VALUATION OF NONPUBLIC COMPANIES

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minus its capital ( xed assets and working capital) needs, it is essentially the same as dividends or dividend-paying capacity The projection of net-free cash ow or dividends is a three-step procedure: 1 Project total cash ow (total revenues less cash expenses) 2 Project the capital needs of the business a Project required capital expenditures b Project required net working capital changes 3 Compute dividend-paying capacity (total cash ow minus total capital needs) The general theory used in estimating the expected rate of return is that investors return expectations are based on past returns In establishing the required rate of return for a nonpublic company, practitioners almost invariably use long-term stock return data compiled by Ibbotson Associates, whose Annual Yearbook includes series of stock return data In deriving the required rate of return for a subject company, it is rst necessary to estimate the rate of return investors expect on the small companies themselves on the valuation date Then, if the appraiser believes that an investment in the subject company is riskier than in the small companies, he must add an increment to their rate of return to re ect that greater risk Conversely, if the appraiser believes the risk is less, the rate of return must be reduced The value of stock is the present value of future returns in perpetuity This axiom requires, at least theoretically, that future dividends or net-free cash ows be projected and their present value be determined in perpetuity or, as a practical matter, so far into the future that present value increments become insigni cant There are three ways of doing this: 1 The arithmetic method 2 The algebraic method 3 The semialgebraic method Under the arithmetic method, each year s dividend is projected and its present value determined using the expected rate of return This is done for all future years until the annual present value increments become insigni cant Then the present values are totaled to give value In the algebraic method, the appraiser used the Gordon Model, which is: value = D ROR g

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where D = dividends for the rst year after the valuation date, ROR = the expected rate of return, and g = expected rate of growth in perpetuity The algebraic method produces the same value as the arithmetic method It is simply a computational shortcut It can be used only if the assumed growth rate of dividends is constant In the semialgebraic method, dividends or net-free cash ows are projected for a few years, usually ve, and then present value is determined Then the Gordon Model is used to determine the value at the end of the projection period, and the present value of that terminal value is added to the present value of the cash ows during the projection period Appraisers rarely use the arithmetic method because it tends to highlight the fact that their valuation depends on a projection of dividends decades into the future Also, appraisers do not commonly use the algebraic method, possibly because it seems embarrassingly simple By far the most common method used is the semialgebraic, probably because it gives the appearance of suitable complexity and tends to obscure the inherently in nite nature of the projection However, unlike the algebraic method, it can accommodate changes in the growth rates and capital needs during the projection period The discounted future net-free cash ow or dividends approach, as a valuation model, is eminently sound However, the problems inherent in its application to a speci c fact situation, primarily

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443 GENERAL PROCEDURE FOR VALUATION

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the inexactitude of the two major inputs, return and bene ts, render the results obtained only as good as the assumption incorporated in its application If the guideline company approach and the discounted future bene ts approach produce substantially different values, the appraiser should carefully analyze the reasons for the difference Such differences usually indicate that the investing public is using a different discount rate and/or growth rate from those used by the appraiser in his discounted bene ts approach (h) USE OF FORMULAS Rev Rul 59 60, the courts, and the Employees Stock Ownership Plan (ESOP) Association have discredited the use of valuation formulas The ESOP Association made the point very clearly: Formula appraisals are totally unacceptable, because they will virtually always result in an unfair, if not absurd, appraisal at some time in the future Valuation formulas can be as simple as Value = net book value, Value = net asset value, or Value = 10 earnings On the other hand, they can be so complex as to defy comprehension Doctors and engineers seem particularly enamored of complex valuation formulas The most widely employed type of formula still in use by some business appraisers is the excess earnings formula The original formula of this type was ARM-34, which was used for many years by IRS in the valuation of closely held companies ARM-34 was as follows: Value = book value + capitalized excess earnings Generally, excess earnings were de ned as earnings in excess of 10 percent of net worth, and a 20 percent capitalization rate was generally used in capitalizing excess earnings so that, in practice, the formula was: Value = book value + 5 1earnings 2 The formula has long since been discredited and abandoned by the IRS as well as the courts because it is arbitrary and not market oriented and can therefore produce very unrealistic values However, a variation of ARM-34 is still in use by some appraisers The basic formula is the same: Value = book value + capitalized excess earnings Excess earnings are de ned as the earnings in excess of the industry s average rate of earnings on stockholders equity Typically, these excess earnings are capitalized at 20 percent (or multiplied by 5) The shortcomings of this approach are fundamentally the same as ARM-34 The underlying assumption that a company is worth its book value if it has an average rate of earnings on net worth for its industry is arbitrary, unsupported, and often absurd In fact, companies in industries marked by low rates of earnings on book value will tend, on average, to have values in excess of book value, sometimes by a factor of 4 or 5 (i) NET ASSET VALUE APPROACH Net asset value is simply computed by adjusting all assets to a market value basis and deducting all liabilities Fundamentally, this is yet another formula approach, the formula being Value = net asset value There is ample evidence in the marketplace that the common stocks of industrial companies can sell appreciably above or below net asset value This is not surprising because the normal expectation of investors is that the bene ts of ownership will be received by them by way of dividends and a rising market price However, if the liquidation of a company is pending, net asset value is of paramount importance Net asset value has greater relevance to the appraisal of holding companies, notably investment companies and real estate holding companies Even here, however, the evidence of the marketplace is that the stocks of such companies almost always trade below net asset value

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