CAPITAL STRUCTURE 2 Two primary funding sources: debt and equity 4 Each source has different risk level 2 Each funding source must be compensated for opportunity cost of what suppliers of funds can earn elsewhere, on investments of equivalent risk 2 In order to be accepted, projects must increase owners’ expected utility of wealth Each project must provide, on a risk adjusted basis, enough CF to pay required returns to equity and debt holders, pay back original investments, and leave something extra to increase owners’ (equity holders’) EU of wealth. 2 Cost of capital: minimum risk adjusted return to shareholders
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CAPITAL STRUCTURE - Michigan State University no debt and CAPM: Cost of Capital = E(kj) k 0 E(k m k 0) j We need to consider effect of debt on the cost of capital Also does capital
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CAPITAL STRUCTURE
� Two primary funding sources: debt and equity
� Each source has different risk level
� Each funding source must be compensated for opportunitycost of what suppliers of funds can earn elsewhere, oninvestments of equivalent risk
� In order to be accepted, projects must increase owners’expected utility of wealth
Each project must provide, on a risk adjusted basis, enoughCF to pay required returns to equity and debt holders, payback original investments, and leave something extra toincrease owners’ (equity holders’) EU of wealth.
� Cost of capital: minimum risk adjusted return toshareholders
� With no debt and CAPM:
� Cost of Capital = E(kj) � k0 � E(km � k0) j
� We need to consider effect of debt on the cost of capital
Also does capital structure really matter?
That is, does a firm’s capital structure impact the firm’svalue?
VALUE OF THE FIRM WITH CORPORATE TAXES
� Value of a Levered Firm
� Modigliani and Miller (1958, 63)
� Capital markets are frictionless� Borrow and lend at the risk-free rate� No cost to bankruptcy� Two types of claims: risk-free debt and (risky)
equity� All firm’s in the same risk class� Only corporate taxes� All CFs are perpetuities (no growth)� No signaling opportunities� Managers maximize shareholder wealth
� Many of the assumptions can be relaxed without changingmajor conclusions
� e.g., risk-free assumption on debt can be relaxedwithout impacting results
� Bankruptcy and personal tax assumptions do have criticalimpact on results
� Clarification: All firms in the same risk class
� Implication: Risky CFs vary only by a scale factor
where = constant scale factorCFi � CFj
In other words, CFs are perfectly correlated
Consider gross returns
rit �CFit � CFit&1
CFit&1
CFi � CFj � rit �CFjt � CFjt&1
CFjt&1
�CFjt � CFjt&1
CFjt&1
� rjt
So if CFs differ only by scale factor, they will have thesame distribution of returns, the same risk, and will requirethe same expected return.
� Assume the firm’s assets generate the same distribution ofoperating CFs each period after-taxes forever.
Thus value of the firm without any debt is
V u �E(c)ku
where
Vu = present value of an unlevered firm
= expected after-tax cash flow in perpetuityE(c)
ku = discount rate for all equity firm
Remember stuff on estimating CF
˜ATCF � ˜NIAT � Dep
� (R � Vc � Fc � Dep)(1 � tc) � Dep
� no other accruals� no interest cost because no debt� no growth
V u �E(c)ku
�E( ˜EBIT)(1 � tc)
ku
We've assumed c is generated in perpetuity.
This implies depreciation each year must be replaced byinvestment in order to keep the same amount of capital inplace.
Thus we're assuming Dep = I where I is capital investmenteach year.
= c ˜NIAT � Dep � I
= ( ˜Rev � Vc � Fc � Dep)(1 � tc) � Dep � I
= ( ˜Rev � Vc � Fc � Dep)(1 � tc)
= ( ˜EBIT)(1 � tc) � ˜NIAT
When all CFs are perpetuities, CFs to investors is the sameas NIAT, so
� Now assume the firm issues debt
After-tax CFs must be split between debt and equityholders
� Equity holders get: ˜NIAT � Dep � I
Debt holders get: kd D
where kd = interest rate on debtD = face value of debt
� Thus to total CF to debt and equity holders is
( ˜NIAT � Dep � I) � kd D �
( ˜Rev � Vc � Fc � Dep � kd D)(1 � tc) � Dep � I � kd D
� Assuming no growth (Dep = I), the total CF is
= ˜NIAT � kd D ˜EBIT(1 � tc) � kd Dtc � �
CF to unlevered Tax shield from firm . Will have using debt (risk-free(c) same risk level. by assumption).
V L �E( ˜EBIT)(1 � tc)
ku
�kd Dtc
k0
� Discounting each CF by the appropriate discount rate forits risk class, we find the value of the levered firm to be
where VL = value of levered firmk0 = risk-free rate
Note: kdD is the perpetual stream of risk-free paymentsto debt holders
This implies the market value of the risk-freedebt is
B = = market value of debt (bonds)kd D
k0
� Rewriting we find,
VL = Vu + Btc
Value of a levered firm is equal to the value of theunlevered firm plus the present value of the tax shieldprovided by debt.
Note that in the absence of any market imperfections(i.e. tc = 0), the value of the firm is not dependent onthe capital structure of the firm
V L � V u (if tc � 0)
This famous result is known as Modigliani-MillerProposition I (MMI).
MMI (Arbitrage argument) (tc = 0)
2 firms, identical except for capital structures
Lever Company Unlevered CompanyE(EBIT) = $200 E(EBIT) = $200VL = ? Vu = $1000BL = 500 Bu = 0EL = ? Eu = 1000kd = .10 ku = .20
V u �E(EBIT)
k u�
200.20
� $1000
Strategy I: Buy 10% of Unlevered
Investment Cash Flow
.10($1000) = $100 .10( ˜EBIT) = .10(Vu)
� Strategy II: Buy 10% of Levered Company’s Equity
Analysis: Effect of financial leverage depends on company’s income.
Possible Argument: Expected income is $1,200,000 so thefirm should take on additional debt.
Argument is flawed. Shareholders canborrow on personal accounts andduplicate effects of company’s leverage.
� Invest $2,000 in levered
Leverage Plan
Recession Expected Expansion
EPS 0 $4 $8
EPS x 100 shares 0 400 800
Initial Cost = 100 Shares @ $20/sh. = $2000
� Invest $2,000 in unlevered
Homemade Leverage (Borrow $2,000 – Buy 200 shares in Unlevered)
Recession Expected Expansion
EPS x 200 sh. $1 x 200 = 200 3 x 200 =600
5 x 200 =1000
Int = .10(2000) 200 200 200
0 400 800
Initial Cost = 200($20) - 2000 = $2000
V L � V u � Btc
� This is another illustration of MMI. In a world withouttransaction costs, capital structure doesn’t matter.
Effectively, increases in expected returns from leverage areoffset by additional risk (more later).
� Doesn’t match reality
� Letting tc > 0,
giving debt preferential tax treatment (allowing a taxdeduction for interest payments) increases the value of thefirm as the firm takes on more and more debt.
� firms should use almost all debt financing.
� Doesn’t match reality
WEIGHTED AVERAGE COST OF CAPITAL (WACC)
Suppose project is funded with
B = $ by debt holdersE = $ by equity holders
I = $ of initial investment
I = B + E
The WACC is defined so that suppliers of capital receive theirrespective required return given the risk they must bear.
� wd and we often assumed set at some "target level" (morelater)
� kw supplies required return to each contributor of capital
V u ku � tcBkd � Eke � Bkd
ke �V u
Eku � (1 � tc)
BE
kd
Relationship between ke and debt
VL = Vu + Btc
� Expected ATCF into levered firm
Vu (ku) + (kd)Btc� �
same risk same risk as as c kd D
� Expected ATCF to debt and equity holders
Eke � Bkd
� Cash inflows = cash outflows (no growth)
Remember
V L � V u � tcB � B � E
so V u � E � B(1 � tc)
Substituting,
ke �E � B(1 � tc)
Eku � (1 � tc)
BE
kd
� ke � ku � (1 � tc) (ku � kd)BE
(MMII)
� Opportunity cost of equity capital increases linearly
with a change in .BE
� With no debt, ke = ku.
Example:
AGFIRM is currently unlevered. It is considering restructuringto allow $200 in debt. Company expects to generate $151.52 inEBIT (perpetuity). Corporate tax rate = 34%. Cost of debt is10%. Unlevered firms in the industry require a 20% return.
� What will AGFIRM’S value be if it restructures?
E( ˜ATCFu) � E( ˜EBIT)(1 � tc)
� $151.52(1 � .34)
� $100
V u �E(ATCF u)
k u�
100.20
� $500
V L � V u � tcB � $500 � 200(.34) � $500 � $68
� $568
Suppose AGFIRM started with 500 shares
Share priceu = V u
shares�
$500500
� $1
Share priceL = V L � B
shares�
$568�$200300
� $1.23
Value of equityL = EL = VL - B = $568 - $200 = $368
� What is the required return on AGFIRM’s equity?
ke � ku � (1 � tc) (ku � kd)BE
� .20 � (1 � .34)(.20 � .10) 200368
� .2359
Use of debt increased required return on equity fromku = .20 to ke = .2359
Check
E L �(E(EBIT) � kd B)(1 � tc)
ke
= $368�(151.52 � .10(200)) (1 � .34)
.2359
� Find AGFIRM’s WACC
wd �B
V L�
200568
� .352 we �368568
� .648
kw = weke + wdkd (1- tc)
= (.648)(.2359) + (.352) (.10)(1 - .34)
= .15286 + .02323
= .1761
The firms WACC decreased from kw = ku = 20% tokw = 17.61% as a result of the debt use.
Check value of the firm
$568V L �E(EBIT)(1 � tc)
kw
�151.52(1 � .34)
.1761�
Suppose the firm holds a $100 in assets. Required paymentto capital suppliers = I · kw
� �CF to unlevered CF to debtfirm after taxes holders after
taxes
So
VL � Vu � B 1 �(1 � tc) (1 � te)
(1 � td)
where B = kdD (1 - td) / kd
Gain from leverage in world with personal taxes
G � B 1 �(1 � tc) (1 � te)
(1 � td)
Notes:
� When te = td, gain is same as in world without personaltaxes
� When te < td, gain from leverage is reduced from worldwithout personal taxes
� Reasons te may be less than td
� capital gains tax break� capital gains may be delayed by reinvestment� gains and losses in a portfolio may offset each other� dividend exclusions for corporations
when te < td, more taxes get paid in a levered firm, thanan unlevered firm at the personal level
$
B
$
B
VL = Vu + tcB when te = td
VL = Vu + B[1-(1-td)
]
when (1-td) > (1-tc)(1-te)
(1-tc)(1-te)
VL = Vu when
(1-td) = (1-tc)(1-te)
� If , gain from leverage is zero.(1 � tc) (1 � te) � (1 � td)
Lower corporate taxes from leverage are exactly offset byhigher personal taxes.
TAX POLICY AND FINANCING INCENTIVES
Before 1986: Corporate Income – 46% maximumInterest and Dividends – 50% maximumCapital Gains – 20%
Suppose firm pays no dividends and capital gains are deferredso that the effective tax rates are te = 10%, td = 50% and tc = 46%.
Interest Equity IncomeIncome before tax $1.00 $1.00Less Corporate tax @ 46% 0.00 0.46Income after Corporate tax 1.00 0.54Less Personal tax (te=.10 and td=.50) 0.50 0.054Income after tax $0.50 $0.496
Small advantage to debt = $.004
Essentially no advantage to debt
1999: Corporate Income – 35% maximumInterest and Dividend – 39.6% maximumCapital Gains – 20%
Suppose effective capital gains rate is 20%/2 = 10% and that nodividends are paid.
Interest Equity IncomeIncome before tax $1.00 $1.00Less Corporate tax (tc = 35) 0.00 0.35Income after Corporate tax 1.00 0.65Personal tax (td=.396 and te=.10) 0.396 0.065Income after tax $0.604 $0.585
Advantage to debt = $0.019
Now suppose the same firm in 1999 pays out 1/2 of equityincome as dividends.
Effective tax rate on equity (.396 + .10)/2 = .248)
Interest Equity IncomeIncome before tax $1.00 $1.00Less Corporate tax (tc=.35) 0.00 0.35Income after Corporate tax 1.00 0.65Personal tax (td=.396 and te=.248) 0.396 0.161Income after tax $.604 $0.489
Advantage to debt = $.115
� Advantage tends to favor debt
� Magnitude not clear and depends on tax rates of equity anddebt holders as well as dividend payout rates
EXAMPLE
(perpetuity)E(EBIT) � $100,00
tc � 34% te � 12% td � 28%
ku (1 � tc) � 15%
Currently all equity, but considering borrowing $120,000at 10%.
V u �$100,000(1� .34)(1� .12)
.15(1� .12)� $440,000
VL � $440,000 � $120,000 1 �
(1 � .34)(1 � .12)(1 � .28)
� $463,200
= $23,230G � VL � Vu � 463,200 � 440,000
Smaller than tcB = .34(120,000) = $40,800
Extra tax on debt (td > te) at personal level lowers gainsfrom debt
� Implications
� Gains from leverage still positive (probably) butsmaller than thought if te < td
� "Grossed" up return on debt to equate after-tax returns(if te < td) offsets same debt advantage
Result
� Framework also lays out arguments for equilibriumaggregate debt levels (another day)
� How firms establish capital structure
� Practical difficulties — no "formula" for optimaldebt structure
� Empirical Evidence
� Most firms have "low" D/E.
U.S. average D/E : .3 to .5
Firms pay substantial taxes but clearly don't issuedebt to point where tax shield is exhausted
� Announced increases (decreases) in anticipatedleverage tend to increase (decrease) firm value
� Capital structures differ by industry
� Profitability� Growth� Intangible assets
� Firms tend to maintain target levels at D/E
FACTORS TO CONSIDER IN DETERMININGTARGET D/E
� Taxes (tax shield)
� Financial Distress Cost
� Variable income � increase probability of financialdistress
� Tangible assets � less financial distress� Intangible assets � more financial distress
� Credit Reserves
� External equity can be expensive to issue relative tointernal equity
� Maintain credit capacity (low D/E) to allow capitalexpenditures without issuing new equity
� Industry D/E Ratios
Reconciling M-M and CAPM
Unifies approach to determining discount rate (cost of capital)
Type ofCapital CAPM MM
Debt kd = krf + (km-krf) d kd = krf , d = 0
Unlevered Equity ku = krf + (km-krf) u ku = ku
Levered Equity ke = krf + (km-krf) L ke = ku + (ku -kd)(1-tc) B/E
WACC kw = weke + wdkd(1 - tc)
kw � ku 1 � tcB
B�E
wd �B
B�Ewc �
EB�E
Can easily modify MM risk-free debt assumption:
kd � krf � (km � krf) d
Relationship between L + u
ke � krf � (km � krf) L � ku � (ku � kd) (1 � tc)BE
Substitute kd � krf � (km � krf) d
ku � krf � (km � krf) u
Rearrange and simplify
L � u � ( u � d) (1 � tc)BE
� u (1 � (1 � tc)BE
) � d (1 � tc)BE
If we observe L, we can estimate u
u �
L � d (1 � tc)BE
1 � (1 � tc)BE
EXAMPLE
Currently wd = .2 (market value)Considering wd = .35
kd = krf = .07 ( d = 0)tc = .5km = .17
L = .5 (wd = .20)
� Find the current values of ke and kw
ke � krf � (km � krf) L
� .07 � (.17 � .07) .5
� .12 or 12% (at wd � .2)
kw � weke � wd kd (1 � tc)
� (.8) (.12) � (.2) (.07)(1 � .5)
� .103 or 10.3% (at wd � .2)
� Find kw if the new target capital is wd = .35
Remember ke will increase as the debt level rises relative toequity
MM’s definition of kw says
kw � ku 1 � tcB
B � E
which implies (using observed results at wd = .20)
ku �kw
1 � tcB
B � E
�.103
1 � (.5)(.2)� .1144
So if wd = .35, MM’s definition of kw says
kw = .1144 (1 - (.5)(.35)) = .09438 or 9.438%
� We could have calculated the new L and ke and precededwith the standard kw approach directly
At wd = .2, Remember d = 0u �L
1 � (1 � tc)BE
�.5
(1 � (1 � .5)(.25))� .4444
So at wd = .35, the new L will be
L � 1 � (1 � tc)BE u
� [1 � (1 � .5)(.5385)] (.4444)
� .5641 (at wd � .35)
Thus ke = krf + (km - krf) L = .07 + (.17 - .07) .5641
= .1264
and
kw � wd ke � wd kd (1 � tc) (at wd � .35)
� (.65)(.1264) � (.35)(.07)(1 � .5)
� 0.944 or 9.44%
� Suppose project has same systematic risk as firm, L, andprovides expected return at 9.25%. Should project betaken?
%
B/E
ke
25% 53.85%
12.6%
12%
10.39.4
ku(1 - tc)kd(1 - tc)
kw = ku (1 - tc (B/B+E))
E(kp) � .0925 < kw � .0944
� Evaluating projects with different risk levels than the firm.
� Find the required return assuming all equityinvestment.
� Adjust for the firm’s capital structure using theapproach(s) from the previous section.
Example: uj � 1.2, krf � .07, km � .17
� = krf + (km - krf) k uj
uj
= .07 + (.17 - .07) 1.2 = .19 or 19%
� kw = ku (1 - (1 - tc) B/B+E)
= .19 (1 - (.5) (.20)) = .171 or 17.1% at wd = .2
= .19 (1 - (.5) (.35)) = .157 or 15.7% at wd = .35