- (a) Show under MM Hypothesis that the payment of dividend has no impact on the value of the firm.
(b) Following are the detail regarding three Companies A Ltd., B Ltd., C Ltd.:
| A Ltd. | B Ltd. | C Ltd. |
| r = 15% | r = 5% | r = 10% |
| k = 10% | k = 10% | k = 10% |
| E = Rs. 8 | E = Rs. 8 | E = Rs. 8 |
r = internal rate of return, k = cost of capital, E = earning per share
Calculate the value of an equity share of each of these companies applying Walter’s formula when divided payment ratio (D\P ratio) is
(A) 25% (B) 75%
(a) Under the Modigliani-Miller (MM) hypothesis, which assumes perfect capital markets and no taxes or transaction costs, the payment of dividends has no impact on the value of the firm. This can be shown as follows:
According to the MM hypothesis, the value of a firm is determined by its underlying cash flows and the risk associated with those cash flows, represented by the discount rate (cost of capital). The dividend policy, whether the firm pays dividends or retains earnings, should not affect the overall value of the firm.
If a firm pays dividends, it reduces its cash balance, resulting in a decrease in the value of cash and an increase in the value of other assets or equity in the balance sheet. This redistribution of value does not change the total value of the firm.
Similarly, if a firm retains earnings instead of paying dividends, it increases its cash balance, resulting in an increase in the value of cash and a decrease in the value of other assets or equity. Again, the total value of the firm remains the same.
Therefore, under the MM hypothesis, the payment of dividends has no impact on the value of the firm.
(b) Applying Walter’s formula, the value of an equity share of each company can be calculated based on the given information and different dividend payment ratios:
(A) Dividend payment ratio = 25% Value of equity share = (E / k) + [(D / k) × (1 – D/P ratio)] For A Ltd.: Value of equity share = (8 / 0.10) + [(0.25 / 0.10) × (1 – 0.25)] = 80 + (2.5 × 0.75) = 80 + 1.875 = 81.875
(B) Dividend payment ratio = 75% For A Ltd.: Value of equity share = (8 / 0.10) + [(0.75 / 0.10) × (1 – 0.75)] = 80 + (7.5 × 0.25) = 80 + 1.875 = 81.875
Therefore, the value of an equity share for A Ltd., regardless of the dividend payment ratio, is Rs. 81.875.
For B Ltd. and C Ltd., the dividend payment ratio does not affect the value of an equity share under Walter’s formula, as the dividend payment ratio is not considered in the formula. Therefore, the value of an equity share for B Ltd. and C Ltd. is Rs. 80 for both scenarios.
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