FREE online courses on Capital Structure of Firms - Capital Structure Theory - II. Modigliani & Miller model with corporate taxes

 

In 1963, Modigliani and Miller published an article that refined their original model by incorporating corporate taxes (but still ignoring any personal taxes). This is commonly known as MM model 2 or MM model with corporate taxes. The presence of corporate tax (i.e. ) “affected” the original two propositions as follows:

 

Proposition 1:	where The reason that the value of an unlevered firm () has changed in this particular model is that the firm needs to pay corporate taxes on its earnings before paying them out as dividends to its shareholders.
Proposition 2:

 

Similarly, we can represent Propositions 1 and 2 of the Modigliani-Miller model with corporate taxes as follows:

 

 

Once again, we need to ask ourselves the question “What do the two propositions and the two graphs depicted above tell us above the Modigliani-Miller model on capital structure in an environment with corporate taxes?” The two lessons that we will learn in this model differ from the earlier MM model without corporate taxes.

 

In Proposition 1, we see that capital structure does have an impact on the value of the firm. In fact, it has a positive impact on the firm's value: as the level of debt employed by the firm increases, so does its value. In other words, there is tax advantage in debt financing, which is represented by the following term:

 

                  

 

Why is there a tax advantage in using debt and not equity? This is because when a firm is determining its taxes, it can write off its interest payments but not its dividend payments. As a result, the firm is receiving a subsidy from the government for using debt to raise capital (but not for using equity).

 

Using what we have learned in Proposition 1, we can try to understand intuitively the meaning of Proposition 2. We know that in an environment with corporate taxes, there are now two “benefits” to using debt financing: (i) debt is a cheaper source of capital than equity and (ii) interest payment represents a tax write off to the firm. From MM model 1, we know that the saving in using the cheaper debt is completely offset by the increased cost in using equity. However, in an environment with corporate taxes, the firm's benefits in using debt (i.e. cheaper form of capital and tax write off) more than offset the increased cost in using equity. Hence, the cost of equity of a levered firm in an environment with corporate taxes rises at a slower rate than the one in an environment without corporate taxes. In other words, the shareholders have a smaller compensation for financial risk (or risk premium) in an environment with corporate taxes.

 

Since the “savings” in using debt outweighs the increased cost in using equity, the weighted average cost of capital faced by the firm decreases as it uses more and more debt.

 

Basically, the Modigliani-Miller model claims that in an environment with corporate taxes, a firm does enjoy a benefit in using debt in the form of an interest tax shield. We know that the value of the firm increases as the level of debt usage increases. From the graphs above, we know that the firm will achieve its highest value and its lowest level of cost when it uses 100% debt financing. Hence, we know the capital structure of a firm has an impact on its value and WACC in an environment with corporate taxes.

 

Example: Lilliput, Inc. and Infants & Babies, Inc. are two infant apparel manufacturers that are identical in every aspect except their financing decision. The management of Lilliput has decided that it is best for the firm if only equity is used in raising money, but the management of Infants & Babies has decided that it is best to used both debt and equity. Both firms have assets with book value of $20 million that are expected to earn before-tax returns of 12%. Currently, the U.S. government is trying to promote domestic infant apparel manufacturing by offering a zero federal-plus-state corporate tax rate for a limited period. The current cost of debt for such firms is 7% and the cost of equity (for an unlevered firm) is 10%. The assumptions of the MM model apply to these two firms.

 

According to the MM model, what are the value and WACC of Lilliput?

Before we can determine the value of Lilliput, we need to first determine its earnings (which is determined by the return it earns on its assets) as follows:

 

         

 

Since Lilliput faces no corporate tax and uses only equity in this particular scenario, we know its value and WACC are:

 

         

         

 

According to the MM model, what are the value, cost of equity, and WACC of Infants & Babies if the management has decided to raise (i) 0 debt, (ii) $10 million debt, and (iii) $20 million debt? What conclusion can you make in terms of the impact of debt financing (or financial leverage) on the firm's value?

 

Since Infants & Babies uses both debt and equity in raising capital, we can use Propositions 1 and 2 of MM model (without corporate tax) to determine the value, the cost of equity, and WACC as follows:

 

                   and    

         

         

 

Infants & Babies issuing zero debt

 

In this particular scenario, Infants & Babies is identical to Lilliput since it is not using any debt. As a result, we know:

         

         

Infants & Babies issuing $10M debt

Since we know from (a) that , using Propositions 1 of the MM model we know:

         

 

In addition, since the firm uses $10M of debt we know the value of the stocks is:

         

As a result, the cost of equity and WACC for Infants & Babies when it uses $10M of debt are:

         

         

Infants & Babies issuing $20M debt

Similarly, using Propositions 1 of the MM model we know:

         

And since the firm uses $10M of debt, we know the value of the stocks is:

         

As a result, the cost of equity and WACC for Infants & Babies when it uses $20M of debt are:

         

         

 

Suppose the U.S. government removed the favorable tax treatment and all infant apparel manufacturers now have to face a 40% federal-plus-state corporate tax rate.

When the U.S. government removed the tax treatment, Lilliput and Infants & Babies will have to pay corporate taxes on their earnings before paying them as dividends to the shareholders. This will have an impact on the firms' values and in some situations the cost of equity and WACC.

 

What are the value and WACC of Lilliput?

In this particular scenario, the value and WACC of Lilliput after paying corporate taxes are as follows:

         

         

 

The value, the cost of equity, and WACC of Infants & Babies if the management uses (1) $10 million debt and (2) $20 million debt.

In this particular scenario, Infants & Babies actually enjoys a tax benefit for using debt because it can use the interest payments to help write off part of the tax liability. As a result, the value and cost of equity of the firm are as follows:

         

         

 

Infants & Babies issuing $10M debt

Using the above formulas and the answer in (i), we know the following:

         

Since the firm uses $10M of debt, we know the value of the stocks is:

         

In addition, we know the cost of equity and WACC for the firm is as follows:

         

         

 

Infants & Babies issuing $20M debt

Similarly, we know the value of Infants & Babies is as follows:

         

Since the firm uses $10M of debt, we know the value of the stocks is:

         

In addition, we know the cost of equity and WACC for the firm is as follows:

         

         

 

What is the maximum dollar amount of debt financing available to Infants & Babies if it is facing a 40% federal-plus-state corporate tax rate? What is the value of the firm at this debt level? What is the cost of debt?

The maximum amount of debt that Infants & Babies can use is 100% debt. In other words,

         

Solving the above equation for  will give us the following:

         

Hence, the value of the firm at a 100% debt level is $24M and the cost of debt remains at 7%.