8.3  Dividends versus Capital Accounts

As we saw in the free cash flow model, many companies do not pay cash dividends.  So the simple dividend model cannot be used to value the stock of such a company, and models such as the free cash flow to equity model use the concept of economic dividends.

To motivate the residual income model, consider the following simple example.  A company sells stock and buys an asset.  The shareholders equity, at this point, equals the book value which equals the asset value.  If the company immediately liquidates, each shareholder would simply receive the book value per share.  So for this “one-day lived” company, the intrinsic value is simply the book value. 

Now, suppose the company uses the asset to generate income (or a loss) during the day.  The claim of the shareholder now changes.  At the end of the day, if the company liquidates, each shareholder would get the initial book value plus income plus any change in the book value; a change in the book value could come about because, for example, the asset may depreciate through use.

For a going concern, let’s define

a_t = I_t + (BV_t – BV_t-1) where I is “income” and BV is the book value.  We will look carefully at how this income is defined in a bit. 

So a_t is the additional equity generated for the stock holders at time t.  It may or may not be paid out in dividends; in fact, we can think of a “capital account” held on behalf of the shareholder at the company; depending on the income generated, cash dividends, and changes in book value, this capital account gets credited or debited.  If d_t is paid out in cash dividends, the amount added to the account is a_t-d_t and if no dividends are paid, the entire amount is added.   So in the simple case, where there is no change in the book value, we are back at the free-cash flow model: the intrinsic value is simply the present value of the income earned by the company. 

More generally,

Intrinsic value =V₀ = a₁/(1+k_e) + a₂/(1+k_e)² + a₃/(1+k_e)³ + ……    .                 3)