A Proof of Dividend Irrelevance
To provide a formal proof of irrelevance, assume that LongLast Corporation, an
unlevered firm manufacturing furniture, has operating income after taxes of $ 100
million, growing at 5% a year, and that its cost of capital is 10%. Further, assume that
this firm has reinvestment needs of $ 50 million, also growing at 5% a year, and that
there are 105 million shares outstanding. Finally, assume that this firm pays out residual
cash flows as dividends each year. The value of LongLast Corporation can be estimated
as follows:
Free Cash Flow to the Firm = EBIT (1- tax rate) – Reinvestment needs = $ 100 million - $ 50 million = $ 50 million
Value of the Firm = Free Cash Flow to Firm (1+g) / (WACC - g) = $ 50 (1.05) / (.10 - .05) = $ 1050 million
Price per share = $ 1050 million / 105 million = $ 10.00
Based upon its cash flows, this firm could pay out $ 50 million in dividends.
Dividend per share = $ 50 million/105 million = $ 0.476
Total Value per Share = $ 10.00 + $ 0.48 = $10.476
The total value per share measures what stockholders gets in price and dividends from
their stock holdings.
Scenario 1: LongLast doubles dividends
To examine how the dividend policy affects firm value, assume that LongLast
Corporation is told by an investment banker that its stockholders would gain if the firm
paid out $ 100 million in dividends, instead of $ 50 million. It now has to raise $ 50
million in new financing to cover its reinvestment needs. Assume that LongLast
Corporation can issue new stock with no issuance cost to raise these funds. If it does so,
the firm value will remain unchanged, since the value is determined not by the dividend
paid but by the cash flows generated on the projects. Since the growth rate and the cost of
capital are unaffected, we get:
Value of the Firm = $ 50 (1.05) / (.10 - .05) = $ 1050 million
The existing stockholders will receive a much larger dividend per share, since dividends
have been doubled:
Dividends per share = $ 100 million/105 million shares = $ 0.953
In order to estimate the price per share at which the new stock will be issued, note that
after the new stock issue of $ 50 million, the old stockholders in the firm will own only
$1000 million of the total firm value of $ 1050 million.
Value of the Firm for existing stockholders after dividend payment = $ 1000 million
Price per share = $ 1000 million / 105 million = $ 9.523
The price per share is now lower than it was before the dividend increase, but it is exactly
offset by the increase in dividends.
Value accruing to stockholder = $ 9.523 + $ 0.953 = $ 10.476
Thus, if the operating cash flows are unaffected by dividend policy, we can show
that the firm value will be unaffected by dividend policy and that the average stockholder
will be indifferent to dividend policy, since he or she receives the same total value (price
+ dividends) under any dividend payment.