Developing Capitalization Rates For Valuing a Business

By Jeffrey W. Lippitt and Nicholas J. Mastracchio, Jr.

Most businesses are valued by using one of two models that capitalize an income stream. Regardless of the model used, the major problem is determining the capitalization rate to be used in the calculation. The authors explain how the use of the regression analysis features of a spreadsheet program can be used to help provide answers.

In recent years there has been a substantial growth in the demand for business valuations. This growth stems from a combination of tax, legal, and business factors, including the growth in the use of employee stock ownership plans, the classification of many closely held businesses as marital property in divorce actions, and the growth in legislation protecting oppressed minority shareholders.

In most circumstances, businesses are valued by some methodology that capitalizes the income stream. This is another way of saying that the value of a business is a function of the earnings stream it produces and is likely to continue to produce. The two most commonly used models in estimating values are the earnings capitalization model and the excess earnings model.

Although rates can be developed from comparable publicly traded firms for use in the earnings capitalization model, there is no generally recognized method for developing an excess earnings rate from information available on public companies. However, by using the simple regression functions available with most spreadsheet software, it is possible to develop rates for excess earnings calculations. To understand this approach, it is first necessary to review the nature of the two capitalization rate models.

Earnings Capitalization Model

The earnings capitalization model estimates the value of the company by calculating the present value of the adjusted accounting earnings in perpetuity. Since it assumes the earnings will continue indefinitely, the value is computed simply by dividing the earnings by a capitalization factor expressed as a percentage. For example, a company whose normal earnings are $1,000 and for which a capitalization rate of 20% is chosen would have a value of $5,000 ($1,000 ÷ .2). One of the most problematic aspects of this process is determining an appropriate capitalization rate. This is accomplished either by reference to rates implicit in the value the marketplace gives to comparable publicly traded companies or through a process known as the "buildup method." In the "buildup method" the valuator begins with the risk free rate and adds subjectively to that rate an amount appropriate for the investment risk of the firm being valued. Once an appropriate rate has been determined, the value of the firm is calculated rather quite simply by dividing the adjusted earnings by the capitalization rate.

Excess Earnings Model

The excess earnings model is based upon the contention that excess earning or earnings resulting from goodwill are riskier than earnings that provide a normal return on tangible assets. Consequently, the earnings stream is divided into two portions‹earnings attributable to tangible assets and those attributable to intangible assets. The present value of each portion is calculated using a capitalization rate appropriate for the level of risk associated with the two earnings streams. The rate used for the earnings attributable to intangible assets is generally higher, since the investment risk associated with these earnings is generally perceived to be greater. Arriving at these rates is the most problematic aspect of implementing the excess earnings model.

To illustrate the excess earnings model, consider the simple example presented in Tables 1 and 2. The example seeks to value a physician's practice where the doctor earns $200,000 a year after all expenses, including net rent expense of $30,000. Assume the practice has no material investment in tangible assets and the appropriate capitalization rate for a physician's practice is 20% (reflecting the value of the practice is primarily goodwill). In addition, assume the rent for the building produces a net 10% return to the owner, and the value of the land and building in total is not expected to diminish over time.

The value of the practice using the conventional earnings capitalization method and a 20% rate would be $1,000,000 (see Table 1). If the same practice were to purchase the building for $300,000, via an infusion of funds from the physician, the income would rise to $230,000 since there no longer would be a rent expense. If we were to continue to use the same capitalization rate, however, the value of the practice would only increase to $1,150,000.

We would expect the value of the practice and the building to be worth $1,300,000, the value of the practice prior to the purchase of the building, plus the value of the building. The theory used in the excess earnings model says the earnings, for purposes of valuing the practice, should not include earnings attributable to tangible assets such as the building. Consequently, the earnings would be split into earnings attributable to the building and to the practice. Therefore the earnings would be reduced by a fair return on the building, $30,000, and the remainder would be capitalized at the rate appropriate for the practice, 20%. The practice value would then be added to the value of the building. In this case, the value would be the expected $1,300,000 as shown in Table 2.

The need for valuing investments in assets that, such as in the example above, would command a yield different from that of the predominant business is well recognized. In fact, sophisticated use of the earnings capitalization model would suggest that unless real property is single use, it should be valued separately from the rest of the business.

The Right Rate

As noted earlier, the most problematic aspect of using an earnings-based model is determining the appropriate capitalization rates. The estimated value of a company is very sensitive to the rate chosen, and the choice is often very subjective, depending to a great extent on professional judgment. In the September 1993 issue of The CPA Journal, Idelle A. Howitt ("Valuing Closely Held Stock," p. 47) indicates using the market price of comparable publicly traded companies to calculate a capitalization rate is one approach to the valuation. Being able to draw a convincing link to a market determined rate can enhance the credibility of the valuation. This is important, particularly in litigation and other adversarial settings. However, there are several problems in attempting to make this link to market rates:

* Finding a firm or group of firms comparable to the firm being valued that has publicly available values is often difficult.

* Selecting an appropriate rate from a group of comparables, which often individually imply a range of rates is a subjective decision.

* After selecting a comparable, allowances must be made for differences in the nature of the firm being valued and that being used as comparable, such as marketability and control differences.

* The excess earnings model requires two capitalization rates, one for return on tangible assets and one for return on intangible assets. Since there is no generally available method for splitting observed rates of returns on publicly traded companies into these two components, rates for the excess earnings model are generally developed using the buildup method.

The Appropriate Use of Both Methods

For valuing businesses for which tangible assets are not a major factor, the two methods would presumably produce similar results. For example, in valuing the practice element of a physician's business, tangible assets are not normally a significant component. Therefore the capitalization rate in the earnings capitalization method approximates the rate on intangibles in the excess earnings model. The excess earnings method produces a level of refinement and sophistication when tangible assets are significant to the earnings process. For example, in valuing a manufacturing business with a large investment in property and equipment, it would be important to consider the return on tangible assets. By introducing a lower rate for those tangibles, the derived value better reflects the risks to the purchaser/investor.

Use of the excess earnings model is not uncommon. For example, in the land-mark New York State case, Seagrott Floral, the Court of Appeals affirmed the excess earnings methodology used in an oppressed minority action. The method has come under criticism, however, because of a lack of a recognized way to develop a link to the value of comparable publicly traded firms. The IRS has criticized the excess earnings model stating, "You hope to get a good answer based upon two bad guesses...to get two fairly accurate rates, one for tangibles and the other for intangibles, other than by the use of pure guesswork, is impossible." [Internal Revenue Service, IRS Appellate Conferee Valuation Training Program (Chicago: Commerce Clearing House, 1978)].

Contrary to the IRS statement, it is not impossible to develop capitalization rates other than as a matter of pure guesswork. It can be done by using the regression function of commonly used spreadsheet software such as Lotus 1-2-3, Excel, and Quattro Pro.

Calculating Capitalization Rates

This procedure permits the extraction of rates for both the earnings capitalization model and the excess earnings model from a collection of publicly traded comparables. In the October 1994 issue of The CPA Journal ("Discount and Capitalization Rates in Business Valuations," pps. 41-42), Randy Swad discusses the selection of comparable publicly traded companies and the consideration that should be given to various attributes of the company. His procedure develops rates that are characteristic of the industry as a whole, thereby reducing the subjectivity associated with the judgmental selection of an individual comparable. It also provides a practical method of using comparables to determine a rate for the excess earnings method.

Returning to the proposed rate estimation procedure, an example using data obtained from the Compustat Data PC Plus Database, is illustrative. For this example, we selected a group of publicly traded firms that have the same two digit SIC--electrical manufacturing‹with a value of less than $100 million. Alternative sources of such data are becoming increasingly available as information technology provides increased access to many diverse data bases. Currently, an alternate source of information in electronic form is available in Lexus/Nexus. In addition, the AICPA's CD­NAARS resources are available. Information also can be obtained from more traditional sources such as Value Line Investment Survey and annual SEC registration statements, which are available in many libraries. There may be many other sources on the Internet.

The 141 firms in our sample are far more than is necessary to arrive at defensible capitalization and excess earnings rates. We recommend a minimum of about 25 to 30 firms be included in any analysis. Clearly, the firms would have to be screened to obtain a subset that is reasonably comparable to the firm being valued. However, it is not necessary for each firm to be comparable in all respects, because it is the characteristics and risks of the industry as a whole that will determine the rates, not any individual firm.

Estimation Procedure

The procedure uses linear regression analysis. Our computations were all made using the regression feature of Lotus 1-2-3, but as we noted earlier, nearly any spreadsheet or statistical package will accommodate regression analysis quite easily.

The end-of-year share market value, the earnings for the year, and end-of-year net tangible assets for all 141 companies were entered in three columns of the spreadsheet, in that order. The program requires a decision be made as to an intercept point. For all calculations, a zero intercept point was designated. For the earnings capitalization rate calculation, the market value column was designated as the Y variable and the earnings column as the X variable. For the excess earnings calculation, both the earnings column and the net tangible assets column were designated as the X range.

Running the regression function produces output as shown in Table 3. The earnings capitalization model section of the Table on the X-coefficient line produces an earnings multiple (10.52) which is the statistical best estimate for the group of firms. It can be used to determine an unadjusted value (before liquidity and control adjustments) of a similar company by multiplying it by that company's earnings. More typically it is converted to a capitalization rate (9.5%)--See Table 4.

The excess earnings model section of Table 3 shows two X coefficients, the first of 6.39 represents the multiple to be applied to earnings and the second coefficient (.5) represents the multiple to be applied to net tangible assets. Table 4 converts the multiples to the more commonly used capitalization rates. It is noteworthy that the excess earnings rates are at the lower end of the ranges suggested in Revenue Ruling 68-609, which suggests a rate on tangible assets of eight to 10% and a rate on intangibles of 15 to 20%.

The mathematical formulas used in the Lotus calculations and Table 4 can be obtained from Michael J. Rosencrantz at The CPA Journal, 530 Fifth Avenue, New York NY 10036-5101.

Other Factors

The use of regression techniques to establish a link to publicly traded firms for the excess earnings method simplifies the choice of comparable firms since a whole segment of an industry may be selected. It also simplifies the determination of a rate. Once the firms are chosen, the regression will calculate the mathematically most appropriate rate. The regression technique can be used for both earnings capitalization and excess earnings models. Generally, it is difficult to use publicly traded firms as comparables when dealing with small, closely held firms. The techniques discussed here do not solve that problem. Finally, adjustments are always needed when using publicly traded firms. Differences in growth and leverage between the industry and the firm being valued need to be considered. In addition, the estimate of firm value is based upon minority trades, ignoring any control or marketability issues. These factors would have to be carefully considered anytime publicly traded firms are used to value closely held companies. *

Jeffrey W. Lippitt, PhD, is an associate professor at Siena College in Loudenville, NY. Nicholas J. Mastracchio, Jr., PhD, CPA, is an assistant professor at the State University of New York at Albany and is a former managing director of Marvin & Co., PC.

NOVEMBER 1995 / THE CPA JOURNAL

Without Building With Building

Earnings $ 200,000 $ 230,000

Rate 20% 20%

Value $1,000,000 $1,150,000

Practice earnings $ 230,000

Less earnings attributable to the building
($300,000 X 10%) 30,000

Adjusted practice earnings 200,000

Practice rate 20%

Practice value 1,000,000

Real estate earnings $30,000

Real estate rate 10%

Real estate value 300,000

Total value $1,300,000

TABLE 3

Earnings Capitalization Model

Constant 0

Standard error of Y estimate 14.21

R squared 0.64

No. of observations 141

Degrees of freedom 140

X coefficient 10.52

Standard error of coefficient 0.39

Excess Earnings Model

Constant 0

Standard error of Y estimate 11.19

R squared 0.78

No. of observations 141

Degrees of freedom 139

X coefficients 6.39 0.50

Standard error of coefficient 0.54 0.05

Earnings Capitalization

Capitalization rate 1/10.52 .095

Excess Earnings Model

Tangible asset rate (1-.50)/6.39 .078

Intangible asset rate 1/6.39 .156