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How to calculate Irrelevance Dividend theories?


Modigliani and Miller’s Approach: Under this approach the dividend policy of a company does not change the value of the firm. If company give dividend or doesn’t give dividend to its shareholders it does not affect the value of the firm. The decision to give dividend in constant rate, regular rate and irregular rate to its shareholders does not change the value of the firm.

Assumptions of Modigliani and Miller’s Approach in Irrelevance dividend theory:
·         There is no corporate tax.
·         There is a perfect market condition.
·         The investors are rational.
·         There is no risk or uncertainty.

Formula:
P0 = D1 + P1 / (1+Ke)
P1 = P0 (1+Ke) - D1 
Number of new shares: M*P1 = I – (X – nD1)
Where,
P0 = Market price of shares
D1 = Dividend at the end of period one
P1 = Market price of share at the end of period one
Ke = Cost of equity
M = Number of new shares issued
P1 = Price of new shares to be issued
I = Amount of investment required
nD1 = Dividend paid in the period
X = Total net profit in the period

Example: Find out the prevailing market price of share if the dividend received by shareholders is Rs.2.60 per share. The capitalisation rate is 10%.The market rate is Rs. 5 per share at the end of the month.
Solution: P0 = D1 + P1 / (1+Ke)
= 2.60 + 5 / (1+0.1)
= 7.60 / 1.1
= Rs. 6.90

Example: Company XYZ has net profit of Rs. 7, 00,000. The company has issued 50,000 shares and the capitalisation rate is 9%. The company has invested Rs. 3, 20,000 in a new project. The current market price of share is Rs. 4.20 per share. The dividend given by XYZ Company is Rs.2.50 per share. With the help of MM approach find out the market price of shares at the end of the period according to dividend policy.
·         If dividend is paid to shareholders @Rs. 2.50 per share.
·         If Company doesn’t provide any dividend to its shareholders.

Solution:
If dividend paid to its shareholders @ Rs. 2.50 per share:
P0 = D1 + P1 / (1+Ke)
4.20 = 2.50 + P1 / (1+0.09)
4.20 = 2.50 + P1 / 1.09
4.20*1.09 = 2.50 + P1
4.578 = 2.50 + P1
P1 = 4.578 – 2.50
=Rs. 2.078
If Company doesn’t provide any dividend to its shareholders then,
P0 = D1 + P1 / (1+Ke)
4.20 = 0 + P1 / (1+0.09)
4.20 (1+ 0.09) = 0 + P1
4.578 = 0 + P1
P1 = Rs. 4.578

 Value of the firm:

Particulars
Dividend given by Company XYZ
Dividend is not given by Company XYZ
Net profit
7, 00, 000
7, 00, 000
Dividend paid
1, 25, 000
-----
Retained earnings
5, 75, 000
7, 00, 000
Amount Invested
8, 20, 000
8, 20, 000
Amount raised through  new shares (amount invested –retained earnings)
2, 45, 000
1, 20, 000
Market price per share (P1)
2.078
4.578
Number of new shares issued
(Amount raised through new shares / market price of per share)
1, 17, 901.8
26, 212.3
Total number of shares
1, 67, 901.8
76, 212.3
Market share value of the firm
3, 48, 899.9
3, 48,899.9



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