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Financial distress significantly impacts firm valuation, necessitating methodologies that accurately incorporate its effects. This paper explores two distinct approaches to valuing firms under financial distress: the adjustment within the Discounted Cash Flow (DCF) valuation and the modification of the Adjusted Present Value (APV) model. Further, it delves into the application of multiple valuation techniques for distressed firms, highlighting the limitations and proposing practical solutions. Through theoretical frameworks and practical examples, including a detailed case study of Global Crossing, this paper aims to enhance the accuracy of firm valuation in the presence of financial distress, offering insights into the probabilistic modeling of distress scenarios and their impact on firm value.

Adjustments The DCF model, while robust, necessitates modifications to incorporate financial distress accurately.

One approach involves adjusting the model to factor in the probability of distress and the expected proceeds from a distress sale. The formula for firm value considering financial distress is as follows:

V_F=Going concern value*(1-π_Distress )+Distress sale value*π_Distress

Where VF is the firm value and π_Distress is the cumulative probability of financial distress.

Here the liquidation value comes again into importance.

If the cumulative probability of financial distress π_Distress is set at 100%, the firm value of the above formula will be similar to the liquidation value. Nevertheless, the possibility for the financially distressed firm to become stable again is considered in this formula. Hence, this formula can be regarded as a modification of the liquidation value.

The probability of distress can be estimated via three different approaches.

Either through a statistical approach by comparing firms, similar in size, profitability, leverage, that have recently gone bankrupt with such that are healthy, by evaluating the firm’s bond rating and the historical default rates in its respective rating, or by using the firm’s bond prices.

The distress sale proceeds can be as well estimated via three different approaches. First of all, a set percentage of less than 100% of the PV resulting from a typical discounted cash flow valuation can be assumed to be the distress sale value. Secondly, the PV of the cash flows arising from only the assets in place can be used. This means the calculation is based on a growth rate of 0%. The most practical way, however, is to consider a percentage of the book value of assets concerning comparable companies that have experienced a distress sale.

To apply the theoretical approaches to a practical example, the case of former telecommunications giant “Global Crossing” is suitable, which filed for bankruptcy in early 2002. Assessing Global Crossing’s probability of experiencing financial distress in late 2001, its bond rating was at a staggering CCC, which historically would lead to default in 51.38% based on a 10-year time span. When estimating the probability of default through the third approach, Global Crossing’s bond price trading at $653 would lead to a cumulative probability of distress of 76.63%. Because of the stagnant economic growth in the early 2000s and as well the defaults of several telecommunication firms, the distress sale proceeds could not be high for Global Crossing. In fact, only about 15% of its book value would have been received as the proceeds. With a book value of $14,531 million, the sale proceeds would only equal $2,180 million.

After making several assumptions about Global Crossing exiting the distress situation and becoming profitable again, Damodaran obtains a going concern value of the operating assets of the firm of approximately $5,530 million. If this is put into the formula for dealing separately with distress, the following value of Global Crossing can be obtained:

V_F=$5,530*(1-0.7663)+$2,180*0.7663=$2,962.90 million

Thus, the value of Global Crossing, when considering financial distress separately, with $2,962.9 million, is significantly lower than when assuming it would become financially healthy again, $5,530.

As introduced, the value of the firm arising from the APV model depends on three components, of which one is the negative effect of expected bankruptcy costs. Because this component does not incorporate the full magnitude of the systematic distress costs, Almeida and Philippon (2007) introduce two approaches to vary the APV model. Firstly, they use historical corporate bond yields to estimate the risk-adjusted probability of default. Secondly, they derive the risk-adjusted default probabilities from historical data on default probabilities.

Damodaran (2009) introduces a practical example of how to value a company with the APV model. Following the three steps of the APV model, he initially calculates the value of Las Vegas Sands without any leverage. He obtains an unlevered value of the firm’s assets of $7,003 million. He then continues to compute the tax benefits as 38% of the debt value, $.7,565 million. Noticeable is the fact that tax benefits for distressed firms are meager, due to likely and substantial losses in operating income. Finally, he estimates the bankruptcy costs as the difference between the going concern value and the distress sale estimate of $2,769 million, as well as the probability of distress as 76.66%. The adjusted present value of Las Vegas Sands then amounts to:

V_LVS=7,003+0.38*7,565-0.7666*(7.,003-2,769)=$6,632 million

Adding back the cash and marketable securities and subtracting the market value of debt, he then receives the value of the firm’s equity as $2,107 million. Compared to the current market value of Las Vegas Sands’ equity of $2,728, the firm is indeed overvalued, because the overall impact of systematic distress cost is not fully incorporated.

There are nonetheless certain limitations to Damodaran’s framework on incorporating financial distress in DCF valuation. For example, it is of immense difficulty to estimate the cumulative probability of financial distress for the entire valuation period. This could lead to the problem that expected cash flows might not fully consider the effects of financial distress.

As well, it is questionable how meaningful the results are after assembling the going concern and the distressed sale models in one model since both models make drastically different assumptions about how markets operate and how distressed firms evolve over time.

The multiple valuation approach, often referred to as relative valuation, is compared to the DCF approach based upon the assumption that a specific asset should have the same value as a similar asset. This is also referred to as the law of one price, which states that in an efficient market, all identical goods must have the same price. Multiples are often used in practice, which is stated by the results of Imam et al. (2008). The main reasons why multiples are used is the lack of detailed information about the financial data of a firm and as well to conduct a robustness check towards results arising from other valuation methods, mostly the DCF approach.

In multiple valuation, we distinguish between two general categories of multiples, the trading and the transaction multiples. Trading multiples are derived from current stock market prices, for example, the market price over the current earnings, when transaction multiples are derived from prices paid in recent acquisitions, for example, the takeover price over the current earnings. As well, we distinguish between so-called enterprise value multiples, which use the market or transaction price of the entire capital (i.e., equity and debt), and the equity value multiples using the market or transaction price of the equity. The most frequently used multiples are the following:

Enterprise Value to EBITDA ratio (EntV/EBITDA):

EntV/EBITDA=(Market value of equity+Book value of debt-Excess Cash)/EBITDA

Enterprise Value to Sales ratio (EntV/Sales):

EntV/Sales=(Enterprise Value)/sales

Equity value multiples:

Price to earnings ratio (P/E):

P/E=(market price per share)/(earnings (net income) per share)

Price to book value ratio (P/BV):

P/BV=(market price per share)/(book value per share)

Price to sales ratio (P/S):

P/S=P/E*(earnings per share)/sales

which consists of the price to earnings ratio multiplied by the return on sales.

The general approach to multiple valuation is subdivided into three essential steps. Initially, comparable firms have to be detected and their mostly publicly available data has to be retrieved. The comparable firms in this so-called peer group should be similar to the to be valued firm in terms of the business and financial risk, the growth potential, and the payout characteristics. In addition, Damodaran mentions that analysts often mainly look for comparable firms in the same industry. The second step is to scale the market prices to a standardized level, to make them comparable. This is basically the calculation of the multiple for each firm. The third and final step is to adjust for differences between the peers and eradicate the non-meaningful values (i.e., negative ratios), calculate the mean or median of the multiple using all the retrieved multiples, and finally apply the mean or median to the financial data of the to be valued firm. This then leads to the value of the entire entity or its equity stake, depending on which multiple is used.

Comparing the most important valuation methods, the DCF and multiple valuation, they distinguish themselves significantly. In DCF valuation, the assumption holds that if markets make mistakes, they will correct these in the long term, wherein multiple valuation, the assumption holds that markets may make mistakes on individual stocks, but will correct these on average. This is one primary driver for the results in both approaches diverging massively.

There are a few reasons why one might suit better. In the case of trying to study cross-industry differences amongst stocks, relative approaches seem to be more useful, while analyzing pricing differences and their correction over time, the intrinsic approach might be the better choice. One reason why analysts find DCF models more important is of technical motivation. Cash flows are simply less vulnerable to accounting manipulation by the management than earnings. In contrast, the results of a multiple valuation are more comfortable to defend, meaning when analysts have negative expectations and opinions on a specific asset, they tend to use multiples. Finally, often they tend to make use of a mix of both approaches in order to counter-check the results arising respectively from the models.

As relative valuation is a frequently used valuation tool, it finds its relevance in the valuation of distressed firms as well. However, there are two important issues that multiples face with distressed firms, mentioned by Damodaran (2006b). Because distressed firms often have negative earnings and EBITDA, the equity multiples mentioned, price to earnings and price to book value, cannot be calculated. A market price divided by negative earnings would lead to a negative multiple, hence, non-meaningful. Therefore, analysts use numbers that can potentially be positive, which are rather the EBITDA or the sales. Sometimes even, only the sales multiple is useful. Generally spoken, only the entity multiples may be useful for the valuation of distressed assets.

If analysts are aware of financial distress, they often consider it subjectively at a specific case. If a firm trades at a significantly lower multiple than the average of its peer group, however, has a much higher default risk, it might not be considered as undervalued. The major problem of subjective adjustments is that any misevaluation can somehow be justified.

How can financial distress correctly be considered in multiple valuation? The following section will introduce the usage of multiples for the valuation process of distressed firms in practice and lead on with a framework on how to sufficiently consider financial distress.

Again, looking at the study by Gilson, Hotchkiss, and Ruback (2000) , they as well estimate the value of the 63 firms that have filed for bankruptcy in the United States based on comparable company multiples. The multiple they test is the median ratio of total capital to EBITDA. This multiple was earlier introduced as the Enterprise Value to EBITDA ratio. For the several industry median ratios, they use companies that have the same four- (three- or two-) digit SIC code and generate sales above $20 million. They hereby assume that the industry average of the ratio matches the risk and growth of the firm in financial distress.

While using the multiple valuation, they obtain even more extreme results compared to the DCF results. The valuation error is, in fact, characterized by stronger outliers, ranging from -269.3% to 115.8%. Similarly to the DCF results, only about 20% of the estimated values are within a range of 15% of the actual market values. Thus, the multiple valuation seems not fully to incorporate financial distress into its results.

Damodaran (2006b) gives two possible solutions on how to do so, despite the fact that these adaptions tend to be far less accurate than the ones made in the DCF valuation. The first possibility to adequately incorporate financial distress is simply to exchange the peer group with comparable firms that as well experience financial distress. Thereby, the value of these firms that the market is willing to pay can be obtained. The downside of this approach is the fact that a large number of firms in an entire industry would have to fall into financial difficulties. Besides, the respective causes of the financial problems might be different and, therefore, not comparable. A possible solution to that would be to expand the distressed peer group to the entire market and not only one industry.

**Table 1: Distressed Telecommunication 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% |

Table 1 shows a selection of the peer group for Global Crossing, entirely consisting of 19 distressed telecommunication firms. The industry average of the value to book capital, earlier introduced as the price-to-book ratio, that arises from this peer group is at 0.87. Global Crossing’s price-to-book ratio, however, trades at 0.5, which is lower than the industry average. Under the assumption that the comparable firms experience the same degree of financial distress, this could be a hint for Global Crossing being highly undervalued.

The second approach is not focused on the peer group anymore but now on the multiple itself. Whatever multiple it is, concerning sales, EBITDA, or operating income, by looking at the respective multiple in all rating classes, the discount between these classes made by the market can be obtained. In the case of Global Crossing, Damodaran estimates the price-to-book ratios at the end of 2001 by bond rating class for the entire industry of telecommunication companies. He finds that healthy companies with an A rating should have a price-to-book ratio of 1.70 while companies rated CCC, as Global Crossing is, should only have about half of the ratio’s value, 0.88.

As well as for the DCF valuation, Damodaran suggests considering financial distress separately. The going concern value then is derived by using an industry multiple based on a peer group consisting of healthy firms. The formula then looks like this:

V_F=Going concern relative value*(1-π_Distress )+Distress sale value*π_Distress

The probability of distress π_Distress and the proceeds of a distress sale are estimated just like in the case of the DCF valuation. As stated above, the going concern value can only be derived when the comparable firms are in a healthy financial situation. But what if the entire industry is in financial distress?

In cases like this, Damodaran gives the solution to use forecasted revenues or operating earnings to obtain the going concern value. Global Crossing is expected to generate an EBITDA of $1,371 million in five years and the average industry EV⁄EBITDA multiple is at 7.2. The expected firm value in year five thus is the EBITDA5 multiplied by the multiple, which is $9,871 million. This value discounted back for five years by the cost of capital of Global Crossing, 1.138, results in a PV of $5,172 million. Using the possibility of distress from above, 76.63%, and the estimated proceeds from a distress sale, $2,180, he calculates the following estimated firm value:

V_F=5,172*(1-0.7663)+2,180*0.7663=$2,879 million

This estimation is very similar to the firm value obtained when considering financial distress separately in the DCF valuation.

The limitations in the framework for considering financial distress in relative valuation have been shortly addressed in the previous sections. Adapting the peer group towards a group of financially distressed firms is nearly impossible, since mostly only a few firms comparable in operations, size, and further factors are experiencing similar financial problems. As well, the firms in this peer group ought to experience the same degree of financial distress. One possible occasion for that would be an industry-wide crisis, for example, in the automotive industry from 2008 to 2010.

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