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choice also causes future abnormal earnings to be lower, for two reasons. First, future
earnings will be lower (by $100) in a later period, when the customer actually defaults
on the payments and receivables will have to be written off. Second, in the meantime,
the benchmark for normal earnings, the book value of equity, will be higher by $100.
Let™s say the accounts receivables are not written off until two years after the current pe-
riod. Then assuming a discount rate of 13 percent and the impact of the current aggres-
sive accounting, the subsequent write-down on our calculation of value is as follows:
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Dollar Impact Present Value
Increase in current abnormal earnings (and $100 $100.00
book value)
Decrease in abnormal earnings of year 1,
· 1.13 =
due to higher book value (.13 — $100) “13 “11.50
Decrease in abnormal earnings of year 2,
due to higher book value (.13 — $100) “13
due to lower earnings from accounts
receivable write-off “100
· 1.132 =
“113 “88.50
Impact of accounting choice on present value $0.00

The impact of the higher current abnormal earnings and the lower future abnormal
earnings offset exactly, leaving no impact of the current underestimation of the allow-
ance for uncollected receivables on estimated ¬rm value.
The above discussion makes it appear as if the analyst would be indifferent to the ac-
counting methods used. There is an important reason why this is not necessarily true.
When a company uses “biased” accounting”either conservative or aggressive”the an-
alyst is forced to expend resources doing accounting analyses of the sort described in
Chapter 3. These additional analysis costs are avoided for ¬rms if the accounting is “un-
biased”.
If a thorough analysis is not performed, a ¬rm™s accounting choices can, in general,
in¬‚uence analysts™ perceptions of the real performance of the ¬rm and hence the fore-
casts of future performance. In the above example, the managers™ allowance and receiv-
ables estimates, if taken at face value, will in¬‚uence the analyst™s forecasts of future
earnings and cash ¬‚ows. If so, the accounting choice per se would affect expectations of
future earnings and cash ¬‚ows in ways beyond those considered above. The estimated
value of the ¬rm would presumably be higher”but it would still be the same regardless
of whether the valuation is based on DCF or discounted abnormal earnings.11
An analyst who encounters biased accounting has two choices”either to adjust cur-
rent earnings and book values to eliminate manager™s accounting biases, or to recognize
these biases and adjust future forecasts accordingly. Both approaches lead to the same
estimated ¬rm value. For example, in the above illustration, a simple way to deal with
manager™s underestimation of current default allowance is to increase the allowance and
to decrease the current period™s abnormal earnings by $100. Alternatively, as shown
above, the analyst could forecast the write-off two periods from now. Which of the two
approaches is followed will have an important impact on what fraction of the ¬rm™s
value is captured within the forecast horizon, and what remains in the terminal value.
Holding forecasting horizon and future growth opportunities constant, higher
accounting quality allows a higher fraction of a ¬rm™s value to be captured by the current
book value and the abnormal earnings within the forecasting horizon. Accounting can
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be of low quality either because it is unreliable or because it is extremely conservative.
If accounting reliability is a concern, the analyst has to expend resources on “accounting
adjustments.” If accounting is conservative, the analyst is forced to increase the forecast-
ing horizon to capture a given fraction of a ¬rm™s value, or to rely on relatively more
uncertain terminal values estimates for a large fraction of the estimated value.

A number of ¬rms have negative
DEALING WITH NEGATIVE BOOK VALUES.
earnings and book values of book equity. One category of ¬rms with negative equity are
those in the start-up phase, or in high-technology industries. These ¬rms incur large in-
vestments whose payoff is uncertain. Accountants write off these investments as a matter
of conservatism, leading to negative book equity. Examples of ¬rms in this situation in-
clude biotechnology ¬rms, Internet ¬rms, telecommunication ¬rms, and other high-
technology ¬rms. A second category of ¬rms with negative book equity are those that
are performing poorly, resulting in cumulative losses exceeding the original investment
by the shareholders.
Negative book equity makes it dif¬cult to use the accounting-based approach to value
a ¬rm™s equity. There are several possible ways to get around this problem. The ¬rst ap-
proach is to value the ¬rm™s assets (using, for example, abnormal operating ROA, or ab-
normal NOPAT) rather than equity. Then, based on an estimate of the value of the ¬rm™s
debt, one can estimate the equity value. Another alternative is to “undo” accountants™
conservatism by capitalizing the investment expenditures written off. This is possible if
the analyst is able to establish that these expenditures are value creating. A third alterna-
tive, feasible for publicly traded ¬rms, is to start from the observed stock and work back-
wards. Using reasonable estimates of cost of equity and steady-state growth rate, the
analyst can calculate the average long-term level of abnormal earnings needed to justify
the observed stock price. Then the analytical task can be framed in terms of examining
the feasibility of achieving this abnormal earnings “target.”
It is important to note that the value of ¬rms with negative book equity often consists
of a signi¬cant option value. For example, the value of high-tech ¬rms is not only driven
by the expected earnings from their current technologies, but also the payoff from tech-
nology options embedded in their research and development efforts. Similarly, the value
of troubled companies is driven to some extent by the “abandonment option””share-
holders with limited liability can put the ¬rm to debt holders and creditors. One can use
the options theory framework to estimate the value of these “real options.”12

Firms with excess
DEALING WITH EXCESS CASH AND EXCESS CASH FLOW.
cash balances, or large free cash ¬‚ows, also pose a valuation challenge. In our valuation
projections in Table 12-2, we implicitly assumed that cash beyond the level required to
¬nance a company™s operations will be paid out to the ¬rm™s shareholders. If a ¬rm has
a large excess cash balance (after taking into account the ¬rm™s operating needs and the
¬nancial leverage policy) on its balance sheet at the beginning of the forecasting period,
our approach requires that the excess cash balance is treated as a one-time cash payout
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to the shareholders. This payout can simply be added to the estimated value of the ¬rm
from the rest of the calculations. On an ongoing basis, excess cash ¬‚ows are assumed to
be paid out to shareholders either in the form of dividends or stock repurchases. Notice
that these cash ¬‚ows are already incorporated into the valuation process when they are
earned, so there is no need to take them into account when they are paid out.
It is important to recognize that both the accounting-based valuation and the dis-
counted cash ¬‚ow valuation assume a dividend payout that can potentially vary from pe-
riod to period. This dividend policy assumption is required as long as one wishes to
assume a constant level of ¬nancial leverage, a constant cost of equity, and a constant
level of weighted average cost of capital used in the valuation calculations. As discussed
in a later chapter, ¬rms rarely have such a variable dividend policy in practice. However,
this in itself does not make the valuation approaches invalid, as long as a ¬rm™s dividend
policy does not affect its value. That is, the valuation approaches assume that the well-
known Modigliani-Miller theorem regarding the irrelevance of dividends holds.
A ¬rm™s dividend policy can affect its value if managers do not invest ¬rms™ free cash
¬‚ows optimally. For example, if a ¬rm™s managers are likely to use excess cash to un-
dertake value-destroying acquisitions, then our approach overestimates the ¬rm™s value.
If the analyst has these types of concerns about a ¬rm, one approach is to ¬rst estimate
the ¬rm according to the approach described earlier and then adjust the estimated value
for whatever agency costs the ¬rm™s managers may impose on its investors. One ap-
proach to evaluating whether or not a ¬rm suffers from severe agency costs is to examine
how effective its corporate governance processes are.


SUMMARY
We illustrate in this chapter how to apply the valuation theory discussed in Chapter 11.
The chapter discusses the set of business and ¬nancial assumptions one needs to make
to conduct the valuation exercise. It also illustrates the mechanics of making detailed
valuation forecasts and terminal values of earnings, free cash ¬‚ows, and accounting rates
of return. We also discuss how to compute cost of equity and the weighted average cost
of capital. Using a detailed example, we show how a ¬rm™s equity values and asset val-
ues can be computed using earnings, cash ¬‚ows, and rates of return. Finally, the chapter
raises and discusses ways to deal with some commonly encountered practical issues, in-
cluding accounting distortions, negative book values, and excess cash balances.


DISCUSSION QUESTIONS
1. Verify the forecasts in Table 12-2. How will the forecasts change if the assumed
growth rate in sales from 1999 to 2003 is changed to 15 percent (and all the other
assumptions are kept unchanged)?
2. Recalculate the forecasts in Table 12-2 assuming that the NOPAT profit margin de-
clines by 1.5 percent per year (keep all the other assumptions unchanged).
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3. Recalculate the forecasts in Table 12-2 assuming that the ratio of net operating
working capital to sales is 30 percent, and the ratio of net long-term assets to sales
is 50 percent. Keep all the other assumptions unchanged.
4. Calculate Sigma™s dividend payments in the years 1999“2003 implicitly assumed
in the projections in Table 12-2. How will these payments change if the ratio of net
debt to net capital is changed from 40 percent to 50 percent?
5. Verify the present value calculations in Table 12-3. How will the present values in
the table change if the cost of equity changes to 15 percent?
6. Verify the terminal value calculations in Table 12-9. How will the terminal values
in Table 12-9 change if the sales growth in years 2004 and beyond is 5 percent
(keeping all the other assumptions in the table unchanged)?
7. Calculate the proportion of terminal values to total estimated values of equity and
assets under the abnormal earnings method and the discounted cash flow method.
Why are these proportions different?
8. Can accounting analysis improve accounting-based valuations? Explain why or
why not.
9. Can accounting distortions, if not recognized by an analyst, affect cash flow-based
valuations? Construct a numerical example to verify your answer.
10. Nancy Smith says she is uncomfortable making the assumption that Sigma™s divi-
dend payout will vary from year to year. If she makes a constant dividend payout
assumption, what changes does she have to make in her other valuation assump-
tions to make them internally consistent with each other?


NOTES
1. As discussed in Chapter 9, using the beginning-of-period balances in these ratios ensures
that operating activities such as sales and expenses in a time period are compared to the resources
available at the beginning of the time period. In practice, it may not make much difference for
companies which are not growing rapidly if the end-of-period balances are used.
2. An alternative approach to making projections involves starting with a beginning balance
sheet, making assumptions about asset turnover to forecast sales, NOPAT margin, and after-tax in-
terest rate assumptions to project net income, a book value growth rate assumption to project end-
ing book value, and a debt-to-equity ratio assumption to project total capital and assets at the end
of the year. The approach discussed in this chapter, which starts with a sales growth assumption,
is more traditional. However, it requires a one-time restructuring of the beginning balance sheet
to conform to the rest of the assumptions.
3. Recall that the balance sheet at the beginning of 2004 shown in Table 12-2 is based on the
assumption that sales in 2004 will growth at 3.5 percent. This balance sheet has to be recalculated
with zero sales growth to re-estimate the cash flows in 2003. Then the free cash flow to debt and
equity in 2003 will be $113 million and the free cash flow to equity will be $92 million.
4. See T. Copeland, T. Koller, and J. Murrin, Valuation: Measuring and Managing the Value
of Companies, 2nd Edition (New York: John Wiley & Sons, 1994). Theory calls for the use of a
short-term rate, but if that rate is used here, a difficult practical question rises: how does one reflect
the premium required for expected inflation over long horizons? While the premium could, in
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principle, be treated as a portion of the term [E(rm ) “ rf ], it is probably easier to use an interme-
diate- or long-term riskless rate that presumably reflects expected inflation.
5. The average return reported here is the arithmetic mean, as opposed to the geometric mean.
Ibbotson and Associates explain why this estimate is appropriate in this context (see Stocks,
Bonds, Bills, and Inflation, 1998 Yearbook, Chicago).
6. One way to estimate systematic risk is to regress the firm™s stock returns over some recent
time period against the returns on the market index. The slope coefficient represents an estimate
of β . More fundamentally, systematic risk depends on how sensitive the firm™s operating profits
are to shifts in economy-wide activity, and the firm™s degree of leverage. Financial analysis that
assesses these operating and financial risks should be useful in arriving at reasonable estimates
of β.
7. Ibbotson and Associates, op. cit.
8. See “Toward an Implied Cost of Capital” by William R. Gebhardt, Charles M. C. Lee, and
Bhaskaran Swaminathan, Cornell University, working paper, 1999; and “The Equity Premium Is
Much Lower Than You Think It Is: Empirical Estimates from a New Approach” by James Claus
and Jacob Thomas, Columbia University, working paper, 1999.
9. Analysts often estimate the value of a firm™s assets and then estimate the value of equity by
subtracting the book value of debt from the estimated asset value. Notice that for Sigma this ap-
proach leads to an estimated value of equity that is somewhat different from the equity value es-
timated directly. This difference is attributable to the fact that the WACC estimate here is based on
book values of debt and equity, rather than market values. Unfortunately, as discussed earlier, it
is difficult in practice to avoid this problem because WACC estimates based on market value lever-
age ratio are hard to implement. Our recommendation, therefore, is to estimate equity values di-
rectly, as illustrated here.
10. Valuation based on discounted abnormal earnings does require one property of the fore-
casts: that they be consistent with “clean surplus accounting.” Such accounting requires the fol-
lowing relation:
End-of-period book value =
Beginning book value + earnings “ dividends ± capital contributions/withdrawals
Clean surplus accounting rules out situations where some gain or loss is excluded from earnings
but is still used to adjust the book value of equity. For example, under U.S. GAAP, gains and losses
on foreign currency translations are handled this way. In applying the valuation technique de-
scribed here, the analyst would need to deviate from GAAP in producing forecasts and treat such
gains/losses as a part of earnings. However, the technique does not require that clean surplus ac-
counting has been applied in the past”so the existing book value, based on U.S. GAAP or any

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