Modigliani Miller

This reading calculates the weighted-average cost of capital and explains the internal and external factors, including the life cycle stage, that shape a company's capital structure. It then sets out the Modigliani–Miller propositions with and without taxes, the costs of financial distress, the static trade-off and pecking order theories, and how a target capital structure is estimated.

LOS 25.a — Calculating and interpreting the WACC

A company's weighted-average cost of capital (WACC) is the blended required return of all its capital providers. With debt and common equity only:

where $w_d$ and $w_e$ are the weights of debt and equity ($w_d+w_e=1$), $r_d$ is the pretax cost of debt, $t$ is the marginal tax rate, and $r_e$ is the cost of equity. If the firm has preferred stock, add $w_p{r}_p$. Preferred dividends are not tax-deductible, so this term has no tax adjustment.

Key points:

• Debt costs less than equity because debtholders are paid first from the firm's cash flows and have a senior claim on its assets.
• Interest is tax-deductible in most jurisdictions, so the pretax cost of debt is converted to an after-tax cost of debt, $r_d(1-t)$. The cost of equity gets no tax adjustment.
• The weights can be target weights or market value weights. Market values reflect conditions today, so they are the right basis for measuring today's opportunity cost of capital. LOS 25.d explains how an analyst estimates a target capital structure that the company does not disclose.
• The WACC is the discount rate for computing the NPV of an expansion that mirrors the existing business and is financed in the firm's normal proportions.

LOS 25.b — Factors affecting capital structure and the WACC

Firms usually aim for the capital structure that minimizes the WACC, and they try to match the maturity of their financing to the life of their assets. The factors that shape capital structure are essentially those that determine a company's capacity to service debt.

• Internal factors: business and industry characteristics, life cycle stage, existing leverage, and the corporate tax rate.
• External factors: conditions in the market and the business cycle, regulation, and industry norms.

The corporate tax rate matters because interest is tax-deductible: the higher the rate, the larger the tax saving from each unit of debt.

Features of a company that let it carry more debt:

• Revenue that is growing or stable, and cash flow that is growing and predictable.
• Low business risk (operational risk and demand risk).
• Plenty of liquid, tangible assets that can be pledged as collateral. Creditors prefer tangible assets that can be sold without much loss of value, or that are fungible, over intangible assets. A firm that owns its productive assets outright has more collateral than one that uses assets owned by others, as in a franchise model.
• Low cost and ready availability of debt.
• Low existing leverage and low earnings volatility. Analysts gauge debt capacity with leverage ratios (debt-to-equity, debt-to-operating profit) and coverage ratios, such as interest coverage $=\text{EBIT}/\text{interest expense}$.

Other things equal:

The life cycle stage shows these factors at work:

A start-up's debt would be very risky, so lenders would demand high interest rates, and its small base of receivables and fixed assets offers little collateral. Convertible debt suits a start-up with a fast-rising share price because it costs less than straight debt and postpones the dilution of existing shareholders.

Top-down factors are macroeconomic conditions (inflation, real GDP growth, monetary policy and exchange rates) that move benchmark rates and credit spreads. In downturns, lenders demand wider spreads, especially from companies in cyclical industries. Some industries benefit from particular conditions; for example, spreads of oil producers tend to narrow when oil prices rise.

LOS 25.c — The Modigliani–Miller propositions

The assumptions

The capital structure propositions of Modigliani and Miller (MM) rest on these assumptions: capital markets are perfectly competitive, with no taxes, transactions costs or bankruptcy costs; all investors hold homogeneous expectations; borrowing and lending are available to investors at the risk-free rate; agency costs are absent; and financing choices have no effect on investment decisions, so the firm's operating income does not depend on its mix of debt and equity.

MM Proposition I (no taxes): capital structure irrelevance

With these assumptions in place, changing the capital structure does not change firm value: $V_L=V_U$, where $V_L$ is the value of the levered firm and $V_U$ the value of an otherwise identical unlevered (all-equity) firm. The size of the "pie" (the value of the firm's operating earnings, EBIT) stays the same however it is divided between debtholders and shareholders. An investor who owned all of the debt and equity of a levered firm would receive the same EBIT as the owner of an identical all-equity firm.

MM Proposition II (no taxes): cost of equity and leverage

The cost of equity rises linearly with the debt-to-equity ratio. Debtholders have a prior claim, so the residual cash flows left to shareholders become riskier as debt increases:

where $r_e$ is the cost of equity, $r_0$ is the cost of equity of the firm if it had no debt (all equity), $r_d$ is the cost of debt and $D/E$ is the debt-to-equity ratio. Promised payments to debtholders are more certain than the residual cash flows to shareholders, so $r_d<r_e$. The formula follows from Proposition I: if the WACC equals $r_0$ whatever the mix, then $\frac{D}{V}{r}_d+\frac{E}{V}{r}_e=r_0$, and solving for $r_e$ gives the line above. $r_0$ reflects the business risk of the firm's operations, which the financing mix does not change. As $D/E$ rises, the cost of equity rises while the cost of debt stays the same. The benefit of using more low-cost debt is exactly offset by the higher cost of equity, so the WACC is unchanged. This is consistent with Proposition I.

MM with taxes

When interest is tax-deductible, debt creates a debt tax shield worth $t\times D$:

With taxes, the government's slice of the pie shrinks as debt rises. Firm value is therefore maximized, and the WACC minimized, at 100% debt. The cost of equity still rises with leverage, but more slowly:

The figure draws both cases with the example inputs ($r_0=11\%$, $r_d=5\%$, $t=20\%$).

Costs of financial distress

In practice firms do not use 100% debt or anything close to it. MM themselves suggested that differences in investors' tax rates on dividends and on interest income could help explain observed capital structures. Current theory points instead to a cost the model leaves out, the costs of financial distress: the extra costs a firm faces when falling earnings make its fixed financing costs hard to pay. These costs rise with leverage. Expected costs of financial distress have two components:

1. The costs incurred if distress occurs. Direct costs are the legal and administrative fees of bankruptcy. Indirect costs include forgone investment opportunities and the lost trust of customers, suppliers, creditors and employees. Conflicts between managers (acting for shareholders) and debtholders add the agency costs of debt.
2. The probability of financial distress, which rises with operating and financial leverage and with weak management and corporate governance.

Other things equal, higher expected costs of financial distress discourage heavy use of debt.

LOS 25.d — Optimal and target capital structures

Static trade-off theory

The static trade-off theory balances the value of the debt tax shield against the expected costs of financial distress:

As debt increases, the tax shield keeps increasing, but beyond some point the extra expected distress costs outweigh the extra tax benefit. The optimal capital structure is the debt level at which firm value is maximized and the WACC is minimized. Because $V_U$ is constant, this is also where $V_L-V_U$ is largest.

• Firm value first rises and then falls as leverage increases; the WACC first falls and then rises (a U shape).
• The cost of equity rises throughout as leverage increases.
• The optimum differs across firms. It depends on business risk, the tax rate, corporate governance, industry and other factors.

The figure shows firm value and the costs of capital with illustrative numbers: an unlevered firm worth 1,000, a 25% tax rate and distress costs that start once debt passes 150.

Target capital structure

The target capital structure is the mix a firm aims for on average over time, reflecting management's view of the optimal structure. WACC weights should reflect the target, measured at market values. An analyst can use management's stated target when one is given, but most firms do not publish a target, so an external analyst estimates it from (1) the current market-value capital structure, (2) the current structure adjusted for a visible trend, or (3) industry-average weights.

Book values are also common in practice. Analysts often estimate target weights from the book values of debt and equity, and managers often think in book values for three reasons: short-term market swings do not change the appropriate amount of debt, management cares about how capital is deployed to projects, and rating agencies use book values.

Actual capital structures fluctuate around the target because of:

• changes in market values, especially of equity;
• management exploiting opportunities, such as issuing equity after a temporary share-price rise;
• external capital being raised in minimum-size lots.

Deviations caused by these three reasons are a normal part of how an actual capital structure moves around its target.

Asymmetric information, signaling and pecking order theory

Costs of asymmetric information arise because managers know more about the firm's prospects than investors do. They are higher for firms with complex products or opaque financial statements, and they raise required returns on both debt and equity. The larger the share of equity in the capital structure, the higher the cost of asymmetric information. Investors read financing choices as signals. Taking on debt, a commitment to fixed payments, signals confidence; issuing equity is often read as a sign that management believes the shares are overvalued.

Pecking order theory says managers prefer the financing least likely to send a negative signal, ranked by visibility to investors:

1. Internally generated funds (retained earnings), the most preferred source;
2. Debt;
3. New external equity, the least preferred source.

Capital structure is then a by-product of individual financing decisions rather than a deliberate target.

Agency costs of equity

Agency costs of equity stem from conflicts between managers and shareholders. Managers without an ownership stake do not bear the cost of excessive pay or of taking too much or too little risk, so shareholders spend money to limit the conflict. The net agency costs of equity that result have three components:

Under the free cash flow hypothesis, more debt reduces agency costs because interest payments leave managers less free cash flow to spend for their own benefit.