INTRODUCTION TO
VALUATION
Discounted cash flow and relative
valuations are designed to value healthy firms and fall short when used to value firms where there
is a substantial probability that the firms may not be in
existence in 6 months, a year or two years, because of their inability to make
debt payments or cover operating expenses. The degree to
which traditional valuation models misvalue distressed firms will vary,
depending upon the care with which expected cash flows are estimated,
the ease with
which these firms can access external capital market and the consequences of distress. In this paper, we
will begin by looking at the underpinnings of discounted cash flow valuation, why
DCF models do not explicitly consider the possibility of distress and when analysts can get away with
ignoring
distress.
We will follow up by considering ways in which we can adjust discounted
cashflow models to explicitly allow for the possibility of distress. In the final part
of the paper, we consider how distress is considered (or as is more often,
ignored) in relative valuation and ways of adjusting multiples for the possibility of
failure.
Consider how we
value a firm in a discounted cash flow world. We begin by projecting expected cash flows for a period, we
estimate a terminal value at the end of the period that captures what we
believe the firm will be worth at that point in time and we then discount the cash flows back at a
discount rate that reflects the riskiness of the firmÕs cash flows. This approach
is an extraordinarily flexible one and can be stretched to value firms ranging
from those with predictable
earnings
and little growth to those in high growth with negative earnings and cash flows.
Implicit
in this approach, though, is the assumption that a firm is a going
concern, with potentially an infinite life. The terminal value
is usually estimated by assuming that earnings grow at a constant rate forever
(a perpetual growth rate). Even when the terminal value is estimated using a multiple of
revenues or earnings, this multiple is derived by looking at publicly traded
firms (usually healthy ones).
Growth is not
inevitable and firms may not remain as going concerns. In fact, even
casual empirical observation suggests that a very large number of firms,
especially smaller and higher growth firms, will not survive and will go out of
business. Some will fail because they borrow money to fund their operations and
then are unable to make these debt payments. Other will fail because they do
not have the cash to cover their operating needs.
But
what are the consequences of financial failure? Firms that are
unable to make their debt payments have to liquidate their assets, often at
bargain basement prices, and use the cash to pay off debt. If there is any cash
left over, which is highly
unlikely, it will be paid out to equity investors. Firms that are unable to
make their operating payments also have to offer themselves to the highest
bidder, and the proceeds will
be distributed to the equity investors.
Given the
likelihood and consequences of distress, it seems foolhardy to assume that we can ignore
this possibility when valuing a firm, and particularly so, when we are valuing
firms in poor health and with substantial debt obligations. So, what you might
wonder, are the arguments offered by proponents of discounted cash flow valuation for not
explicitly considering the possibility of firms failing? We will consider five
reasons often provided by for this oversight. The first two reasons are offered by
analysts who believe that there is no need to consider distress explicitly, and the last
three reasons
by those who believe that discounted
cashflow valuations already incorporate the effect of distress.
It is true that
the likelihood of distress is lower for larger, more established firms, but experience
suggests that even these firms can become distressed. The last
few months of 2001 saw the astonishing demise of Enron, a firm that had a
market capitalization in excess of $ 70 billion just a few months previously At
the end of 2001, analysts were openly discussing the possibility that large firms like Kmart and Lucent
Technologies would be unable to make their debt payments and may have to
declare bankruptcy.
The other problem
with this argument, even if you accept the premise, is that smaller,
high growth firms are traded and need to be valued just as much as larger
firms. In fact, you could argue that the need for valuation is greater for
smaller firms, where the uncertainty and the possibility of pricing errors are greater.
In
valuation, as in much of corporate finance, we assume that a firm with good
investments has access to capital markets and can raise the funds it needs to
meet its financing and investment needs. Thus, firms with great growth
potential will never be forced out of business because they will be able to
raise capital (more likely equity than debt) to keep going.
In
buoyant
and developed financial markets, this assumption is not
outlandish. Consider, for instance, the ease with which new
economy companies with negative earnings and few if any assets were able to
raise new equity in the late 1990s.
However,
even in a market as
open and accessible as the United States, access to capital dried up as investors drew
back in 2000 and 2001. In summary, then,
you may
have been able to get away
with the assumption that firms with valuable assets will not be forced into a distress
sale in 1998 and 1999, but that assumption would have been untenable in 2001.
The
discount rate is the vehicle we use to adjust for risk in
discounted cash flow valuation. Riskier firms have higher costs of
equity, higher costs of debt and usually have
higher costs of capital than safer firms. A reasonable
extension of this argument would be that a firm with a greater possibility of
distress should have a higher cost of capital and thus a lower firm value.
The
argument has merit up to a point. The cost of capital for a distressed firm,
estimated correctly, should be higher than the cost of capital for a safer firm.
If the distress is caused by high financial leverage, the cost of equity should
be much higher. Since the cost of debt is based upon current borrowing rates,
it should also climb as the firm becomes more exposed to the risk of bankruptcy and the effect
will be exacerbated if the tax advantage of borrowing also dissipates (as a
result of operating losses).
Ultimately though, the adjustment to
value that results from using a higher discount rate is only a partial one. The
firm is still assumed to generate cash flows in perpetuity, though the present value is lower. A
significant portion of the firmÕs current value still comes from the terminal
value. In other words, the biggest risk of distress that is the loss of all
future cash
flows
is not adequately captured in value.
To
better understand this adjustment, it is worth reviewing what the expected
cash flows in a discounted cash flow valuation are supposed to measure. The expected
cash flow in a year should be the probabilityweighted estimate of the cash flows under all
scenarios for the firm, ranging from the best to the worst case. In other
words, if there is a 30% chance that a firm will not survive the next year, the
expected cash
flow
should reflect both this
probability and the resulting cash flow. In practice, we tend to be far sloppier in our
estimation of expected cash flows. In fact, it is not uncommon to use an exogenous
estimate of the expected growth rate (from analyst estimates) on the current
yearÕs
earnings or revenues to generate future values. Alternatively, we often map out
an optimistic path to
profitability for unprofitable firms and use this path as the
basis for estimating expected cash flows.
We
could estimate the expected cash flows under all scenarios and use the expected values in our valuation.
Thus,
the expected cash flows would be much lower for a firm with a significant
probability of distress. Note, though, that contrary to conventional wisdom,
this is not a risk adjustment. We are doing what we should have been doing in
the first place and estimating the expected cash flows correctly. If we wanted to
riskadjust the cash flows, we would have to adjust the
expected cash
flows
even further downwards using a certainty equivalent.[1] If we do this,
though, the discount rate used would have to be the riskfree rate and not the
riskadjusted cost of capital.
As
a practical matter, it is very difficult to adjust expected cash flows for the
possibility of distress. Not only do we need to estimate the probability of
distress each year, we have to keep track of the cumulative probability of
distress as well. This is because a firm that becomes distressed in year 3
loses its cash flows not just in that year but in all subsequent
years.
The
problem with distress, from a DCF standpoint, is not that the firm ceases to
exist but that all cash flows beyond that point in time are lost. Thus, a firm
with great products and potentially a huge market may never see this
promise converted into cash flows because it goes bankrupt early in its life. If we assume that
this firm can sell itself to the highest bidder for a distress sale value that
is equal to the present value of expected future cash flows, however,
distress does not have to be considered explicitly.
This
is a daunting assumption because we are not only assuming that a firm in distress
has the bargaining power to demand fair market value for its assets, but we are
also assuming that it can do this not only with assets in place (investments it
has already made and products that it has produced) but with growth assets
(products that it may have been able to produce in the future).
In summary, the
failure to explicitly consider distress in discounted cash flow valuation will
not have a material impact in value if any the following conditions hold:
1. There is no possibility of bankruptcy, either
because of the firmÕs size and standing or because of a government guarantee.
2. Easy and free access to capital markets allows
firms with good investments to raise debt or equity capital to sustain
themselves through bad times, thus ensuring that these firms will never be
forced into a distress sale.
3. You used expected cash flows that incorporate
the likelihood of distress and a discount rate that is adjusted for the higher
risk associated with distress. In addition, the firm will receive sale proceeds
that are equal to the present value of expected future cash flows as a going
concern in the event of a distress sale.
When will the
failure to consider distress in discounted cash flow valuation have a
material impact on value? If the likelihood of distress is high, access to
capital is constrained (by internal or external factors) and distress sale
proceeds are significantly lower than going concern values, discounted cash flow valuations will
overstate firm and equity value, even if the cash flows and the discount rates are
correctly estimated. In this section, we will consider several ways of
incorporating the effects of distress into the estimated value.
In traditional valuation, we estimate expected
values for each of the input variables. For instance, in valuing a firm, we may assume an expected growth
rate in revenues of 30% a year and that the expected operating margin will be 10%. In
reality, each of these variables has a distribution of values, which we
condense into an expected value. Simulations attempt to utilize the information
in the entire distribution, rather than just the expected value, to arrive at a
value. By looking at the
entire distribution, simulations provide us with an opportunity to deal explicitly
with distress.
Before you begin
running the simulations, you will have to decide the circumstances which will
constitute distress and what will happen in the event of distress. For example,
you may determine that cumulative operating losses of more than $ 1
billion over three years will push the firm into distress and that it will sell
its assets for 25% of book value in that event. The parameters for distress
will vary not only across firms, based upon their size and asset
characteristics, but also on the state of financial markets and the overall
economy. A firm that has three bad years in a row in a healthy economy with
rising equity markets may be less exposed to default than a similar firm
in the middle of a recession. The steps in the simulation are as follows:
Step 1: The first step
involves choosing those variables whose expected values will be replaced by
distributions. While there may be uncertainty associated with every variable in
valuation, only the most
critical variables might be chosen at this stage. For instance,
revenue growth and operating margins may be the key variables that you choose
to build distributions for.
Step 2: You choose a
probability distribution for each of the variables. There are a
number of choices here, ranging from discrete probability distributions
(probabilities are assigned to specific outcomes) to continuous distributions
(the normal or exponential distribution). In making this choice, the following
factors should be considered:
á
the range of feasible outcomes for the variable;
(e.g., the revenues cannot be less than zero, ruling out any distribution that
requires the variable to take on large negative values, such as the normal
distribution).
á
the experience of the company on this variable.
Data on a variable, such as operating margins historically, may
help us determine the type of
distribution that best describes it.
While no distribution will provide a perfect fit,
the distribution that best fits the data should be used.
Step 3: Next, the parameters
of the distribution chosen for each variable are estimated. The number of
parameters will vary from distribution to distribution; for instance, the mean
and the variance have to be estimated for the normal distribution, while the
uniform distribution requires estimates of the minimum and maximum values for
the variable.
Step 4: One outcome is
drawn from each distribution; the variable is assumed to take on that value for
that particular simulation. To make the analysis richer, you can repeat this
process each year and allow for correlation across variables and across time.[2]
Step 5: The expected cash flows are estimated
based
upon the outcomes drawn in step 4. If the firm meets the criteria for a going concern,
defined before the simulation, you will then discount the cash flows to arrive at a
conventional estimate of discounted cash flow value. If it fails to meet the criteria, you will
value it as a distressed firm.
Step 6: Steps 4 and 5 are
repeated until a sufficient number of simulations have been conducted. In
general, the more complex the distribution (in terms of the number of values
the variable can take on and the number of parameters needed to define the
distribution) and the greater the number of variables, the larger this number
will be.
Step 7: Each simulation will generate a value, going
concern or distressed as the case may be, for the firm. The average across all
simulated values will be the value of the firm. You should also be able to
assess the probability of default from the simulation and the effect of
distress on value.
The primary
limitation of simulation analysis is the information that is required for it to
work. In practice, it is difficult to choose both the right
distribution to describe a variable and the parameters of that distribution.
When these choices are made carelessly or randomly, the output from the
simulation may look impressive but actually conveys no valuable information.
You
can adapt discounted cash flow valuation to reflect some or most of the effects
of distress on value. To do this, you will to bring in the
effects of distress into both expected cash flows and discount rates.
To
consider the effects of
distress into a discounted cash flow valuation, you have to incorporate the probability that
your firm will not survive into the expected cash flows. In its most
complete form, this would require that you consider all possible scenarios,
ranging from the most optimistic to the most pessimistic, assign probabilities
to each scenario and cash flows under each scenario, and estimate the expected cash flows each year.
where p_{jt }is the probability
of scenario j in period t and Cashflow_{j}_{t} is the cashflow
under that scenario and in that period. These inputs have to be
estimated each year, since the probabilities and the cash flows are likely to
change from year to year.
A
shortcut, albeit an approximate one, would require estimates for only two
scenarios Ð the going concern scenario and the distress scenario. For the going
concern scenario, you could use the expected growth rates and cash flows estimated under
the assumption that the firm will be nursed back to health. Under the distress
scenario, you would assume that the firm will be
liquidated for its distress sale proceeds. Your expected cash flow for each year
then would be:
In
conventional valuation, we often estimate the cost of equity using a regression
beta and the cost of debt by looking at the market interest rates on publicly
traded bonds issued by the firm. For firms with a significant probability of
distress, these approaches can lead to inconsistent estimates. Consider first
the use of regression betas. Since regression betas are based upon past prices
over long periods (two to five years, for instance), and distress
occurs over shorter periods, you will find that these betas will understate the
true risk in the distressed firm.[3] With the interest
rates on corporate bonds, you run into a different problem. The yields to maturity on the corporate
bonds of firms that are viewed as distressed reach extremely high levels, largely because the
interest rates are computed based upon promised cash flows (coupons and face
value) rather than expected cash flows. The presumption in a going concern
valuation is that the promised cash flows have to be made for the firm to remain a going
concern, and it is thus appropriate to base the cost of debt on promised rather
than expected cash flows. For a firm with a significant likelihood of
distress, this presumption is clearly unfounded.
What
are the estimation options for distressed firms? To estimate the cost of
equity, you should use the bottomup unlevered beta (the weighted average of unlevered betas of the businesses
that your firm operates in) and the current market debt to equity ratio of the
firm. Since distressed firms often have high debt to equity ratios, brought
about largely as a consequence of dropping stock prices, this will lead to
levered betas that are significantly higher than regression betas[4]. If you couple
this with the reality that most distressed firms are in no position to get any
tax advantages from debt, the levered beta will become even higher.
Levered beta = Bottomup Unlevered beta (1 + (1
tax rate) (Debt to Equity ratio))
Note, though, that
it is reasonable to reestimate debt to equity ratios and tax rates for future
years based upon your expectations for the firm and adjust the beta to reflect
these changes. To estimate the cost of debt for a distressed firm, we would
recommend using the interest rate based upon the firmÕs bond rating. While this will
still yield a high cost of debt, it will be more reasonable than the yield to
maturity when default is viewed as imminent.[5]
Finally,
to compute the cost of capital, you need to estimate the weights on debt on
equity. In the initial year, you should use the current market debt to capital
ratio (which may be very
high for a distressed firm). As your make your forecasts for future years and
build in your expectations of improvements in profitability, you should adjust
your debt ratio towards more reasonable levels. The conventional
practice of using target debt ratios for the entire valuation period (which reflect
industry averages or the optimal mix) can lead to misleading estimates of value
for firms that are significantly over levered.
The biggest
roadblock to using this approach is that even in its limited form, it is difficult
to estimate the cumulative probabilities of distress (and
survival) each year for the forecast period. Consequently, the
expected cash
flows
may not incorporate the effects of distress completely. In addition, it is difficult to
bring both the going concern and the distressed firm assumptions into the same
model. We attempt to do so using probabilities, but the two approaches make
different and sometimes contradictory assumptions about how markets operate and
how distressed firms evolve over time.
An
alternative to the modified discounted cash flow model presented in the last section is to separate
the going concern assumptions and the value that emerges from it from the
effects of distress. To value the effects of distress, you estimate the
cumulative probability that your firm will become distressed over your forecast
period, and the proceeds that you estimate you will get from the distress sale.
The value of the firm can then be written as:
Firm Value = Going
concern value * (1p_{Distress} )+ Distress sale value
* p_{Distress}
where p_{distress }is the cumulative
probability of distress over the valuation period. In addition to
making valuation simpler, it also allows us to make consistent assumptions
within each valuation.
You
may wonder about the differences between this approach and the far more
conventional one of estimating liquidation value for deeply
distressed firms. You can consider the distress sale value to be a
version of liquidation value, and if you assume that the probability of
distress is one, the firm value will, in fact, converge on liquidation value. The advantage of
this approach is that it allows us to consider the possibility that even
distressed firms have a chance (albeit small) of becoming going concerns.
To
value a firm as a going concern, you consider only those scenarios where the
firm survives. The expected cash flow is estimated only across these scenarios and thus
should be higher than the expected cash flow estimated in the modified discounted cash flow model. When estimating
discount rates, we make the assumption that debt ratios will, in fact, decrease
over time, if the firm is over levered, and that the firm will
derive tax benefits from debt as it turns the corner on profitability. This is
consistent with the assumption that the firm will remain a going concern. Most discounted cash flow valuations that
we observe in practice are going concern valuations, though they may not come
with the tag attached.
A
key input to this approach is the estimate of the cumulative probability of
distress over the valuation period. In this section, we will consider three ways in
which we can estimate this probability. The first is a statistical approach (a
probit) where we relate the probability of distress to a firmÕs observable
characteristics Ð firm size, leverage and profitability, for instance Ð by contrasting firms that have
gone bankrupt
in prior years with firms that did not. The second is a less data intensive
approach, where we use the bond rating for a firm, and the empirical default
rates of firms in that rating class to estimate the probability of distress. The third
is to use the prices of corporate bonds issued by the firm to back out the
probability of distress.
The fact that hundreds of firms
go bankrupt every year provides us with a rich database that can be examined to evaluate both why
bankruptcy occurs and how to predict the likelihood of future bankruptcy. One of the
earliest studies that used this approach was by Altman (1968), where he used linear
discriminant analysis to arrive at a measure that he called the Z score. In this first
paper, that he has since updated several times, the Z score was a function of
five ratios:
Z = 0.012 (Working
capital/ Total Assets) + 0.014 (Retained Earnings/ Total Assets) + 0.033 (EBIT/
Total Assets) + 0.006 (Market value of equity/ Book value of total liabilities)
+ 0.999 (Sales/ Total Assets)
Altman argued that you could compute the Z scores
for firms and use them to forecast which firms would go bankrupt, and he
provided evidence to back up his claim. Since his study, both academics and practitioners
have developed their own versions of these credit scores.
Notwithstanding its usefulness in
predicting bankruptcy, linear discriminant analysis does not provide a probability of
bankruptcy. To arrive at such an estimate, we use a close variant Ð a probit.
In a probit, we begin with the same data that was used in linear discriminant
analysis, a sample of firms that survived a specific period and firms that did
not. We develop
an indicator variable, that takes on a value of zero or one, as follows:
Distress Dummy = 0 for any
firm that survived the period
=
1 for any firm that
went bankrupt during the period
We then consider
information that would have been available at the beginning of the period that may have allowed us to separate
the firms that went bankrupt from the firms that did not. For instance, we
could look at the debt to capital ratios, cash balances and operating margins of all of the
firms in the sample at the start of the period Ð you would
expect firms with high debt to capital ratios, low cash balances and negative
margins to be more likely to go bankrupt. Finally, using
the dummy variable as our dependent variable and the financial ratios (debt to capital
and operating margin) as independent variables, we look for a relationship:
Distress Dummy = a
+ b (Debt to Capital) + c (Cash Balance/ Value) + d (Operating
Margin)
If the
relationship is statistically and economically significant, we have the
basis for estimating probabilities of bankruptcy.[6]
One
advantage of this approach is that it can be extended to cover the likelihood
of distress at firms without significant debt. For instance, you could relate
the likelihood of distress at young, technology firms to the cashburn ratio,
which measures how much cash a firm has relative to its operating cash needs.[7]
Many firms, especially
in the United States, have bonds that are rated for default risk by the ratings
agencies. These bond ratings not only convey information about default risk (or at least
the ratings agencyÕs perception of default risk) but come with a rich history. Since bonds have
been rated for decades, we can look at the default experience of bonds in each
ratings class. Assuming that the ratings agencies have not significantly
altered their ratings standards, we can use these default probabilities as
inputs into discounted cash flow valuation models. Altman (2001) has estimated the
cumulative probabilities of default for bonds in different ratings classes over
five
and
tenyear periods and the estimates are reproduced in the table
below:
Table: Bond Rating and
Probability of Default Ð 1971  2001
Rating 
Cumulative Probability
of Distress 

5 years 
10 years 

AAA 
0.03% 
0.03% 
AA 
0.18% 
0.25% 
A+ 
0.19% 
0.40% 
A 
0.20% 
0.56% 
A 
1.35% 
2.42% 
BBB 
2.50% 
4.27% 
BB 
9.27% 
16.89% 
B+ 
16.15% 
24.82% 
B 
24.04% 
32.75% 
B 
31.10% 
42.12% 
CCC 
39.15% 
51.38% 
CC 
48.22% 
60.40% 
C+ 
59.36% 
69.41% 
C 
69.65% 
77.44% 
C 
80.00% 
87.16% 
As elaboration, the cumulative default probability for a BB
rated bond over ten years is 16.89%.[8]
What
are the limitations of this approach? The first is that we are delegating the
responsibility of estimating default probabilities to the ratings agencies and
we assume that they do it well. The second is that we are assuming that the
ratings standards do not shift over time. The third is that the table measures
the likelihood of default on a bond, but it does not indicate whether the defaulting firm goes out
of business. Many firms continue to operate as going concerns after default.
We can illustrate
the use of this approach with Global Crossing. At the end of
2001, Global Crossing had been assigned a bond rating of CCC by Standard and
Poors.
Based upon this bond rating and the history of defaults between 1971 and 2001,
we would have
estimated
a cumulative
probability
of bankruptcy of 51.38% over 10 years for the firm.
The conventional approach
to valuing bonds discounts promised cash flows back at a cost of debt that incorporates a
default spread to come up with a price. Consider an alternative approach. You could discount the
expected cash
flows
on the bond, which would be lower than the promised cash flows because of the
possibility of default, at the riskfree rate to price the bond. If we assume that
a
constant annual probability of default, we can write the bond price as follows
for a bond with fixed coupon maturing in N years.
Bond Price =
Global
Crossing has a 12% coupon bond with 8 years to maturity trading at $ 653. To
estimate the probability of default (with
a treasury bond rate of 5% used as the riskfree rate):
653 =
p_{Distress } = Annual probability of default = 13.53%
To estimate the
cumulative probability of distress over 10 years:
Cumulative
probability of surviving 10 years = (1  .1353)^{10} =
23.37%
Cumulative
probability of distress over 10 years = 1  .2337 = .7663 or 76.63%
Once
you have estimated the probability that your firm will be unable to make its
debt payments and will cease to exist, you have to consider the logical
followup question. What happens then? As noted earlier in the paper, it is not
distress per se that is the problem but the fact that firms in distress have to
sell their assets for less than the present value of the expected future cash
flows
from existing assets and expected future investments. Often, they may
be unable to claim even the present value of the cash flows generated even
by existing investments. Consequently, a key input that we need to estimate is
the expected proceeds in the event of a distress sale. We have
three choices:
a. Estimate the
present value of the expected cash flows in a discounted cash flow model, and assume that
the distress sale will generate only a percentage (less than 100%) of this
value. Thus, if the discounted cash flow valuation yields $ 5 billion as the value of the
assets, you may assume that the value will only be $ 3 billion in the event of
a distress sale.
b.
Estimate the present value of expected cash flows only from existing investments as the distress sale value.
Essentially, you are assuming that a buyer will not pay for future investments
in a distress sale. In practical terms, you would estimate the distress sale
value by considering the cash flows from assets in place as a perpetuity (with no
growth).
c. The most practical way of estimating distress
sale proceeds is to consider the proceeds as a percent of book value of assets,
based upon the experience of other distressed firms. Thus, the fact that
distressed telecomm companies are able to sell their assets for 20% of book
value would indicate that the distress sale proceeds would be 20% of the book
value of the assets of your firm.
Note that many of
the issues that come up when estimating distress sale proceeds Ð the need to
sell at below fair value, the urgency of the need to sell Ð are issues that are
relevant when estimating liquidation value.
To
estimate the expected proceeds in the event of a distress sale, we considered
several factors. First, the sluggish growth in the economy clearly does not
bode well for any firm trying to sell its assets in a liquidation. Second, the fact that a large number of
telecomm firms are in distress and looking for
potential buyers is also likely to weigh down the proceeds in a sale. In fact,
PSInet, another telecomm firm that had recently been forced into a distress
sale, was able to receive less than 10% of its book value in the sale. For
Global Crossing, we will assume that the distress sale proceeds will be 15% of the book
value of the noncash assets.
Book value of noncash assets =
$14,531 million
Distress sale
value = 15% of book value = .15*14531 = $ 2,180 million
Since the firm has
debt outstanding (in face value terms) of $7,647 million, the equity investors
will receive nothing in the event of a distress sale, even if we consider the
cash and marketable securities of
$2,260 million that the firm has on its books.
To
value Global Crossing with distress valued separately, we will begin with a
going concern valuation of Global Crossing and then consider the distress sale
proceeds:
1. Valuing Global
Crossing as a going concern
Global Crossing provides managed data and voice
products over a fiber optic network. Over its threeyear history, the firm has
increased revenues from $420 million in 1998 to $4,040 million in 2001,
but it has gone from an operating income of $120 million in 1998 to an
operating loss of $1,895 million in 2001[10]. In addition, the firm is capital intensive and
reported substantial capital expenditures ($4,289 million) and depreciation ($1,436 million) in 2000.
In
making the valuation, we assume that there will be no revenue growth in the
first year (to reflect a slowing economy) and that revenue growth will be brisk
for the following
4 years
and then taper off to a stable growth rate of 5% in the terminal phase, that
EBITDA as a percent of sales will move from the current level (of about Ð10%) to a industry
average of 30%. by the end of the tenth year and that capital
expenditures will be ratcheted down over the next two years to maintenance
levels. Table 1 summarizes our assumptions on revenue growth,
EBITDA/Sales and reinvestment needs over the next 10 years.
Table 1: Assumptions
for Valuation

EBITDA/ Revenues 
Growth rate in Capital Spending 
Growth rate in Depreciation 
Working capital as % of Revenue 

1 

3% 
20% 
10% 
3.00% 
2 
40.00% 

50% 
10% 
3.00% 
3 
30.00% 
5.00% 
30% 
10% 
3.00% 
4 
20.00% 
10.00% 
5% 
10% 
3.00% 
5 
10.00% 
15.00% 
5% 
50% 
3.00% 
6 
10.00% 
18.00% 
5% 
30% 
3.00% 
7 
10.00% 
21.00% 
5% 
5% 
3.00% 
8 
8.00% 
24.00% 
5% 
5% 
3.00% 
9 
6.00% 
27.00% 
5% 
5% 
3.00% 
10 
5.00% 
30.00% 
5% 
5% 
3.00% 
For both revenue
growth and improvement in EBITDA margins, we assume that the larger changes
occur in the earlier years. Note that the changes in depreciation lag the
changes in capital spending Ð the capital spending is cut first and
depreciation drops later. Finally, we assume that the firm will need to set
aside 3% of the revenue change each year into working capital based upon the
industry averages.
With
these forecasts, we estimated revenues, operating income and aftertax
operating income each year for the high growth period in Table 2. To estimate
taxes, we consider the net operating losses carried forward into 2001 of $2,075
million and add on the additional losses that we expect in the first few years
of the projection.
Table 2: Expected aftertax operating income to firm: Global
Crossing
Year 
Revenues 
EBITDA 
Depreciation 
EBIT 
NOL at beginning of
year 
Taxes 
EBIT (1t) 
1 
$3,804 
$95 
$1,580 
$1,675 
$2,075 
0 
$1,675 
2 
$5,326 
$0 
$1,738 
$1,738 
$3,750 
$0 
$1,738 
3 
$6,923 
$346 
$1,911 
$1,565 
$5,487 
$0 
$1,565 
4 
$8,308 
$831 
$2,102 
$1,272 
$7,052 
$0 
$1,272 
5 
$9,139 
$1,371 
$1,051 
$320 
$8,324 
$0 
$320 
6 
$10,053 
$1,809 
$736 
$1,074 
$8,004 
$0 
$1,074 
7 
$11,058 
$2,322 
$773 
$1,550 
$6,931 
$0 
$1,550 
8 
$11,942 
$2,508 
$811 
$1,697 
$5,381 
$0 
$1,697 
9 
$12,659 
$3,038 
$852 
$2,186 
$3,685 
$0 
$2,186 
10 
$13,292 
$3,589 
$894 
$2,694 
$1,498 
$419 
$2,276 
Terminal 
$13,957 
$4,187 
$939 
$3,248 
$0 
$1,137 
$2,111 
Year 
EBIT (1t) 
Capital
Expenditures 
Depreciation 
Change
in working capital 
FCFF 
1 
$1,675 
$3,431 
$1,580 
$0 
$3,526 
2 
$1,738 
$1,716 
$1,738 
$46 
$1,761 
3 
$1,565 
$1,201 
$1,911 
$48 
$903 
4 
$1,272 
$1,261 
$2,102 
$42 
$472 
5 
$320 
$1,324 
$1,051 
$25 
$22 
6 
$1,074 
$1,390 
$736 
$27 
$392 
7 
$1,550 
$1,460 
$773 
$30 
$832 
8 
$1,697 
$1,533 
$811 
$27 
$949 
9 
$2,186 
$1,609 
$852 
$21 
$1,407 
10 
$2,276 
$1,690 
$894 
$19 
$1,461 
Terminal 
$2,111 
$2,353 
$939 
$20 
$677 
The firm uses debt liberally to fund these
investments and had book value of debt outstanding
of $7,647 million at the
end of 2001. We estimated a market value for the debt of $4,923 million.[12] Based upon its market capitalization (for equity) of $1,649 million at the
time of this valuation, we estimated a market debt to capital ratio for the
firm.
Debt to capital
Equity to capital
To estimate the bottomup beta, we begin with an
unlevered beta of 0.7527 (based upon all publicly traded telecomm services
firms) and
estimate the levered beta for the firm:
Levered beta = Unlevered beta ( 1 + (1 tax rate)
(Debt/Equity))
=
0.7527 (1 + (10) (4923/1649)) = 3.00
Using a bottomup
beta of 3.00 for the equity
and a cost of debt of 12.80% based upon the current rating for the firm, we
can estimate a cost of capital for the next 5 years. (The riskfree rate is 4.8% and the risk
premium is 4%.)
Cost of equity =
4.8% + 3 (4%) = 17.40%
Aftertax cost of
debt = 12.8% (10) = 12.8%
(The firm does not pay taxes)
Cost of capital = 16.80% (0.2509) + 12.8% (0.7491) =
13.80%
In stable growth,
after year 10, we assume that the beta will decrease to 1.00 and that the
pretax cost of debt will decrease to 8%. The adjustment occurs in linear
increments from years 6 through 10 as shown in Table 4
Table 4: Cost of capital Ð Global Crossing
Year 
15 
6 
7 
8 
9 
10 
Terminal 
Tax Rate 

0% 
0% 
0% 
0% 
16% 
35% 
Beta 
3.00 
2.60 
2.20 
1.80 
1.40 
1.00 
1.00 
Cost of Equity 
16.80% 
15.20% 
13.60% 
12.00% 
10.40% 
8.80% 
8.80% 
Cost of Debt 
12.80% 
11.84% 
10.88% 
9.92% 
8.96% 
6.76% 
5.20% 
Debt Ratio 
74.91% 
67.93% 
60.95% 
53.96% 
46.98% 
40.00% 
40.00% 
Cost of Capital 
13.80% 
12.92% 
11.94% 
10.88% 
9.72% 
7.98% 
7.36% 
Value of the operating assets
of the firm = $5,529.92
+ Cash and Marketable
Securities = $2,260.00
Market Value of Debt = $4,922.75
Market Value of Equity = $2,867.17
Value of Options
Outstanding (See option worksheet) = $14.31
Value of Equity in
Common Stock = $2,852.86
Value of Equity per
Share = $3.22
In
illustration 1 we estimated the cumulative probability of
distress for Global Crossing to be 76.63% over the next 10 years, and in
illustration 2, we estimated the distress sale proceeds to be 15% of book value, based upon how
much the
assets of other bankruptcy telecomm firms were receiving in the market place
currently. Combining these two inputs, we arrive at an estimate of an expected
value for the operating assets with distress built into the assumptions:
Expected Value of
Operating Assets = 5530 (1  .7663) + 2180 (.2337) = $2,962.90 million
If we add back the
cash and marketable securities and net out the debt, we arrive at an adjusted
value of equity for the firm.
Value of the firm = $2,962.90
+ Cash and Marketable
Securities = $2,260.00
Market Value of Debt = $4,922.75
Market Value of Equity
= $2,031.98
Value of Options
Outstanding (See option worksheet) = $14.31
Value of Equity in
Common Stock = $2,017.67
Value of Equity per
Share = $0.02
One
limitation of this approach is that it does not consider the fact that equity
has limited liability. In other words, if distress occurs and the value of the
operating assets is less than the debt outstanding (as is inevitable), equity investors
will get nothing from their investment but will not be required to make up the
difference. We can estimate a more realistic value of equity by
taking a weighted average of equity per share:
Value of equity =
$3.22 (1 .7663) + $ 0.00 (.7663) = $0.75
One way to read
this difference is to consider the first estimate of value ($0.02) as the value
without limited liability and the second estimate ($0.75) as the value to equity
investors
of limited
liability.
In the adjusted present value (APV) approach, we
begin with the value of the firm without debt. As we add debt to the firm, we
consider the net effect on value by considering both the benefits and the costs
of borrowing. To do this, we assume that the primary benefit of borrowing is a
tax benefit and that the most significant cost of borrowing is the added risk
of bankruptcy.
We estimate the value of the firm in three steps.
We begin by estimating the value of the firm with no leverage. We then consider
the present value of the interest tax savings generated by borrowing a given
amount of money. Finally, we evaluate the effect of borrowing the amount on the
probability that the firm will go bankrupt, and the expected cost of
bankruptcy. It is in this last element that we can consider the possibility of
distress and its consequences for value.
The
first step in this approach is the estimation of the value of the unlevered
firm. This can be accomplished by valuing the firm as if it had no debt, i.e.,
by discounting the expected free cash flow to the firm at the unlevered cost of
equity. In the special case where cash flows grow at a constant rate in
perpetuity, the value of the firm is easily computed.
Value of Unlevered Firm =
where FCFF_{0}
is the current aftertax operating cash flow to the firm, r_{u} is the unlevered
cost of equity and g is the expected growth rate. In the more general case, you
can value the firm using any set of growth assumptions you believe are
reasonable for the firm.
The
inputs needed for this valuation are the expected cash flows, growth rates
and the unlevered cost of equity. To estimate the latter, we can compute the
unlevered beta of the firm.
where
bunlevered = Unlevered beta of the firm
bcurrent = Current equity beta of the firm
t = Tax rate for the
firm
D/E = Current
debt/equity ratio
This unlevered
beta can then be used to arrive at the unlevered cost of equity.
The
second step in this approach is the calculation of the expected tax benefit
from a given level of debt. This tax benefit is a function of the tax rate of
the firm and is discounted at the cost of debt to reflect the riskiness of this
cash flow. If the tax savings are viewed as a perpetuity,
Value of Tax
Benefits
The tax rate used
here is the firmÕs marginal tax rate and it is assumed to stay constant over
time. If we anticipate the tax rate changing over time, we can still compute
the present value of tax benefits over time, but we cannot use the perpetual
growth equation cited above.
The
third step is to evaluate the effect of the given level of debt on the default
risk of the firm and on expected bankruptcy costs. In theory, at least, this
requires the estimation of the probability of default with the additional debt
and the direct and indirect cost of bankruptcy. If p_{a} is the
probability of default after the additional debt and BC is the present value of
the bankruptcy cost, the present value of expected bankruptcy cost can be
estimated.
PV of Expected
Bankruptcy cost
You can use the approaches
described in the last section to arrive at an estimate of the probability of
bankruptcy. You can also consider the difference between the value of a firm as
a going concern and the distress sale value as the cost of bankruptcy. Thus, if
the present value of expected cash flows is $ 5 billion Ð the going concern
value Ð and the distress sale proceeds is expected to be only 25% of the book
value of $ 4 billion, the bankruptcy cost is $ 4 billion.
Expected bankruptcy cost = $ 5 billion  .25 (4
billion) = $ 4 billion
The
adjusted present value approach is best suited for firms that are distressed
because they have too much debt. It cannot be used for firms that face the
possibility of distress because they have insufficient cash to meet their
operating obligations. The estimation challenges abound. In particular,
attaching a value to expected bankruptcy cost can be problematic.
To
value Global Crossing on an adjusted present value basis, we would first need
to value the firm as an unlevered entity. We can do this by
using the unlevered cost of equity as the cost of capital.
Unlevered beta for
Global Crossing[14] = 0.7527
Using the riskfree
rate of 4.8% and the market risk premium of 4%,
Unlevered cost of
equity for Global Crossing = 4.8% + 0.7527 (4%) = 7.81%
We use this cost
of equity as the cost of capital and discount the expected free cashflows to
the firm shown earlier in table 3. (Note that the terminal value is left
unchanged. We will continue to assume that the firm will earn its cost of
capital on investments after year 10)
Table 5: Present Value
of FCFF at Unlevered Cost of Equity
Year 
FCFF 
Terminal
Value 
PV
at 7.81% 
1 
$3,526 

$3,270.85 
2 
$1,761 

$1,515.31 
3 
$903 

$720.38 
4 
$472 

$349.17 
5 
$22 

$15.02 
6 
$392 

$249.55 
7 
$832 

$491.64 
8 
$949 

$519.81 
9 
$1,407 

$715.26 
10 
$1,461 
$28,683 
$14,210.82 
The
unlevered firm value is $14,211 million. To this we should add the expected
tax benefits of debt. Since the firm is losing money and has substantial net
operating losses, the expected tax benefits accrue almost entirely after year 10. Consequently, we
assume no significant tax benefits[15]. To estimate the
bankruptcy cost, we consider the difference between the going concern value of
$14,211
million
and the distress sale proceeds estimate of $2,180 million (estimated in
illustration 2) as the bankruptcy cost. Multiplying this
by the probability of bankruptcy estimated in illustration 1 yields the
expected cost of bankruptcy:
Adjusted Present
Value of Global CrossingÕs assets = Unlevered firm value + Present value of tax
benefits Ð Expected bankruptcy costs =
14,211 + 0 Ð 0.7663 ( 14,211 Ð 2,180) = $4,992 million
Adding back the
cash and marketable securities and subtracting out debt yields a value of
equity for Global Crossing:
APV of Global
Crossing Assets = $ 4, 992 million
+ Cash &
Marketable Securities = $
2,260 million
 Market value of
Debt = $
4,923 million
Value of Equity = $2,259
million
Value per share =
$2,259 million/ 886.47 = $2.55
Most
valuations, including those of distressed firms, are relative valuations. In
particular, firms are valued using multiples and groups of comparable
firms. An open question then becomes whether the effects of distress are
reflected in relative valuations and, if not, how best to do so.
It
is not clear how distress is incorporated into an estimate of relative value.
Consider how relative valuation is most often done. You choose a group of firms
that you believe are comparable to your firm. Usually, you pick firms in the
same business that your firm is in as your comparable firms. You then
standardize prices by computing a multiple Ð price earnings, price to
book, enterprise value to sales or enterprise value to EBITDA. Finally, you
examine how your firm measures up on this multiple, relative to the comparable
firms. While this time honored approach is used for distressed firms as well, the issues listed
below generally are unique to distressed firms:
1. Revenue and EBITDA
multiples are used more often to value distressed firms than healthy firms. The
reasons are pragmatic. Multiple such as price earnings or price to book value
often cannot even be computed for a distressed firm. Analysts therefore move up
the income statement looking for a positive number. For firms that make heavy
infrastructue investments, where depreciation and amortization is a significant
charge against operating income and there are substantial interest expenses, the EBITDA is
often positive while net income is negative. For some firms, even EBITDA is
negative and revenue multiples are
only multiples that yield positive values.
2. Analysts who
are aware of the possibility of distress often consider them subjectively when
they compare the
multiple for the firm they are analyzing to the industry average. For example,
assume that the average telecomm firm trades at 2 times revenues and that the
firm you are analyzing trades at 1.25 times revenues. Assume also that the firm
that you are analyzing has substantially higher default risk than the average
telecomm firm. You may conclude that the firm is not undervalued even though it
trades at a significant discount on the average, because of the potential for
default.
The
perils of subjective adjustment are obvious. Barring the most egregious
misvaluations, analysts will find a way to justify their prior biases about
firms.
Is
there a way in which relative valuation can be adapted to cover distressed
firms? We believe so, though the adjustments tend to be much more approximate
than those described in the discounted cash flow section.
To
value a distressed firm, you can find a group of distressed firms in the same
business and look at how much the market is willing to pay for them.
For instance, you
could value a
troubled telecomm firm by looking at the enterprise value to sales (or book capital) multiples at which other
troubled telecomm firms trade. While there is promise in this approach, it
works only if a large number of firms in a sector slip into financial trouble
at the same time. In addition, by categorizing firms as distressed or not
distressed firms, you run the risk of lumping together firms that are distressed to
different degrees.
One
possible way to expand this approach is to look at distressed firms across the
whole market, rather than just the sector in which your firm operates. This
will allow for a larger sample though there is the possible disadvantage that a
troubled grocery store may be in a better position (in terms of generating
distress sale proceeds) than a troubled technology company.
To
value Global Crossing, we considered only telecomm service firm with negative operating income and high leverage (market debt to capital
ratios that exceed 75%). We measured book capital as the sum of the book
values of equity and debt at the end of the most recent financial year. Our objective was
to arrive at a sample of telecomm firms that have a significant likelihood of
distress. Table 6 summarizes the enterprise value/ book capital
ratios for these firms:
Table 6: Distressed
Telecomm Firms
Company Name 
Value to Book
Capital 
EBIT 
Market Debt to Capital Ratio 
SAVVIS
Communications Corp 
0.80 
83.67 
75.20% 
Talk America
Holdings Inc 
0.74 
38.39 
76.56% 
Choice One Comm. Inc 
0.92 
154.36 
76.58% 
FiberNet Telecom
Group Inc 
1.10 
19.32 
77.74% 
Level 3 Communic. 
0.78 
761.01 
78.89% 
Global Light Telecom. 
0.98 
32.21 
79.84% 
Korea Thrunet Co.
Ltd Cl A 
1.06 
114.28 
80.15% 
Williams
Communications Grp 
0.98 
264.23 
80.18% 
RCN Corp. 
1.09 
332.00 
88.72% 
GT Group Telecom Inc
Cl B 
0.59 
79.11 
88.83% 
Metromedia Fiber 'A' 
0.59 
150.13 
91.30% 
Global Crossing Ltd. 
0.50 
15.16 
92.75% 
Focal Communications
Corp 
0.98 
11.12 
94.12% 
Adelphia Business
Solutions 
1.05 
108.56 
95.74% 
Allied Riser
Communications 
0.42 
127.01 
95.85% 
CoreComm Ltd 
0.94 
134.07 
96.04% 
Bell Canada Intl 
0.84 
51.69 
96.42% 
Globix Corp. 
1.06 
59.35 
96.94% 
United Pan Europe
Communicatio 
1.01 
240.61 
97.27% 
Average 
0.87 


Global Crossing
trades at 50% of book capital invested, significantly lower than the average
ratio across these distressed firms. We could view this as indicative of the fact that
Global Crossing is under valued on a relative basis, though that conclusion
would be justified only if we assume that the firms are exposed to equal
degrees to financial distress.
A
second possibility is to look for objective ways of adjusting the multiple for
distress. Consider one possible solution. You could examine the
multiple of revenues or operating income at which firms in different ratings
classes trade at to get a measure of the discount (if any) that is being applied
by the market for the degree of distress to which a firm is exposed. If there are
enough firms in the sector that you are analyzing in each ratings class, you
could do this on a sector basis. If there are not, you could look at the
multiple across the entire market and examine differences across bond rating
classes.
Looking
at all telecomm firms,
and categorizing them based upon bond ratings, we were able to estimate the
value to book ratios by bond rating class:
Bond Rating Value to Book Capital Ratio
A 1.70
BBB 1.61
BB 1.18
B 1.06
CCC 0.88
CC 0.61
The differences
between ratings classes provide us with an indication of the discount that you
would apply when valuing distressed firms. For instance, Global Crossing with
its CCC ratings should have a multiple that is roughly half that of a healthy A rated firm in the same
sector.
One
of the adaptations that we suggested for discounted cash flow valuation was an
explicit assessment of default risk and a firm value that was a weighted
estimate of a going concern value and a distress sale value. For a distressed
firm in a sector where the average firm is healthy, this approach offers promise.
You can estimate the value of the distressed firm using the comparable firms
and consider it the going concern value. For instance, if
healthy firms in the business trade at 2 times revenues, you would multiple
your firmÕs revenues by 2 to arrive at the going concern value. You could then
estimate the firm value as follows:
Firm Value = Going concern relative value * (1p_{Distress} )+ Distress sale
value * p_{Distress}
The probability of
distress and the distress sale value would be estimated just as they were in the last
section.
This
approach makes the most sense when valuing a firm that is distressed in a
sector containing mostly healthy firms, since the prior two approaches could
not be used here.
In
some cases, you may have to use forecasted values for revenues and operating
income to arrive at the going concern value, especially if current
revenues and operating income are adversely impacted by the overhang of
distress.
Consider
the forecasts of revenues and EBITDA made in table 2
for Global Crossing. While the firm is losing a substantial amount of money
currently, we are forecasting a return to financial health. In year 5, for
instance, Global Crossing is expected to have an EBITDA of $1,371 million on
revenues of $9,139 million. Using the average enterprise value/EBITDA multiple
of 7.2 at
which healthy telecomm firms[16] trade, we can
estimate an expected enterprise value in year 5.
Expected
Enterprise value in year 5 = EBITDA_{5} * EV/ EBITDA_{Current for
healthy telecomm firms}
=
1,371 * 7.2 = $9,871 million
You can estimate
the present value of this estimated value by discounting back at Global
CrossingÕs cost of capital.
Enterprise value
today =
9871/1.138^{5} = $5,172 million
This, of course,
is based upon the assumption that Global Crossing will become a healthy firm.
Using the probability of survival (23.37%) and distress (76.63%) estimated
earlier, we can value Global
CrossingÕs operating assets today:
= Going Concern Value (p_{Going Concern}) + Distres Sale
Value (1  p_{Going Concern})
= 5172 (.2337) +
2180 (.7663) = $2,879 million
Note that the
estimate of the distress sale value of $2,180 million was made earlier in
illustration 2. Adding back the cash balance of the firm ($ 2,260 million)
and subtracting out debt ($4923 million) yields a value for the equity:
Enterprise Value =
$ 2,879 million
+ Cash &
Marketable Securities =
$ 2,260 million
 Debt =
$4,923 million
Value of Equity =
$216 million
Value per share = $216/ 886.47 =$ 0.24
In conventional
valuation, you subtract the market value of the debt from firm value to arrive
at equity value. When valuing distressed firms, you have to consider two
specific issues. The first is the shifting debt load at these firms, since
these firms are often in the process of restructuring and renegotiating debt,
can make identifying the dollar debt due sat a point in
time a hazardous exercise. The
second is that equity in distressed firms often take on option
characteristics and may need to be analyzed as options.
In addition to
having a substantial amount of debt, distressed firms often have very
complicated debt structures. Not only do they owe money to a number of different
creditors, but the debt itself often is usually complex Ð convertible, callable and
filled with special features demanded by the creditors for their own
protection. In addition, distressed firms are often in the process of
negotiating with debt holders, trying to convince them to change the terms of
the debt and, in some cases, convert their debt into equity. Consequently, the
value of the debt can change dramatically from day to day, thus affecting the
value of equity, even if the enterprise value does not.
When
estimating the value of debt in a distressed firm, you should consider doing
the following:
In
distressed firms with a substantial debt obligation, equity takes on the
characteristics of an option. In particular, if the value of the firmÕs assets is
less than the face value of the outstanding debt, as is often the case with a distressed
firm, you can argue that equity investors have the option to liquidate the
firm if the asset value climbs above the face value of the debt but cannot
lose more than their equity investment, if asset value drops below:
If Value
of assets > Face value of debt: Asset
value Ð Face Value of debt
Value
of assets < Face value of debt: 0
So
what are the implications for valuation? To the extent
that equity investors value equity as an option, you can argue that the
equity in a deeply distressed firm should be the greater of two values Ð the conventional
value of equity, obtained by subtracting the market value of debt from firm
value and the value of equity as an option Ð with the
liquidation value of the assets representing the value of the underlying
asset
and the face value of debt the strike price. This approach
to valuing equity in deeply distressed firms is described more fully in
Damodaran (2001).[17]
Every
asset, financial as well as real, has a value. The key to successfully
investing in and managing these assets lies in understanding not only what
the value is but also the sources of
the value. Any asset can be valued, but some assets are easier to value than
others and the details of valuation will vary from case to case. Thus, the
valuation of a share of a real estate property will require different
information and follow a different format than the valuation of a publicly
traded stock. What is surprising, however, is not the differences in
valuation techniques across assets, but the degree of similarity in basic
principles. There is undeniably uncertainty associated with valuation. Often
that uncertainty comes from the asset being valued, though the valuation
model may add to that uncertainty.
E. either A, B, or C. Distressed
firms, i.e., firms with negative earnings that are exposed to substantial likelihood of
failure, present a challenge to analysts valuing them because so much of
conventional valuation is built on the presumption that firms are going
concerns. In this paper, we have examined how both
discounted cash flow and relative
valuation deal (sometimes partially and sometimes not at all) with distress.
With discounted cash flow valuation, we
suggested four ways in which you can incorporate distress into value Ð simulations
that allow for the possibility that a firm will have to be liquidated,
modified discounted cash flow models, where the expected cash flows and
discount rates are adjusted to reflect the likelihood of default, separate
valuations of the firm as a going concern and in distress and adjusted
present value models. With relative valuation, you can adjust your
multiples for distress or use other distressed firms as your comparable
firms.
References
Altman, E.I.,
1968, Financial Ratios, Discriminant Analysis and the Prediction of
Corporate Bankruptcy, Journal of Finance, v23, pp 589609.
Altman,
E.I., 2002, Bankruptcy, Credit Risk and
High Yield Junk Bonds, Blackwell.
Altman, E.I.
and V. Kishore, 2000, The Default Experience of U.S. Bonds, Working
Paper, Salomon Center, Stern School of Business, New York
University.
Altman, E.I, and P. Arman, 2002, Defaults and
Returns on High Yield Bonds, Analysis through 2001, Working Paper, Salomon Center, Stern School of
Business, New York University.
Damodaran,
A.,
2002, Investment
Valuation (Second Edition), John Wiley
& Sons.
Damodaran, A., Estimating Equity Risk
Parameters, Working paper, www.stern.nyu.edu/~adamodar/New_Home_Page/papers.html.
[1] A certainty equivalent cashflow replaces an
uncertain cash flow with an equivalent riskless cashflow. Thus, an expected
cashflow of $ 125 million will be replaced by a riskless cashflow of $ 100
million. The more uncertain the cash flow, the greater the downward adjustment.
[2] For example, you may increase the likelihood of
the earnings being low if the earnings in previous years were low and the
likelihood of negative margins if revenue growth is low.
[3] As an extreme example, consider estimating a beta
for Enron at the end of 2001. The beta estimate from Bloomberg, using 2 years
of data, was 1.45. Over threequarters of this period, Enron was viewed
(rightly or wrongly) as a healthy firm with positive earnings. It is only in
the last part of the regression period that you see the effects of distress on
stock prices and the debt to equity ratio of the firm.
[4] For more on bottomup betas, refer to Damodaran
(2000).
[5] The yields to maturity on bonds issued by
companies where there is a significant probability of distress will be
stratospheric, because they are based upon the promised cash flows on the bond,
rather than expected cashflows.
[6] This looks like a multiple regression. In fact, a
probit is a more sophisticated version of this regression with constraints
built in ensuring that the probabilities do not exceed one or become negative.
[7] Cash Burn Ratio = Cash Balance/ EBITDA. With
negative EBITDA, this yields a measure of the time that it will take the firm
to burn through its cash balance.
[8] Altman estimates the probability of default only
for AAA, AA, A, BBB, BB, B and CCC bonds. We interpolated to get the rest of
the table.
[9] With a 10year bond, it is a process of trial and
error to estimate this value. The solver function in excel accomplishes the
same in far less time.
[10] While the financial statements for 2000 had not
been
released, the trailing 12month numbers were used for most of the inputs in
November 2001
[11] The tax rate in year 10 is less than 35% because
of the net operating losses carried forward from the previous year.
[12] To estimate the market value, we discounted the
face value of debt and the interest payments back at the estimated pretax cost of
debt of 12.80%.
[13] The BlackScholes model was used to estimate the
value of the options outstanding. In fact, these options
had lost a substantial portion of value because of the drop in the stock price.
[14] We used the unlevered beta of telecomm services
firms as the unlevered beta for Global Crossing.
[15] This is conservative. There will be tax benefits
after year 10. We could estimate these tax benefits and consider them in
present value terms.
[16] We considered only firms with positive operating income and low debt to capital ratios (less than 30%) as healthy firms.
[17] See chapter 30 of the second edition of Investment Valuation for more details on valuing equity in a deeply distressed firm as an option.
[18]This is most
visible in takeovers, where the decision to acquire a firm often seems to
precede the valuation of the firm. It should come as no surprise, therefore,
that the analysis almost invariably supports the decision.
[19]In most years, buy
recommendations outnumber sell recommendations by a margin of ten to one. In
recent years, this trend has become even stronger.
[20]This is extracted
from Mr. Buffett's letter to stockholders in Berkshire Hathaway for 1993.
[21]On a chart, the
support line usually refers to a lower bound below which prices are unlikely to
move and the resistance line refers to the upper bound above which prices are
unlikely to venture. While these levels are usually estimated using past
prices, the range of values obtained from a valuation model can be used to
determine these levels, i.e., the maximum value will become the resistance
level and the minimum value will become the support line.
[22]Most corporate
financial theory is constructed on this premise.
[23]The motivation for
this has been the fear of hostile takeovers. Companies have increasingly turned
to 'value consultants' to tell them how to restructure, increase value and
avoid being taken over.