Deeper Learning and thinking of Modigliani & Miller Theorem (Blog 4) 17.11.2019

Deeper Learning and Thinking of Modigliani & Miller Theorem (Blog 4)

In last week's lectures, Prof. Roman explained to us two schools of academic circles on dividend policy and dividends, namely, dividend irelevance and dividend relevance, which focused on Modigliani & Miller theorem in dividend irelevance and "bird in the hand" theory in dividend relevance. The author is interested in Modigliani & Miller theorem, so he decided to study Modigliani & Miller theorem deeply in this blog.

Definition of Modigliani & Miller Theorem

As for the definition of Modigliani & Miller theory, the definition points out that the market value of a company is calculated by using its profitability and the risk of the underlying assets, regardless of the way the company finances or distributes dividends for investment. Companies can choose three financing methods: borrowing, paying profits (rather than distributing profits to shareholders in the form of dividends) and directly issuing shares (Brealy, Myers and Allen, 2008). Although the theorem is very complex, its simplest form is based on the view that under certain assumptions, there is no difference between debt financing and equity financing (Chen, 2019).

In his book financial innovation and market volatility, Merton Miller, a famous economist of Chicago school who won the Nobel Prize in economics in 1990, explained Modigliani & Miller theory clearly through the following analogy: we think of this company as a large basin of whole milk. Farmers can sell whole milk intact. Or he could separate the cream and sell it at a higher price than whole milk. (this is similar to a company selling low yield, high price debt securities.) But, of course, the rest of the farmers will be skimmed milk with low fat content, and the price will be much lower than that of whole milk. This is equivalent to leverage. Modigliani & Miller theory noted that without the cost of separation (and, of course, without the government's dairy support program), cream plus skim milk would bring the same price as whole milk. "

Deeply Learning and Analysis of Modigliani & Miller theorem in various propositions

According to the relevant information inquired by the author, As for capital structure, the capital structure of a company is the proportion of debt and equity used to finance its assets. We can write the value of the company as v = D + e, where V is the value of the company, and D and E are the market value of the company's debt and equity respectively.

The concept of optimal capital structure is that there is a certain proportion of debt and equity financing to maximize value.Modigliani & Miller theory provides a good starting point for the company to seek the optimal capital structure. 

However, they need some assumptions, such as: (1) there is a fully effective market, there is no transaction cost, (2) there is no financial distress and agency cost, (3) the ability to borrow and lend at a risk-free rate, etc (Milken Insititute, 2015).

Meanwhile, in this assumptions, Modigliani & Miller theorem offer two proposals in two environments: without tax and with tax.

The first proposition is under the condition of no tax. In this case, Modigliani & Miller theory shows that the value of leverage company and non leverage company are the same. In the symbol, VL=VUwhere VLand VU are the values of the levered and unlevered firms respectively (CPI, 2019).

This result is also based on the assumption that individuals and companies can borrow at the same interest rate without tax.

If they do, and the price of a leveraged company is higher than that of an unlevered company, investors can buy an unlevered company on margin.

By doing so, investors create leveraged companies, which increase the value of these companies and earn investors' profits.

The second proposition is that under the condition of no tax, the cost of equity has a linear relationship with leverage ratio. According to the formula: 

RE=R0+DE(R0−RD)${\displaystyle )}$, where:

• RE is the return on equity.
• R0 is the return on the firm's unlevered equity.
• RD is the return on the firm's debt.
• D and E are the market values of the firm's debt and equity respectively.

In general, the cost of debt is usually lower than the cost of equity. That is, if a company pays a 5% debt yield, it will have to earn, say, 8% equity yield. As a result, it is often thought that companies should borrow money to take advantage of cheaper interest rates.

Modigliani & Miller's second proposition says that if you increase your borrowing to get a cheaper interest rate, you will also increase the amount of equity you have to pay. In fact, both will completely offset your (total) weighted average cost of capital (Milken Insititue, 2015).

So in fact, you can't reduce your capital cost by debt to equity.

If tax is now allowed under the first proposition including tax, the company can increase its value through debt financing. This is because debt allows companies to pay less tax.

The tax credit for debt in a particular period is tcI, where tc is the corporate tax rate and I is the interest paid during that period.

If we assume that the company pays "I" of the same amount in each period, the present value of this tax shield is tcD, where D is the total outstanding debt. This can be seen by noting the present value of a perpetuity which pays `I` every period is 

IrD, and I${\displaystyle I}$ is simply rDB (where rD is the per-period cost of debt.

Therefore, in the case of perpetual liabilities, the value of the leverage company is VL=VU+tcD

From the previous discussion, debt is valuable to the company because it has the ability to protect the company from tax.

Without taxes, companies cannot benefit from debt financing.

Finally, under the second proposition including tax, there is still a positive correlation between leverage and equity cost, but equity cost is lower than the level when no tax is imposed. The exact relationship is:

RE=R0+DE(1−tc)(R0−RD)

Note that by setting tc=0, the equation will be reduced to Modigliani & Miller proposition II, excluding tax.

In the author's last blog, we talked about weighted average cost. Its relationship with Modigliani & Miller theory is as follows, the market value of a leveraged company can be written as VL=E+D , so its weighted average cost of capital (WACC) is:

$RWAC=EVLRE+DVLRD(1−tc)$

This is also a good solution to the author's doubts in last week's structure. Why is the formula of WACC in the classroom different from the formula found by myself? This week's blog learning clearly solves this problem. This formula will be more explicit and take tax into account.

Critical Thinking and personal opinion

In this week's in-depth study of Modigliani & Miller's theorem, the author sums up two conclusions based on experts' views. First, the capital structure of a business is irrelevant without taxes. If there is tax, the capital cost of a company can be reduced by issuing bonds. This highlights the importance of debt as a tax shield. 

At the same time, with regard to the dividend policy, the author personally tends to, if the company's management intends to reduce dividends to invest, deal with policies or other options, it is better to communicate effectively and reasonably with investors and shareholders to avoid short-sighted investors affecting the company's stock price, although the dividend drop often means better prospects for development!

References

Brealey, R., Allen, F., & Myers, S. (2006). Corporate finance. Boston: McGraw-Hill Irwin.

Corporatefinanceinstitute. (2019). M&M Theorem - Overview, Assumptions, Propositions. Retrieved 17 November 2019, from https://corporatefinanceinstitute.com/resources/knowledge/finance/mm-theorem/

Chen, J. (2019). Modigliani-Miller Theorem (M&M). Retrieved 17 November 2019, from https://www.investopedia.com/terms/m/modigliani-millertheorem.asp

Milken Insititue. (2015). The Modigliani and Miller Propositions | 5-Minute Finance. Retrieved 17 November 2019, from https://www.5minutefinance.org/concepts/modigliani-and-miller-propositions