3. Smaller Initial Dividend

Now let us assume that the firm announces a change in the dividend policy. Instead of paying out the full cash flow, it announces that it will retain some of the initial cash flow and invests that cash in a new project that generates a rate of return of 10%.

Put differently, this new project has a Net Present Value of 0, as the return it generates is equal to the cost of capital. Let us assume that of the initial cash flow of 100, 60 are reinvested at 10% and 40 are paid out to shareholders.

 

How will the share price react to this announcement?

 

Originally, shareholders have expected to receive 100 today and 110 in 1 year. Now the firm has informed them that today's dividend will drop to 40. In exchange, the dividend of year 1 will increase to 176, namely 110 from the originally expected cash flow plus the payoff of 66 from the reinvested capital (= 60 × 1.1):

 

Initial Dividend (Div0) = 40

Dividend in 1 year (Div1) =  110 + 60 × 1.1 = 176.

 

With this information, we can now compute the value of the firm's equity as well as the theoretical stock price under the revised dividend policy. Since the reinvested capital has a net present value of zero (put differently, it does not add or destroy value), it is not surprising, that the revision of the dividend policy does not affect the firm's valuation. The equity value after the announcement and right before the payment of the dividend, denoted with the prime symbol ('),  is still 200 and the theoretical stock price remains at 20:

 

\( E' = Div_0 + \frac{Div_1}{(1+k_A)} = 40 + \frac{176}{1.1} = 200 \)

   

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

 

This is a first important takeaway: In principle, as long as the firm reinvests capital in NPV-zero projects, it does not matter whether cash is paid out to shareholders or reinvested in the firm.

 

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

 

\( E^* = \frac{Div_1}{(1+k_A)} = \frac{176}{1.1} = 160 \)

 

\( P^* = \frac{E^*}{N} = \frac{160}{10} = 16 \)

 

In sum, total shareholder wealth will therefore remain at 200, namely 40 of cash from the dividend and 160 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 4 of cash from the dividend and 16 worth of stocks.