Question

ABC Ltd. belongs to a risk class for which the appropriate capitalization rate is 10%. It currently has outstanding 5,000 shares selling at TZS.100 each. The firm is contemplating the declaration of dividend of TZS .6 per share at the end of the current financial year. The company expects to have net income of TZS.50,000 and has a proposal for making new investments of TZS.100,000. Show that under the MM hypothesis, the payment of dividend does not affect the value of the firm.

Answer 1

Current share price, P₀ = 100

Situation 1: The company pays dividend D₁ = 6 at the end of the current financial year

Capitalization rate, K_e = 10%

Price at the end of the current financial year = P₁ = P₀ x (1 + K_e) - D₁ = 100 x (1 + 10%) - 6 = 110 - 6 =104

Net income = 50,000; Dividend paid = 6 x Nos. of shares outstanding = 6 x 5,000 = 30,000

Addition to the retained earnings = Net income - dividends paid = 50,000 - 30,000 = 20,000 = Retained earnings available for reinvestment

Proposed amount for making new investments = 100,000

External equity to be raised = Proposed investment amount - Retained earnings available for reinvestment = 100,000 - 20,000 = 80,000

Number of new shares required to be issued = N = 80,000 / P₁ = 80,000 / 104 =  769.23

Numbers of shares currently outstanding, N₀ = 5,000

Total nos. of shares at the end of year, N₁ = N₀ + N = 5,000 +  769.23 = 5,769.23

Total value of the company at the end of the year = P₁ x N₁ = 104 x 5,769.23 = 600,000

Situation 2: The company pays no dividend at the end of the current financial year. Hence, D₁ = 0

Capitalization rate, K_e = 10%

Price at the end of the current financial year = P₁ = P₀ x (1 + K_e) - D₁ = 100 x (1 + 10%) - 0 = 110 - 0 =110

Net income = 50,000; Dividend paid = 0

Addition to the retained earnings = Net income - dividends paid = 50,000 - 0 = 50,000 = Retained earnings available for reinvestment

Proposed amount for making new investments = 100,000

External equity to be raised = Proposed investment amount - Retained earnings available for reinvestment = 100,000 - 50,000 = 50,000

Number of new shares required to be issued = N = 50,000 / P₁ = 50,000 / 110 =   454.55

Numbers of shares currently outstanding, N₀ = 5,000

Total nos. of shares at the end of year, N₁ = N₀ + N = 5,000 +   454.55 = 5,454.55

Total value of the company at the end of the year = P₁ x N₁ = 110 x 5,454.55 = 600,000

Thus, the total value of the company at the end of year remains same whether dividend is paid or not. This is in line with MM hypothesis I.