Lecture_22-23 Optimal Capital Structure and Tradeoff Theory

8/17/2019 Lecture_22-23 Optimal Capital Structure and Tradeoff Theory

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Professor Sang Byung [email protected]

Optimal capital structure and

tradeoff theory



Deviations from M&M assumptions

• The M&M world provides a very useful startingpoint.

• The M&M Propositions essentially give us a “laboratory

control” of corporate financing decisions.

• If some of the assumptions do not hold in the

real world, capital structure decisions do

matter and affect the value of a firm.

1. Corporate taxes

2. Cost of financial distress



Corporate taxes

• What happens if we include corporate taxes in the

model? Does the M&M propositions then change?

• Under the U.S. tax code, and that of many countries,debt interest payments are tax deductible.

• This implies that capital structure is no longer irrelevant tofirm value.

• M&M world + corporate taxes

= +

• : The value of levered firm

•

: The value of unlevered firm (100% equity)



Interest tax shield

•EBIT are taxed at the corporate rate.

• Interest expenses and dividends are taxed

differently:• Corporations can deduct interest payments as business

expense.

• Interest payments are NOT taxed at the corporate level, giving

rise to an interest tax shield.• Retained earnings and dividends are taxed at the corporate

level.



Example

•

You own all the equity of Space Babies Diaper Co.The company has no debt, i.e. its current capitalstructure is 100% equity. The company’s annualearnings before interest and taxes (EBIT) is $1,000.The corporate tax rate is 40%.

• You have the option to exchange ½ of your equityposition for bonds with a face value of $1,000. Thecurrent interest rate you need to pay for issuingdebt is 10%.

• Should you?

• If so, why or why not?



Example

All Equity 1/2 DebtEBIT $1,000 $1000

Interest payment @10% $0 $100

EBT $1000 $900

Taxes @40% $400 $360

Net Income $600 $540

Total CF to investors $600 $540+100 = $640

•

Note that• $600 (all equity firm) < $640 (1/2 Debt firm)

• The difference ($40): interest tax shield



PV of the tax shield

• What is the present value of the tax shield?

• If the same savings occur every year, we can find the PV of the taxshield as a perpetuity.

• If the savings are as risky as the debt, we can discount them at cost ofdebt:

= ℎ

= × ×

=

• : corporate tax rate

• For the Space Babies Diaper Co. example, we have:



Firm value and corporate taxes

•If we simplify and assume that the cash flows toall stakeholders occurs forever, then we can

again value that cash flow as a perpetuity.

• Note that we use a different discount rate on the

interest tax shield.

• That shield is only as risky as the debt part of our capital

structure: No debt, no interest!

= 1 −

+ × ×

= +

The value of unlevered firm ()PV (interest tax shield)



Corporate taxes and M&M Prop I

• Proposition I (with corporate taxes)

• Firm value increases with leverage.

= +

• Firm’s cost of capital () is no longer invariant to

leverage (D/E ratio).

=

+ +

+ −

•

Intuitively, we reduce cost of debt by 1 − because the debtinterest is tax-deductible to the firm.

• Here, the cost of capital is called (post-tax) WACC:

= =

+

+

+

−



Corporate taxes and M&M Prop II

• In the WACC equation, how do we calculate the cost of

equity () under the M&M world with corporate taxes?

• Proposition II (with corporate taxes)

• Some of the increase in equity risk and return is offset by the interesttax shield:

= +

− −

• is the return on equity cost of equity

• ℎ ℎ

• ℎ ℎ

• ℎ

• ℎ

• ℎ ( )



Corporate taxes & the cost of capital

T l h fl i d h



Total cash flow to investors under each

capital structure with corporate taxes

• The levered firm pays less in taxes than does the all-equity firm.

• Thus, the sum of debt (D) and equity (E) of the levered firm is greater than theequity of the unlevered firm.

• This is how cutting the pizza differently can make the pizza larger!

• The government (T) takes a smaller slice of the pizza if the firm is levered!

• That is, financial leverage adds firm value.



Limits to the use of debt

• The above analysis would suggest that firmsshould maximize PV(tax shield), such that weexpect 100% debt.

• Yet, outside the financial sector, D/(D+E) tendsto be below 40%.

•

Why don’t companies fully take advantage ofthe tax shield?

• Personal taxes (small effects)

• Costs of financial distress (most important limit to

debt’s use)



Personal Taxes

• What happens if we have both a corporate tax and a

personal tax that is imposed on investors?• Merton Miller has extended the above model to account for

personal taxes:

• For large public firms, it is in practice difficult to consider personal tax rates when setting the optimal leverage.

• The bottom line is that any effect from personal taxes is

likely to be small.

Note: in the case

where = , wereturn to M&M with

only corporate tax.



Costs of financial distress

• With more debt, there is a greater chance that the

firm will be unable to make its obligations.

• Bankruptcy is a long and complicated process that imposesboth direct and indirect costs on the firm and its investors.

• They are called “bankruptcy cost” or more generally “costs of

financial distress.”

• Bankruptcy risk vs Bankruptcy costs

•

Note that higher bankruptcy itself does not lower value.• Debtholders are rewarded by a higher return on debt.

• It is the costs associated with bankruptcy that lower value.

• Costs of financial distress is something that the assumption ofperfect capital markets ignores.



Costs of financial distress

•

Direct bankruptcy costs• Legal and administrative costs

• Hiring lawyers, consultants, accountants, etc.

• Tend to be a small percentage of firm value; around 3-5%

• Indirect costs

• Impaired ability to conduct business

•

For example, nobody wants to be a customer of a firm that may gobankrupt.

• Agency costs

• Conflicts of interest between stockholders and bondholders.

• Tend to be substantial; 10 to 20% of firm value.



Coprate taxes + financial distress costs

•

Recall: M&M world + corporate taxes: = + tax shield

•

M&M world + corporate taxes + costs of financialdistress:

= + tax shield

−(Financial distress costs)

• The value of the firm is equal to [the value of firmif all equity financed] plus [PV of tax shield] minus[financial distress costs].



Optimal capital structure

•This is a powerful way of thinking about whatcapital structure should be.

• The benefits of leverage from the interest tax shield

• The costs of financial distress

Determine the amount of debt that a firm should issue to

maximize its value

• This approach to optimal capital structure is

called the tradeoff theory.

• Debt’s benefits vs costs



Tradeoff theory

Loss of PV(Financial distress costs)

= + tax shield − (Financial distress costs)



Different levels of financial distress costs

Lecture_22-23 Optimal Capital Structure and Tradeoff Theory

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