**Dividend Irrelevance **

** **Modigliani and Miller give a comprehensive argument for the irrelevance if dividends. M-M argue that dividend policy does not effect the wealth of the share holders and value of the firm depends upon the earnings power of the firm’s assets or its investment policies. The manager in which the earnings stream is split between dividends retained earnings does not affect the value of the firm.

M-M hypothesis is based upon following assumptions

- The firm operates in perfect capital market where investors, are rational information is available to all investors at no cost and transaction and flotation costs does not exist.
- There is no corporate taxes.
- The investment policy of a firm is fixed.
- Risk and uncertainty does not exist.

The rate of return for a shareholder for one year is equal to

= [D_{1}+ (P_{1}-P)]/P

Where is the rate of return, P_{0} is the market price at t = 0, P_{1} is the market price at t = 1, and D_{1} is the dividend at time 1. The r should be same for all shares. If it is not so then low yielding shares should be sold by the investors and they will purchase high yielding shares. This process will tend to reduce the price of low yielding shares and increase the price of high yielding shares. This switching will continue until the difference in rate of return are eliminated.

The above equation can be used for deriving the valuation model, which is

r = [D_{1}+ (P_{1}-P_{0})]/P_{0}

rP_{0}= D_{1} + P_{1} – P_{0}

P (I + R) D_{1} + P_{1}

P_{1} = (D_{1} + P_{1})/ (I +r) or,

P_{1} = (D_{1} + P_{1})/ (I +k) (Since r = k, perfect)

Capital market assumptions)

The value of the firm can be obtained by multiplying both sides by the number of shares outstanding ‘n’

V = nP_{1} = (nD_{1} + nP_{1})/ (1+K)

If the firm sells m number of new shares at time 1 at price the value of firm at time 0 will be

V = nP_{1 }= [(nD_{1}+nP_{1}+mP_{1}+mP_{1})] / (1+k)

[nD_{1 }+ P_{1 }(m + n) mP_{1})] / (1+k)

The total amount of new shares issued in

mP_{1 }1 – (X – nD_{1})

Where 1 is the total new investment during period 1 and X is the net profit earned by the firm (X – nD_{1}) depicts the retained earnings investment retained earnings is the amount to be raised by issuing new shares.

Thus the above value of situation becomes

V = nP_{1 }= [(nD_{1}) + (X_{n}D_{1})]/ (1+k)

= [(m + n) (P_{1} – 1 +X)]/ (1+k)

Dividend does not appear directly in a long equation and (m + n) P_{1}. 1, X and k are assumed to be independent to D_{1}M-M concludes that current value of firm is independent of dividend policy. What investor gains in increased dividends is offset exactly by the decline in the terminal value of his stock.