Modigliani-Miller Assumptions

EXERCISE 01

Assume perfect markets apart from the taxes expressly mentioned; assess each claim.

A.Without tax, a debt-funded buyback reduces equity value, so shareholders should avoid it.
B.Without tax, cheaper debt reduces WACC.
C.Corporate tax lowers a levered company’s net income relative to a no-tax world, so debt should be avoided.
D.With corporate tax, the levered equity return falls below the unlevered return.
E.Adding personal taxes always eliminates the debt tax advantage.

A.

False. The remaining equity value falls because cash is distributed to sellers. Total shareholder wealth, including the payout, is unchanged.

B.

False. Increased financial risk raises the cost of equity enough to offset the higher weight on cheaper debt.

C.

The comparison confuses tax and financing effects. Compare levered and unlevered firms under the same tax system; deductible interest creates a tax shield.

D.

False for ordinary positive risk-premium debt financing. MM II gives RE = RU + (1−Tc)(D/E)(RU−RD). Tax reduces the leverage increment, not generally below RU.

E.

False. The advantage depends on corporate tax, personal tax on interest and personal tax on equity income. It vanishes only at the corresponding tax-neutrality condition.

Modigliani-Miller Assumptions

EXERCISE 02

Assess each statement under the stated tax and market assumptions.

A.Without taxes, borrowing increases EPS, total equity value and share price.
B.Without taxes, replacing expensive equity with cheaper debt reduces WACC.
C.With corporate tax, debt lowers aggregate dividends but raises dividends per share, so unlimited borrowing is always desirable.
D.Corporate tax lowers both the pretax debt rate and the equity rate, and hence WACC.
E.The debt tax advantage increases with corporate tax and decreases with both personal interest and dividend tax.

A.

False. EPS can rise or fall depending on operating return relative to debt cost. In frictionless MM, fair share price and total shareholder wealth including distributions are unchanged; remaining equity value falls by cash paid out.

B.

False. The rise in required equity return offsets the financing-weight change, leaving WACC equal to the unlevered cost.

C.

Per-share dividends need not rise. Tax-only MM rewards usable interest tax shields, but practical debt limits, distress, agency costs and tax-shield capacity invalidate an unconditional unlimited-debt prescription.

D.

Interest deductibility lowers the effective after-tax debt cost, not mechanically the contractual pretax rate. At fixed operating risk and D/E, tax dampens the MM II equity leverage increment. Separate these mechanisms.

E.

The net advantage per unit debt is 1−(1−Tc)(1−TE)/(1−TD). It increases with Tc and TE, but decreases with TD. Personal equity tax favours debt relative to equity.

Modigliani-Miller Assumptions

EXERCISE 03

Assess each statement under the stated tax and market assumptions.

A.Without tax, higher leverage raises equity risk, equity cost and WACC.
B.The leverage-related rise in equity risk is independent of operating risk.
C.Corporate taxes make financing irrelevant because leverage changes total and per-share earnings in opposite directions.
D.Corporate tax has no effect on the leverage-related increase in equity cost.
E.Higher personal interest and dividend taxes both increase levered firm value.

A.

The first two generally hold for positive operating risk; the last does not. MM keeps WACC constant.

B.

False. RE = RU + (D/E)(RU−RD) without tax; the operating risk premium affects the leverage increment.

C.

False. Interest deductibility adds tax-shield value; financing is relevant in tax-only MM. Accounting EPS changes are not the proof.

D.

False. Under the standard fixed-debt MM assumptions, the increment is (1−Tc)(D/E)(RU−RD).

E.

For a fixed unlevered benchmark, the relative debt advantage increases with equity-income tax but decreases with interest-income tax. Absolute values can also change through investor discount rates and the benchmark.

Modigliani-Miller Assumptions

EXERCISE 04

Assess each statement under the stated tax and market assumptions.

A.Without tax, equity issuance to retire debt raises both equity cost and WACC.
B.With corporate tax, a debt-funded buyback increases both firm value and total remaining equity value.
C.Debt tax shields raise the unit prices of both outstanding bonds and shares.
D.Raising corporate tax increases the pretax debt return and reduces equity return.
E.An IPO used to retire debt raises net income and therefore necessarily raises share value.

A.

False. Deleveraging reduces financial risk and equity cost; frictionless no-tax WACC stays constant.

B.

Firm value increases by the added tax shield, but remaining equity falls by (1−Tc) times the debt-funded payout under the standard assumptions.

C.

Shareholders receive the financing gain under risk-free debt assumptions; existing risk-free bond prices do not rise merely because the issuer gains a tax shield. Risky debt can be affected through credit risk.

D.

The pretax debt rate does not mechanically rise. The equity leverage increment falls at fixed RU, RD and D/E, but changes in operating cash flow and market values can alter those inputs.

E.

Lower interest can raise total accounting income, but share issuance dilutes ownership and debt retirement loses tax shields. Value depends on all financing effects, including possible distress-cost savings, not earnings alone.

Modigliani-Miller Assumptions

EXERCISE 05

Assess each statement under the stated tax and market assumptions.

A.Levered firm value exceeds unlevered value because equity holders require a higher return.
B.The leverage-induced rise in equity risk is independent of business risk.
C.DCF must include the debt tax shield directly in unlevered FCF.
D.At trade-off-optimal leverage, WACC and the gain over unlevered value are both maximal.
E.MM contradicts CAPM because CAPM rewards beta rather than leverage.

A.

False explanation. The added value is the present value of usable interest tax shields. The higher equity return compensates higher financial risk.

B.

False. Both unlevered beta and the operating risk premium influence the equity response to leverage.

C.

Not with after-tax WACC: doing so double-counts it. Under APV, calculate and value the shield separately from unlevered FCF.

D.

Firm value is maximal when marginal tax benefits equal marginal expected distress and other financing costs. Under consistent cash-flow assumptions WACC is minimised, not maximised.

E.

False. Leverage changes equity beta, so the two theories can be consistent.

Modigliani-Miller Assumptions

EXERCISE 06

Assess each statement under the stated tax and market assumptions.

A.Equity issuance to retire debt raises share price because shares become riskier.
B.A moderate leverage increase that leaves default risk unchanged raises both debt and equity required returns.
C.Personal taxes always enlarge the debt tax advantage relative to corporate tax alone.
D.With distress costs, higher debt certainly raises share price.
E.Firms with lower default risk tend to choose less debt.

A.

False. Deleveraging reduces equity financial risk; in tax-only MM it destroys tax-shield value and lowers the fair announcement share price.

B.

Equity financial risk generally increases. The debt return need not change if its risk and market conditions are unchanged.

C.

False. The outcome depends on personal equity and interest tax rates. Use 1−(1−Tc)(1−TE)/(1−TD).

D.

False. Beyond the optimum, incremental expected distress costs can exceed tax benefits.

E.

Other things equal, lower expected distress costs permit more debt, not less. Industry assets, tax capacity and other frictions also matter.

Modigliani-Miller Assumptions

EXERCISE 07

Assess each statement under the stated tax and market assumptions.

A.Corporate tax makes financing relevant because debt changes unlevered operating FCF.
B.Optimal trade-off leverage minimises both debt and equity costs separately.
C.Without tax or distress, a buyback leaves asset beta fixed, equal to the value-weighted debt and equity betas.
D.Personal taxes are irrelevant for debt shields.
E.Without tax or distress, more debt lowers WACC because both debt and equity costs fall.

A.

Financing is relevant through interest tax shields, but these do not belong in unlevered operating FCF; value them through WACC or separately with APV.

B.

False. It maximises firm value by balancing marginal benefits and costs; neither component financing cost must be at its minimum.

C.

True if the operating assets and their risks are unchanged. BetaA = (D/V)betaD + (E/V)betaE.

D.

False. Interest and equity-income taxes alter the relative after-tax benefit of debt.

E.

False. MM leaves WACC constant; equity cost generally rises with financial leverage.