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Miller and Modigliani Model (MM Model)

Miller & Modigliani Model Assignment / Homework Help
Miller and Modigliani Model assume that the dividends are irrelevant. Dividend irrelevance implies that the value of a firm is unaffected by the distribution of dividends and is determined solely by the earning power and risk of its assets. Under conditions of perfect capital markets, rational investors, absence of tax discrimination between dividend income and capital appreciation, given the firm’s investment policy, its dividend policy may have no influence on the market price of the shares, according to this model.

Assumptions of MM model
  • Existence of perfect capital markets and all investors in it are rational. Information is available to all free of cost, there are no transactions costs, securities are infinitely divisible, no investor is large enough to influence the market price of securities and there are no floatation costs.
  • There are no taxes. Alternatively, there are no differences in tax rates applicable to capital gains and dividends.
  • A firm has a given investment policy which does not change. It implies that the financing of new investments out of retained earnings will not change the business risk complexion of the firm and thus there would be no change in the required rate of return.
  • Investors know for certain the future investments and profits of the firm (but this assumption has been dropped by MM later).

Argument of this Model
  • By the argument of arbitrage, MM Model asserts the irrelevance of dividends. Arbitrage implies the distribution of earnings to shareholders and raising an equal amount externally. The effect of dividend payment would be offset by the effect of raising additional funds.
  • MM model argues that when dividends are paid to the shareholders, the market price of the shares will decrease and thus whatever is gained by the investors as a result of increased dividends will be neutralized completely by the reduction in the market value of the shares.
  • The cost of capital is independent of leverage and the real cost of debt is the same as the real cost of equity, according to this model.
  • That investors are indifferent between dividend and retained earnings implies that the dividend decision is irrelevant. With dividends being irrelevant, a firm’s cost of capital would be independent of its dividend-payout ratio.
  • Arbitrage process will ensure that under conditions of uncertainty also the dividend policy would be irrelevant.

MM Model:
Market price of the share in the beginning of the period = Present value of dividends paid at the end of the period + Market price of share at the end of the period.

P0 = 1/(1 + ke) x (D1 + P1)

Where: P0 = Prevailing market price of a share
ke = cost of equity capital
D1 = Dividend to be received at the end of period 1 and
P1 = Market price of a share at the end of period 1.

Value of the firm, nP0 = (n + ∆ n) P1 – I + E
(1 + ke)

Where: n = number of shares outstanding at the beginning of the period
∆ n = change in the number of shares outstanding during the period/ additional shares issued.
I = Total amount required for investment
E = Earnings of the firm during the period.

A company whose capitalization rate is 10% has outstanding shares of 25,000 selling at $100 each. The firm is expecting to pay a dividend of $5 per share at the end of the current financial year. The company's expected net earnings are $250,000 and the new proposed investment requires $500,000. Prove that using MM model, the payment of dividend does not affect the value of the firm.

  • Value of the firm when dividends are paid:

    • Price per share at the end of year 1:

      P0 = 1/(1 + ke) x (D1 + P1)
      $100 = 1/(1 + 0.10) x ($5 + P1)
      P1 = $105
    • Amount required to be raised from the issue of new shares:

      ∆ n P1 = I – (E – nD1)
      => $500,000 – ($250,000 - $125,000)
      => $375,000
    • Number of additional shares to be issued:

      ∆n = $375,000 / 105 => 3571.42857 shares (unrounded)
    • Value of the firm:

      => (25,000 + 3571.42857) (105) - $500,000 + $250,000
      (1 + 0.10)
      => $2,500,000
  • Value of the firm when dividends are not paid:

    • Price per share at the end of year 1:

      P0 = 1/(1 + ke) x (D1 + P1)
      $100 = 1/(1 + 0.10) x ($0 + P1)
      P1 = $110
    • Amount required to be raised from the issue of new shares:

      => $500,000 – ($250,000 -0) = $250,000
    • Number of additional shares to be issued:

      => $250,000/$110 = 2272.7273 shares (unrounded)
    • Value of the firm:

      => (25,000 + 2272.7273) (110) - $500,000 + $250,000
      (1 + 0.10)
      => $2,500,000

Thus, according to MM model, the value of the firm remains the same whether dividends are paid or not. This example proves that the shareholders are indifferent between the retention of profits and the payment of dividend.

Limitations of MM model:
  • The assumption of perfect capital market is unrealistic. Practically, there are taxes, floatation costs and transaction costs.
  • Investors cannot be indifferent between dividend and retained earnings under conditions of uncertainty. This can be proved at least with the aspects of i) near Vs distant dividends, ii) informational content of dividends, iii) preference for current income and iv) sale of stock at uncertain price.

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