Modigliani and Miller Proposition I and II
Discuss about the Business Operations By Making Suitable Combination.
In financial aspects, a systematic approach applied for financing the business operations by making a suitable combination of equity and liability is basically known as capital structure theory. These theories reflect relation between debt and equity financing and the market value of firm. There are various capital structure theories which clearly reflect an understanding about the need of optimal capital structure for the business and companies. Such theories are as follows:
The two professors Millar and Modigliani developed a capital structure irrelevance proposition. According to them, the capital market used by the companies does not matter in the situations of perfect market. The propositions I and II assumes that there are no taxes and no transaction and bankruptcy cost. Proposition I states that value of the company does not depends upon its capital structure (Modigliani and Miller, 1958). According to the proposition, the businesses having same operations will have same assets and will only differ in their liabilities that are the way of financing their activities. One may have a capital structure where the portion of equity is more and debt is less whereas other’s capital structure may reflect high portion of bonds and less equity (Harris and Raviv, 1991). Therefore, M&M I say that in an entity, the structure of its equity and debt is irrelevant and the value is determined by its real assets.
On the other hand, Proposition II states that the value of financial leverage is directly proportional to the value of cost of equity. As the debt component increases, the cost of equity also rises (Bradley, Jarrell and Kim, 1984).
Proposition I (no taxes)
Value of unlevered firm (VU) = Value of levered firm (VL)
Proposition II (no taxes)
re = ru + (ru – rb) B / S (Harris and Raviv,1991).
re = Cost of Equity
ru= Cost of Capital
rb = Cost of Debt
B = Value of Debt
S = Value of Equity
Initial investment = $6000
EBIT = $2000
ru= 10%
rb = 5%
B = $1000
Proposition I = VL = VU
VU = S = Value of Equity
S = EBIT / ru
= $2000 / 0.1 = $20,000
Value of unlevered firm = $20,000
VL = B + S = Vale of Debt + Value of Equity
B + S = [Interest + (EBIT – Interest)] / ru
= $2000 / 0.1 = $20,000
Proposition I and II (with tax)
S = VL – B = $20,000 – $1,000 = $19,000
Value of levered Firm = $20,000
Hence, it is proved that the value of levered and unlevered firm is equal irrespective of the capital structure applied to the firms.
Proposition II = re = ru + (ru – rb) B / S
VU =ru = 0.10 + (.10 – 0.05) x ($0 / $20,000)
Value of unlevered firm = 10%
VL = re = 0.10 + (.10 – 0.05) x ($1000 / $19,000)
Value of levered firm = 10.26%
Proposition I and II (with tax)
The hypothesis given by MM is valid only in perfect market condition. In real world, such condition does not prevail and imperfection arises in the capital market and the capital structure of the firm. All such imperfections affect the valuation as corporate taxes are present there.
As it is a fact that when taxes are imposed, debt financing is the most beneficial method because interest paid on debt is a tax deductible item whereas the dividends are non-tax deductible. Thus, if the major portion of capital structure is covered by debt capital then more income will be there for the equity and debt holders (Modigliani and Miller, 1963). In other words, the levered firm will have high value than the unlevered firm. The trade-off theory suggests that the firm can capitalize it requirements with debt as long as the bankruptcy cost exceed the tax benefit. Thus, if the debt increases within a given threshold, it will add value to the company. MM approach with taxes promotes tax savings and thus states that a change in debt equity ratio will affect WACC which means higher the portion of debt, lower will be the value of WACC and vice-versa (Miller, 1988).
Proposition I (with tax)
Value of levered firm (VL) = Value of unlevered firm (VU)+ tB
Where, t = Corporate tax rate
B = Value of debt
Proposition II (with tax)
re = ru + (B / S) (1 – t) (ru – rb)
For example:
ru(for unlevered firm) = 10%
t = 34%
|
Unlevered |
levered |
|
|
Cash flows |
||
|
EBIT |
$ 2,000.00 |
$ 2,000.00 |
|
(-) Interest |
$ 50.00 |
|
|
EBT |
$ 2,000.00 |
$ 1,950.00 |
|
(-) Tax (34%) |
$ 680.00 |
$ 663.00 |
|
Net Income |
$ 1,320.00 |
$ 1,287.00 |
|
Cash flows debt + equity |
$ 1,320.00 |
$ 1,337.00 |
Income tax savings = Interest expense * tax rate
= $50 * 34% = $17
Proposition I
VU = EBIT (1 – t) / ru = 680 / 0.1 = $6,800
VL = VU + tB = $6,800 + (0.34 x $1000) = $7140
S = VL– B = $7140 – $1000 = $6140
Proposition II
ru = .10 + ($0 / $6,800) (1–.34) (.10 – .05) = 10%
Pecking Order Theory
re = .10 + ($1,000 / $6,140) (1 – .34) (.10 – .05) = 10.54%
The MM theory with taxes relates to trade off theory in a manner that both of them focus on the benefits provided to the levered firm due to the imposition of tax. As per the trade-off theory, companies having leverage are having benefits until the optimum capital structure is attained. Both the theories recognize the tax benefits from interest payments and say that the levered firm has high value as compare to unlevered firm.
The empirical findings from this theory is that the approaches given by Modigliani and Miller are not applicable in real world. The proposition I and II does not take into account the taxes and any type of transaction cost. Also, they believe that in calculating the value of the firm, capital structure does not matter. However, the assumptions taken were unrealistic in today’s world.
This theory is considered as an alternative approach to trade off theory. Instead of bringing corporate taxes and financial distress in the framework of MM, the theory assumes that managers have more knowledge than investors and their actions give investors an idea about the scenarios of the firm. According to the theory, a hierarchy is followed by managers in selecting the sources of finance (Leary and Roberts, 2010).
As per the hierarchy, managers first go for internal financing and when it is not enough they opt for external financing. In raising funds from external source, managers issue debt to generate funds and when it is not possible to issue more debt, they go for equity financing. As the risk increases the cost of finance also increases. The theory view equity as last option because of the amount of transaction cost associated with each form of financing. Internal source finance has low transaction cost than the cost incurred in issuance of debt and shares (Frank and Goyal, 2003). Pecking theory is based on assumption of asymmetric information which means unequal distribution of information. Such asymmetric information affects the affects the options related to internal and external financing as a result of which, a pecking order exist in order to finance the new projects (Tong and Green, 2005).
Generally, the theory does not have a targeted capital structure it only prioritize the three major sources of finance. The pecking order is important because it gives an idea about the performance of the company. If the firm is focused on internal financing then it is strong, if it goes for debt financing then it is confident about paying its obligations and if the firm opts for issue of shares, then it is considered to be a negative signal (Rajan and Zingales, 1995).
It can be empirically found out that pecking order theory believes in following a hierarchy for raising finance. It does not provide a targeted capital structure but it do gives investors an idea about the scenario of firm’s capital structure. It shows the percentage of internal and external financing done by the managers.
It is another capital structure theory which explains the relationship between the principals and agents. In this, the principals are the shareholders of the firm and agents are firm’s executives. Under this relationship, the agents are hired by the principals to perform and work and it is assumed that both have self-interest which leads to various types of conflicts. As a result of which, agency cost arises. In corporate finance, agency cost arises when managers seeks to perform in their own interest instead of maximizing the value of firm. Such costs can also be a result of the conflict between debt and equity holder (Vilasuso and Minkler, 2001). The agency theory highlights the fact that firm using more debt has more benefits of tax and along with that they have high bankruptcy costs. However, the theory suggested that firm can only have an optimal capital structure and can only maximize the firm value by matching its debt cost with their benefits. It states that there is a positive relation between the firm’s profitability and its leverage (Leland, 1998). The optimal capital structure is identified by agency cost theory by adjusting the debt and the investments made by the firm. This will reduce the conflict between managers, debt holders and shareholders. By resolving the equity debt conflicts, the company can attain an optimal capital structure. Agency cost theory suggests various methods to solve the conflicts so that the managers can have a preferred capital structure in their firm (Berger and Di Patti, 2006).
From all the above capital structure theories, one thing is clear that the need for having an optimal capital structure does exists and managers do strive for the same. As pecking order theory also provides a hierarchy of raising the finance clearly indicates that managers look for a suitable capital structure within their firm. In addition to this, as suggested by agency theory that reducing the conflict or minimizing the agency cost will result in optimal capital structure for the firm. So, it is true that for a company to grow and function successfully, managers must focus to improve and employ preferred structure of capital within the business.
It is found out that the agency cost theory believes that an optimal capital structure exists in the company and firm can improve it and increase its value by matching the cost and benefits of its debt. Resolving the issues between the principal and agent and adjusting the investments and debt component will lead to a preferred capital structure.
From the above theories, it is clear that the need for finding the optimal structure of capital do exist. As it is clear that lowering the amount of WACC will maximize the shareholder’s wealth so managers are required to find out a mixture of debt and equity component that will lower down its WACC. In real life instances, the company can do this by increasing its debt component as it is cheaper than equity. Hence it can be said that the hunt for an optimal capital structure continues. Also managers should have knowledge about pecking order theory as it follows a totally different approach and ignores the concept of preferred structure of capital.
The policy of dividend are directly related to the theories of capital structure. If the company pay dividends out of its earnings, then its capacity of raising funds internally reduces and it goes for external financing. MM theory of irrelevance in both dividend and capital structure cases does not work in real world. The theories given by other authors concludes that taking a decision related to capital structure is as difficult as deciding the dividend policy for the firm. Companies do consider the theories in both the aspects in order to make appropriate dividend policy and choose the suitable financing option for their business (Franc-Dabrowska, 2009).
Modigliani and Miller, the authors who were famous for their capital structure theories have also provided dividend irrelevance theory. According to them, in a perfect market the dividend policy is irrelevant. They claimed that the policy of dividend of the firm does not affect its share prices and its capital structure. They prove this by giving a notion that if an investor gets more dividend than the expected one, then he can re-invest the same in company’ stock with the surplus cash flow. On the other hand, if the received amount of dividend is low then the investor can sell a part of his shares to recover the desired cash flow. Hence, the fact about the dividend policy followed by the firm is irrelevant for the investor (Miller and Modigliani, 1961).
In order to prove the above notion, certain assumptions are to be made by the investors which are as follows:
- Personal and corporate taxes does not exist
- No flotation and no transaction costs
- Capital budgeting of the firm is not affected by its dividend policy.
- The information is readily available to the investors.
- Zero impact of leverage is there on company’s cost of capital (Baker, 2009).
P0 = 1/ (1 + ke) x (D1 + P1)
Where,
P0 = Market price of share
ke= Cost of equity
D1 = Dividend received at the end of the period 1
P1 = Market price of the share at the end of period 1 (Brigham and Houston, 2012).
Value of firm = nP0 = [(n + ? n) P1 – (I +E)] / (1 + Ke)
Where,
n = Number of outstanding shares at beginning of period
? n = Change in number of shares during the period / additional shares issued
I = Investment amount
E = Firm’s earning during the period (Brigham and Houston, 2012).
The firm has a capitalization rate of 10%, outstanding shares 30000 selling at $100 each. Dividend is expected to be at $7 per share at the end of the financial year. The net earnings of the company amounted to $300,000 and the new proposed investment worth $600,000.
- Firm’s value when dividends are paid
Per share price at the end of year 1
P0 = 1/ (1 + ke) x (D1 + P1)
$100 = 1 / (1+ 0.10) x ($7 + P1)
P1 = $103
Amount needed to be raised through equity shares
? n P1 = I – (E – nD1)
= $600,000 – ($300,000 – $210,000)
= $510,000
Additional shares to be issued
? n = $510,000 / 103 = 4951.456 shares
Value of the firm
= [(30,000 + 4951.456) (103) – ($600,000 + $300,000)] / (1 + 0.10)
= $2454545.45
- When dividend is not paid
Per share price at the end of year 1
$100 = 1 / (1+ 0.10) x ($0+ P1)
P1 = $110
Amount needed to be raised
= $600,000 – ($300,000 – $0)
= $300,000
Shares to be issued in addition
? n = $300,000 / 110 = 2727.27273 shares
Value of the firm
= [(30,000 + 2727.27273) (110) – ($600,000 + $300,000)] / (1 + 0.10)
= $2454545.45
Form the above example it is proved that the dividend policy and the amount of dividend paid by the company is irrelevant to the value of firm and its capital structure. However, this theory has some limitations like its assumptions does not exist in real world and the market has imperfections along with the corporate taxes.
It can be empirically found out that this theory focused on the fact of not having a dividend policy, as it does not have any impact on the share price and value of the firm. MM approach says that firm’s value remain same irrespective of its dividend policy. However, this theory also assumes that there are no corporate taxes and no sort of flotation costs.
In contrast to MM irrelevance theory, Myron Gordon has given a theory on dividend which states the relevancy of dividends in context of the company. It is also known as bird-in-hand theory and focuses on the fact that value of current dividends is much more needed while determining the value of firm. The model provided by Gordon calculates firm’s value by using its dividend policy (Gordon, 1959). The main crux of Gordon’s theory is that company’s dividend pay-out policy affects its share price and the relationship between its rate of return (r) and cost of capital (k). It is shown as below:
The theory is based on certain assumptions which are as follows:
- It is assumed that no debt is there and the company is totally financed through equity.
- No external financing is there.
- Perpetual earnings are there.
- It is assumed that there is a constant IRR
- Constant cost of capital (k) is there.
- No taxes are there and k>g that is cost of capital is more than the growth rate (Frankfurter, Wood and Wansley, 2003).
According to the model, the value of market price per share is calculated by applying the following formula:
P = [EPS x (1-b)] / (k-g)
Where,
P = per share market price
EPS = Earnings per share
b = retention ratio
k = cost of capital
g = growth rate = b*r (Chandra, 2011).
The model states that the market value of share is equal to the sum of the present values of future dividends. This notion can be clearly understand by a practical example.
The EPS of the company is $20. Its cost of capital is 10% and dividends grow annually at the rate of 5%. The company retain 80% of its earnings. So, the value of company’s share will be:
E = $20
k = 10%
g = 5%
b = 80%
Market price per share = P = [$20 x (1-0.80)] / (0.10 – 0.05) = $80
As per Gordon’s theory, the policies of dividend followed by the firm do impact its value. For a growing firm, reinvesting the dividends will give more benefits to the shareholders whereas for a declining firm, distributing the dividends to the shareholders is more beneficial than reinvesting them. However, this theory also has certain limitations like it is difficult to measure the constant internal rate of return and cost of capital. Along with this, external financing do exists in the companies (Chandra, 2011).
It is analysed that Gordon’s model is totally in contrast of MM irrelevance theory. It considers that dividend policies of a firm do affect the value of company and its shares. As per this theory the present value of future dividends determine the market value of company’s share.
It is a theory which explains Clientele effect which arises with the reaction of investors when a company changes its policies and procedures related to dividend, tax or others. The clientele effect clearly explains the movement in company’s stock prices due to the changes in its policy. The theory assumes that investors are attracted towards a company due to its policies and once the company changes them, the investors seek to adjust their stocks accordingly. As a result the stock price changes (Elton and Gruber, 1970). There is basically two side of such effect. The first side describes the manner in which investor chooses a particular type of stock. Such as some prefer to invest in stocks with high dividend while some go for the one which has a potential to generate high capital gains.
The other side deals with the reactions of current investors as and when the company changes its policies or procedures. For example, a stock which pay no dividends and reinvest all the profits in the company will first attract the growth investors. Then, if company decided to pay dividends instead of reinvesting, the high growth investors then may exit and look for other stocks. However, such change in policy will attract the investors who are seeking the dividend income. So, this how clientele theory works and it clearly states the dividend polices are very much relevant for measuring the value of firm (Dhaliwal, Erickson and Trezevant, 1999).
It can be empirically concluded that the theory is mainly focused on the reactions of investors when a company changes its policies. According to this theory, the investors believes that change in the dividend policy of the company will impact its stock prices. Hence, it shows the need of having an optimal policy of dividend.
This theory of dividend suggests that when a company made an announcement about increase in its dividend pay-outs then it is considered as the positive future prospects. The theory is linked to game theory and it provides a notion that dividend signaling does occur. Increase in pay-outs forecast positive future performance of the company whereas a decrease in dividend pay-outs shows company’s negative performance in future (Nissim and Ziv, 2001). When this theory was tested, it was found out that the stock prices of a company rise when there is an increase in dividend pay-outs and it fall when the pay-outs reduces. In other words, dividends signal some information about company’s profitability. The signaling theory suggested that firm paying high dividend is more profitable than the one offering lower dividends. Thus, it can be assumed that dividends can be considered as predictor for forecasting the future earnings of the firm. This theory also proves the relevancy of dividends in determining the share price of a firm (Connelly et al., 2011).
This theory also critically explains the need of having an optimal dividend policy. It says that the firm’s stock prices rises as and when its dividend pay-out increases and vice versa. Also dividends give signals about the profitability of the company.
This theory concerns with the dividend policy of an enterprise. It claims that investors prefer the companies which have lower pay-outs for tax reasons. Also the rate of corporate taxes influences company’s decision regarding their dividend policies. Reason being, the taxes affect the net income after tax of the firm which shows its capability of paying dividends and the net value received by the shareholders. According to this theory tax rate plays a major role in determining the amount of dividend to be declared and paid by the company (Elton, Gruber and Blake, 2005).
So from all of the above theories, it can be said that dividend payments do matter while calculating the share price of the company. Apart from MM irrelevance theory, the other theories claim that the dividend and the related policies are the integral part of the firm’s stock prices. Changes in the dividend amount do affect the share prices of the firm
This theory also considers the dividend policy of the firm. The crux of the theory is that investors prefer those company’s stock who offers lower pay-outs for tax purposes. Also the tax rates decide the firm’s policy of dividend which eventually reflects its capability of distributing the dividends to its shareholders.
Thus, it can be said a need of having optimal dividend policy does exist in present world. All the theories focused on this fact except MM approach. The firm can have the same by having high pay-outs which means it distributes more dividend to the investors. Optimal and preferred dividend policy will definitely increases the value of firm and maximize the shareholder’s wealth.
References
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