Dealing with
Distress in Valuation
CHAPTER 1
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.
The Underpinnings
of Discounted Cash flow Valuation
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).
The Possibility and Consequences of Financial
Distress
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.
Distress in
Discounted Cash flow Valuation
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.
1. We value only
large, publicly traded firms and distress is very unlikely for these firms.
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.
2. We
assume that access to capital is unconstrained
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.
3. We adjust the
discount rate for the possibility of distress
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.
4. We adjust the
expected cash
flows
for the possibility of distress
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 probability-weighted 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
risk-adjust 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
risk-adjusted 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.
5. 5.We assume that
even in distress, the firm will be able to receive as proceeds the present
value of expected cash flows from its assets
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).
RecappingÉ
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.
Adapting
Discounted Cash flow Valuation to Distress Situations
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.
Simulations
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.
Steps in
Simulation
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.
Limitations
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.
Modified Discounted
Cash
flow
Valuation
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.
Estimating
Expected Cash
flows
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 pjt is the probability
of scenario j in period t and Cashflowjt 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
short-cut, 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:
Estimating
Discount Rates
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 bottom-up 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 = Bottom-up Unlevered beta (1 + (1-
tax rate) (Debt to Equity ratio))
Note, though, that
it is reasonable to re-estimate 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.
Limitations of
Approach
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.
Dealing with
Distress Separately
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 * (1-pDistress )+ Distress sale value
* pDistress
where pdistress 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.
Going Concern DCF
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.
Estimating the
Probability of Distress
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.
a. Statistical Approaches
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 cash-burn ratio,
which measures how much cash a firm has relative to its operating cash needs.[7]
b. Based upon Bond
Rating
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
ten-year 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% |