Value, much like beauty, is in the eyes of the beholder. And like beauty, there will never be unanimity of opinion when it comes to the reorganization value of a debtor. The process of valuation, regardless of the specific methodology employed, cannot avoid some fair degree of subjectivity, which inevitably gives rise to discrepancies and disagreement among parties in interest over value. A sufficiently narrow range of values that parties in interest can agree on would be considered an optimal outcome. From there, remaining differences of opinion over value can be negotiated and resolved to arrive at an acceptable going-concern value for the reorganized entity.

The determination of a debtor's weighted average cost of capital (WACC), the discount rate used to bring a stream of relevant cash flows to present value under the discounted cash flow (DCF) method, is a highly subjective exercise—not to mention one of the most critical determinants of value. The acute sensitivity of net present value (NPV) to relatively small changes in WACC allows for bias to be insinuated into the valuation process through subtle adjustments to WACC.

In this article, we present a modification to the standard DCF method that reduces some of the subjectivity intrinsic to the calculation of WACC and, at a minimum, helps to present the DCF method of valuation in a more forthright manner. We applied this modified DCF method to an actual debtor that emerged from bankruptcy within the last year (herein referred to as X Corp.) and compared our valuation results to those presented by the company in its disclosure statement.

X Corp. presented four-year operating projections (adjusted and summarized in Exhibit A) of the reorganized company in its disclosure statement, which were utilized in applying three valuation methodologies (comparable company analysis, DCF analysis and comparable transaction analysis) to estimate X Corp.'s enterprise value range as a going concern. We focused solely on the DCF method, for which the company used discount rates ranging from 20-25 percent. No additional details were provided.

We tried to identify and value an appropriate cash flow stream and then compare it to the debtor's enterprise value range. In a non-bankruptcy setting, net operating profit after taxes (NOPAT) is typically the line-item that is capitalized and present valued. However, in X Corp.'s case, we felt that NOPAT was inappropriate because depreciation expense was a poor proxy for normalized capital expenditures due to the significant downward revaluation of non-current assets in the application of fresh start accounting. Our best proxy for a cash flow stream to value was EBITDA minus Maintenance Capital Expenditures minus Taxes on EBIT. We assumed that two-thirds of estimated capital expenditures in X Corp.'s four-year projections were non-expansion-related outlays. Finally, we applied an assumed industry multiple of 12 to this line item in 2007 for a terminal value. Our resulting enterprise value range (see Exhibit B) was quite close to that derived by X Corp.—within about 10 percent.

Our contention with the standard approach to the DCF method of valuation is that only one operating scenario is presented, and the projected cash flows of the reorganized entity are expressed as a mathematical certainty, even though there is a fair likelihood that this scenario will not materialize. The risk of significant forecast error, which we will herein refer to as execution risk, is indirectly accounted for via the use of a subjectively high WACC to discount the designated cash flow stream.

We wonder whether the paramount risk inherent to any reorganized entity—that is, the execution risk of its business plan—could be better captured explicitly in the forecasted cash flows rather than implicitly through the discount rate applied to those cash flows. This approach would be unconventional in that the reorganization scenario would have to explicitly provide for the possibility of re-failure. No emerging debtor ever believed it would fail again—yet many have. Keeping execution risk embedded in the discount rate is a highly appealing practice since it accounts for the risk of re-failure without having to address it directly. As we will discuss shortly, the probability of re-failure is not an insignificant one, statistically speaking, and a direct approach to dealing with execution risk may be more intuitively appealing than making adjustments to WACC.

A theoretical weakness of the DCF method as it is widely used is that there is no systematic way to link WACC with execution risk. In a typical calculation of value in a reorganization, WACC (or more specifically, its cost of equity (COE) component) is usually determined by a subjective adjustment to some mathematically rigorous approximation, such as "add an extra risk premium of Y percent to COE as determined by the Security Market Line (CAPM)," or worse yet, some traditional rule of thumb. The linkage between WACC and execution risk is understood to be directionally correct, but it is not expressed in the form of an explicit relationship. Moreover, the determination of WACC leaves ample room for creativity. As a result of this imprecise relationship and the difficulty in achieving agreement on a single WACC, financial advisors typically provide a range of reorganization values using a band of discount rates. When a single value is provided, it is usually the midpoint of a valuation range. In X Corp.'s case, the difference in value between discount rates of 20 and 25 percent in Exhibit B is about 19 percent.

One way to incorporate the execution risk of a reorganized entity directly into the cash flow forecast is through scenario analysis. Several months ago we published an article that examined re-failure rates (chapter 22's) and trends between 1995 and 2001. Overall, 55 public companies re-filed for bankruptcy during this period. Their second lives were generally short ones; the median time period between emergence and re-filing was approximately 41 months. Only 36 percent of these chapter 22's filed between 1995 and 2001 were out of bankruptcy longer than 55 months before re-filing. Rounding down the median time of 41 months to the closest full year, these 55 re-filings represented at least 19 percent of the 295 public companies that emerged from bankruptcy between 1992 and 1998. (It should be noted that the term "public company" means that the entity was publicly owned when it originally filed for chapter 11, but not necessarily afterwards. Furthermore, we say "at least 19 percent" because New Generation Research (our data source) indicated that their listing of chapter 22 filers was thorough, but not necessarily exhaustive because smaller-emerged companies that became entirely creditor-owned or subsidiaries of other entities might not have been flagged if they subsequently failed a second time or were simply liquidated.) Retailers fared the worst of any industry, accounting for 25 of these 55 chapter 22 filers—far above their representative proportion of all companies that emerged from chapter 11—with a median time between emergence and re-filing of only 31 months. In the first half of 2003 alone, Wherehouse Entertainment, Today's Man, Clothestime Stores, Eagle Food Centers and Penn Traffic added their names to the list of retail chapter 22s. Historical re-failure rates, preferably by relevant industry and size, provide a credible starting point from which we can attempt to quantify an emerging entity's execution risk.

For illustration, let's imagine that there are only two possible outcomes with respect to X Corp.'s reorganization after it emerges from chapter 11; it will either achieve its presented business plan to the penny or it will stumble badly, fail within four years and be forced to file chapter 11 again. We could undertake to assign probabilities to each outcome and then compute the expected value of the reorganization scenario. We could, for example, assign a probability of, say, 25 percent to a chapter 22 outcome with an assumed recovery of zero to unsecured creditors receiving new stock in the initial reorganization, and a probability of 75 percent to the successful execution of the business plan contained in the disclosure statement. The expected value of the reorganized entity would be the sum of the payoffs from each outcome multiplied by the expected probability of occurrence.

Unfortunately, reorganization outcomes aren't binary, and we don't mean to oversimplify matters other than for illustrative purposes. Rather than two discrete outcomes, there are an infinite number of possible outcomes. Perhaps the payoff under a re-fail scenario is greater than zero. At the other end of the complexity spectrum, it may be possible to run a Monte Carlo simulation, where hundreds or thousands of outcomes can be generated to estimate expected cash flows and the value of the reorganized company if (and only if) we know the specific probability distributions of critical input variables, such as sales and gross margins. This is quite difficult to ascertain, and we aren't suggesting anything so abstract for purposes of valuation—just the idea that we move execution risk "upstairs" (i.e., into the cash flows).

After adjusting our cash flows, we must reduce WACC to remove the execution risk that is embedded in the discount rate range of 20-25 percent. Initially, we calculated the cost of equity (COE) of industry peers that had speculative-grade issuer credit ratings from Standard & Poor's. Beta is the average of historical beta for this peer group as of April 2003, calculated over the 60-month time period ending with that month.

Cost of Equity = Rf + [Historical Levered Beta *(10-Year Avg. Return on S&P500 - Rf)]
= 2.85% + 1.003 * (9.90-2.85%)
= 9.92% for speculative-grade rated peers

In order to calculate a COE for X Corp., we must first unlever the industry beta and then re-lever beta for X Corp.'s pro forma capital structure, where:

Unlevered Beta = Levered Beta/[1+ (1-Tax Rate)*(Debt/Equity Market Value)]

This calculation works out to an unlevered industry beta of .733 and a re-levered beta for X Corp. of 1.444 based on the mid-point of X Corp.'s estimated equity market value range and its projected capital structure upon emergence. Therefore:

Cost of Equity for X Corp. = 2.85% + 1.444*(9.90%-2.85%)
= 13.03%

Next, utilizing a 10.73 percent pre-tax cost of debt based on actual market yields for its speculative-grade peers, an assumed tax rate of 35 percent, and the company's pro forma capital structure, we computed a weighted average cost of capital for X Corp.

WACC for X Corp. = [Cost of Debt * (1-Tax Rate) * (Debt/Market Value Capitalization)] + [Cost of Equity * {1-(Debt/Market Value Capitalization)}]
= 9.51%

Based on a WACC of 9.51 percent and an assumed 25 percent probability of a chapter 22 filing, we then calculated the enterprise value of a reorganized X Corp., as shown in Exhibit C.

Our estimated enterprise value was about 16 percent above the high end of X Corp.'s valuation range as indicated in its disclosure statement. This discrepancy can be attributed to either of two variables in our model; our probability of re-failure was too low or our adjusted WACC was too low—either of which could produce a value that is higher than the value range in the disclosure statement. However, it would be hard to beat up on our revision to WACC since it was derived strictly in accordance with traditional financial literature on the subject, using third-party data for historical market returns, the company and its peer group.

We aren't suggesting that somebody should rewrite the playbook here. What we are suggesting is that this fairly straightforward modification to the traditional DCF method of valuing an entity as a going concern can strip away much of the opacity and subjectivity of WACC, enabling creditors to understand the key drivers of reorganization value in more direct and obvious terms, as well as providing a useful reality check on the reorganization value of a debtor as provided in its disclosure statement.