MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Definition: Capital Structure refers to the mix of securities used to finance the firm’s investment
projects. Note: this is the mix of all securities of the firm outstanding, not just new securities
issued to finance new projects. When considering capital structure we always look at the market
values of debt and equity and the market rates of return on each. If market values are not
available, then estimates of market values should be used.
A. Miller and Modigliani (M+M) Theories with no taxes.
Miller & Modigliani’s Proposition 1
In a world with no taxes, the firm’s capital structure does not matter.
The firm’s value is determined by its real assets, not by the securities issued against them.
See “pies”
Miller & Modigliani’s Proposition 2:
The expected rate of return on common stock of a levered firm (firm with debt financing)
increases in proportion to the debt/equity ratio. (Note: D/E ratios must be using market values,
not book values.)
E.g., if a firm’s debt has its expected rate of return held constant at RD, then as the proportion of
debt increases, the expected rate of return on equity must increase.
Recall firm is due to the firm’s assets, firm doesn’t change as financing changes.
firm = X E E+(1-XE)D
If X E  1-X E 
E  to maintain firm. For moderate levels of debt, D does not change.
Note: X D = proportion of firm financing which is debt = (1-XE)
D V
   so there is no equity and the debt risk must be the same as the overall
E 0
risk of the firm’s assets.
When XD = 1,
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 2 of 8
Now, look at firm’s WACC (no taxes) with changes in capital structure:
Assets = A
E
D
Assets =  E +  D
V
V
Rearranging terms we get  E  A 
D
(  D )
E A
In the example below we assume debt is risk free. With this simplifying assumption, D = 0 and
thus we get a simpler form for the equity beta as follows: E=V/E A
The equity beta increases relative to the asset beta because of financial risk– i.e., risk due to
leverage. Note that asset beta is the result of cyclicality of output and revenues and the degree of
operating leverage – these two determine the operating risk or asset risk.
E[rE] = rf + E[E(rm) - rf]
Firms WACC =
E
D
 E[r E ]  E[r D ]
V
V
If (for simplicity) D = 0, we can replace E[rD] with rf. Now we can also substitute in the CAPM
(somewhat rearranged) for E[rE]:
E
D
WACC =  β E E[r m ]  rf (1  β E )  [rf ]
V
V
E
V
E
E V
E 

=  β A E[r m ]  rf  rf   β A   rf  rf 
V
E
V
V E
V 

= E[rm]A-A rf + rf
= rf + A[E(rm) - rf]  independent of proportion in E or D
We have seen that with zero taxes, WACC of the firm doesn’t change with changes in the firm’s
mix of securities because betas of securities change so as to keep the  of the firm constant.
Summary:
As D/E increases, the value of the firm doesn’t change, the WACC doesn’t change, and the asset
beta doesn’t change. However, as D/E increases, the market values of D and E obviously change,
and the risk and expected return of equity both increase. For very high levels of debt, the debt
beta will also increase.
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 3 of 8
Do investors prefer to hold stock in firms with different capital structures?
Assumptions: perfect capital markets
- no transaction costs, no taxes
- lending & borrowing rates are same
- competitive markets
Let rf = .10 [E[rm]-rf] = .09
Two firms hold exactly same assets  is same overall for firms.
Firm 1
Firm 2
1.2
1.2
 assets
75% = X = .75
50% = X = .50
% in Equity
25%
50%
% in Debt
0.1
0.1
 of debt
Note:  of equity is solved from assets = X(e) + (1-X)D so 1.2 = Xe + (1-X)0.1
2.3
e
1.5 6
E[re] = rf+e(E[rm]-rf)
.24
.307
E[re] =
Suppose an investor currently has a well diversified portfolio with  = 1.56. Suppose the
investor prefers a portfolio with  = 1.56, will the investor pay a premium for firm 1’s stock
because it possesses that  whereas firm 2 stock has a higher ?
No. Why? The investor can achieve the same desired  using either stock.
E.g.
Using Firm 1: just buy the stock,  = 1.5 6 E[rp] = .24
Using Firm 2: Want  = 1.5 6 , then buy a combination of firm 2’s stock & risk-free asset.
p = X(2) + (1-X)0 rf
1.56 = X(2.3)
1.56
 0.678260870
X=
2.3
So, for each additional dollar invested in the portfolio, invest $.678260870 in firm 2’s stock and
$.32173913 in risk free asset.
E[rp] = X(E(re2)) + (1-X)rf
= .67826087(.307) + (.32173913)(.10) = 0.24
With no transaction costs, etc., the investor is indifferent between the two possibilities, therefore
no premium will be paid for a particular capital structure of a firm.
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 4 of 8
B. Taxes in the M&M analysis
Previously with taxes we saw the WACC decreases as the proportion of the firm financed
through debt increased because interest expenses are tax deductible.
WACC = D/VE[rD] (1-TC) + E/VE[rE]
D
increases, E[rE] will
V
increase as before (similar to the no tax case) but unlike the no tax case, the higher proportion of
financing with tax-subsidized debt results in WACC decreasing.
Assume over moderate levels of debt that E[rD] does not change. Then as
Note: E[rD] cannot always be constant; as D/V approaches 1, the debt becomes as risky as the
firm.
MM adjust their proposition one in the presence of taxes to …
MM Proposition I corrected to reflect corporate income taxes
Value of firm = value if all equity financed + PV tax shield from debt interest payments
VL = Vu+TcD
Why? Because in after tax cash flows, introducing debt will incur interest charges but part of
these will be paid by government through reduced taxes  more of the firm’s financing cash
flows are paid by the government. In effect, more of EBIT is available for security holders and
less goes to the government. Thus the total value of the firm (D+E) goes up.
E.g. for simplicity assume a risk free firm with EBIT of $100,000 per year in perpetuity.
Before tax: EBIT = $100,000 (assume risk free)
Tc = 40% Let rf = 10%
Consider an all-equity financed firm, all income (after taxes) is paid out as dividends.
Income before tax = 100,000, tax = 40,000, therefore Income after tax = 100-40 = 60,000.
PVdiv = 100,000(1-TC)/rf = 60,000/0.10 = 600,000 = VU = E
Now consider a levered firm …
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 5 of 8
Consider a firm that has perpetual bond financing with interest per year = 20,000
Earnings before interest and tax (EBIT) = 100,000
Earnings after interest = 80,000
Tax = 32,000
Earnings after interest and tax = 48,000
PVdiv = 48,000/0.10 = 480,000 = value of equity = E
PVint = 20,000/0.10 = 200,000 = value of debt = D
PVfirm = Value of firm = 680,000 = D+E = VL
Or using M+M revised Proposition 1:
VL = Vu+TcD
PVfirm = 600,000 + PVinterest tax shields
The annual tax shield is the change in tax due to the interest, 40,000-32,000, or calculated as
TC  Interest = 8,000/yr.
PVinterest tax shield = 8,000/0.10 = 80,000
PVfirm = 600,000 + 80,000 = 680,000
C. Other Considerations
Why not finance the firm entirely with debt? WACC drops and MM say value increases.
Personal taxes
Investors generally face higher tax rates on interest income than on capital gains or dividend
income.
- interest income is taxed at the investor’s personal tax rate.
- tax on capital gains can be deferred until the capital gain is realized (when the stock is sold)
- tax on dividend income is reduced by the dividend tax credit.
Counterargument to personal tax reason:
Some investors (e.g. pension funds, RRSP’s) are exempt from paying tax on interest income (or
any other income)  firms could increase their value by financing with debt placed to these tax
exempt investors and the firms still get a tax reduction because of interest payment  more funds
available to be paid out.
But . . .
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 6 of 8
Merton Miller - Debt & Taxes, Journal of Finance, May 1977, argues that all firms will try
to exploit the ability to issue debt to zero-tax investors. As there are fewer tax exempt
institutions left to buy the firms debt, firms will try to place their debt with low-tax investors. In
order to entice more investors to the firm’s debt, the firm will have to raise the interest payments
(yield or return) on the debt. As firms try to place more debt, the tax rates of the “newly enticed”
investor will creep up and the firm will have to pay even higher interest rates to entice these
investors. Eventually, the point will be reached where the tax advantage to the firm of debt is
offset by the high rate of interest required … resulting in indifference to debt or equity financing.
Result: there will be an optimal debt/equity ratio for the economy, but individual firms will be
indifferent to debt or equity financing.
Miller shows that with both corporate and personal taxes, the following holds:
 1  Tc 1  TPE 
VL  Vu  D  1 
1  TPD  

where the subscripts on the tax rates T refer to tax on the following kinds of income:
C = corporate income
PE = personal equity income
PD = personal debt income
Bankruptcy Costs and Costs of Financial Distress
The likelihood of bankruptcy costs or costs of financial distress (being perceived as unlikely to
be able to meet debt obligations) increases as debt levels increase.
It is more likely the firm won’t be able to meet fixed obligations (i.e. coupon or interest
payments) as the fixed obligations increase.
Investors may then value firm as
VL = VU + PVnet interest tax shields - PVexpected costs of financial distress
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 7 of 8
Costs of financial distress:
Direct costs: Legal and admin (e.g., 5.3% of pre-bankrupt market value for railways)
Indirect costs Loss of value of intangible assets
Lost ability to invest in + NPV projects; not able to finance them – less flexibility
Loss of preferential terms given by suppliers
Loss of customers (when after sales support is important)
Loss of best employees
There will be higher bankruptcy costs for firms with intangible assets, e.g., reputation, brand
names, human capital, etc. vs. tangible assets, e.g., buildings, land, etc.
Limit to debt financing
Want to increase debt until the marginal benefit from the increase in PV of interest tax shields
equals the marginal cost from the increase in the PV of bankruptcy costs.
More Indirect Costs of for firms in financial distress:
Adverse incentive problems
1. Select high risk projects
-shareholders benefit as there is a chance of a payout to them but bondholders are hurt because
what is left for them is more risky and there is a greater chance of even less being available for
them. (When near bankruptcy, it is best to view the equity as an out-of-the money call option on
the firm’s assets. As the assets are more variable, there is more value for the option holder – the
stockholders.)
2. Pass up +NPV projects because shareholders won’t provide financing.
- the benefits would only (or mainly) go to the bondholders
3. Pay a large dividend
-shareholders benefit by receiving cash they otherwise would not get; bondholders are hurt by
having less left to pay to them.
Copyright © 2002 David A. Stangeland
MBA 8415
Capital Structure and Theories
Dr. D.A. Stangeland
Page 8 of 8
Agency Costs and Capital Structure
Recall the Stockholder - Manager conflict
- If the manager owns less than 100% of the firm, then less than a 100% proportion of the cost
will be borne by the manager if perquisites or shirking are done
e.g.
Manager owns 50% of firm
Manager consumes $100 of perquisites
Cost to manager  personal shares drop by $50
 total firm’s shares drop by $100
There is an incentive for a non-owner manager to consume perquisites or to shirk on his/her
duties. Jensen, 1986, states that this problem is more severe when managers control a greater
amount of “free cash flow” from the firm. If “free cash flow” at management’s discretion can be
reduced, the costs of undesired perquisites and shirking can be reduced too and thus the total
value of the firm can be increased. Jensen states that higher debt levels reduce discretionary cash
flow and thus reduce these costs.
M&M irrelevancy assumes operating cash flows of the firm are unaffected by capital structure.
The argument now is that capital structure can affect the size of the operating cash flows, EBIT.
Signalling
Information about firms is not symmetric between the firm’s managers and investors in the
capital markets. With asymmetric information, managers’ actions can be analyzed to try to infer
additional information about their firms.
Capital structure changes may signal what managers think about the future or what they think
about the current market values of their securities. E.g., an increase in debt usually signals that
managers think the debt payments can be supported by better performance in the future. A stock
issue may signal that managers think the stock is currently overvalued.
This leads to the pecking order theory of financing in that managers will (if possible) first
finance with retained earnings, then with debt, and, as a last resort, with equity.
D. Setting Debt Policy — putting it all together
Each firm (or industry) will likely have a different optimal capital structure. The optimal
structure depends on balancing benefits of interest tax shields and reduced agency costs of equity
against expected costs of financial distress & bankruptcy and the lack of flexibility that results
from too high debt levels. The following equation helps to illustrate this:
+ PV
+ PV
– PV
VL = VU net benefit from
of expected reduction of
of expected financial
interest tax shields
Copyright © 2002 David A. Stangeland
agency costs of equity
distress costs