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A blog on financial markets and their regulation

July 1, 2005

Posted by on 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

track record

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