4. Larger Initial Dividend

The same conclusion applies when the firm pays a larger initial dividend.

To see this, let us assume that it is the firm's 100th birthday and that the firm wants to celebrate this event by paying out a special dividend of 60 on top of the expected dividend of 100 today. To finance the additional dividend, we assume that the firm raises 60 at the cost of capital of 10%. Therefore, the new investors will require a payback of 66 in one year, namely the capital of 60 plus an interest payment of 10% on that capital.

 

How will the (original) shareholders react to the announcement of this change in the firm's dividend policy?

 

The shareholders learn that they receive more money today (160 instead of 100) but that year one's dividend will drop by 66 because the firm will first have to repay the additional capital that was raised for today's special dividend. Consequently, the original shareholders , the original shareholders only receive what is left over after repaying the new investors, namely 110 - 66 = 44. The dividends to the original shareholders, therefore are:

 

Initial Dividend (Div0) = 100 + 60 = 160

 

Dividend in 1 year (Div1) =  110 - 60 × 1.1 = 44.

 

With this information, we can again compute the value of the firm's equity as well as the theoretical stock price right after the announcement of the change in the dividend policy ('):

 

\( E' = Div_0 + \frac{Div_1}{(1+k_A)} = 160 + \frac{44}{1.1} = 200 \)

   

\( P' = \frac{E'}{N} = \frac{200}{10} = 20 \)

  

As we can see, announcing the extra dividend leaves the theoretical valuation of the firm and its equity unaffected. Again, the reason is that the financing decision that allows the firm to increase today's dividend is a zero-NPV project: Expressed in present values, the additional dividend the firm pays today (60) is equal to the dividend cut in one year (66/1.1 = 60).

  

Right after the initial dividend payment of 160 (or 16 per share), the market value of the firm's equity (E*) will drop to 40 and each share will have a value of 4 (P*):

 

\( E^* = \frac{Div_1}{(1+k_A)} = \frac{44}{1.1} = 40 \)

 

\( P^* = \frac{E^*}{N} = \frac{40}{10} = 4 \)

 

In sum, total shareholder wealth will therefore remain at 200, namely 160 of cash from the dividend and 40 as the firm's remaining equity value after the dividend. Also on a per-share basis, wealth will be unaffected, as each shareholder will hold 16 of cash from the dividend and 4 worth of stocks.