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Capital Structure and Theories

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Capital Structure and Theories

Definition: Capital Structure The mix of securities used to finance the firms investment projects.

 Note, this is the mix of all securities of the firm outstanding, not just new securities issued to finance new projects.

A. Miller and Modigliani (M+M) Theories with no taxes.

Miller & Modigliani’s Proposition 1.

In a world with no taxes, the firms capital structure does not matter.

- Firm’s value is determined by its real assets, not by the securities issued against them.

Miller & Modigliani’s Proposition 2:

Expected rate of return on common stock of a levered firm (firm with higher debt/equity ratio) increases in proportion to the debt/equity ratio.

Note: D/E ratio’s must be using market values, not book values.
E.g. If firm’s debt has its expected rate of return held constant at RD, then as proportion of debt increases, expected rate of return on equity must increase.
Recall firm is due to firms assets, doesn’t change as financing changes.

firm = X EE+(1-X)D

If X E  1-X E

E  to maintain firm

Note: X D = proportion of firm financing which is debt = (1-XE)

When XD = 1, so there is no equity and the debt risk must be the same as the overall risk of the firm’s assets.

Now, look at firm’s WACC (no taxes) with changes in capital structure:

Let D = 0 for simplicity

Assets = A

Assets =  E + D

A =

this is the effect of financial risk on equity beta – i.e., risk due to leverage

Note that A 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 =

= if D = 0


= 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 firms mix of securities because s of securities change so as to keep  of firm constant.

Do investors prefer to hold stock in firms with different capital structures?

Assumptions: perfect capital markets

- info. freely available

- 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 = 1.2

2 = 1.2

% in Equity

75% = X = .75

50% = X = .50

% in Debt same debt contrast



 of debt



 of equity from f = X(e) + (1-X)D

1.2 = Xe + (1-X)0.1




E[re] = rf+e(E[rm]-rf)

E[re] =



Suppose investor currently has a well diversified portfolio with  = 1.56. Suppose 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? Investor can achieve same desired  using either stock.
E.g. Firm 1: just buy stock,  = 1.5 E[rp] = .24

Firm 2: Want  = 1.5, then can buy a combination of firms stock and risk free asset.

p = X(2) + (1-X)0 rf

1.56 = X(2.3)

X =
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
VIII. B. Taxes in the M&M analysis

Introduce Taxes: with taxes we saw the WACC decreases as proportion of firm financed through debt increased because interest expenses are tax deductible.

Assume debt is still riskless, then as increased, E[rE] will increase as before (no tax case) but unlike no tax case, is decreasing WACC decreases.
Note: Debt can’t be riskless when .
MM adjust their proposition one in the presence of this to …

MM Proposition I corrected to reflect corp. income taxes.

Value of firm = value if all equity financed + PV tax shield from debt interest pmts

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 firms financing cash flows paid by government  value of firm up.
E.g. for simplicity assume a risk free firm with EBIT of $100,000 per year in perpetuity.
Before tax: income = $100,000 (assume risk free)

Tc = 50% Let rf = 10%

All equity financed firm, all income (after taxes) paid out as dividends.
Income before tax = 100, tax = 50, therefore Income after tax = 100-50 = 50

PVdiv =

Now let firm have perpetual bond financing with Interest/year = 25,000
Income before tax and interest = 100,000

Income after interest = 75,000

Tax = 37,500

Income after interest and tax = 37,500

PVdiv = = value of equity = E
PVint = = value of debt = D
PVfirm = Value of firm = 625,000 = D+E
Or using M+M revised Proposition 1:
VL = Vu+TcD
PVfirm = 500,000 + PV tax shields

Annual tax shield is the change in tax, 50,000-37,500, or TC  Interest = 12,500/yr.

PV =

PVfirm = 500,000 + 125,000 = 625,000

VIII. C. Other Considerations
Why not finance the firm entirely with debt? WACC drops and MM say value increases.
Reasons: 1. Investors’ taxes
Investors generally face higher tax rates on interest income than on capital gains or dividend income.

- interest income is taxed at the investors 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 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.

< firm gets tax reduction because of interest payment  more funds available to be paid out>
But Merton Miller - Debt & Taxes JF May 1977 pp. 261-276, argues that all firms will try to exploit this. As there are fewer tax exempt institutions buying the firms debt, firms will try to place their debt with low-tax investors. In order to entice more investors for the firm debt, the firm will have to raise the interest payments on the debt. As firms try to place more debt, the tax rates of the “newly enticed” investor will creep up - 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’s Debt & Taxes argument.
Miller shows that with both corporate and personal taxes, the following holds:
(Equation 4)

VIII.C. 2. Bankruptcy Costs and Costs of Financial Distress
Bankruptcy costs or costs of financial distress likelihood of bankruptcy (not being able to meet debt obligations) increases as debt level increases.
- More likely won’t be able to meet fixed obligations (i.e. coupon payments) as fixed obligations increase.
Investors may then value firm as
V = V if all equity + PV interest tax shields

- PV costs of financial distress

Bankruptcy is result of a decline in performance of the firm. Firm cannot meet obligations due to poor performance  its value decreases.

bankruptcy  result

Performance is cause
Costs of financial distress:
Direct costs: 1. Legal and admin 5.3% of pre-bankrupt market value for railway

2. Loss of value of intangible assets

3. Lost ability to invest in NPV projects

Indirect costs: 3. Indirect costs may not be able to finance good projects when near bankrupt.

* higher bankruptcy costs for firms with intangible assets - e.g. capital reputation market recognition vs. tangible assets - buildings, land.
 Limit to debt financing

Want to increase debt till marginal benefit increase in PV of int tax shield = marginal cost increase in PV of bankruptcy costs.

Costs of financial distress:

indirect: - adverse incentives

- select high risk projects

-shareholder benefit bondholder hurt

- pass up +NPV prj. - benefits  bondholder

- liquidate when not optimal

- receive higher liq. value but pass up possibility of saving firm

- produce inferior goods, provide less safe work environment

Characteristics of firms with high costs of fin distress
- Co’s whose products require after sale service or support.

- customer buy here

-Goods where quality is a key concern.


- Prod with switching costs

- computers

- high growth opportunities - value lost if period firm will go bankrupt.

- intangibles - employees, reputation, brand names, etc.

- large tax shields - lost value if no + earnings.
3. Agency Costs and Capital Structure
a. Stockholder - Manager conflict

- If manager owns less than 100% of the firm, then less than a 100% proportion of the cost will be born by manager if perquisites paid for by firm.

e.g. Manager owns 50% of firm

Consumers $100 of perquisites

Cost to manager  personal shares drop by $50

 total firm’s shares drop by $100

Incentive for non-owner manager to consume perks, etc.

Implication - may want high ownership stakes for managers

- also risk aversion problem

- only perfectly aligned when manager = owner

- M&M irrelevancy assumes op c.f.’s of firm unaffected by capital structure.

- argument have is that too much equity fin  lower op c.f.

Solutions: Finance more of firm with debt.

- less equity owned by non-managers, less of an incentive problem

- more of the costs of suboptimal decision born by managers
Many LBO’s were justified with this reasoning.
Kaplan 1989 JFE, Vol. 24, pp. 217-254 finds that op. per. of firms increased after LBO’s supporting reduction in agency costs.
“The effects of management buyouts on op perf and value” Jenson 1986 - reduces free cash flow.
B. Stockholder Bondholder Conflict
If there is a high level of debt financing then there is an incentive for shareholders and managers to redirect wealth from bondholder to shareholder via value of stock as an option on firms assets. - invest in high risk projects

- potentially - ve NPV

In addition there is a potential for a higher probability of bankruptcy costs or costs of financial distress.
- Partially remedied through restrictive covenants improved by bondholder on management.

- monitoring and bonding costs, reputation and future financing

- when too high, debt can’t be used

- observable

- verifiable
Why use debt when there are these costs

- may be less than costs associated with new equity

C. Signaling (see next page)
VIII. D. Setting Debt Policy
- balance benefits of interest tax shields, reduced agency costs of equity against restriction on managers. Agency costs of debt, and costs of financial distress. - most visible - financial distress - ensure c.f. will cover debt costs.
V. C. 4c. Signaling - c.s. issues may signal managers think stock is overvalued - trying to raise money when sec. can be sold for more than they’re worth (Pecking order)
V. C. 4d. Agency Costs - high debt levels may encourage management to take very risky projects because all losses borne by debt holder

- c.s. get gain

bondholder - bear loss

- high equity levels - where managers don’t own any

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