Simple Valuation of Compounded Deferred Tax Assets Using a Binomial Algorithm

Introduction

The tax return of a company is based on its accounting financial statements. To provide comparable information, financial statements are prepared according to the International Financial Reporting Standards (IFRS), issued by the International Accounting Standards Board (IASB). The IASB was formed in 2001 to replace the International Accounting Standards Committee that issued International Accounting Standards (IAS). Since the previously issued IASs remain effective, we have that the main body of standards that are used worldwide by several countries are comprised of IFRSs and IASs. The companies’ income, depicted by the IFRSs and IASs (refereed to simply by the Generally Accepted Accounting Principles GAAP) are their accounting profits, but these may be (and are) different than the taxable profit, since the taxable profit is calculated as a function of the tax law inherent to each country. The number of factors that lead to differences between tax and accounting returns is huge and varies from country to country. One of those factors is of relevance to the present work – the deferral of taxes.

The relationship of DTAs with the creditworthiness of a company as already deserved some work from academic community. The effects of book-tax differences on a firm’s credit risk were analysed in (Crabtree & Maher 2009), (Ayers et al. 2010), (Edwards 2011) and (Gallemore 2011); all agreeing that great amounts of deferred taxes were associated with higher risks and lower earnings quality, resulting in a decline of creditworthiness. Additionally, studies of the impact of DTAs on credit ratings led to the conclusion that deferred tax positions are substantial for many firms (between 5% and 10% of all assets according to (Poterba et al 2011)).

Under normal circumstances, a company’s DTAs usually originate in the carry-over of losses (though it can also arise from overpaying some taxes). The corresponding rights are registered in the balance sheet as assets, although in (Amir and Sougiannis 1999) it also argued that DTA may have implications for the perception of the firm as a going concern (dubbed as the information effect), since if the DTA arose from past operating losses, future losses would be likely to incur; this means that future liabilities could be more than likely, and thus such “assets” should be regarded with great suspicion).

These assets may be hard to value, since they are time-limited and may never be used at all. Their value is contingent on the future earnings of the company, and they can be used to shield these future profits from taxation – IAS 12 states that “a DTA should be recognised for all deductible temporary differences, to the extent that it is probable that taxable profit will be available against which the deductible temporary difference can be utilised”. Since corporate income taxation works on an annual basis, the shielding opportunities occur once a year. This is equivalent to saying that we are faced with a compound European option (or an annual Bermuda option) that might be exercised until the last year in which the law will permit shielding, or until the DTAs value has been completely depleted by its use. Consistent with this line of thinking, there is an ongoing debate regarding the appropriateness of including DTA in the banks’ regulatory capital calculation, since by doing so we are assuming its “full” worth; something that is clearly misleading.

Another aspect that must be taken into consideration is that a company can have several DTAs, each with different expiry dates; in this situation it will naturally use the DTA’s with the nearest expiry date first. Thus being, the probability of a certain DTA being used is dictated by all DTAs with shorter expiration dates being used or expired, and that the company generates enough profit to cover the DTA. Such scenario may seem hard to quantify at first, but as we will show, it is rather simple via the use of a binomial algorithm.