Firms can choose to finance themselves with a number of securities: shares, bonds, preferred shares, convertible bonds, etc. These securities can be classified into two broad categories, debt and equity, and each comes with its own cost. Capital structure describes the way a firm finances itself.

*Data from Statistics Canada, 2009*

Capital structure can be represented as a ratio of debt financing to equity financing (financial leverage), or debt financing to overall financing. The ratios can be significantly different over time. In the US, the debt to book equity ratio decreased from ~0.6 in the 1970s to ~0.4 in the 2010s. The average debt to book equity also differs from industry to industry — the pharmaceutical industry is under 0.05, while the entertainment industry is over 0.5. The optimal amount is different for each firm within an industry, and will depend on factors such as tax and bankruptcy costs.

### Is Debt Better or Equity Better?

Given that a firm’s primary objective is to maximize shareholder value, the first thing that comes to mind might be: a firm should finance itself with the cheapest source of finance. To determine which is cheaper, we can go through the calculations for each.

Cost of debt is easy to estimate, it is the return that a shareholder receives through interest payments. To calculate cost of debt, we take risk free rate plus a premium, which accounts for all the risks associated with lending to your firm. You can use the credit ratings as a proxy on the risk premiums demanded by lenders to find the cost of debt, or just look at the financials of a firm to see how much they actually pay.

Cost of equity is harder to calculate, as the firm does not owe the shareholders a fixed stream of payments. The firm can pay the shareholders a dividend, but using that would be inconsistent, as it is a choice not an obligation. The way we calculate cost of equity is through the CAPM, or some sort of Multi Factor Model.

However, even without calculating the cost of each, we know equity must be more expensive than debt. This is due to the fact that shareholders have the residual claims on the assets and cash flows of the company, after the debtholders, and therefore hold much more risk than the debtholders. If we were to naively interpret this information, we would probably conclude that debt is better than equity. However, we would have failed to account for the fact that cost of equity increases with the amount of debt, as equity holders will demand a higher return for the extra risk from the additional debt.

#### Modigliani & Miller Theorem – Proposition I

Franco Modigliani & Merton Miller addressed this idea in their proposition in 1958. Under a certain set of conditions, they proposed, the value of the firm stays the same, regardless of capital structure. This also means that weighted average cost of capital must stay the same, as the value of the firm is the sum of its discounted cash flows. In other words, the firm should be agnostic towards the way they choose to finance themselves, as it has no bearing on the overall financing costs. The assumptions are as follows:

- No taxes: interest from debt would not be shielded from tax
- No transaction costs: investors can freely buy and sell stocks to rebalance their portfolio
- Stocks can be freely traded at market prices: buying and selling stocks would not change prices
- Symmetric information: taking on debt does not signal information to shareholders
- No agency problem: managers are working for their shareholders and maximizing their value
- Financing does not affect operations: significant debt burden would not change interactions with customers or suppliers

To understand why the value of the firm stays constant with different debt levels, consider a firm with no debt and with debt of $1,000. If an investor is able to borrow $1,000 at the same rate as the firm and invest in the firm with no debt, the investor will get the same return compared to the firm with $1,000 debt. Therefore, the investor should not care about the firm’s debt levels.

#### Modigliani & Miller Theorem – Proposition II

As the WACC stays constant with different levels of debt, the cost of equity must increase with increasing debt levels. The increase in cost of equity would offset the use of cheap debt. The relationship can be described by the equation below:

*r _{E }= r_{U} + D/E * (r_{U}-r_{D})*

Where *r _{E}* is the cost of equity,

*r*is the WACC, and

_{U}*r*is the cost of debt. As the debt to equity ratio increases, so does

_{D}*r*.

_{E}As mentioned in our example above, in a perfect world, investors can rebalance their own portfolio freely and use debt to trade risk for return. However, if any of the assumptions are violated, capital structure will affect the value of the firm. In the real world, these assumptions do not hold true, the most important being the tax assumption.

#### Modigliani & Miller Theorem with Tax

Tax is important in capital structure because interest payments to debtholders are tax deductible, while dividend payments to shareholders are not. Specifically, as interest comes before tax in the income statement, interest reduces the taxable income by *D * r _{D}*, and lower tax payments by

*D * r**

_{D}*t*. This provides a “tax shield” for the shareholders, and increases both firm and equity value by the present value of the debt tax shields. To find PV(debt shield), we would discount the tax shields back by the cost of debt, with the final tax shield a perpetuity of

*t * D*.

The cost of equity still increases with debt in a tax world, but it does not perfectly offset the additional cheaper financing.

*r _{E }= r_{U} + D/E * (r_{U }– r_{D}) * (1 – t)*

As a result, WACC would decrease with increasing debt levels, thus increasing firm value, consistent with the PV(debt shield) calculation.

Would this mean you should maximize debt to maximize shareholder value? Not necessarily. There are other costs to holding too much debt, the main one being cost of financial distress. Insolvency will cost the shareholders money, both directly through lawyer fees and indirectly through loss of talent and distortion of management incentives. These costs are hard to estimate and firm specific, but can be estimated through PV calculations. If we were to include these costs in the equation, the firm value would be:

*V _{l }= V_{u}+ PV(Tax Shields) – PV(Bankruptcy Costs)*

Where *V _{l}* would be the optimum firm value.

Statistics 101 | · · · |
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