CFA Program Level I

Modigliani-Miller and the trade-off theory: CFA Level I

In perfect capital markets, Modigliani and Miller showed that firm value is the present value of its cash flows and does not depend on the debt-equity mix. Allowing interest to be tax deductible makes value rise with debt. The trade-off theory adds the costs of financial distress, so a firm borrows until the marginal tax saving equals the marginal expected distress cost.

Irrelevance without taxes

Modigliani and Miller (1958) showed that in perfect capital markets the value of the firm is independent of how its debt and equity claims are structured. What determines value is on the asset side: the present value of the cash flows the firm generates.

Replacing equity with cheaper-looking debt does not raise value in this world. The cash flows are the same; only their division among claimholders changes.

Adding tax-deductible interest

When interest is deductible, each extra dollar of interest lowers the tax bill. This interest tax shield increases the total after-tax return to investors, so value rises with debt.

Example: a firm adds USD1,000 of debt at 5%. Interest is USD50 a year. At a 25% tax rate the firm pays 50 x 0.25 = USD12.50 less tax each year, cash that now goes to claimholders instead of the government.

Taken alone, this would imply financing almost entirely with debt.

The static trade-off theory

Too much debt raises the probability of financial distress. The trade-off theory says a firm borrows to the point where the marginal value of the tax shield equals the expected marginal cost of financial distress.

A firm below that point gains by borrowing more. A firm above it, where one more unit of debt adds more expected distress cost than tax saving, gains by borrowing less.

The pecking order theory is the main alternative. Because managers know more than investors, the market may read a share issue as a sign the stock is overvalued. Firms therefore prefer internal funds, and when they need outside money they issue the least risky securities, debt before equity.

Where the exam catches people

Believing that in the no-tax Modigliani-Miller world cheaper debt raises firm value: value is unchanged because cash flows are unchanged.
Believing added debt lowers firm value once interest is deductible and distress costs are ignored: the tax shield makes value rise with debt.
Believing the optimal structure is where the tax saving is largest: it is where the marginal tax saving equals the marginal expected distress cost.
Believing a firm whose next unit of debt costs more in distress than it saves in tax should hold its debt level: it is past the optimum and should carry less debt.

Written from CFA Institute's documentation

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

In a world with no taxes, where investors can borrow and lend as easily as corporations, Talmo Industries replaces part of its equity with debt that carries a lower required return than its equity. According to Modigliani and Miller, Talmo's firm value will most likely:
Right. In the game that’s Renown for your Corporate Finance building.
Not that one: B is right. In the game your Corporate Finance building would lose a little Renown, and this question would come back later.
Your answerA.Rise, as cheaper debt replaces costlier equityDebt does carry a lower required return than equity, which makes the swap look like a saving. But under Modigliani and Miller firm value is fixed by the present value of expected cash flows, and splitting them differently among claimholders leaves it unchanged.The answerB.Stay the same, as its expected cash flows are unchangedThe Modigliani-Miller theorem says that where investors can borrow and lend as easily as corporations, a firm's value is the present value of its expected cash flows and does not depend on how those cash flows are divided among claimholders.Your answerC.Fall, as the added debt raises riskAdding debt changes who receives Talmo's cash flows, not the cash flows themselves. With no taxes and investors able to borrow and lend like the firm, value neither rises nor falls.
Show the full explanation and doc quotes
Swapping equity for debt changes only the division, so Talmo's value is unchanged: capital structure is irrelevant.
Written from www.nber.org/system/files/working_papers/w17760/w17760.pdf
An analyst applies the Modigliani-Miller framework but, as Modigliani and Miller themselves did, allows for the deductibility of interest expense. Ignoring any costs of financial distress, as Orsk Shipping adds debt to its capital structure, its firm value should most likely:
Right. In the game that’s Renown for your Corporate Finance building.
Not that one: A is right. In the game your Corporate Finance building would lose a little Renown, and this question would come back later.
The answerA.Rise, as more of its earnings are shielded from taxModigliani and Miller acknowledged the tax deductibility of interest, and allowing for it implies that firm value should increase with leverage: each added unit of debt means more interest deducted and less tax paid, leaving more cash for claimholders.Your answerB.Stay unchanged, as its financing mix is irrelevantIrrelevance holds in the Modigliani-Miller world without taxes. Once interest is deductible, borrowing reduces the tax the firm pays, so firm value increases with leverage instead of staying fixed.Your answerC.Fall, as added debt raises financial riskAdded debt does raise financial risk for shareholders, but in this framework the stem sets aside the costs of financial distress. What remains is the benefit of deductible interest, which raises value.
Show the full explanation and doc quotes
With financial distress costs ignored, nothing offsets that gain, so Orsk's value rises as it adds debt.
Written from www.nber.org/system/files/working_papers/w17760/w17760.pdf
Interest on Fenmore Logistics' debt is tax deductible, and heavier borrowing raises its chance of financial distress. Its analyst estimates that, at Fenmore's current debt level, the tax saving from one more unit of debt would fall short of the added expected costs of financial distress. Under the static trade-off theory, Fenmore's optimal capital structure most likely has:
Right. In the game that’s Renown for your Corporate Finance building.
Not that one: A is right. In the game your Corporate Finance building would lose a little Renown, and this question would come back later.
The answerA.Less debt than it now carriesIn the static trade-off theory, the optimal capital structure is reached where the tax advantage of borrowing is balanced, at the margin, by the costs of financial distress.Your answerB.As much debt as it now carriesThe current level would be optimal only if the tax saving from the last unit of debt just equalled its added expected distress cost. Here the distress cost is larger, so the balance point lies at a lower debt level.Your answerC.More debt than it now carriesInterest deductibility does make debt attractive, but the trade-off theory sets that advantage against the costs of financial distress. Once the marginal distress cost exceeds the marginal tax saving, adding debt lowers value, so the optimum lies below the current level.
Show the full explanation and doc quotes
At Fenmore's current level, one more unit of debt costs more in expected distress than it saves in tax, so Fenmore has passed that balance point. Its optimum therefore carries less debt than it has now.
Written from www.nber.org/papers/w1393