Chapter 9: Optimal Capital Structure: M&M
I.
Modigliani and Miller (1958): The NO-TAX Arbitrage Argument
M&M Proposition 1 (No taxes): Value of the Levered Firm = Value of the Unlevered Firm
M&M Proposition II: (No taxes): The WACC is the same for both
-
M& M show that the EPS argument for leverage is misleading. They show that the corporation
should not try to increase EPS since the greater EPS also comes with greater risk.
-
M&M argue that the correct action is to try to maximize firm value. Only changes that increase
the value of the firm are beneficial to shareholders.
-
M&M show that changes in leverage alone does not affect value. If two firms have identical
cash flows, then their value must be the same, regardless of differences in leverage.
-
Their famous arbitrage proof demonstrates that investors, by creating homemade leverage, will
cause two firms with identical cash flows to have identical values:
M&M Proposition 1 (No taxes): Firm value is indifferent to financial leverage
Firm Value
Firm Value = Assets = Debt + Equity
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|_____________________________________________Value of the firm
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|______________________________________________
Debt/Assets
M&M Proposition 2 (No taxes): The WACC is indifferent to financial leverage
Cost of capital
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|______________________________________________WACC
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|______________________________________________
Debt/Assets
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 1
M&M Proposition 2: Debt does not affect the WACC
-
As the firm adds debt to its capital structure, the variability (risk) of EPS rises. Stockholders
demand a higher rate of return.
-
The stockholders’ required rate will increase just enough to offset the benefit of adding low-cost
debt.
-
The WACC will remain constant, so that value is constant.
kSU
Cost of capital
|
kSL
|
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|____________________________________WACC
|
|_____________________________________kD
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|______________________________________________
Debt/Assets
kSL
kSU
kSL
=
=
=
Required return for levered stock
Required return for unlevered stock
kSU + D/S (kSU – kD)
kSL
=
kSU
+
compensation for leverage risk.
Example:
D/S = 40/60
kSU = .10
=
.10
=
.1167 =
WACC
+
kD = .075
.40/.60 (.10 - .075)
Cost of equity for the levered firm
=
D/V(kD )
+
S/V(kSL)
=
.4(.075)
+
.6(.1167)
=
.03
+
.07
=
.10
=
Cost of equity for the unlevered firm
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 2
II.
M&M with Taxes
Proposition 1 with Taxes:
When interest is tax deductible, there is a tax advantage to adding debt to the capital structure. Using
debt allows the government to subsidize the firm and increases the cash flows to the firm.
The advantage of tax deductibility of debt from taxable earnings is called the tax shield from debt.
Compare a firm with no debt to a firm with $4,000 of 5% debt:
EBIT
Interest
EBT
Taxes (.35)
Net Income
Unlevered Firm
$ 1,000
0
1,000
350
$650
Levered Firm
$1,000
200
800
280
520
Total cash flow to stockholders and bondholders:
No Debt Firm: $650
Debt Firm: $520 + 200 = $720
The difference is $70
Tax shield from debt:
TCk DD
=
.35(.05)($4,000) = $70
Assuming a similar savings every year into perpetuity, the present value of this tax shield is:
TCkDD/ kD = $70/.05 = $1,400
Adding debt will raise the value of the firm by $1,400!
Proposition I with Taxes:
Firm Value
|
VL
|
|
|
|
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|__________________________________
Debt/Assets
Cash Flows of the Levered Firm = Cash flows of the Unlevered Firm + Tax Shield
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 3
Unlevered Firm:
Taxable income:
Total Taxes (.35):
Earnings after Taxes:
EBIT
EBIT x Tc
EBIT (1-Tc)
$1,000
$350
$650
The total cash flow to the all-equity firm is $650 after taxes
Levered Firm:
Taxable income:
EBIT – kDD
= $1,000 - .05($4,000) = $800
Total Taxes:
Tc(EBIT – kDD)
= .35(1,000 – 200) = $280
Earnings to Stockholders:
EBIT – kDD - Tc(EBIT – kDD) =
1,000 – 200 - .35(1000-200) = $520
Earnings to Stock and Bond Holders
EBIT – kDD - Tc(EBIT – kDD)+ kDD
Cancel and Rearrange:
EBIT - Tc(EBIT – kDD)
=
EBIT(1 - Tc) + TckDD
=
$650
+
$70
=
Unlevered cash flows plus tax-shield value
The total cash flow to the debt/equity firm is $720 after taxes
Bottom Line: The value of the debt tax-shield adds value to the firm
VU
Firm Value
|
VL
|
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|__________________________________
Debt/Assets
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 4
Proposition 2 with Taxes
kSL
=
kSU + D/S (1-Tc)(kSU – kD)
The WACC will fall as debt is added due to the effect of the tax shield on the costs of debt
Cost of capital
kSU
|
kSL
|
|
|
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WACC
|_______________________________________________kD
|
|________________________________________________
Debt/Value
Limits to the Use of Debt: Costs of Financial Distress
Costs of Financial Distress offset the Tax Benefit of Debt:
-
Financial distress includes all costs, including the direct costs of bankruptcy.
-
Direct costs of financial distress are the legal and administrative charges that occur during
bankruptcy proceedings and that are taken from the cash flows that otherwise would go to the
bondholders and stockholders.
-
Indirect costs of financial distress include:
*
Impaired ability to conduct business
*
Agency costs
-
Incentives by managers to take on excessive risk
Under-investment by existing stockholders
Excessive dividend payout
Excessive bond covenants
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 5
III.
M&M with Taxes and Financial Distress: The Trade-off Theory
-
Debt adds value up to a point
-
After that point, the effects of financial distress offset entirely the tax benefits
-
Setting the target capital structure that maximizes value is not a perfect science
-
The capital structure that maximizes value will be the one that minimizes the WACC.
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 6
The Trade-Off Theory of Capital Structure refers to the idea that a company chooses
how much debt and how much equity to use by balancing the costs and benefits.
An important purpose of the theory is to explain the fact that corporations usually are
financed partly with debt and partly with equity. It states that there is an advantage to
financing with debt, the tax benefits of debt and there is a cost of financing with debt, the
costs of financial distress including bankruptcy costs of debt and non-bankruptcy costs
(e.g. staff leaving, suppliers demanding disadvantageous payment terms, bondholder and
stockholder infighting, etc). http://upload.wikimedia.org/wikipedia/commons/7/79/TradeOff.png
Following Modigliani and Miller's pioneering work on capital structure, we are left with
the question: "Is there such a thing as an optimal capital structure for a company? In
other words, is there a best way to finance the company: an optimal debt/equity ratio?"
According to the trade-off theory, the answer is yes - in fact, you might even say that
there is an optimal range. There is a specific debt/equity ratio that will minimize a
company's cost of capital. (This is also the point at which the value of the company will
be maximized.)
There is a danger of getting outside of this range however. The cost of capital will
increase rapidly once you get outside the range.
http://campus.murraystate.edu/academic/faculty/larry.guin/FIN330/Optimal%20Capital%
20Structure.htm
Conclusion: Capital Structure Theory
A.
The Effect of Taxes
B.
The Effect of Bankruptcy Costs
C.
The Trade-Off Theory
D.
Signaling Theory
E.
Using Debt Financing to Constrain Managers
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 7
Appendix 1: M&M’s Arbitrage Proof for Proposition 1: Debt does not affect Firm Value
If two firms have identical cash flows, they should have identical value, regardless of differences in
leverage. M&M demonstrate that investors can arbitrage any profitable opportunities by substituting
homemade leverage for corporate leverage
If the stock of the levered firm is more highly valued than the stock of the unlevered firm, investors will
sell their shares in the levered firm, and purchase shares of the unlevered firm. They will substitute
homemade leverage by borrowing enough on a personal basis to replicate the risk they were exposed to
indirectly through the corporation. Since the risk level of the investor’s total investment is unchanged
and the expected cash flows are unchanged, then the total value of the investment should be the identical
with or without debt
Proof:
Two firms:
Unlevered (U) and Levered (L)
The cost of equity is 10 percent
The cost of debt is 7 ½ percent
You own 100% of L
Firm U has $900,000 in equity
Firm L has $400,000 in debt and $600,000 in equity
Expected operating cash flows (EBIT) is identical for both firms: $90,000.
Firm U
$90,000
$
0
$90,000
EBIT
Interest
NI
Firm L
$90,000
$30,000
$60,000
Value U
=
90,000/. 10
=
Value L
=
60,000/. 10
+ 30,000/. 075
Value of L’s stock
=
$900,000
=
$1,000,000
$600,000
Since Firm L has more value than Firm U, this violates M&M Proposition I since the operating cash
flows to the firms are identical. Your Arbitrage Action: Sell overvalued L shares and buy undervalued U
shares
You get $600,000 for your shares. You also borrow an amount equal to L’s debt ($400,000). You buy
all of U’s stock for $900,000. (Leaving you with $100,000 extra cash!)
Old Net Income:
New Net Income:
Less interest due
Total new net income
$60,000
$90,000
$30,000
$60,000
Thus your net income hasn’t changed, but you have an additional $100,000 to play with!
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 8
Appendix 2: M&M Proposition 2 (No Taxes) Proof
S = Value of Common Stock D= Value of Debt D+S = A
=Total Asset Value
RD = cost of debt RSU = Cost of unlevered equity RSL = Cost of levered equity
1.
From Proposition 1, we know that the WACC for the levered firm must equal the
WACC for the unlevered firm (ie unlevered cost of equity), if their values are equal
(which was proved in Proposition 1).
WACC = (D/D+S) x RD + (S/D+S) x RSL = RSU
WACC for levered and unlevered firms are equal (from Proposition 1)
2.
Begin to use algebra:
RSL
=
{RSU - (D/D+S) x RD}/(S/D+S)
=
{RSU x (D+S) – D x RD}/S
=
{D x RSU + S x RSU – D x RD}/S
=
RSU + {D x RSU – D x RD}/S
=
RSU + {RSU – RD} x D/S Quod Erat Demonstrandum (Q.E.D.)
A detailed power point can be found at the following:
http://home.olemiss.edu/~lpkugele/WEB338/PPT_LPK/FIN338_Ch16_lpk.ppt
Explanation with Taxes can be found at the following:
Robert H. Smith School of Business
Fin 336: Chapter 9 - Optimal Capital Structure: M&M, p. 9