Cost of Capital &
Risk Analysis
MBA Fellows
Corporate Finance Learning Module
Part II
1
Class Topics
 Incorporating risk in Capital Budgeting
 Cost of Capital Components: cost of
debt, preferred stock, common equity.
 Calculating the Weighted Average Cost
of Capital (WACC)
 Capital Structure Decisions
 EVA
2
Capital Budgeting and Risk
 Prior discussion of alternative projects
assumed that the level of risk
associated with each project was the
same.
 How do you evaluate projects when
they have different levels of risk?
3
Project Risk
 Reflects the the potential variability of
returns.
 Portfolio effect - if a project’s proposed
returns are not perfectly correlated with the
returns from the firm’s other projects.
 Diversification - influences risk. The total
risk of the firm may be reduced by
accepting the proposed project, if its
returns are not perfectly correlated with the
returns from the firm’s other investments.
4
Types of Project Risk




Stand-alone Risk
Corporate/Within Firm Risk
Market/Beta Risk
All Risk is not equal - some risk can
be diversified away, and some cannot.
5
Stand-Alone Risk
 The risk associated with a particular
project, ignoring the firm’s other
projects/assets and firm/shareholder
diversification.
 Measured by the  (standard deviation) or
CV (coefficient of variation) of NPV, IRR, or
MIRR.
 Methods for estimating stand-alone risk:
Sensitivity Analysis, Scenario Analysis,
Monte Carlo Simulation
6
Stand-alone risk
 Stand-alone risk is easiest to
measure, more intuitive.
 Core projects are highly correlated
with other assets, so stand-alone risk
generally reflects corporate risk.
 If the project is highly correlated with
the economy, stand-alone risk also
reflects market risk.
7
Coefficient of Variation
(COV)
 COV is a relative measure of stand-alone
risk used. It used to compare the risk of 2
or more assets because it enables us to
choose between 2 investments when one
has a higher expected rate of return, but
the other has a lower standard deviation.
 It measures the the risk per unit of return.
COV = Standard Deviation
Expected Return
8
Measuring Stand-Alone Risk
 Entails determining:
1. the uncertainty inherent in the
project’s cash flows.
2. the nature of the individual cash flow
distributions and their correlations
with each other to determine the
nature of the NPV probability
distribution.
9
Probability Density
Flatter distribution,
larger , larger
stand-alone risk.
0
E(NPV)
NPV
10
Corporate Risk





The risk that the project contributes to the firm as
a whole (the effect of the project on the earnings
and cash flow variability of the firm).
Corporate risk considers the fact that some of the
project's risk will be “diversified away” when the
project is combined with the firm’s other projects.
However, corporate risk ignores shareholder
diversification.
Depends on the project’s , and its correlation
with returns on the firm’s other projects.
Measured by the project’s beta.
11
Profitability
Project X
Total Firm
Rest of Firm
0
Years
1. Project X is negatively correlated to
firm’s other assets.
2. If r < 1.0, some diversification benefits.
3. If r = 1.0, no diversification effects.
12
Market Risk
 The effect (risk) of the project on a
well diversified stock portfolio.
 It takes in consideration the
stockholders’ other assets
(investments).
 Depends on project’s  and its
correlation with the stock market.
 Measured by the project’s market
beta.
13
Variables that Influence a Project’s NPV
and IRR







Market Size
Selling Price
Market Growth Rate
Market Share (unit volume sales)
Residual Value of Investment
Operating/Fixed Costs
Investment required
14
Sensitivity Analysis
 Answers the question “what if”
 Shows how changes in one variable affects
NPV or IRR.
 The value of one variable is changed while
holding all other variables constant.
 Provides some idea of stand-alone risk.
 Provides breakeven information.
15
Why is sensitivity analysis useful?
 Provides some idea of stand-alone
risk.
 Identifies dangerous variables.
 Provides breakeven information.
16
Sensitivity Analysis
 Each variable is changed by several
percentage points above and below
its expected value (while holding the
other variables constant).
 Then a new NPV is calculated using
each of these values.
 Finally the set of NPV’s is plotted
against the variable that was
changed.
17
Example
Change from
Base Level
-30%
-20
-10
0
+10
+20
+30
Resulting NPV (000s)
Unit Sales Salvage
k
$ 10
$78
$105
35
80
97
58
81
89
82
82
82
105
83
74
129
84
67
153
85
61
18
NPV
(000s)
Unit Sales
Salvage
82
k
-30
-20
-10 Base 10
Value
20
30
19
Sensitivity Analysis
 Slope of the lines in the graphs show how
sensitive NPV is to changes in each of the
inputs.
 The steeper the slope, the more sensitive
the NPV is to a change in the variable.
 Comparison of 2 projects - the one with the
steeper slope (sensitivity lines) would be
riskier, because for that project a relatively
small error in estimating a variable would
produce a large change in the project’s
expected NPV.
20
Results of Sensitivity Analysis
 Steeper sensitivity lines show greater
risk. Small changes result in large
declines in NPV.
 Unit sales line is steeper than salvage
value or k, so for this project, should
worry most about accuracy of sales
forecast.
21
Weaknesses of
Sensitivity analysis
 Does not reflect diversification.
 Says nothing about the likelihood of
change in a variable, i.e. a steep sales
line is not a problem if sales aren’t
expected to fall.
 Ignores the relationships among
variables.
22
Scenario Analysis
 Considers both the sensitivity of NPV to
changes in key variables and identifies the
range of possible outcomes under the
worst, best, and most likely case.
 It considers the impact of simultaneous
changes in key variables on the project.
 It provides a range of possible outcomes.
23
Scenario Analysis
 Standard Deviation of NPV:
 NPV 
n
2
P
[
NPV

E
(
NPV
)]

i
i 1
 Coefficient of Variation:
 NPV
CVNPV =
E (NPV )
24
Scenario Analysis
 The project’s COV can be compared with
the COV of the company’s average project
to get an idea of the relative riskiness of
the project under consideration.
 Although scenario analyze can provide
useful information about a project’s stand
alone risk, it is limited because it only
considers a few discrete outcomes (NPVs),
even though there can be an infinite
amount of possibilities.
25
Assume: all variables are known with
certainty except unit sales, which could
range from 900 to 1,600.
Scenario
Probability NPV(000)
Worst
0.25
$
15
Base
0.50
82
Best
0.25
148
E(NPV) = $ 82
(NPV) = 47
CV(NPV) = (NPV)/E(NPV) = 0.57
26
If the firm’s average project has a CV of 0.2
to 0.4, is this a high-risk project? What type
of risk is being measured?
 Since CV = 0.57 > 0.4, this project
has high risk.
 CV measures a project’s standalone risk. It does not reflect firm
or stockholder diversification.
27
Would a project in a firm’s core
business likely be highly correlated with the
firm’s other assets?
 Yes. Economy and customer demand
would affect all core products.
 But each product would be more or less
successful, so correlation < +1.0.
 Core projects probably have correlations
within a range of +0.5 to +0.9.
28
How do correlation and  affect a project’s
contribution to corporate risk?
 If P is relatively high, then project’s
corporate risk will be high unless
diversification benefits are significant.
 If project cash flows are highly
correlated with the firm’s aggregate
cash flows, then the project’s corporate
risk will be high if P is high.
29
Would correlation with the
economy affect market risk?
 Yes.
 High correlation increases
market risk (beta).
 Low correlation lowers it.
30
Subjective risk factors should also be
considered
 A numerical analysis may not
capture all of the risk factors
inherent in the project.
 For example, if the project has the
potential for bringing on harmful
lawsuits, then it might be riskier
than a standard analysis would
indicate.
31
Weaknesses of Scenario Analysis
Only considers a few possible out-comes.
Assumes that inputs are perfectly
correlated--all “bad” values occur together
and all “good” values occur together.
Focuses on stand-alone risk, although
subjective adjustments can be made.
32
Monte Carlo Simulation
 A computerized version of scenario
analysis.
 Computer randomly selects a value for each
variable and combines these values to
determine the NPV/IRR of the project.
 The process is repeated many times (1,000
or more) until a probability distribution of
the project’s NPVs/IRRs is developed with
its own expected value and standard
deviation.
33
Monte Carlo Simulation
 The inputs to a simulation include all of the
principal factors affecting the project’s
profitability, and the simulation output is a
probability distribution of NPVs or IRRs for
the project.
 The project is accepted if the decision
maker feels that enough of the distribution
lies above the normal cutoff criteria (NPV
>0) or (IRR> Required Rate of Return).
34
Simulation Results (1000 trials)
Mean
St. Dev.
CV
Max
$353,238
Min
($45,713)
Prob NPV>0
Units
1260
201
Price
$202
$18
1883
$248
685
$163
NPV
$95,914
$59,875
0.62
97%
35
Interpreting the Results
 Inputs are consistent with specified
distributions.
 Units: Mean = 1260, St. Dev. = 201.
 Price: Min = $163, Mean = $202,
Max
= $248.
 Mean NPV = $95,914. Low
probability of negative NPV (100% 97% = 3%).
36
Histogram of Results
Probability
-$60,000
$45,000
$150,000
$255,000
$360,000
NPV ($)
37
Probability Density
xxxx
xxxxxxx
xx xxxxxxx
xxx xxxxxxxx
xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxx
0
E(NPV)
NPV
Also gives NPV, CVNPV, probability
of NPV > 0.
38
Advantages of Monte Carlo Simulation
 Reflects the probability
distributions of each input.
 Shows range of NPVs, the
expected NPV, NPV, and CVNPV.
 Gives an intuitive graph of the
risk situation.
39
Weaknesses of simulation
 Difficult to specify probability
distributions and correlations.
 If inputs are bad, output will be bad:
“Garbage in, garbage out.”
40
Project Risk Analysis
 Sensitivity, scenario, and simulation
analyses do not provide a decision rule.
They do not indicate whether a project’s
expected return is sufficient to compensate
for its risk.
 Sensitivity, scenario, and simulation
analyses also ignore diversification. As a
result, they measure only stand-alone risk,
which may not be the most relevant risk in
capital budgeting.
41
Risk Adjusted Discount Rate
 Calculate the NPV of a project, using a
discount rate that has been adjusted for the
riskiness of the project.
 Risk premiums applied to individual
projects are chosen in a subjective manner.
 Projects assigned to risk classes and then
the same discount rate is assigned to all
projects in each class.
42
Cost of Capital
 Capital : amount of money raised by a
corporation from creditors and investors
through the issuance of bonds (debt),
preferred stock, and/or common stock.
 Cost: the rate of return required by
investors and creditors who supply capital
to the firm, or
 The cost to the corporation of raising funds
from investors and/or creditors, or
 The minimum rate of return required on
new investments undertaken by the firm.
43
Capital Structure
 The proportion of a firm’s total assets
financed by debt, preferred stock,
and common stock.
 Component cost - the required rate of
return on each source of capital
(debt, preferred stock, common
stock)
 Target Capital Structure percentages are set for different
financing sources.
44
Weighted Average Cost of Capital
(WACC)
 The average (after-tax) cost of the sources
of capital weighted by the proportion of
each component in the firm’s capital
structure.
 EVA - firms create value if their income
exceeds the cost of capital used to finance
their operations.
 For a project to be accepted, it must
generate a return greater than its WACC.
45
WACC
 The WACC is based on the weighted costs
of the individual components of capital.
The weights are equal to the proportion of
each of the components in the target
capital structure.
 The appropriate component costs to use
are the marginal costs or the costs
associated with the next dollar of capital to
be raised. These may differ from the
historical costs of capital raised in the past.
46
Marginal Cost of Capital
 The primary objective of managers is to
maximize shareholder value. To do this
managers must select projects that are
expected to earn more than the firm’s cost
of capital.
 To evaluate a project that requires raising
and investing new capital, managers must
compare the marginal cost of capital to
the project’s expected return.
47
Cost of Debt
 The after-tax cost of debt is used
in the calculation of WACC
because of the tax savings that
result from the deductibility of
interest.
kd = ( 1- Tax rate)
48
Component Cost of Debt
 Interest is tax deductible, so the
after tax (AT) cost of debt is:
rd AT
= rd BT(1 - T)
= 10%(1 - 0.40) = 6%.
 Use the nominal rate.
49
Cost of Preferred Stock
 The rate of return investors require on the firm’s
preferred stock adjusted for flotation costs.
 kps = Dps/Pn
 Because of the non-deductibility of preferred stock
dividends, the cost of preferred stock is higher than
that of debt. As a result, firms prefer to issue debt
rather than from preferred stock.
50
Cost of Preferred Stock
 PP = $113.10; 10%Q; Par = $100; F = $2
Use this formula:
rps 
Dps
Pn
0.1 $100 

$113.10  $2.00
$10

 0.090  9.0%.
$111.10
51
Picture of Preferred Stock
0
-111.1
rps = ?
1
...
2.50
2.50
$111.10 
rPer
2
DQ
rPer

2.50
$2.50

.
rPer
$2.50

 2.25%; rps ( Nom )  2.25%(4)  9%.
$111.10
52
Cost of Common Stock (ks)
 The rate of return required by investors in
the firm’s common stock.
 Equity capital can be raised internally
through retained earnings or through the
sale of new common.
 The cost of retained earnings is the
opportunity cost, i.e. the return that
investments could earn in alternative
investments.
53
Cost of Common Stock (ks)
 Funds generated through earnings can
either be paid out as dividends or retained
to be reinvest them in the firm.
 If the funds are paid out as dividends,
stockholders can reinvest these dividends
elsewhere to earn an appropriate rate of
return.
 The cost of internal equity to the firm is
less than the cost of new common stock,
because the sale of new stock requires the
payment of flotation costs.
54
Two ways to determine the
cost of equity, ks:
1. Capital Asset Pricing Model
ks = kRF + (kM - kRF)b
= kRF + (RPM)b.
2. Dividend Growth Model
ks = D1/P0 + g
55
Capital Asset Pricing Model
 The rate of return investors require on the
firm’s common stock is a function of the
risk free rate (kRF – Treasury Bond rate),
the market risk premium, and the firm’s
beta.
 rs = rRF + (RPM )bi
Equity/Market Risk Premium: RPM =
kRF)
(rM -
 The additional return that investors require to
invest in risky equities.
56
Estimating Beta
 Run a regression with returns of the
stock in question plotted on the Y axis
and returns on the market portfolio
plotted on the X axis.
 Historical beta: based on the past
relationship between a stock’s return
and the returns of the market
portfolio.
57
Cost of equity based on the CAPM
rRF = 7%, RPM = 6%, b =
1.2
rs = rRF + (rM - rRF )b.
= 7.0% + (6.0%)1.2 =
14.2%.
58
Dividend Growth Model
 ks = D1/P0 + g
D1 - dividend to be paid next year
P0 - current price of the stock
g - expected growth rate of dividends
g = (Retention Rate)(ROE) or
g = (1- Payout Ratio)(ROE)
59
Dividend Growth Model
 Future dividends are assumed to
grow at a constant rate.
 Payout ratio - the proportion of
earnings (net income) paid out in the
form of dividends.
 Retention rate - the proportion of
earnings not paid out as dividends
(i.e. retained and reinvested in the
firm).
60
What’s the DCF cost of equity, rs?
Given: D0 = $4.19;P0 = $50; g = 5%.
D0 1  g 
D1
rs 
g
g
P0
P0
$4.191.05

 0.05
$50
 0.088  0.05
 13.8%.
61
Weighted Average Cost of Capital
WACC = wdkd(1-T) + wpskps+ wceks
 Represents the average cost of each new or
marginal dollar of capital supplied.
 Percentage capital components (wd, wps,
wce) are based on accounting book values,
current market values of the components,
or the targeted capital structure.
62
Determining WACC
1) Calculate the cost of capital for each
individual component.
 kd = ( 1- Tax rate),
 kps = Dps/Pn
 ks = D1/P0 + g
2) Compute the weighted (marginal)
cost of capital for each increment of
capital raised.
63
Factors Affecting WACC






Interest Rates
Market Risk Premium
Tax Rates
Capital Structure Policy
Dividend Policy
Investment Policy
64
Estimating Project Risk
 The (marginal) cost of capital is a function
of project’s risk.
 The firm’s WACC is closely related to the
degree of risk associated with new
investments, existing assets, and the
firm’s capital structure.
 The 3 risks associated with a project are:
1. Stand-alone risk
2. Corporate or with-in firm risk
3. Market or beta risk
65
Divisional Beta
 Security Market Line - expresses the
risk return trade-off:
ks = kRF + (kM - kRF)bi
bi - the beta of a division.
ks - required rate of return on the
division’s
investment.
66
Estimating Project Risk
 Stand Alone risk - the project’s diversifiable
risk. It is measured by the variability of the
project’s expected returns.
 Corporate/Within Firm Risk - the project’s
contribution to the firm’s overall risk (the
fact that the project represents only one of
the firm’s portfolio of assets. It is measured
by the project’s impact on uncertainty
about the firm’s future earnings.
67
Estimating Project Risk
 Market/Beta Risk - project's risk as viewed
by the a well diversified stockholder who
recognizes that the project is only one of
the firm’s assets and that the firm’s tock is
but one part of the investor’s total portfolio.
 Measures by the project’s impact on the
firm’s beta.
 Market Risk directly affects the stock prices.
68
CAPM and Project Risk
 Using the CAPM to estimate a
project’s risk adjusted cost of
capital:
kproject = kRF + (kM - kRF)bproject
69
Capital Asset Pricing Model
 Market (systematic) risk is the only
relevant risk for capital budgeting
purposes.
 Firm can be viewed as a portfolio of
assets, each having its own beta.
 The beta of a firm is the weighted
average betas of its individual assets.
70
Mistakes in Estimating WACC
 Using the current cost of debt instead of
the interest rate on new debt.
 Using the historical average rate return on
stocks instead of the current expected rate
of return on stocks to estimate the risk
premium.
 If the targeted capital structure is unknown
use the market values to obtain the
weights.
71