Valuation of tax loss carryforwards

A large number of firms have accumulated tax losses (Graham 1996a; Miller and Skinner 1998; Bauman and Das 2004); a look at the 2008–2009 annual statements in Compustat reveals that, after deleting firms with missing data, about 75 % of US firms (3,989 out of 5,291) were carrying tax losses. Moreover, tax losses can be significant in terms of magnitude; for instance, tax carryforwards accounted for 30.4 % of total assets in the Bauman and Das (2004) sample of internet firms, while firms in the Miller and Skinner (1998) sample had average deferred tax assets of about 10 % of total assets.

There are some papers on this topic that use a random walk process to model the earnings stream, e.g., Graham (1996a, b), Shevlin (1990). However, this way of modeling earnings has a significant drawback, i.e., earnings volatility will be significantly under-estimated under the random walk process. This has been pointed out and discussed at some length in a recent paper by Blouin et al. (2010). Given this weakness of the random walk process, it is not surprising that the contingent-claim modeling literature has extensively used the lognormal process for this purpose, including the papers just mentioned above. If we had used the random walk process instead of lognormal, the earnings volatility would have been under-estimated in our model; as a result, both the TLC value and the marginal tax rate (MTR) would have been over-estimated by our model.

The lognormal process, while a popular way of modeling earning in the Finance literature, is not the only process that can be used to depict the earnings process. In the early Accounting literature, for instance, some papers showed empirical support for the random walk, seasonal random walk with drift and other AR processes (Lev 1983; Lang 1991), although other papers disagreed with this (Lieber et al. 1983; Freeman et al. 1982). Further, Lipe and Kormendi (1994) provided evidence of mean reversion in the earnings process. In the trade-off between tractability and realism, we use the lognormal process that is commonly used in the Finance literature.

Constant coupon payment is a simplifying assumption for reasons of tractability. In real life, companies tend to reduce debt level when the benefits of debt are smaller (as in the case of large TLC). Reducing debt level will result in higher TLC values, since (as shown later in the paper) a lower leverage ratio increases TLC value, everything else remaining unchanged. On the other hand, companies with large TLC are generally in financial trouble and might not have the necessary cash to buy back debt. Hence the final effect of this is not clear and must be evaluated on a case-by-case basis.

Even if earnings are negative, the company does not necessarily default on its debt. This assumption might raise the question: where does the money to make coupon payment come from? We make the implicit assumption, as in Leland (1994), Goldstein et al. (2001), etc., that this money comes from shareholders. The argument is as follows. As long as the equity has some value, rational shareholders will keep the company alive even if they have to make out-of-pocket payments (see Leland 1994 for the detailed argument). This argument also has empirical support (Bhagat et al. 2005).

There is also some statutory progressivity, as pointed out by Graham and Smith (1999, p. 2243), because there are two tax rates: 15 % if profits are below $100,000 and 34 % if profits exceed $100,000. We examine the effect of this statutory progressivity in Sect. 3.2.

We assume, as in Leland (1994), that cash shortfalls are met by shareholders. Thus, when cash from operations fall short of the company’s coupon obligation (x < c), shareholders keep the company alive by paying the difference. If, however, earnings fall to a sufficiently low level, shareholders will not find it worthwhile to keep the company alive, and the company will file for bankruptcy (as in Leland 1994; Goldstein et al. 2001). This is consistent with actual corporate and shareholder behavior; as Bhagat et al. (2005) show, in loss-making firms it is the equity holders who invest in the company in order to keep it alive.

In Shevlin’s (1990) study of marginal corporate tax rates with NOL, there are four scenarios (see his Table 1): (a) negative taxable income and zero NOL, (b) negative taxable income and positive NOL, (c) positive taxable income and zero NOL, and (d) positive taxable income and positive NOL. In our model, the corresponding scenarios are (4), (2), (3) and (1) respectively.

This is because of the continuous-time nature of the model. In a discrete-time model, at year-end the outstanding TLC might be smaller than the taxable profit, in which case there would be a tax liability. In a continuous-time model, tax is paid continuously, but only after L is exhausted; therefore, when the company pays taxes, we must have L = 0. After L is exhausted, the firm is in region (3) and will be paying tax.

Bonds of companies with interest coverage ratio of over 8.5 (12.5 for smaller and riskier firms) are rated AAA, which is the highest safety rating possible and denotes negligible bankruptcy risk (for bond ratings and associated coverage ratios, please see http://​pages.​stern.​nyu.​edu/​~adamodar/​New_​Home_​Page/​datafile/​ratings.​htm). Therefore, a coverage ratio of 50 should imply negligible bankruptcy risk.

A rigorous empirical study could, of course, use market (analyst) expectations, if available, to compare model and market values to examine the usefulness of the model. However, such a study is beyond the scope of our paper.

Note that our main objective is to value TLC and not the value of the firm’s equity. However, TLC are not traded, making it very difficult to evaluate the model’s performance. Therefore, to check for model’s reliability, we look at model versus market values for equity, since the equity market values are available.

The particular solution will depend on the function ς(x).