8.3 Dividends versus Capital Accounts
Equity Added
for
stock holders is Income plus change in Book Value.
This may or may not be paid out as a dividend..
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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
at =
It + (BVt – BVt-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 at
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 dt
is paid out in cash dividends, the amount added to the account is at-dt
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+ke) + a2/(1+ke)2
+ a3/(1+ke)3 + ……
.
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