Modigliani-Miller (MM) supports irrelevance in dividend, how?

According to M-M, under a perfect market situation, the dividend policy of a firm is irrelevant, as it does not affect the value of the firm. They argue that the value of the firm depends on the firm’s earnings, which results from its investment policy. Thus, when investment decision of the firm is given, dividend decision –the split of earnings between dividends and retained earnings- is of no significance in determining the value of the firm

M-M constructed their arguments on the following assumptions:

• Perfect capital markets: The firm operates in perfect capital markets where investors behave rationally, information is freely available to all and transactions and flotation costs do no exist. Perfect capita; markets also imply that no investor is large enough to affect the market price of a share.

• No taxes: taxes do no exist or there are no differences in the tax rates applicable to capital gains and dividends. This means that investors value a rupee of dividend as much as a rupee of capital gains.

• Investment opportunities are known: the firm is certain with its investment opportunities and future profits.

• No risk: Risk of uncertainty does not exist i.e. investors are able to forecast future prices and dividends with certainty, and one discount rate is appropriate for all securities and all time periods. Thus, r=k for all t

According to M-M, r should be equal for all shares. If it is not so, the low return yielding return shares will be sold by the investors who will purchase the high- return yielding shares. This process will tend to reduce the price of the low-return shares and increase the prices of the high-return shares. This switching or arbitrage will continue until the

differentials in rates of return are eliminated. The discount rate will also be equal for all firms under M-M assumptions since there are no risk differences.

Thus the rate of return for a share held for one year may be calculated as follows:

r = Dividends+ Capital gains (or loss)

Share price

r = Div1 + (P1-P0)


Po = Div1 + P1


Since it is assumed that there exist perfect markets r = k; we can write the above equation as:

Po = Div1 + P1


So we can equate both of them:

Po = Div1 + P1 Div1 + P1

        (1+ r) (1+k)

Where P0 is the market or purchase price per share at time 0.

P1 is the market price per share at time 1.

Div 1 is the dividend per share at time 1.

k is the cost of capital

As hypothised r should be equal for all shares.

If we multiply both the equation by the number of shares outstanding, n, we will the total value of the firm:

V = nPn (DIV1 + P1)


You can note an important point here that MM allows for the issue for the new shares, unlike Walter’s and Gordon’s model. Therefore, a firm can pay dividends and raise funds to undertake the optimum investment policy.

Taking to the above note, suppose that the firm sells m number of new shares at time 1 at a price P1, the value of the firm at time 0 will be:

NPn (Div1 +P1) + mP1-mP1


Or if we simplify we get:

NPo = nDiv1 + P1(m-n)-m P1


MM believes that the investment programmes of a firm in a give period of time can be financed either by retained earnings or the issue of new shares or both. Thus, the amount of new shares issued will be:

m P= I1 – (X1– n Div 1) = I1-X+ nDiv1

Where Irepresents the total amount of investment during first period and X1is the total net profit of the firm during first period.

I hope you are not lost in the complexity of the formulae. Ok! I will make you understand by taking a practical example.

Lets assume that a company currently has 10,000 outstanding shares selling at Rs 100 each. The firm has net profits of Rs 10,00,000 and wants to make new investments of Rs 20,00,000 during the period. The firm is also thinking of declaring a dividend of Rs 5 per share at the end of the current fiscal year. The firm’s opportunity cost of capital is 10%. We want to know the price of the share at the end of the year if: (i) dividend is not

declared,(ii) a dividend is declared , (iii) The number of new shares to be issued by applying MM approach?

We know that the price of the share according to MM approach at the end of the current fiscal year is:

Po = Div1 + P1


Or P1 = P(1+k)- Div1

Lets apply the formula for getting the value of Pwhen dividend is not paid:

P1 = Rs 100(1.10)-0 = Rs 110

We have taken Div= 0 because the firm has not paid dividend.

Now, can you tell me the share price when the firm is paying dividends! Is it Rs 105! Yes, you are right.

You can note a point here that the wealth of shareholders will remain the same whether or not dividend is paid. When the dividend is not paid, the shareholder will get Rs 110 by way of the price per share at the end of the current year.

If you see the other side of the coin, when dividend is paid, the shareholder will realise Rs 105 by way of the price per share at the end of the current fiscal year plus Rs 5 as dividend.

Now, if we want to know the number of new shares to be issued by the company to finance its investments, we will follow the formula as discussed above.

m P= I1 – (X1– n Div 1) = I1-X+ nDiv1

105 m = 20,00,000 – 10,00,000 + 5,00,000

105 m = 15,00,000 or m = 15,00,000/105


Do you think that there are some drawbacks in MM approach? 

There are some critics who argue that the assumptions made by MM dividends are irrelevant. According to them dividends matter because of the uncertainty characterising the future, the imperfections in the capital market, and the existence of taxes. We will discuss the implications of these as follows:

1. Information About Prospects :In a world of uncertainty the dividends paid by the company, based as they are on the judgment of the management about future, convey information about the prospects of the company. A higher dividend payout ratio may suggest that the future of the company, as judged by management, is promising. A lower dividend payout ratio may suggest that the future of the company as considered by management is uncertain. Gordon has eloquently expressed this view. An allied argument is that dividends reduce uncertainty perceived by investors. Hence investors prefer dividends to capital gains. So shares with higher current dividends, other things being equal, command a high in the market.

2. Uncertainty and Fluctuations: Due to uncertainty, share prices tend to fluctuate, sometimes rather widely. When share prices fluctuate, conditions for conversion of current income into capital value and vice versa may not be regarded as satisfactory by investors. Some investors who wish to enjoy more current income may be reluctant to sell a portion of their shareholding in a fluctuating market. Such investors would naturally prefer, and value more, a higher payout ratio. Some investors who wish to get less current income may be hesitant to buy shares in a fluctuating market. Such investors would prefer, and value a lower payout ratio.

3. Offering of Additional Equity at Lower Prices: MM assume that a firm can sell additional equity at the current market price. In practice, firms following the advice and suggestions of merchant bankers offer additional equity at a price lower than the current market price. This practice of ‘underpricing’ mostly due to market compulsions, ceteris paribus, makes a rupee of retained earnings more valuable than a rupee of dividends. This is because of the following chain of causation:

4. Issue cost: The MM irrelevance proposition is based on the premise that a rupee of dividends be replaced by a rupee of external financing. This is passib1e when there is no issue cost. In the real world where issue cost is incurred, the amount of external financing has to be greater than the amount of dividend paid. Due to this, other things being equal, it advantageous to retain earnings rather than pays dividends and resort to external finance.

5. Transaction Costs: In the absence of transaction costs, current income (dividends) and Capital gains are alike-a rupee of capital value can be converted into a rupee of current income and vice versa. In such a situation if a shareholder desires current income (from shares) greater than the dividends received, he can sell a portion of his capital equal in value to the additional current income sought. Likewise, if he wishes to enjoy current income less than the dividends paid, he can buy additional shares equal in value to the difference between dividends received and the current income desired. In the real world, however, transaction costs are incurred. Due to this, capital value cannot be converted into an equal current income and vice versa. For example, a share worth Rs 100 may fetch a net amount of Rs 99 after transaction costs and Rs 101 may be required to. buy a share worth Rs 100. Due to. transaction costs, shareholders who have preference

Higher dividend payout

Greater dilution of the value of equity

Greater volume of under priced equity issue to financea given level of investment far current income, would prefer a higher payout ratio and shareholders who have preference for deferred income would prefer a lower payout ratio.

6. Differential Rates of Taxes: MM have assumed that the investors are indifferent between a rupee of dividends and a rupee of capital appreciation, This assumption is true when the taxation is the same for current income and capital gains. In the real world, the effective tax on capital gains is lower than that for current income. Due to this difference, investors would prefer capital gains to current income.

Let us try some problems to make the concept clearer.


Voltas Ltd. had 50000 equity shares of Rs.10 each outstanding on Jauary1, 1993. The shares are currently being quoted at par in the market. In the wake the removal of the dividend of Rs.2 per share for the current calendar year. It belongs to a risk class whose appropriate capitalization rate is 15%. Using Modigliani-Miller model and assuming no taxes, ascertain the price of the company’s share as it is likely to prevail at the end of the year (1) when dividend is declared,

And (2) when no dividend is declared.

Also find out the number of new equity shares that the company must issue to meet its investment needs of Rs.2 Lakhs, assuming a net income of Rs1.1 lakhs and also assuming that the dividend is paid.


a. Price of the share, when dividend are paid

D1 + P1

Po = —————


Rs.2+ P1

Rs.10 = ————–


Rs.115 = Rs.2+P1

Rs.9.5 = P1

b. Price of the share, When dividends are not paid:


Rs. 10 = ———-


Or P1 = 11.5

c. Number of new equity shares to be issued:


Δn = ———————–



Δn = ——————————-





Thus 20000 new equity shares are to be issued to meet investment needs of the company.