2. Dividends Equal to Cash Flows

If the firm pays dividends equal to cash flows, the shareholders collect 100 today (Div0) and 110 in 1 year (Div1). At a cost of capital of 10% (kA), the value of the firm's equity right before the payment of the dividend (E0), therefore, is 200:

 

\( E_0 = Div_0 + \frac{Div_1}{(1+k_A)} = 100 + \frac{110}{1.1} = 200 \)

 

Consequently, given that there are 10 shares outstanding (N), the current stock price (P0) is 20:

 

\( P_0 = \frac{E_0}{N} = \frac{200}{10} = 20 \)

 

Right after the firm pays the expected dividend of 100 (or 10 per share), the market value of the firm's equity (E*) will drop to 100 and each share will have a value of 10 (P*):

 

\( E^* = \frac{Div_1}{(1+k_A)} = \frac{110}{1.1} = 100 \)

 

\( P^* = \frac{E^*}{N} = \frac{100}{10} = 10 \)

 

In sum, total shareholder wealth will remain at 200, namely 100 of cash from the dividend and 100 as the firm's remaining equity value after the dividend.