# Valuing a Small Business: Implications of Different Income Tax Models

## Article excerpt

Introduction

A common method used to value a small business1 involves applying an aftertax discount rate to future aftertax returns (See, for example, Fishman, Pratt, Griffith, and Wilson 2003, chapter 5). The reason for using an aftertax discount rate is simply that it is aftertax discount rates that are observed (Bowles and Lewis 2000). To be consistent, aftertax discount rates must be applied to aftertax returns.2 Of course, estimating future aftertax returns requires an estimate of future average tax rates. This paper presents three different methods of modeling taxes in applying the discounted future returns method and compares the accuracy of each. These methods are outlined below:

1. Forecast aftertax returns based on a historical aftertax growth rate. In this instance, the future average tax rate is forecast implicitly.

2. Forecast before-tax returns based on a historical before-tax growth rate. Next, calculate future aftertax returns using the average tax rate of the base year. Again in this instance, the forecast of the future tax rate is implicit. For all future years, it is assumed to equal the average tax rate during the base year.

3. Forecast before-tax returns based on a historical before-tax growth rate. Unlike method (2), however, in this instance calculate future aftertax returns based on an estimated average tax rate which may be different for each future year.

The objectives of this paper are to (i) demonstrate the magnitude of errors that are possible from applying equation (1) or (2) rather than (3) in valuing a small business (using hypothetical company data) and (ii) review and demonstrate different approaches to estimating k^sub t^, which of course is required if equation (3) is to be applied. For example, it is demonstrated that for a high growth rate small business (e.g., g > 9%) the value of the business arrived at by applying equation (1) or (2) generally will result in a business value that is different than the true value7 in the range of 1% to 10% due to the wrong average tax rate.

Two types of small business entities will be considered. Those whose income is taxed at individual income tax rates (i.e., sole proprietorships, limited liability companies, partnerships, and S-corporations) and taxable business entities (i.e., C-corporations). This is necessary since the income tax rate scheme is different for individuals versus corporations. Moreover, the focus will be on average or effective income tax rates rather than marginal tax rates. When dealing with C-corporations, the reason is obvious: The corporation is a taxable entity and the forecast of aftertax earnings must be based on an estimate of the average tax rate. For entities taxed of individuals rates, the reason is more subtle. Generally, in the context of divorce litigation or gift and estate tax planning and compliance the business is valued without reference to a known buyer or, indeed, and implied sale (see, for example, Fishman, Pratt, Griffith and Wilson 2003,Chapters 10 and 12). Therefore, a reasonable and common assumption is that the business income will be taxed at an average rather that a marginal rate.8

Application of the Three Different Methods

To demonstrate that different business value estimates can be obtained by applying equation (1) or (2) rather than (3), consider the parameters provided in table 1. Essentially, table 1 assigns a number to each of 32 hypothetical firms, each corresponding to a combination of one of the levels of NBIT and one of four growth rates, 0, 3, 9, and 15%. First, it is assumed that the small business being appraised is a C-corporation. Then the analysis will be conducted assuming the business income is taxed at individual rates. The procedures applied to estimate the value of the business using the three different equations are outlined below.9, 10

Steps in Applying Equation 1

1. Determine NIBT for 1988-1992.

2. …