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 firm’s 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 firm’s 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 year’s 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).

Recapping…

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 firm’s 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:

Š      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).

Š      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 – 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:

where pGoing concern, t is the cumulative probability that the firm will continue as a going concern through period t. The probabilities of distress will have to be estimated for each year and the cumulative probability of surviving as a going concern can then be written as follows:

where pdistress, t is the probability that the firm will become distressed in period t. For example, if a firm has 20% chance of distress in year 1 and a 10% chance of distress in year 2, the cumulative probability of surviving as a going concern over two years can be written as:

Cumulative probability of survival over 2 years = (1- .20) (1 - .10) = .72 or 72%

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 firm’s 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 firm’s observable characteristics – firm size, leverage and profitability, for instance – 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 – 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 – 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 agency’s 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 – 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.

c. Based upon Bond Price

            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 =

This equation can now be used, in conjunction with the price on a traded corporate bond to back out the probability of default.

            While this approach has the attraction of being a simple one, we would hasten to add the following caveats in using it. First, note that you not only need to find a straight bond issued by the company – special features such as convertibility will render the approach unusable – but the bond price has to be available. If the corporate bond issue is privately placed, this will not be feasible. Second, the probabilities that are estimated may be different for different bonds issued by the same firm. Some of these differences can be traced to the assumption we have made that the annual probability of default remains constant and others can be traced to the mis-pricing of bonds. Finally, as with the previous approach, failure to make debt payments does not always result in the cessation of operations.

Illustration 1: Estimating the probability of bankruptcy using bond price: Global Crossing

            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 =

Solving for the probability of bankruptcy[9], we get

pDistress  = 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%

Estimating Distress Sale Proceeds

            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 follow-up 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 – the need to sell at below fair value, the urgency of the need to sell are issues that are relevant when estimating liquidation value.

Illustration 2: Estimating Distress Sale Proceeds in January 2002: Global Crossing

            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 non-cash assets.

Book value of non-cash 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.

Illustration 3: Valuing Global Crossing with Distress valued separately

            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 three-year 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 –10%) 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

 

Revenue

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 – 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 after-tax 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 after-tax operating income to firm: Global Crossing

Year

Revenues

EBITDA

Depreciation

EBIT

NOL at beginning of year

Taxes

EBIT (1-t)

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

The accumulated losses over the first nine years shield the firm from paying taxes until the tenth year. After that point, we assume a marginal tax rate of 35%.[11]

            Finally, we estimated free cash flows to the firm with our assumptions about capital expenditures and working capital.

Table 3: Expected free cashflows to the firm: Global Crossing

Year

EBIT (1-t)

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 bottom-up 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 + (1-0) (4923/1649)) = 3.00

Using a bottom-up 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%

After-tax cost of debt = 12.8% (1-0) = 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 pre-tax 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 – Global Crossing

Year

1-5

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%

To estimate the reinvestment rate in the terminal year, we assume that Global Crossing would earn its cost of capital of 7.36% in perpetuity after year 10, and that the expected growth rate would be 5%. This yields a reinvestment rate of 67.93%.

Reinvestment rate in stable growth

Expected FCFF in terminal year

Terminal value

Discounting the operating cashflows and the terminal value back to the present, we arrive at an estimate of the value of the operating assets of $5,530 million. Note, though, that almost of this value comes from our presumption that Global Crossing will not only survive but become profitable, which is the source of the large terminal value. Adding back the cash and marketable securities held by the firm ($2,260 million) and subtracting out the value of debt ($4,923 million) and the estimated value of management options outstanding ($14.3 million)[13], we arrive at a value of equity of $2.852 billion. Dividing by the number of shares outstanding results in a value per share of $3.22.

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

Valued as a going concern, you would assign a value of $3.22 per share to Global Crossing’s equity.

Dealing with Distress

            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.

Adjusted Present Value (APV)

            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. 

Steps in APV

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 FCFF0 is the current after-tax operating cash flow to the firm, ru 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 firm’s 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 pa 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 the going concern value – 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

Limitations

            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.

Illustration 4: Valuing Global Crossing: Adjusted Present Value

            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 Crossing’s assets = Unlevered firm value + Present value of tax benefits Expected bankruptcy costs = 14,211 + 0 – 0.7663 ( 14,211 – 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

Relative Valuation

            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.

Distress in Relative Valuation

            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 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.

Adapting Relative Valuation to Distress

            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.

 

Choosing the Comparables

            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.

Illustration 5: Choosing comparables

            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.

Adjusting the Multiple

            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.

Illustration 6: Adjusted Multiple: Global Crossing

            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.

Considering the Possibility of Distress Explicitly

            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 firm’s 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 * (1-pDistress )+ Distress sale value * pDistress

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.

Illustration 7: Forward Multiples and 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 = EBITDA5 * EV/ EBITDACurrent 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 Crossing’s cost of capital.

Enterprise value today = 9871/1.1385 = $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 Crossing’s operating assets today:

Estimated Enterprise Value

= Going Concern Value (pGoing Concern) + Distres Sale Value (1 - pGoing 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

From Firm to Equity Value in Distressed Firms

            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.

The Shifting Debt Load

            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 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:



[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 three-quarters 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 bottom-up 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 10-year 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 12-month 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 pre-tax cost of debt of 12.80%.

[13] The Black-Scholes 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.