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A blog on financial markets and their regulation
Karpoff, Jonathan M., Lee, Dale Scott and Martin, Gerald, “The Cost to
firms of Cooking the Books” (June 14, 2005)
http://ssrn.com/abstract=652121 provide an interesting analysis of the penalties for
financial misreporting in the United States.
They claim that the legal penalties are dwarfed by what they call
the reputational penalty imposed by the market:
“the reputational penalty is twelve times the sum of all penalties imposed
through legal and regulatory processes.”
The difficulty is in the way that the reputational penalty is estimated. The authors
take the drop in market value of the firm when an investigation is announced and subtract
from this the monetary penalty imposed by the regulator as well as the amount paid in
any class action suit. They then proceed to subtract the valuation
impact of the accounting write-off required to reverse the financial misreporting. What
is left is the authors’ estimate of the reputational penalty imposed by the
market. The authors assume that the valuation impact of the accounting write-off
is captured by multiplying the amount of the write-off by the price to book ratio.
consider the hypothetical example of an all-equity firm that has book value of
assets equal to $100 and a market-to-book ratio of 1.5. The market value of the
firm’s assets, and its shares, is $150. Assume the company then issues a
misleading financial statement that overstates its asset
values by $10. If the firm’s market-to-book ratio stays the same, its share
values will increase temporarily by ($10 x 1.5) to $165. But when the
financial misrepresentation is discovered, the book value will be restated
by $10, back to $100. If there is no other impact, the market value
will fall by $15, back to $150. Thus, a $10 restatement in the firm’s
books implies a $15 change in the market. This $15 drop in market value is
what we seek to capture with the accounting write-off effect.
This estimate can be badly wrong because the accounting restatement can change
the price to book ratio itself. A restatement that is relatively small in relation
to the net worth of a company can make a large difference to the growth rate in
earnings. If this changes the estimate of future growth opportunities, then the price to
book ratio can fall dramatically. This is because the price to book reflects the
relative importance of the present value of growth opportunities (PVGO) in relation to
the present value of continuing operations (PVCO) and a relatively small change
in growth rates can make a large change to the PVGO.
This is best seen in the context of a constant dividend growth model. Under this
model, the market capitalization of the company is given by E(1-b)/(k-g) where E
is the earnings of the company next year, b is the fraction of earnings that is retained
(1 minus the payout ratio), k is the cost of equity and g is the growth rate in
earnings and dividends. In this model E/k is the present value of continuing
operations (PVCO) and is a rough estimate of what the book value would be.
The balance is the present value of growth opportunities (PVGO).
Let us consider a numerical example. If last year’s earnings are
$108 million, the dividend payout ratio is 40%, the cost of equity is 10% and
the growth rate is 8%, the dividend growth model predicts a market capitalization
of about $2.3 billion since the projected earnings
next year are $116 million and the price earnings multiple (1-b)/(k-g)is 20.
Of this, the PVCO is
only about half ($108 million discounted at 10%), while PVGO accounts for slightly
more than half. Assuming that book value is a rough approximation to the PVCO, the price
to book for this company would be about 2. Consider an accounting restatement that
changes the earnings last year from $108 million to $106 million. as against
$100 million the year before last. This reduces the observed growth rate from 8% to 6%.
If the market regards 6% as the true estimate of future growth, then the price
earnings multiple would fall to 10 and the price to book ratio would fall to 1
as the PVGO simply vanishes. (The 6% growth amounts to only the required 10%
return on the 60% of earnings that is retained and ploughed back into the business
every year.) The market capitalization would then halve from $2.3 billion to
$1.1 billion or a loss of over $ 1 billion. As against this, the authors’
estimate of the valuation effect would be $2 million times the price to book
ratio of 2 or $4 million. The true valuation effect is then about 250 times
what the authors estimate it to be.
If this is so and the bulk of the alleged reputational penalty is
actually a valuation effect of the restatement itself, then the author’
findings can be interpreted very differently. The legal penalties are only a small
fraction (only 1/12 or around 8%) of the true losses suffered by investors. Considering
that creditors recover about 60% of the value of a defaulted bond, this is a very poor