Capital Structure: Modigliani–Miller, Tax Shields, Distress, and Financing Incentives

A company can finance the same factory with more debt or more equity. Does changing that financing mix create value, or merely redistribute the factory’s cash flows and risks? Modigliani–Miller starts with a frictionless benchmark in which the mix does not matter. Taxes, distress, information, and incentives then explain the conditions under which it can matter.

Learning goals and notation

You should finish able to reproduce the M–M value argument, explain why cheap debt does not lower frictionless WACC, value a conditional tax shield, compare financing theories, and calculate shareholder–creditor conflicts.

Symbol	Meaning
$V_U$	Value of an otherwise comparable unlevered firm
$V_L$	Total value of the levered firm
$D$, $E$	Market values of debt and equity
$r_A$ or $r_U$	Required return on unlevered operating assets
$r_D$, $r_E$	Required debt and equity returns
$\tau_c$	Corporate marginal tax rate in the model
$L$	Contractual debt payment due at a future date

Use market values for financing weights, not historical book values. Distinguish debt’s market value $D$ from its promised face repayment $L$. The basic model keeps operating assets and investment policy fixed, and excludes excess-cash complications.

1. Lecture 4: the financing question

The left-hand side of an economic balance sheet is the value of operating assets and investment opportunities. The right-hand side consists of the claims issued against those assets. In the simple debt-and-equity structure:

$$V=D+E.$$

Issuing debt and retaining the proceeds as cash temporarily adds both an asset and a liability. A leveraged recapitalization instead uses the borrowing to distribute cash or repurchase shares, changing the financing mix of the existing business. Keep these transactions distinct when comparing values.

Capital structure includes more than a debt percentage: priority, maturity, collateral, covenants, conversion rights, and control rights can all matter once frictions are introduced.

2. M–M Proposition I: the frictionless cash-flow pie

The no-tax M–M benchmark assumes fixed investment policy, frictionless competitive markets, no distress or transaction costs, no informational or incentive effects, and investor access to the trades needed to replicate financing choices.

Under these conditions:

$$\boxed{V_L=V_U.}$$

Financing divides the same underlying cash-flow pie among claimants. It does not enlarge the pie when it changes neither total state-by-state cash flows nor attainable investment opportunities.

Worked state-by-state proof

Two firms own identical assets. At date 1, asset cash flows are 180 in the strong state and 60 in the weak state. Firm U is all equity financed. Firm L has debt promising 80 and residual equity. Assume limited liability and no bankruptcy cost.

State	U equity	L debt	L equity	L debt plus equity
Strong	180	80	100	180
Weak	60	60	0	60

The combined levered claims exactly reproduce unlevered equity. They must therefore have the same total price under no arbitrage and feasible trading. If U costs 120 while L’s debt and equity together cost 115, buying the L package and shorting U produces an initial 5 with offsetting future payoffs.

Notice that default itself occurs in the weak state, but no resources disappear in this model. A transfer of unpaid promised debt into a lower recovery is different from the destruction of value through legal costs or disrupted operations.

Homemade leverage and undoing leverage

An investor who wants levered exposure can buy unlevered equity while borrowing personally, provided equivalent financing terms and liabilities are attainable. An investor who wants the full asset exposure can combine the firm’s debt and equity to undo the corporate split.

This replication logic fails if investor borrowing costs, shorting constraints, taxes, information, or bankruptcy arrangements differ materially. Those are economic reasons to study departures from the benchmark, rather than reasons to ignore it.

3. M–M Proposition II: the WACC fallacy

Without taxes:

$$r_A=\frac{E}{D+E}r_E+\frac{D}{D+E}r_D.$$

Rearranging gives

$$\boxed{r_E=r_A+\frac{D}{E}(r_A-r_D).}$$

Debt may be safer and have a lower required return, but issuing more of it concentrates residual risk in the remaining equity. Equity’s required return rises; simply replacing equity with “cheap debt” does not lower the total required return on unchanged assets in this setting.

Worked WACC example

An unlevered business is worth 1,000 and has asset cost of capital 10%. Introduce debt with market value 400 and required return 5%. Under M–M, total value remains 1,000 and equity becomes 600:

$$r_E=10\%+\frac{400}{600}(10\%-5\%)=13.3333\%.$$

Then

$$WACC=0.6(13.3333\%)+0.4(5\%)=10\%.$$

A tempting but incorrect calculation holds equity cost fixed at 10% and reports WACC of 8%. It omits the additional risk borne by shareholders. Higher EPS or ROE caused by a smaller equity base is likewise not evidence of newly created value.

With risky debt, a promised yield to maturity may exceed its expected return. Do not substitute a promised yield for the required expected debt return in the frictionless return identity without considering default losses.

How far does irrelevance extend?

Pure repackaging at fair prices is zero NPV when total cash flows and investor opportunities are unchanged. Related frictionless arguments can make payout timing, maturity choices, and hedging irrelevant under their respective assumptions.

This does not mean every financing transaction in reality is zero NPV, or that every version of risk management irrelevance follows from one equation. If hedging preserves valuable investment, financing changes incentives, or a transaction changes taxes or available risks, the premise has changed.

4. Lecture 5: the corporate interest tax shield

In a simplified corporate-tax model, deductible interest reduces tax payments, while ordinary equity distributions are not deductible in the same way. For fully usable deductions:

$$TS_t=\tau_c\,Interest_t.$$

If debt principal $D$ is maintained forever, interest is $r_DD$ each year, the tax rate is constant, all deductions can be used, and the shield is appropriately discounted at $r_D$:

$$PV(TS)=\frac{\tau_cr_DD}{r_D}=\tau_cD,$$

so

$$V_L=V_U+\tau_cD.$$

These assumptions do substantial work. Finite debt, debt tied to future firm value, tax-loss positions, deduction limits, and uncertain tax rates change the cash flows or their risk. The expression $\tau_cD$ is not a universal tax benefit for any amount of borrowing.

Worked perpetual-debt recapitalization

Suppose unlevered value is 1,000, permanent debt is 400, debt rate is 5%, and the corporate tax rate is 25%. Assume the full textbook shield conditions above.

$$Interest=20,\qquad TS=5\text{ per year},\qquad PV(TS)=100.$$

Thus $V_L=1{,}100$ and remaining equity is $1{,}100-400=700$. If the 400 borrowing proceeds are paid to the original shareholders, their combined wealth is 400 in cash plus equity worth 700, totaling 1,100. The 100 gain comes from the modeled tax reduction, not the borrowing proceeds themselves.

For fixed perpetual debt under the corresponding tax model:

$$r_E=r_U+(1-\tau_c)\frac{D}{E}(r_U-r_D).$$

With $r_U=10\%$, the example gives $r_E\approx12.1429\%$. Using market weights:

$$WACC=\frac{700}{1100}(12.1429\%)+\frac{400}{1100}(5\%)(0.75) \approx9.0909\%.$$

Discounting unlevered after-tax operating cash flow of 100 perpetually at that WACC gives value 1,100. Count the shield through WACC or separately through adjusted present value, rather than adding it twice.

A finite shield is smaller

For the same annual tax shield of 5 lasting only three years, discounted at 5%:

$$PV(TS)=\frac5{1.05}+\frac5{1.05^2}+\frac5{1.05^3}\approx13.62.$$

The debt principal does not itself become a tax deduction. Actual deductions and their timing depend on the applicable rules; principal repayment and interest must remain separate in the analysis.

5. Financial distress and the static trade-off

Financial distress means difficulty meeting obligations or maintaining access to finance. It can arise before formal bankruptcy. Direct costs include legal and administrative resources. Indirect costs can include lost customers, disrupted suppliers, employee departures, and forced asset sales that sacrifice going-concern value.

Lower creditor recovery is not automatically an additional social cost: some losses are transfers between claimants. Count actual value destruction and avoid double counting the same operating deterioration in both base cash flows and a distress adjustment.

A one-date expected-cost shorthand is

$$ExpectedCost=p(\mathrm{distress})\times \mathbb E[Cost\mid\mathrm{distress}].$$

For valuation, cash-flow timing, states, and risk adjustment matter. An undiscounted probability-times-cost number is not automatically today’s PV, especially when distress occurs in bad aggregate states.

The static trade-off model summarizes:

$$V_L=V_U+PV(TS)-PV(\text{expected distress costs}).$$

A smooth interior optimum balances the marginal shield benefit against marginal expected distress cost, with other relevant frictions added consistently.

Worked debt comparison

Suppose $V_U=1{,}000$, tax rate is 25%, the simple perpetual shield remains usable at each candidate debt level, and separately modeled distress-cost PVs are:

Debt	Tax-shield PV	Distress-cost PV	Levered value
0	0	0	1,000
200	50	10	1,040
400	100	30	1,070
600	150	110	1,040

Debt of 400 is best among these candidates. Moving from 400 to 600 adds 50 of shield but 80 of expected distress costs. A 100%-debt conclusion follows only if one unrealistically retains the benefits while excluding the costs and constraints that grow with leverage.

This is a model comparison, not an empirical optimal debt ratio. Debt capacity depends on cash-flow stability, collateral, growth needs, and the costs of lost flexibility. Maturity and refinancing concentration can matter even for firms with similar total debt.

6. Lecture 8: information asymmetry and financing signals

Managers may know more about existing assets and investment opportunities than outside investors. If investors expect managers to issue relatively more equity when shares are expensive, an issue announcement can lead them to revise their valuation downward.

That is an adverse-selection argument, not proof that every equity issuer is knowingly overvalued or every issue is bad. Equity can fund valuable growth, reduce excessive leverage, or satisfy other constraints. Rational investors also learn from the decision itself.

The Lecture 8 slides report an approximately -3% equity-issue announcement effect as a historical empirical summary. It should not be read as a current universal average, a mechanical dilution formula, or a prediction for every transaction. Event windows, samples, benchmarks, and offer types matter.

Worked dilution mechanism

Consider a deliberately simplified conditional pricing example. Managers assess existing assets at 150. A new project costs 50 and is worth 60, so its NPV is 10. Suppose investors provisionally value existing assets at 100 but agree on the project’s value of 60.

After the investment, outsiders’ assessed total value is 160. Raising 50 at that valuation requires giving new shareholders $50/160=31.25\%$ of the post-issue company. Managers assess its true post-investment value as $150+60=210$, leaving old shareholders

$$(1-0.3125)(210)=144.375.$$

That is below the 150 managers believe old shareholders would retain without investing. A positive-NPV project can be unattractive to existing shareholders if financing transfers enough value to new investors.

This arithmetic illustrates a mechanism, not a complete equilibrium: in the Myers–Majluf framework investors update beliefs from the issuance decision, which affects the issue price and which firms issue. Issuing fair-value shares merely increases the share count; it does not automatically destroy wealth through “dilution.”

7. The pecking order: internal funds, safer debt, equity

Myers and Majluf (1984) show how private information and managers acting for existing shareholders can affect financing and investment. A familiar resulting hierarchy prefers:

1. Internal funds, avoiding a new security subject to adverse selection.
2. Relatively information-insensitive debt while borrowing capacity remains suitable.
3. Riskier securities, including equity, when other sources are unattractive or insufficient.

Safe debt can be less sensitive to information about upside asset values than equity. Highly risky debt is not immune to adverse selection, and distress costs can make additional borrowing worse than equity.

Internal funds still have an opportunity cost. Retained earnings belong economically to shareholders; calling them first in a financing hierarchy does not make their required return zero. Likewise, accounting retained earnings are not necessarily cash available to spend.

In a pure pecking-order account, leverage reflects cumulative financing deficits and surpluses rather than continuous adjustment toward a fixed target debt ratio. Real firms may combine target ranges, financing flexibility, issuance costs, and information concerns. The model is not a strict universal description of observed behavior.

8. Agency: managers versus shareholders

Managers can prefer empire building, private benefits, or excessive cash retention to payouts that benefit owners. Debt service can discipline spending by committing cash to outsiders and increasing scrutiny.

But more debt does not mechanically improve management. It may encourage short-termism, excessive risk, or cuts to valuable investment. Discipline benefits must be weighed against the firm’s need to fund positive-NPV projects and remain liquid through downturns.

Governance, compensation, covenants, monitoring, and payout policies can also change incentives. Debt is one contractual tool, not a complete substitute for oversight.

9. Agency: shareholders versus creditors

Limited liability makes equity’s payoff convex in asset value. That can create incentives for actions that raise equity value while reducing the value of existing debt or the whole firm. The examples below use one-period terminal amounts, zero interest, and the stated probabilities as valuation weights so the arithmetic is transparent.

Risk shifting or asset substitution

Debt promises 100. A safe existing asset pays 90 for certain: debt receives 90 and equity zero. Shareholders can substitute a gamble paying 150 or 10 with equal probability and no additional investment.

Policy	Expected total asset payoff	Expected debt payoff	Expected equity payoff
Safe	90	90	0
Gamble	80	55	25

The gamble destroys total value of 10 but gives equity 25. Debt loses 35. Creditors anticipating these incentives can demand protective terms or a lower issue price; the transfer is not a free source of value for shareholders indefinitely.

Debt overhang and underinvestment

Existing assets pay 80 and old debt promises 100. A new project costs shareholders 10 today and adds a certain 25 at maturity. Its total NPV is 15 at zero interest.

After investment, total assets pay 105. Debt gets 100 and equity gets 5. Shareholders would pay 10 to receive only 5, so they reject the project if those are their only feasible terms. Debt gains 20 compared with its old payoff of 80, capturing much of the benefit.

Positive total NPV does not ensure existing equity is willing to supply funds when old debt absorbs the gains. Restructuring, renegotiation, or permitted new financing priority can sometimes repair the incentive conflict, subject to contracts and feasibility.

Asset extraction before distress

Distributions or asset transfers that remove resources supporting old debt can shift value from creditors to shareholders. This is the concern behind the outline’s “cash-in-and-run” label. Covenants, security interests, payout restrictions, and legal protections address such conflicts; the value and legality of a transaction depend on its terms and circumstances.

10. Put the explanations together

A broader organizing expression is

$$V_L=V_U+PV(\text{tax benefits})+PV(\text{incentive benefits}) -PV(\text{distress and other financing costs}).$$

Information effects, investment distortions, and transaction costs must be modeled consistently; a simple additive expression is an organizing device, not permission to count the same effect repeatedly.

Framework	Main question	Useful implication	Limitation
M–M	What if financing changes no total cash flow or opportunity?	Pure repackaging cannot create value	Its conditions exclude real financing frictions
Static trade-off	How do tax benefits compare with debt-related costs?	Debt can have an interior value-maximizing range	Inputs are uncertain and policy adjustment is costly
Pecking order	Which financing is least sensitive to private information?	Cash reserves and safe debt capacity can be valuable	It does not explain every issuance or target policy
Agency	How do claims change decisions and transfers?	Financing affects investment and payout incentives	Contracts and governance vary across firms

A practical decision examines operating cash-flow resilience, tax-shield usability, financing maturity, covenant headroom, collateral, future investment needs, and information conditions. The aim is a financing policy that supports valuable investment, not simply the highest EPS or the lowest quoted debt coupon.

11. Practice questions

1. Identical assets pay 140 or 50. Debt promises 70. Find debt and equity payoffs in each state, and show why their sum reproduces the assets under the no-cost M–M assumptions.
2. A no-tax firm has asset cost 12%, debt cost 6%, debt market value 300, and equity market value 600. Find equity cost and WACC.
3. Permanent debt is 200 at 5% interest and tax rate 30%. Under the full usable-shield assumptions, find the annual shield and its PV at 5%. What if it lasts only two years?
4. A firm has unlevered value 800, shield PV 60, and distress-cost PV 25. Find levered value and equity value if debt market value is 240.
5. Existing assets pay 70, debt promises 90, and a new project costs shareholders 8 and adds 25 at maturity. At zero interest, find total project NPV and the shareholders’ net benefit.
6. Debt promises 100. Compare a safe asset paying 85 with a gamble paying 140 or 20 equally likely. Find expected debt and equity payoffs and total value under the stated valuation weights.
7. Why are retained earnings not free capital? Why does the historical -3% announcement figure not imply every equity issue destroys exactly 3% of value?
8. State three reasons why $PV(TS)=\tau_cD$ can fail, and explain why comparing a debt coupon with equity return alone does not identify optimal leverage.

12. Answers and reasoning

1. At 140, debt gets 70 and equity 70. At 50, debt gets 50 and equity zero. The sums are 140 and 50; splitting the claims does not change total state payoffs.
2. $r_E=12\%+(300/600)(12\%-6\%)=15\%$. WACC is $(600/900)(15\%)+(300/900)(6\%)=12\%$.
3. Annual interest is 10 and annual shield is 3. Perpetual PV is $3/0.05=60$. Two-year PV is $3/1.05+3/1.05^2\approx5.58$.
4. $V_L=800+60-25=835$. Equity is $835-240=595$, assuming these components and debt value are consistently specified.
5. Total NPV is $25-8=17$. After investment assets pay 95, debt gets 90, and equity gets 5. Equity’s net benefit is $5-8=-3$, so existing shareholders may refuse despite positive total NPV.
6. Safe: debt 85, equity zero, total 85. Gamble: expected debt $0.5(100)+0.5(20)=60$, equity $0.5(40)=20$, total 80. Equity gains 20 while total value falls 5 and debt loses 25.
7. Internal funds could be distributed or invested elsewhere, so shareholders bear an opportunity cost. An announcement effect is a historical benchmark-adjusted average reflecting information and other effects in a sample, not a universal dilution rule.
8. Examples include finite or changing debt, unavailable or delayed deductions, changing tax rates, and shield risk inconsistent with debt-rate discounting. More leverage changes equity risk and may change debt risk, taxes, distress, and incentives; the coupon comparison omits those effects.

Further reading

• MIT OpenCourseWare, Finance Theory II lecture notes: the Spring 2003 course and section attribution.
• Dirk Jenter, Lecture 4: Capital Structure I: M–M and financing irrelevance.
• Dirk Jenter, Lecture 5: Capital Structure II: taxes and distress considerations.
• Dirk Jenter, Lecture 8: Informational and Agency Considerations: information asymmetry, issuance reactions, and the pecking order.
• Stewart C. Myers and Nicolas S. Majluf (1984), Corporate Financing and Investment Decisions When Firms Have Information That Investors Do Not Have: the financing and investment mechanism under asymmetric information.
• Stewart C. Myers (1984), The Capital Structure Puzzle: trade-off and pecking-order perspectives.

Feynman study lab

Explain it simply

Changing debt and equity changes who bears risk; it does not automatically change the assets’ cash generation.

Concrete example. If assets worth 100 are financed by debt worth 40, equity is worth 60 in a simple balance-sheet valuation.

Teach it back without looking

Close the lesson and explain the idea aloud to a beginner in two minutes. Define each technical term you use, walk through the example, and state one assumption or limitation. Then answer:

Why is cheaper debt not a free way to lower funding costs indefinitely?

Check your explanation after you try

More leverage makes remaining claims riskier. Taxes, distress and other frictions determine whether financing changes total value.

Find the gap and try again

If you hesitated, relied on a formula you could not explain, or missed the self-check, write down the exact gap. Revisit the relevant section of this lesson and work through its example. Close the notes, explain it again in simpler language, then change one number or assumption and predict what changes. Recalculate or check the lesson to test your prediction. Try once more tomorrow from memory.