
Suppose the company 785.com has the
following classes of assets:
2/3 Intangible, good will & New technology
Beta=2.0
1/6 Machine & Plant
Beta=1.3
1/6 Working assets
Beta=0.6
Beta of firm assets
=1.3*(2/3)+1.3/6+0.6/6=1.18
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Same example
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Suppose the same company is owned by
stockholders (70% in value) and debt
holders (30% in value).
Beta of stock=1.51, beta of debt=0.41
Beta of the portfolio that contains all stocks
and debts =0.41*30%+1.51*70%=1.18
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Firm Cost of Capital = WACC
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WACC is the weighted average of the
after-tax cost of each of the sources
capital used by a firm to finance its
project, where the weight reflects the
proportion of total financing raised from
each source.
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Calculating the weighted
average cost of capital
WACC = wdrd(1-T) + wprp + wsrs
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The w’s refer to the firm’s capital
structure weights.
Use market values to determine the
weights (proportions).
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rd , rp , rs
r : cost of debt=required rate of return
for debt investors.
 rp : cost of preferred stock= required
rate of return for preferred stock
holders.
 rs: cost of equity= required rate of
return for common stock holders.
 d
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cost of debt
WACC = wdrd(1-T) + wprp + wcrs
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rd is the cost of debt capital.
The yield to maturity on
outstanding L-T debt is often used as
a measure of rd.
Why tax-adjust, i.e. why rd(1-T)?
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cost of debt
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We are concerned with after-tax cash flows,
so we need to consider the effect of taxes on
the various components of costs of capital.
Interest expense reduces our tax liability
 This reduction in taxes reduces our cost of
debt
 After-tax cost of debt = rd(1-T)
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A 5-year, 12% annual coupon bond sells for
$1,075.81. What is the cost of debt (rd)?
INPUTS
5
N
OUTPUT
I/YR
-1075.81
120
1000
PV
PMT
FV
10
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cost of debt
Interest is tax deductible, so
After-Tax rd
= Before Tax rd (1-T)
= 10% (1 – T)
If T=40%
= 6%
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cost of preferred stock
WACC = wdrd(1-T) + wprp + wsrs
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rp is the cost of preferred stock.
The rate of return investors require on
the firm’s preferred stock.
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What is the cost of preferred
stock?
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The cost of preferred stock can be
solved by using this formula:
rp = Dp / Pp
= $10 / $111.10
= 9%
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cost of preferred stock
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Preferred dividends are not taxdeductible, so no tax adjustments
necessary. Just use rp .
rp = Dp / Pp
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cost of equity
WACC = wdrd(1-T) + wprp + wsrs
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rs is the cost of equity.
The cost of equity is the return
required by equity investors given the
risk of the cash flows from the firm
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Two ways to determine the
cost of common equity, rs
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CAPM: rs = rRF + (rM – rRF) β
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DCF:
rs = (D1 / P0) + g
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If the rRF = 7%, RPM = 6%, and the firm’s
beta is 1.2, what’s the cost of common
equity based upon the CAPM?
rs = rRF + (rM – rRF) β
= 7.0% + (6.0%)1.2 = 14.2%
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If D0 = $4.19, P0 = $50, and g = 5%,
what’s the cost of common equity based
upon the DCF approach?
D1 = D0 (1 + g)
D1 = $4.19 (1 + .05)
D1 = $4.3995
rs = (D1 / P0) + g
= ($4.3995 / $50) + 0.05
= 13.8%
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A firm’s capital consists of has 30% in debt,
10% in preferred stock, and 60% in common
equity. T=40%, rd=10%,rp=9%, rs=14%.
WACC =
=
=
=
wdrd(1-T) + wprp + wcrs
0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
1.8% + 0.9% + 8.4%
11.1%
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The risk of a project
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When calculating the discount rate of a
potential investment project, we have often
assumed that the project to be taken has the
same risk as the existing business or assets
of the firm. If this assumption is valid, then
we can use WACC as our discount rate to
discount future cash flows from a project.
Of course, if the new project has very
different risk from existing business, one
cannot do so.
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Should a company use the composite
WACC as the hurdle rate for any of its
projects?
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Ok for a project with average risk.
The composite WACC reflects the risk of an
average project undertaken by the firm.
Therefore, the WACC only represents the
“hurdle rate” for a typical project with
average risk in the firm.
Not Ok for a project with very different
risk.
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Using WACC for All Projects - Example
What would happen if we use the WACC
for all projects regardless of risk?
 Assume the WACC = 15%
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Project
A
B
C
Required Return Expected Return
20%
17%
15%
18%
10%
12%
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If using one WACC for all projects
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You might mistakenly reject project C
and take project A. That is, you tend to
favor risky projects.
If you keep making such mistakes, the
firm may become more and more risky.
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We should consider the project’s risk
If the project is more risky than the firm, use
a discount rate greater than the WACC
 If the project is less risky than the firm, use a
discount rate less than the WACC
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Questions
What are the approaches for computing
the cost of equity?
 How do you compute the cost of debt
and the after-tax cost of debt?
 How do you compute the capital structure
weights required for the WACC?
 What happens if we use the same WACC
as the discount rate for projects with
very different risks?
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Exercises
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Using the company cost of capital to
evaluate a project is:
A. Always correct
B. Always incorrect
C. Correct for projects that are
about as risky as the average of
the firm's other assets
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If a firm uses the same company cost of capital
for evaluating all projects, which of the
following is likely?
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A. Rejecting good low risk projects
B. Accepting poor high risk projects
C. Both A and B
D. Neither A nor B
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The (pretax) cost of debt for a firm ____.
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A) is always greater than the cost of equity
B) normally cannot be observed, directly or
indirectly, in the marketplace
C) is equal to the yield to maturity on
the firm's outstanding bonds
D) is greater than the average coupon rate on
the firm's outstanding bonds
E) is equal to the average coupon rate on the
firm's outstanding bonds
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A common stock issue is currently selling for
$31 per share. You expect the next dividend to
be $1.40 per share.
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If the firm has a dividend growth rate of 5%
that is expected to remain constant
indefinitely, what is the firm's cost of equity?
A)9.5%
B)11.3%
C)13.8%
D)14.2%
E)15.1%
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