1
Cost of Capital
Models and methods to estimate the appropriate r
Remember the guiding principle: The r should reflect the riskiness of the cash flows
2
Dividend Growth Model Approach
⢠Typically used for equity⢠Future dividends?⢠Future growth rates?
â Analyst forecasts⢠Analyst are optimists! (Realized growth 40-60% lower)
â Historical growth rates
â Other models
Re=(D1/P0) +g
3
Capital Asset Pricing Model (CAPM)
⢠Perfect Competition⢠All investors hold the universe of publicly traded
assets and have unlimited access to borrowing/lending at the risk-free rate
⢠No taxes or transactions costs⢠All investors plan for one identical holding period⢠All investors are mean-variance optimizers⢠All investors have homogeneous expectations
4
Implementing the CAPM Approach
⢠Theoretically can be used on any asset (equity, debt, assets, etc.) â typically used on equity
⢠Ri=Rf+Bi(Rm-Rf)â Only systematic risk (beta) is priced in equilibrium
⢠Computing the componentsâ Risk-free rate: Treasury ratesâ Market risk premium: Expected return on broad based index
such as the S&P 500 or Wilshire 5000â Beta
⢠Many services estimate equity betas: READ THEIR METHODOLOGIES!!!
⢠Estimate with historical equity data
5
How do we estimate CAPM?
⢠Expected Return Model (CAPM)
⢠Realized Return Model (Index Model)
])([)( fMifi rrErRE
itfMtiifit errrR ][
itMtiiit erR ][
6
Estimation Issues⢠Beta is non-stationary
â What estimation period?â How often do you revise?â Beta moves toward one
⢠Data Frequencyâ Daily, Weekly, Monthly?
⢠Market portfolioâ S&P 500?â Other equity indices?â Other real assets?
7
Return on Debt⢠Opportunity Cost of Debt Financing
â Use the YTM of outstanding debt which reflects opportunity cost
â Historical borrowing costs are irrelevantâ Coupon rate is irrelevant
⢠Use credit ratings to estimate cost of debt
⢠Find firms with similar debt risk (probability of bankruptcy)
8
Other Asset Pricing Models
⢠Many other models both proprietary and scholarly ⢠APT: Arbitrage Pricing Theory⢠Fama/French Model
â 3 Factor: Market return, small stock versus big stocks and high versus low book/market (value versus growth stocks)
â 4 Factor: Additional momentum factor discovered by Carhart
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Risk is Difficult to Empirically Measure ⢠Data is necessary for empirical observations⢠Usually estimate equity betas because of data
availability (asset beta is difficult to observe)⢠Equity risk comparables are difficult to find
â Need to have the same capital structure⢠Adjust for different capital structure by levering and unlevering beta
â Need to have the same business (asset) risk ⢠Industry Estimation: May use industry mean/median
⢠Other companies, other projects, divisions, etc.
⢠Usually these measures are a combination of asset or business risk and other types of risk (i.e., capital structure)
â Adjust by levering and unlevering beta
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How Do We Manage This Problem?
⢠We use the relationship between the total firm market value (V), asset (A), equity (E), debt (D) and the NPV of the capital structure/financing ()â Think of the firm value expressed as V=A+= E+Dâ The NPV of the capital structure/financing is the value
created by the capital structure choice of the firm⢠In our simple world with no bankruptcy costs, this is basically the
tax shield of debt⢠In perfect capital markets NPV of financing is zero (no taxes)
⢠The firm (assets) can be viewed as a portfolio of its financing (assume equity, debt and NPV of capital structure/financing)
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The Relationship
⢠The beta of a portfolio is the weighted average of the components therefore
⢠The return of a portfolio is also the weighted average of the componentsâ Substitute return (r) for beta () in the relationship
⢠Note: The use of this relationship is typically called levering and unlevering
DEDE
D
DE
EDEA
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What is the risk of financing NPV()?
⢠Assume BA=B (Case 1)
⢠Assume BD=B(Case 2)
⢠Assume BD=B and D (Case 3)
DEA DE
D
DE
E
DEA DE
D
DE
E
)1(
)1(
)1(
DEA DE
D
DE
E
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Assumptions about NPV of financing ()⢠BA=B
â Asset (business) risk related to the financing risk?⢠More likely if leverage is constant proportion of market value
⢠BD=Bâ Debt risk related to the financing risk?
⢠More likely if leverage is constant dollar amount
⢠Assume BD=B and Dâ Most restrictive assumptionsâ rd is the appropriate rate, debt is constant dollar amount and a
tax deductible perpetuity (D= Drd/rd)⢠How about floating rate debt?
⢠Reasonable assumptions?
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Additional Assumptions
⢠What is the beta of debt?â Can we assume it is zero?â If the firm has fixed rate debt and a low probability of
bankruptcy, its very close to zero
⢠Rule of thumb: Keep the assumptions to a minimum, in other words, lever and unlever only when necessary!
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Computing An Asset Beta⢠Asset beta is usually difficult
to observe⢠How do we estimate an asset
beta?â Strip out the asset risk by
unlevering the betaâ Or find an all equity (pure play)
firm⢠Find the Beta for a new hotel
project. The industry Be is 1.5%, average industry debt level is 20% and Bd is 0.2%. (assume Case 1).
⢠Assume Rf is 3% and Rm is 13%. Does this relationship hold for R also?
1540.0
)03.013.0(24.103.0
24.1
)2.0(2.0)5.1(8.0
A
A
A
A
DEA
R
R
DE
D
DE
E
1540.0
)05.0(2.0)18.0(8.0
A
A
DEA
R
R
RDE
DR
DE
ER
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Estimate return on equity for a new capital structure
⢠Use when you can reasonably estimate⢠New capital structure
⢠Changes in cost of debt
⢠From the previous example, the industry Ra is 15.4%. Your hotel project is going to have a debt level of 40% and the Rd is 7%. What is your Re?
2100.0
)07.0154.0(6
4154.0
)(
E
E
DAAE
r
r
rrE
Drr
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âWhole Firmâ Risk Measures⢠From portfolio theory
â Portfolio risk is the weighted average of the componentsâ risk
â Works with beta and return (but not volatility)
⢠Think of the âwhole firmâ as components of...â Financing: Debt, equity, other financing (i.e., WACC)
â Value: Business (unlevered) and financing flows
â Other logical breakouts?⢠Divisions/business units
⢠Assets in place and growth opportunities
⢠Look to the available data and logical economic components
â Used for any complex asset (does not have to be âwhole firmâ)
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Weighted Average Cost of Capital
⢠When is WACC the appropriate discount rate?â Proposed investment project is similar to the overall
business activities of the firm
â Project is financed with same capital structure weights as the firm
⢠Target weights versus actual weights
⢠Represents cost of the next dollar a firm would raiseâ Simplify the capital structure to debt and equity
⢠View the firm as a portfolio of securitiesâ Cost of Equity
â Cost of Debt
⢠WACC reflects average riskiness of firm's securities
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What if the projects are not similar to company risk?
WACC may lead to poor decisions!
⢠Incorrect Investment Decisions
Rf
Firmâs overall cost of capital
Projectâs security market line
A
B
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Weighted Average Cost of Capital (WACC)
Capital Structure weights (portfolio weights)Use market values
WACC (adjusted) = value-weighted average of after tax cost of capital
WACC = (E/V)Re + [(D/V)Rd*(1-c)]
Tax-Advantage of Debt Implies:
Estimates of Corporate tax rate?
WACC (not adjusted) = value-weighted average of cost of capital
WACC = (E/V)Re + (D/V)Rd
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Bringing it all together: Cash flow and r?
⢠FCF using WACCâ Cash flows are the flows to the total firmâ WACC is based on the firmâs existing capital
structure (RHS of the balance sheet)
⢠Adjusted Present Value (APV)â Most common use: Break the flows into flows
to assets and flows to financingâ NPV plus PV (other benefits or costs)
⢠Flow to Equity Approach (FTE)â Only estimate the flows to the equity holdersâ The appropriate r is the return on equity.
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Comparison of 3 methods
⢠Assume the project is financed with $50 of debt which costs 8% and $50 of equity which costs 12%. The yearly perpetual project cash flow is $8.8, the tax rate is 30% and assume you can perpetually take advantage of the tax shield of debt.
⢠What is the NPV?
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⢠WACC
⢠FTEâ Equity income=cash flow minus after tax cost of debt
088.0)3.01(08.0100
5012.0
100
50WACC
0088.0
8.8100 NPV
012.0
650
6)3.01)(08.0)(50(8.8)1()(
NPV
DrCmeequityincoExp CD