Advanced Project Evaluation
Global Financial Management
Campbell R. Harvey
Fuqua School of Business
Duke University
charvey@mail.duke.edu
http://www.duke.edu/~charvey
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Overview
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“Capital Structure does not matter!”
» Modigliani Miller propositions
– Implications for corporate debt policy
» Capital structure with taxes and bankruptcy costs
Capital structure and required returns
» The weighted average cost of capital (WACC)
» Ungearing betas
Optimal debt policy
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What is “Capital Structure”?
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Definition
The Capital Structure of a firm is the mix of different securities
issued by the firm to finance its operations.
» Bonds, Bank loans
» Equity, Preferences shares
» Warrants
What is the optimal capital structure?
» Debt/equity mix
» Maturity structure of debt
» Option features
» Currency-mix
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Capital Structure Does not Matter!
The Modigliani-Miller Propositions
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Under the assumption that:
» There are no taxes.
» There are no costs of financial distress
» There are no asymmetries of information
» The investment and operating policies of the firm are given.
* the value of a firm is independent of its capital structure
(MM Proposition I).
However,
» Assumptions are not realistic.
» Focus on cases where one of the assumptions are violated.
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Why is This True?
An Example
Two ways of buying the same cash flow:
1.
Buy 1% of an unlevered firm
Outlay:
0.01 VU (Value of unlevered firm)
Payoff:
0.01 OP (Operating Profit)
Can we replicate this for a levered firm?
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Buying a Stake in an Unlevered Firm
YES!
2. Buy 1% of a levered firm:
Outlay:
+
=
0.01 E (Equity of unlevered firm)
0.01 D (Debt of unlevered firm)
0.01 VL (Value of levered firm)
+
=
0.01 I (interest)
0.01 Div (Dividends, OP-I)
0.01 I + 0.01 (OP - I) = 0.01 OP
Payoff:
Conclusion:
Investors who buy 1% of all liabilities of a levered firm have the
same payoffs as investors who buy 1% of the shares in an
unlevered firm. VU = VL
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Who should Borrow?
Firms or Investors?
Assume:
Private investors can borrow and lend on the same terms as the
corporation.
Example
1. Buy 1% of the equity of a levered firm:
Outlay:
0.01 E = 0.01 (VL - D)
Payoff:
0.01 Div = 0.01 (OP - I)
2. Buy 1% of the shares in an unlevered firm and borrow 1% of the
debt level of the levered firm:
Outlay
0.01 VU - 0.01 D
Payoff
0.01 OP - 0.01 I
* If investors can borrow on the same terms, then it does not
matter who borrows. VU = VL.
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Perfect Capital Markets:
Leverage and the Cost of Capital
Firm
Value
VU
VL
DL/EL
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Why Capital Structure is (Ir)relevant
Investor Preferences:
Investors are willing to pay a premium for wider choice of
securities if:
» they prefer certain types of payoffs; (e. g. highly geared
securities, securities offering hedges against certain risks)
– and can’t create the securities themselves (e. g. cannot
borrow)
– and no other firm can offer these securities.
Is this realistic?
» Recall NPV-rule:
– are you protected from competition/imitation?
– can your security be replicated? (Cf. options)
– where could demand come from?
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Leverage and the Cost of Capital
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Consider an unlevered firm with earnings before interest and
taxes of 100 in perpetuity and cost of capital of 10%.
» Firm value is 1000
» How is this affected by leverage?
Suppose the firm issues debt of 400 with interest of 7%.
» Then dividends become:
100-0.07*400=72
» The value of equity becomes:
1000-400=600
» Hence, equity holders return is:
72/600=12%
Hence, the return on the levered firm is unchanged!
0.6*12%+0.4*7%=10%
How does this work generally?
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Leverage and the Cost of Capital:
The General Result
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Modigliani-Miller Proposition II: In a perfect capital market, the firm’s
weighted average cost of capital is invariant to its capital structure.
Hence, r*L = r*U.
This implies the following relationship between the firm’s cost of equity
and its leverage:
L


D
L
L
L
re  r*  r*  rd  L 
E 

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
In a perfect capital market, r*L = r*U =reU. This represents a return to
compensate investors for the inherent business risk of the assets of the
firm.
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Leverage and the Cost of Capital
A Graphical Illustration
Required
Return
rLe
rUe= rU* =rL*
rLd
DL/EL
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What Determines Risk?
Market value balance sheet
Assets
Market value of assets
Total value of company
=
=
=
Liabilities
Debt
Equity
Total value of company
Market value of assets
PV(Cash flow from operations)
PV(Cash flows - interest/principal) + PV(interest/principal)
Value of equity + value of debt
The cost of capital does not depend on gearing.
It depends only on the risk and return of operations.
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The Weighted Average Cost of Capital
WACC
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In a perfect capital market, the
firm’s weighted average cost
of capital (WACC)is calculated
as follows:
L
L




E
D
L
L
r*  re  L   rd  L 
V 
V 
Cost of
Capital
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However, the WACC does not
depend on leverage.
r*U
r* L
DL/EL
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Perfect Capital Markets:
Leverage and the Cost of Capital
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In addition to this business risk, there is a leverage effect.
» The equityholders in the levered firm demand a higher return:
» compensate them for higher risk of equity in a levered firm.
As leverage increases two things happen:
» the equityholders demand higher returns.
» we finance more projects by (relatively cheaper) debt.
In a perfect capital market, these two effects cancel exactly!
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Perfect Capital Markets:
Leverage and the Cost of Capital
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The CAPM can be used to compute all of these discount rates:
» Use the equity beta to compute the return on equity:
E[reL] = rf + beL (E[rm]- rf).
» Use the debt beta to compute the return on debt:
E[rd] = rf + bd (E[rm]- rf).
» Use the asset beta to compute a return commensurate with
the business risk of the assets:
E[reU] = rf + beU (E[rm]- rf).
Note that the beta of equity in an unlevered firm (beU) is also
known as the beta of the assets (ba) since the unlevered firm
has no leverage effect.
The only source of risk in the unlevered firm is the inherent
business risk of the assets themselves.
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Perfect Capital Markets:
Leverage and the Cost of Capital
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The firm’s asset beta is a weighted average of the debt and equity betas:
L
L




D
E
L
L
ba  bd  L   be  L 
V 
V 
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This implies the following relationship between the firm’s equity beta and
its leverage:
L


D
L
L
b e  b a   b a  b d  L 
E 
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Capital Structure and Returns
Macbeth Spot Removers is 100% equity financed and considers a
debt/equity-swap.
Currently:
$12m equity
$2m operating income (perpetuity)
Plan:
Retire equity worth $6m
Expected return on debt: 10%
» What is the required return on equity after the
recapitalization?
» What is the debt placed in the recapitalization worth?
» What is the perpetual stream of dividends and interest?
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MacBeth Spot Removers
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Issue $6m debt, retire $6m equity
» Cash flows to firm remain unaffected
Uses of funds (in perpetuity):
» Interest = 0.1*$6m=$600,000
» Dividends = Operating Income - Interest = $1.4m
» Return on equity = $1.4m/$6m=23.3%
Then cost of capital calculations give us:
» WACC = 0.5*23.3%+0.5*10%=16.7%
» Cost of capital=$2m/$12m=16.7%
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Leverage and Beta
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Assume a riskfree interest rate of rf = 10.0% and a market risk
premium of [E(rM)-rf] = 8.0%.
» Debt beta = 0
» Asset beta =0.833
After the recapitalization we have:
» Equity beta = 1.667
» Debt beta = 0
» Asset beta = 0.5*0+0.5*1.667=0.833
How does shareholder wealth changed?
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The impact of leverage:
Another Example: East Western Airlines
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East Western Airlines has 10 million shares out-standing,
» Share price = $20 and a
» equity beta = 1.0.
» Plan issuing $50 million of 10% debt and using the proceeds to pay a
dividend to shareholders; keep debt constant.
What effect will this capital structure change have on
» the value of the firm
» the WACC
» the equity beta
» the required return on equity
» the wealth of the firm’s shareholders?
Assume a riskfree interest rate of rf = 6.0% and a market risk premium of
[E(rM)-rf] = 8.0%.
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East Western Airlines (cont.)
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Value of the Unlevered Firm:
VU = 10(20) = 200 million.
Cost of Capital for the Unlevered Firm:
E[reU] = rf + beU (E[rm]- rf).
E[reU] = 0.06 + 1.0 (0.08) = 0.14.
Since the firm is unlevered, the value of equity and cost of equity are the
same as for the firm as a whole.
In perfect capital markets, VL = VU and r*L = r*U.
VL = VU = $200 million
r*L = r*U = 14.0%
Since the cost of debt is 10.0%, the cost of equity is determined as
follows:
reL = reU + [reU -rd ](D/E)
reL = 0.14 + [0.14 - 0.10 ](50/150) = 0.1533.
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The impact of leverage - Example
(cont.)
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The equity beta can be determined from the CAPM as follows:
E[reL] = rf + beL (E[rm]- rf).
0.1533 = 0.06 + beL (0.08).
beL = 1.167.
The wealth of the firm’s shareholders has not changed.
Shareholder Wealth = Share Value + Dividend
= $150 + $50 = $200 million
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Corporate Taxes and Leverage
Capital Structure matters if some securities enjoy favourable tax
treatments.
Suppose firm pays out $1 from operating income:
$1 EBIT
Debt
Equity
$1
$1(1-TC)
Hence, on debt value D, pay interest rDD and receive tax shield:
rDDT.
What is the tax shield worth?
How does this affect the cost of capital?
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Valuing the Corporate Tax Shield
Assume capital structure and interest rate are constant. Then:
rD DT
rD DT
rD DT


...

 DT
Value of tax shield =
2
1  rD ( 1  rD )
rD
Value of levered company:
VL = E + D + DT = VU + DT
What is the optimal capital structure now?
What is missing here?
– Ignores personal taxes
– Ignores other costs of debt (financial distress)
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Valuing a Tax Shield
Macbeth Spot Removers
Reconsider Macbeth Spot Removers
Suppose Macbeth pays 10% interest on debt and 34%
corporation tax on income after interest expenses.
What is the income statement before/after the recapitalization?
Capital Structure (Debt)
EBIT
Interest
Pre-tax income
Tax
After tax income
0
6,000
Total income
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Valuing a Tax Shield
Macbeth Spot Removers
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Assume the debt level is constant at $6m. Then the value of the
levered firm is:
VL = VU +TD
VL = $12m +(0.34)($6m) =$14.04m
The value of equity changes from $12m for the unlevered firm
to:
$14.04m - $6m = $8.04m
Hence the price drop on the ex dividend day is:
$12m-$8.04m=$3.96m
Shareholders receive a special dividend of $6m. Then total
shareholder value is:
Share price + dividend = $8.04m + $6m = $14.04m
which is an increase of $2.04m
– where do they come from?
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Who Benefits from the Interest Tax Shields?
East Western Airlines Reconsidered
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Reconsider the East Western Airlines case:
» The firm’s tax rate is 34%.
» How does this capital structure change affect the value of the firm and
the wealth of the firm’s shareholders?
Since the debt is perpetual, the value of the firm will increase as follows:
VL = VU +TD
VL = 200 +(0.34)(50) = 217 million.
Since the debt is issued at fair market value, the value of equity after the
capital structure change is:
Equity Value = $217 - $50 = $167 million.
Since the proceeds from the debt issue are used to pay a dividend to
shareholders, their wealth increases by $17 million. This is the value of
the interest tax shields on debt.
Shareholder Wealth = Share Value + Dividend
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= $167 + $50 = $217 million
The Effect of Corporate Taxes and
Leverage on the Cost of Capital
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Cost of
Capital
r *U
With corporate taxes, the firm’s
weighted average cost of capital
is calculated as follows:
L
L




E
D
L
L
r*  re  L   rd 1    L 
V 
V 
r *L
DL/EL
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Problems of Debt
The costs of financial distress
A firm which is unable, or expects to be unable, to meet its debt
obligations is in financial distress; this is costly:
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Direct costs (legal fees, administrator); usually small (typically
3% of the market value of the firm)
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Costs from losses on asset values in a “fire sale”.
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Losses from business opportunities
» customers and suppliers.
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Losses from constraints on conducting business during
corporate reorganizations.
Indirect costs can be substantial (20% of the value of the firm).
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Identify Firms with Value at Risk
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What are the characteristics of firms with low / high costs of
financial distress?
» Growth opportunities
» Tangible assets
» Riskiness of cash flows
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The “Trade-off Theory”
Firm value with leverage is now:
VL = VU + PV(Tax shield) - PV (Costs of financial distress)
Costs of distress
=
costs of bankruptcy x probability of bankruptcy
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The probability of bankruptcy increases with the debt ratio,
hence higher debt ratios imply higher expected costs of financial
distress.
The optimum debt ratio trades off increases in the costs of
distress against increases in the tax shield:
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The “Trade-off”
A Graphical Presentation
Firm Value
PV(Cost of Distress)
PV(Tax Shield)
Debt Ratio
Optimum
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Problems of Debt
Limited Liability and Risky Investments
Problem:
Managers have incentives to take negative NPV projects if
indebtedness is too high.
Example:
Firm has following asset values:
Debt Equity
Prob = 1/5
100
50
50
Prob = 4/5
25
25
0
Debt has a face value of 50.
What is the investment policy of the firm?
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Investment in a Levered Company
Do Managers Gamble?
Then we have the following market value balance sheet:
Assets
40
Equity
Debt
The firm has the following investment project:
Prob = 1/5
40
Prob = 4/5
0
10
30
- 10
The NPV of this project is -10*4/5+30/5=-2. Will the firm take it?
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Value Implications of Risky Projects
Equity holders decide on the basis of the value implications for
shareholders:
Prob = 1/5
130
Prob = 4/5
15
Debt
50
15
Equity
80
0
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Risky Projects: a Conflict of Interest
The market value balance sheet now looks like:
Assets
38
Equity
Debt
16
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Hence, taking the negative NPV project has:
» reduced the value of the firm by 2
» increased the value of equity by 6
» reduced the value of debt by 8 (6+2).
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Risky projects with negative NPV can induce a conflict of
interest between bondholders and stock-holders.
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If bondholders foresee this, they will either:
» impose covenants, or
» require higher interest; hence, higher cost of capital
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The Debt-Overhang Problem
Now, consider an alternative project the firm may take:
Prob = 1/5
5
Prob = 4/5
15
- 10
The NPV of this project is -10 + 5*1/5 +15*4/5 = +3.
Will equity holders take this project?
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Value Implications
The overborrowing-trap
Prob = 1/5
95
Debt
50
Prob = 4/5
30
30
Equity
45
0
The value of equity has now been reduced to 45*1/5=9.
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The Conflict of Interest - Reversed
The market value balance sheet becomes:
Assets 43
Equity
Debt
9
34
Hence, taking this project:
» increases the value of the firm by 3
» reduces the value of equity by 1
» increases the value of debt by 4 (1+3)
Equity-holders would loose; project cannot be financed through
equity (or junior debt). Positive NPV is lost. Only solution:
» lower gearing
» renegotiate debt
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Factors that Influence Debt
Policy in Practice
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Tax Position of the Corporation
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Costs of Bankruptcy and Financial Distress
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Variability of the Firm’s Earnings and Cash Flows
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Asset Type: Tangible vs. Intangible Assets
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Investment (or Growth) Opportunities
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The Need for Financial and Operating Flexibility
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Informational Asymmetries
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Accounting for Leverage
in Capital Budgeting
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Each investment project has its own cost of capital that depends upon
the risk of the investment.
» NPV must be computed using a discount rate appropriate for the
project, not the firm.
The risk of the investment project depends upon its unlevered (asset)
beta.
The unlevered cost of capital can be estimated using the CAPM.
The project’s leverage ratio should depend upon its own debt capacity,
not on the particular source of funds used to finance the project.
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Accounting for Leverage
in Capital Budgeting
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How do we find this?
» Step 1: Compute the beta of the assets by unlevering another firm’s
equity beta.
» Step 2: Use the CAPM to determine a required return to compensate
investors for bearing this inherent business risk.
» Step 3: Use this required return to find the NPV.
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Capital Budgeting Example
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Your firm is currently in the computer software business, but is considering
investing in the development of a new airline. Information on your firm and
the airline industry are given below:
Your
Firm
1.20
Airline
Industry
1.95
Debt-Equity Ratio
0
67%
Ave. Cost of Debt
-
10%
Equity Beta
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Capital Budgeting Example
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Your airline project is expected to cost $20 million per year for the next 5
years and is expected to generate after-tax cash flows of $10 million per
year indefinitely thereafter.
Because of your firm’s current debt position, you will finance the airline
project with 50% debt, even though this is less than standard for airline
projects.
The corporate tax rate is 34%, the riskfree interest rate is 9%, and the
market risk premium is 8%.
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Capital Budgeting Example
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Step 1: Unlever Equity Beta for Airlines
E
D


b a  b Equity    b Debt  
V
V
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The debt beta, bD comes from the CAPM:
rd  0.10  0.09  b d 0.08
 b d  0.125
b a  1.95 * 0.6  0.125 * 0.4  1.22
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Capital Budgeting Example
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Step 2: Calculate the Unlevered Cost of Capital
r*U  0.09  1.220.08  0.1876
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Step 3: Calculate the NPV of the Project

5
$10
$20
NPV  

 37.61million
 (11738
t
t
(
11738
.
)
.
)
t 6
t 1
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Summary
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Capital structure is irrelevant
» unless there are market imperfections to exploit
Leverage changes the required rates of return on debt and
equity,
» but not the required rate of return on a company
» unless taxes are important
Take into account costs of debt
» costs of financial distress
» costs from overborrowing problem
» induce managers to gamble
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