Cost of Capital

1
Cost of Capital Risk Analysis

• MBA Fellows
• Corporate Finance Learning Module
• Part II

2
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

3
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?

4
Project Risk

• Reflects the the potential variability of
  returns.
• Portfolio effect - if a projects proposed
  returns are not perfectly correlated with the
  returns from the firms 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
  firms other investments.

5
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.

6
Stand-Alone Risk

• The risk associated with a particular project,
  ignoring the firms 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

7
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.

8
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

9
Measuring Stand-Alone Risk

• Entails determining
• the uncertainty inherent in the projects cash
  flows.
• the nature of the individual cash flow
  distributions and their correlations with each
  other to determine the nature of the NPV
  probability distribution.

10
Probability Density
Flatter distribution, larger ?,
larger stand-alone risk.
NPV
0 E(NPV)
11
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 firms
  other projects.
• However, corporate risk ignores shareholder
  diversification.
• Depends on the projects ?, and its correlation
  with returns on the firms other projects.
• Measured by the projects beta.

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Profitability
Project X
Total Firm
Rest of Firm
0
Years
1. Project X is negatively correlated to
firms other assets. 2. If r lt 1.0, some
diversification benefits. 3. If r 1.0, no
diversification effects.
13
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 projects ? and its correlation with
  the stock market.
• Measured by the projects market beta.

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Variables that Influence a Projects NPV and IRR

• Market Size
• Selling Price
• Market Growth Rate
• Market Share (unit volume sales)
• Residual Value of Investment
• Operating/Fixed Costs
• Investment required

15
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.

16
Why is sensitivity analysis useful?

• Provides some idea of stand-alone risk.
• Identifies dangerous variables.
• Provides breakeven information.

17
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 NPVs is plotted against the
  variable that was changed.

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Example
Change from Base Level Change from Base Level Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s) Resulting NPV (000s)
Change from Base Level Change from Base Level Unit Sales Unit Sales Salvage Salvage k
-30 10 78 105
-20 35 80 97
-10 58 81 89
0 82 82 82
10 105 83 74
20 129 84 67
30 153 85 61
19
NPV (000s)
Unit Sales
Salvage
82
k
-30 -20 -10 Base 10 20
30 Value
20
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 projects expected
  NPV.

21
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.

22
Weaknesses ofSensitivity 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 arent expected to fall.
• Ignores the relationships among variables.

23
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.

24
Scenario Analysis

• Standard Deviation of NPV
• Coefficient of Variation
• CVNPV

25
Scenario Analysis

• The projects COV can be compared with the COV of
  the companys average project to get an idea of
  the relative riskiness of the project under
  consideration.
• Although scenario analyze can provide useful
  information about a projects 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.

26
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
27
If the firms 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 gt 0.4, this project has high
  risk.
• CV measures a projects stand-alone risk. It
  does not reflect firm or stockholder
  diversification.

28
Would a project in a firms core business likely
be highly correlated with the firms other assets?

• Yes. Economy and customer demand would affect
  all core products.
• But each product would be more or less
  successful, so correlation lt 1.0.
• Core projects probably have correlations within a
  range of 0.5 to 0.9.

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How do correlation and ? affect a projects
contribution to corporate risk?

• If ?P is relatively high, then projects
  corporate risk will be high unless
  diversification benefits are significant.
• If project cash flows are highly correlated with
  the firms aggregate cash flows, then the
  projects corporate risk will be high if ?P is
  high.

30
Would correlation with the economy affect market
risk?

• Yes.
• High correlation increases market risk (beta).
• Low correlation lowers it.

31
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.

32
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.

33
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
  projects NPVs/IRRs is developed with its own
  expected value and standard deviation.

34
Monte Carlo Simulation

• The inputs to a simulation include all of the
  principal factors affecting the projects
  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 gt0) or (IRRgt
  Required Rate of Return).

35
Simulation Results (1000 trials)

• Units Price NPV
• Mean 1260 202 95,914
• St. Dev. 201 18 59,875
• CV 0.62
• Max 1883 248 353,238
• Min 685 163 (45,713)
• Prob NPVgt0 97

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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).

37
Histogram of Results
38
Probability Density
x x x x x x x x x x x x x x x x x x x x x x x x
x x x x
x x x x x x x
x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x
0 E(NPV) NPV
Also gives ?NPV, CVNPV, probability of NPV gt 0.
39
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.

40
Weaknesses of simulation

• Difficult to specify probability distributions
  and correlations.
• If inputs are bad, output will be badGarbage
  in, garbage out.

41
Project Risk Analysis

• Sensitivity, scenario, and simulation analyses do
  not provide a decision rule. They do not
  indicate whether a projects 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.

42
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.

43
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.

44
Capital Structure

• The proportion of a firms 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.

45
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 firms 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.

46
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.

47
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 firms cost of capital.
• To evaluate a project that requires raising and
  investing new capital, managers must compare the
  marginal cost of capital to the projects
  expected return.

48
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)

49
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.

50
Cost of Preferred Stock

• The rate of return investors require on the
  firms 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.

51
Cost of Preferred Stock

• PP 113.10 10Q Par 100 F 2

Use this formula
52
Picture of Preferred Stock
?
0
1
2
rps ?
...
2.50
-111.1
2.50
2.50
53
Cost of Common Stock (ks)

• The rate of return required by investors in the
  firms 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.

54
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.

55
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
56
Capital Asset Pricing Model

• The rate of return investors require on the
  firms common stock is a function of the risk
  free rate (kRF Treasury Bond rate), the market
  risk premium, and the firms beta.
• rs rRF (RPM )bi
• Equity/Market Risk Premium RPM (rM - kRF)
• The additional return that investors require to
  invest in risky equities.

57
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 stocks return and the returns of the
  market portfolio.

58
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.

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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)

60
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).

61
Whats the DCF cost of equity, rs?Given D0
4.19P0 50 g 5.
62
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.

63
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.

64
Factors Affecting WACC

• Interest Rates
• Market Risk Premium
• Tax Rates
• Capital Structure Policy
• Dividend Policy
• Investment Policy

65
Estimating Project Risk

• The (marginal) cost of capital is a function of
  projects risk.
• The firms WACC is closely related to the degree
  of risk associated with new investments, existing
  assets, and the firms capital structure.
• The 3 risks associated with a project are
• Stand-alone risk
• Corporate or with-in firm risk
• Market or beta risk

66
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 divisions
• investment.

67
Estimating Project Risk

• Stand Alone risk - the projects diversifiable
  risk. It is measured by the variability of the
  projects expected returns.
• Corporate/Within Firm Risk - the projects
  contribution to the firms overall risk (the fact
  that the project represents only one of the
  firms portfolio of assets. It is measured by the
  projects impact on uncertainty about the firms
  future earnings.

68
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 firms assets
  and that the firms tock is but one part of the
  investors total portfolio.
• Measures by the projects impact on the firms
  beta.
• Market Risk directly affects the stock prices.

69
CAPM and Project Risk

• Using the CAPM to estimate a projects risk
  adjusted cost of capital
• kproject kRF (kM - kRF)bproject

70
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.

71
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.