09 Nov, 2017

# Company Valuation Methods. Goodwill-Based Methods (Part 4)

Generally speaking, goodwill is the value that a company has above its book value or above the adjusted book value. Goodwill seeks to represent the value of the company’s intangible assets, which often do not appear on the balance sheet but which, however, contribute an advantage with respect to other companies operating in the industry (quality of the customer portfolio, industry leadership, brands, strategic alliances, etc.). The problem arises when one tries to determine its value, as there is no consensus regarding the methodology used to calculate it.

These methods apply a mixed approach: on the one hand, they perform a static valuation of the company’s assets and, on the other hand, they try to quantify the value that the company will generate in the future. Basically, these methods seek to determine the company’s value by estimating the combined value of its assets plus a capital gain resulting from the value of its future earnings: they start by valuing the company’s assets and then add a quantity related with future earnings.

**1. The «Classic» Valuation Method**

This method states that a company’s value is equal to the value of its net assets (net substantial value) plus the value of its goodwill. In turn, the goodwill is valued as n times the company’s net income, or as a certain percentage of the turnover.

According to this method, the formula that expresses a company’s value is:

V = A + (n x B), or V = A + (z x F),

where: A = net asset value; n = coefficient between 1.5 and 3; B = net income; z = percentage of sales revenue; and F = turnover.

The first formula is mainly used for industrial companies, while the second is commonly used for the retail trade. When the first method is applied to the hypothetical company Alfa Inc., assuming that the goodwill is estimated at three times the annual earnings, it would give a value for the company’s equity amounting to 213 million euro (135 + 3×26).

A variant of this method consists of using the cash flow instead of the net income.

**2. The Simplified «Abbreviated Goodwill Income» Method or the Simplified UEC Method**

According to this method, a company’s value is expressed by the following formula:

V = A + a_{n }(B — iA),

where: A = corrected net assets or net substantial value; a_{n} = present value, at a rate t, of n annuities, with n between 5 and 8 years; B = net income for the previous year or that forecast for the coming year; i= interest rate obtained by an alternative placement, which could be debentures, the return on equities, or the return on real estate investments (after tax); a_{n} (B — iA) = goodwill.

This formula could be explained in the following manner: the company’s value is the value of its adjusted net worth plus the value of the goodwill. The value of the goodwill is obtained by capitalizing, by application of a coefficient an, a «superprofit» that is equal to the difference between the net income and the investment of the net assets «A» at an interest rate «i» corresponding to the risk-free rate.

In the case of the company Alfa Inc., B = 26; A = 135. Let us assume that 5 years and 15% are used in the calculation of a_{n}, which would give a_{n }= 3.352. Let us also assume that i = 10%.

With this hypothesis, the equity’s value would be: 135 + 3.352 (26 — 0.1×135) = 135 + 41.9 = 176.9 million euro.

**3. Union of European Accounting Experts (UEC) Method**

The company’s value according to this method is obtained from the following equation:

V = A + a_{n} (B — iV) giving: V = [A + (a_{n} x B)] / (1 + ia_{n})

For the UEC, a company’s total value is equal to the substantial value (or revalued net assets) plus the goodwill. This calculated by capitalizing at compound interest (using the factor an) a superprofit which is the profit less the flow obtained by investing at a risk-free rate i a capital equal to the company’s value V.

The difference between this method and the previous method lies in the value of the goodwill, which, in this case, is calculated from the value V we are looking for, while in the simplified method, it was calculated from the net assets A.

In the case of the company Alfa Inc., B = 26; A = 135, a_{n} = 3.352, i = 10%. With these assumptions, the equity’s value would be: (135 + 3.352×26) / (1 + 0.1×3.352) = 222.1 /1.3352 = 166.8 million euro.

**4. Indirect Method**

The formula for finding a company’s value according to this method is the following:

V = (A + B/i)/2, which can also be expressed as V = A + (B — iA)/2i

The rate i used is normally the interest rate paid on long-term Treasury bonds. As can be seen in the first expression, this method gives equal weight to the value of the net assets (substantial value) and the value of the return. This method has a large number of variants that are obtained by giving different weights to the substantial value and the earnings' capitalization value.

In the case of the company Alfa Inc., B = 26; A = 135, i = 10%. With these assumptions, the equity’s value would be 197.5 million euro.

**5. Anglo-Saxon or Direct Method**

This method’s formula is the following: V = A + (B — iA) / t_{m}

In this case, the value of the goodwill is obtained by restating for an indefinite duration the value of the superprofit obtained by the company. This superprofit is the difference between the net income and what would be obtained from placing at the interest rate i, a capital equal to the value of the company’s assets.

The rate t_{m} is the interest rate earned on fixed-income securities multiplied by a coefficient between 1.25 and 1.5 to adjust for the risk. In the case of the company Alfa Inc., B = 26; A = 135, i = 10%. Let us assume that tm = 15%. With these assumptions, the equity’s value would be 218.3 million euro.

**6. Annual Profit Purchase Method**

With this method, the following valuation formula is used: V = A + m (B — iA).

Here, the value of the goodwill is equal to a certain number of years of superprofits. The buyer is prepared to pay the seller the value of the net assets plus m years of superprofits. The number of years (m) normally used ranges between 3 and 5, and the interest rate (i) is the interest rate for long-term loans.

In the case of the company Alfa Inc., B = 26; A = 135, i = 10%. With these assumptions, and if m is 5 years, the equity’s value would be 197.5 million euro.

**7. Risk-Bearing and Risk-Free Rate Method**

This method determines a company’s value using the following expression:

V = A + (B — iV) / t giving V = (A + B/t) / (1 + i/t)

The rate i is the rate of an alternative, risk-free placement; the rate t is the risk-bearing rate used to restate the superprofit and is equal to the rate i increased by a risk ratio. According to this method, a company’s value is equal to the net assets increased by the restated superprofit.

As can be seen, the formula is a variant of the UEC’s method when the number of years tends towards infinity. In the case of the company Alfa Inc., B = 26; A = 135, i = 10%. With these assumptions, if t = 15%, the equity’s value would be 185 million euro.

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Company Valuation Methods: Part1, Part2, Part3, Part4, Part5, Part6, Part7, Part8

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