FREE online courses on Capital Structure of Firms - Capital Structure Theory - I. MM model without taxes

 

Using an arbitrage proof, MM showed that when all the assumptions hold and there are no taxes, the value of an unleveled firm is identical to that of a levered firm ():

         

         

This is because all earnings are paid out as dividends and the earnings are expected to be constant for an indefinite period of time. As a result, the common stocks of the firm behave like preferred stocks. If you remember, the intrinsic value of a preferred stock () is determined as follows:

 

         

 

This is known as the Proposition 1 of the MM model without tax. Basically, what this proposition claims is that the value of a firm is independent of its financing strategy (i.e. capital structure). In other words, the value of a firm depends on how the business is operated and not on how the money is raised for the projects.

 

Since the values of identical levered and unleveled firms are the same, the MM model (without tax) claims that the weighted average costs of capital (WACCs) are also identical for the two firms.  This leads to Proposition 2 of the MM model:

 

 

         

 

What does Proposition 2 of the MM model tells us? Before we address that question, we need to look at how the changes in a firm's financing decision affects the shareholders' behaviors. We know that as the firm increases its debt usage, it also faces a greater constraint on its cash flows to meet the increased interest payments. According to Proposition 1, the changes in financing decision (or capital structure) will have no impact on the firm's value. In other words, the shareholders are facing an increased financial risk without being compensated with an increased in firm value. Hence, the shareholders will demand a higher return to compensate the increase in risk and this will translate into a higher cost of using common stock for a levered firm. As a result, we can see from the following equation that the second term of the cost of common stock for a levered firm represents the compensation for the additional financial risk (due to the usage of debt):

 

         

 

We know that in general the cost of debt is cheaper than the cost of common stock. As a result, a firm is experiencing a “saving” when it switches from equity financing to debt financing. However, we can infer from Proposition 1 that the WACCs are identical for a levered and an unleveled firm. What this means is that the “savings” from the use of debt is completely offset by the increased costs of using common stock.

 

We can graphically represent Propositions 1 and 2 of the MM model (without tax) as follows:

 

 

What do the two propositions and the two graphs depicted above tell us above the Modigliani-Miller model on capital structure in an environment without any corporate taxes? We can learn two main lessons from this model assuming that the four assumptions hold:

 

In an environment without any corporate taxes, the value of a firm is not influence by the firm's capital structure. In other words, the value of a firm is not affected by the amount of debt used by the firm. As a result, we also know that the weighted average cost of capital of a firm is also unaffected by its capital structure.

 

We have discussed earlier that as a firm uses more and more debt, its current and prospective shareholders will view the firm as getting riskier. This is because the firm needs to pay a greater amount of interest payments as the amount of debt increases. Since a firm cannot skip its interest payments, it faces a greater cash constraint as its debt usage increases. As a result, the shareholders will “require” a higher return to induce them to hold the stocks, which translates into a higher cost of equity for the firm. In this case, we know that the firm enjoys a bigger and bigger saving when it uses more and more debt because it is cheaper for it to use debt than it is to use equity. However, the cost of using equity rises as the firm increases its debt usage. In this particular MM model, we know that the savings resulted from using debt is completely offset by the increased cost in using equity. As a result, the WACC faced by the firm remains unchanged.

 

Basically, the MM model claims that a firm enjoys no benefit in using debt: whatever savings a firm enjoys in using debt is offset by the increased cost in using equity. Hence, the capital structure of a firm has no impact on its value and WACC.