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1Valuation with Leverage
Lecture 13
Class 12: Summary
The required return on debt is lower than the required return on
equity: Debt is senior
Modigliani-Miller (M&M) irrelevance results. Under perfect
capital markets:
1. Leverage by itself does not increase firm value1. Leverage
(debt financing) increases the risk of equity2. The benefit of
debts lower cost is exactly offset by the higher equity cost
of capital (higher equity risk)2. The WACC is unaffected by
financing
M&M: the capital structure benchmark M&M: focus on the
key source of value Cash flows, cash flows, cash flows!
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2Beyond M&M
Capital structure decisions seem to matter. Evidence: Stock
prices react to financing decisions
Increase if firms: increase leverage Decrease if firms: decrease
leverage
Corporations spend resources on capital structure design Ex.
Investment banking fees
Managers are reluctant to change them: Tell a CFO that debt
policy does not matter
M&M does not predict any patterns for capital structure But,
capital structure shows lots of patterns
Across time for a given firm: life cycle Across industries:
different asset or cash-flow characteristics Across countries:
different institutional factors
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MM relied on perfect or frictionless capital markets MM: any
capital structure is as good as any other!
Thus, capital structure must matter due to some market
imperfection that affects cash-flows/value Corporate income taxes
Bankruptcy costs Agency costs (incentives) Differences in
information Security mispricing
Corporate income taxes: Can leverage be used to reduce the
corporate income taxes that
the firm must pay, and thereby increase its value for
investors?
Leverage and Taxes
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Interest expenses deducted before tax
The Corporate Income Tax
Income Statement2010 2011 2012 2013 2014
Sales Revenues 4,405 4,669 4,985 5,347 5,747Cost of Goods Sold
-2,908 -3,059 -3,240 -3,448 -3,679
SG&A Expenses -705 -747 -797 -856 -920Depreciation -132 -140
-149 -160 -172
Operating Income 660 724 799 883 976Other Income 13 10 15 20
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EBIT 673 734 814 903 1,000Interest Expense -65 -65 -80 -100
-100
Income Before Tax 608 669 734 803 900Taxes (35%) -213 -234 -257
-281 -315Net Income 395 435 477 522 585
No corresponding deduction for dividends or share
repurchases
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Gain from Leverage
With vs. Without Leverage (2014)
What is the benefit? Total income to all investors:
All equity firm = $650 Levered firm = 100 + 585 = $685
Gain from leverage = 685 650 = $35 Tax savings = 350 315 =
$35
All Equity Firm Levered Firm
EBIT $1000 $1000
Interest Paid to Debt Holders $0 $100
Pre-Tax Income $1000 $900
Tax at 35% $350 $315
Net Income to Equity $650 $585
$100
$585
Levered Firm
$650
All Equity Firm
$685
(debt)
(equity)
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The Interest Tax Shield
Debt gives the firm an interest tax shield which reduces taxes
each year:
Tax reduction = Corporate Tax Rate Interest Payments This tax
shield:
Reduces the taxes paid by the firm Increases the net-of tax
cash-flows available to both debt and equity Increases the value of
the firm:
PV(future interest tax shields) = Tc PV(future interest
payments)Tc : corporate tax rate
Value of the Interest Tax Shield
Special and simplest case: Firm increases debt by D permanently:
perpetually rolled over Each period, the tax shield is = Tc D rD.
Given that D is permanent, the
present value of tax shields is:
Gain from leverage: V(Levered Firm) = V(Unlevered) + Tc D Change
in value: V(Levered Firm) = 1 + Tc D
V(Unlevered) V(Unlev) Are these effects meaningful?
If Tc= 35%: for D / V(Unlev)= 20%, firm value increases by about
7% for D / V(Unlev)= 50%, firm value increases by about 17.5%
Bottom line: debt tax shields matter! What happens if a
competent CEO does not want to lever up?
8Offer !!!! Do it! or someone will do it for you!Call
DTr
rDTITSPV cD
Dc )(
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Weighted Average Cost of Capital
The After-Tax Cost of Debt Each $1 of interest paid gives the
firm a $0.35 tax benefit Net after-tax cost of paying $1 in
interest is only $0.65! Effective after-tax interest rate on debt =
rD (1 Tc)
Pretax WACC:
WACC with Taxes:
WACC E DE Dr r r
D E D E
(1 )WACC E D CE Dr r r T
D E D E
ur
u C DDr T r
D E
Unchanged by leverage ratio
Decreasing with leverage
u-unlevered
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Weighted Average Cost of Capital
0%
5%
10%
15%
20%
25%
30%
35%
40%
0% 20% 40% 60% 80% 100%% Debt-to-Value Ratio D/(E+D)
Equity Cost of Capital rE
Debt Cost of Capital rD
After-Tax Debt Cost of Capital rD(1c)
WACC with taxes
pretax WACC
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611
2/5/2015
For years, RadioShack the retailer that helped bring personal
computers to the masses outlasted untold predictions that it would
buckle in the face of bigger rivals and online competitors. But its
clock has finally run out. RadioShack which listed $1.2 billion in
assets and nearly $1.4 billion in total debt could still survive in
a much smaller form.
Mexico
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713
Optimal Leverage
Fact: firms dont fully exploit the interest tax shield What is
the tradeoff?
Interest/EBIT
0
10
20
30
40
50
60
1975 1980 1985 1990 1995 2000 2005 2010
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Direct and indirect costs of financial distress
If debt tax savings are so large what limits debt use?
Direct bankruptcy costs: Cost of the legal proceedings around
reorganization or liquidation Any costs directly related to the
event of bankruptcy:
Legal fees Accounting fees Advisory fees
Indirect costs of financial distress: Loss of (or damage to)
intangibles, such as brands Difficulty retaining valuable employees
Difficulty of maintaining relationships with customers and
suppliers Distortions to investment behavior when firm is close to
default Distortions to managers incentives when firm is close to
default
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815
Example cost of financial distress: GM
This idea that you just go into Chapter 11 and hang around for
three months and agree to reduce your debt obligations and don't
pay your retirees, this is a fantasy. Most people will stop buying
the cars of a bankrupt company.
Rick Wagoner (Source: Reuters, Nov 16, 2008)
Trade-Off theory of capital structure
Firms trade off tax benefits of debt against bankruptcy and
financial distress costs
Optimal leverage ratio is determined by: a. The value and
probability of using tax shields, and b. The costs and probability
of financial distress
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Characteristic EffectonOptimalLeverageProfitability Positive
Nondebttaxshields(eg.Depreciation) NegativeTangibilityofassets
Positive
Volatilityofcashflows NegativeSize Positive
Indirectcostsoffinancialdistress*
Negative*Customerconfidence,laborforcemightleave,supplierswon'tship,etc)
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Tradeoff Theory
Optimal leverage balances tax advantages and direct and indirect
bankruptcy costs
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Valuation with Leverage
Main methods for valuing a firm or project with leverage
WACC: Weighted Average Cost of Capital Method: this class Cash
Flows: Unlevered Free Cash Flow Discount Rate: WACC (after tax)
using constant leverage ratio Determines: Enterprise Value
APV: Adjusted Present Value Method (Corporate finance class,
etc.) Cash Flows: Unlevered Free Cash Flow
Interest Tax Shield Discount Rates: Unlevered (Asset) Cost of
Capital
Tax Shield Cost of Capital Determines: Enterprise Value
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Example: Diptron Incs expansion
A manufacturer of electronic switches is evaluating an
expansion: $60 million expansion Expected to increase its FCF by
$7.5 m the first year, with 4% growth thereafter Diptrons tax rate
is 40% The debt-equity ratio is 1/3 or D/(D+E)=25% The equity cost
of capital is 14.33%, and its cost of debt is 5% (pre-tax)
Questions:1. What is the WACC?2. What is the NPV of this
project?3. How large are the expected tax savings from using debt
financing?
Solution
Unlevered Cost of Capital: Diptrons pre-tax WACC:
NPV without leverage
Tax savings:
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WACC Method: Assumptions
Assumptions: Risk: Expansion has similar risk to the rest of the
firm Leverage: Diptron D/E = D/E project today and in the
future
How much debt will Diptron use to fund the expansion? Capital
structure = 75% equity + 25% debt (market value)
25% $60 million investment = $15 million25% $40 million inc. in
mkt value = $10 millionTotal new debt = $25 million
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Adjusted Present Value (APV) Method
Unlevered Cost of Capital: Diptrons pre-tax WACC:
rUnlevered = (E/V) rE + (D/V) rD = 75% 14.3333% + 25% 5.0%=
12%
NPV without leverage
NPVU = -60 + 7.5/(12% - 4%) = -60 + 93.75 = $33.75 million
Interest Tax Shield
First Year: $25 million 5% 40% = $0.5 million PV(Int Tax Shield)
= 0.5/(12% - 4%) = $6.25 million
Adjusted Present Value
APV = NPVU + PV(Int Tax Shield) = 33.75 + 6.25 = $40 million
Increases by 4%/yr
Same risk as project
U-unlevered
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Alternative Leverage Policies
Suppose Diptron will not maintain a fixed D/E ratio Instead
Diptron plans to:
Borrow $60 million initially Repay $60 million after 2 years
NPV without leverageNPVU = -60 + 7.5/(12% - 4%) = -60 + 93.75 =
$33.75 million
Interest Tax Shield
APV (at 5%) = 33.75 + 2.23 = $35.98 million
Sum Year1 Year2Interest 3,000 3,000
Interesttaxshield 1,200 1,200PresentvalueITS(at12%) 2,028 1,071
957PresentvalueITS(at5%) 2,231 1,143 1,088
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Valuation Methods in Practice
WACC is the most common method Easiest to apply when the project
has a constant target D/E ratio Implicitly assumes that the debt
tax savings are as risky as the
projects cash flows Important note:
Many firms calculate a single firm-wide WACC and apply it to all
new projects: that is typically wrong!
Only valid if all projects have: (a) same target D/E as the firm
and (b) similar business risk
APV is useful if the leverage ratio (D/E) is not constant
Easiest to apply when future debt levels are known Easy to use a
different (lower) discount rate for the debt tax
savings Easy to adjust for other costs or benefits of debt
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Big picture
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Belgium: Notional Interest Deduction
Since 2006, firms receive a tax deduction based on the book
value of equity (deduction=Equity*rD) Level the financing playing
field
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Source: Panier, Perez-Gonzalez and Villanueva (2014)
30%
32%
34%
36%
38%
40%
42%
44%
2002 2003 2004 2005 2006 2007 2008 2009
Percentages
Equitytoassetsratio
PreReform PostReform
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Summary
M&M: capital structure affects value if D,E affect cash
flows Corporate income taxes: Interest payments are tax-deductible.
Debt financing can increase the net-of-tax cash flows and hence
value M&M intuition holds
Trade-off theory of capital structure. Firms choose an optimal
level of debt financing that balances: 1. The tax benefit of using
debt financing (tax-shield) against2. The costs of financial
distress (ex. bankruptcy costs)
Valuation methods to capture the effect of debt tax shields on
firm value: WACC: discount FCFs using the weighted average of
after-tax debt costs and
equity costs Adjusted Present Value (APV). Two steps:
1. Value projects as if 100% equity financed: FCFs &
all-equity cost of capital2. Add the present value of the tax
shield of debt: using the expected interest
tax shield and the tax shield cost of capital