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Valuation multiples size adjustment and their relationship with the cost of capital

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Valuation multiples size adjustment and their relationship with the cost of capital

The Guideline public company method (GPC) under the market approach of securities valuation uses value multiples of similar publicly traded companies to determine the valuation for the subject entity. These similar public companies are usually much larger than the subject private company. This raises the question of whether value multiples derived from these multi-billion-dollar companies are relevant for the valuation of relatively much smaller subject private companies, even if their business descriptions are similar.

In this post, we will discuss the above-mentioned issue, its solution, and criticisms in detail.

Requirement of Size adjustment

Guideline public companies are usually much larger than the subject private company. Empirical evidence suggests that smaller companies have commanded higher expected returns and are riskier than larger companies. Value multiples used in the GPCM are inverse of the capitalization rate and vice versa. A riskier company should command a higher capitalization rate and, consequently, a lower valuation multiple. Using multiples of guideline public companies causes overstatement of the subject company’s fair value, as the excess risk component for the smaller company is not considered in the capitalization rate. Therefore, value multiples of guideline public companies must be adjusted for the relatively smaller size of the subject company to avoid any biases in fair valuation.

Essential considerations in the valuation multiple size adjustment:

  1. The following things should be kept in mind before moving ahead with the value multiples size adjustments:
    • Equity multiples: These are multiples with the value of equity or market capitalization in the numerator. Examples of equity multiples are the Price/Earnings ratio, Price/Cashflows ratio, etc.
    • Invested capital multiples: These are multiples with the Market value of Invested Capital (MVIC) in the numerator. Examples of Invested capital multiples are MVIC/EBITDA, MVIC/Revenue, etc.
  2. There are two types of valuation multiples derived from guideline public companies; they are:
  3. Value multiple is an inverse of a capitalization rate or vice-versa. For example, the Price to Earnings ratio is an inverse of Earnings yield (Earnings/Price). This explanation is important to be understood while performing multiple size adjustments, as we will see going ahead.
  4. Companies listed on stock exchanges can be classified in deciles based on market capitalization as a size measure. Size premium is computed for each decile which is equal to the difference between actual excess return and excess return estimated by a return-generating model such as CAPM for the stock. Actual excess return is the historical return on the stock over and above the risk-free rate, while excess CAPM return is the equity risk premium (ERP) affected by the beta. Thus, a company in the 10th decile will be smaller than the company in the 7th decile and, therefore, command a higher size premium.
  5. Size adjustment in multiples depends on the type of multiple. Size premium is estimated based on market capitalization, i.e., equity value. Therefore, while dealing with Invested capital multiples, the difference between the size premium of the subject company and the guideline company is adjusted for the ratio of equity value to invested capital of the guideline company.
  6. Size premium differences between the subject company and guideline company represent a capitalization rate of earnings, so while dealing with revenue multiples, an additional adjustment for the ratio of revenue to earnings must be made in size premium difference.

 

Numerical Illustration

Suppose the subject company is a privately held company that falls under the 10th decile, and one of the guideline public companies falls under the 8th decile with the following information:

 

Price to Earnings

               11.11

MVIC to After-tax EBIT

               12.50

Price to Revenue

                  1.39

Revenue to Earnings

                  8.00

Revenue to After-tax EBIT

                  3.20

Equity to MVIC

40.0%

 

 

 

Adjusting PE ratio for Size

Size premium difference between 10th and 8th decile

3.56%

Guideline PE ratio

        11.11

Equity capitalization rate (1 / 11.11)

9.00%

Adjusted capitalization rate (9.00% + 3.56%)

12.56%

Size Adjusted PE ratio (1 / 12.56%)

          7.96

Adjusting MVIC to After-tax EBIT for size

Guideline MVIC/After-tax EBIT ratio

        12.50

MVIC Capitalization rate (1 / 12.5)

8.00%

Equity to MVIC (Given)

40.00%

Adjusted Capitalization rate (8% + (3.56% x 40.00%))

9.42%

Size-adjusted MVIC/After-tax EBIT ratio (1 / 9.42%)

        10.61

 

Adjusting Price/Revenue Multiple

Price to Revenue Multiple

          1.39

Revenue to Earnings (Given)

          8.00

Equity capitalization rate (1 / 1.39)

71.94%

Adjusted Capitalization rate (71.94 % + (3.56% *8))

100.42%

Size Adjusted Price to Revenue Multiple

          1.00

Criticisms of Value multiples Size adjustment

The following points are often mentioned in the criticism of Valuation multiple size adjustments:

  • The existence of size premiums is still an issue of debate.
  • The calculation methodology of size premium is considered inappropriate or ambiguous by many.
  • Size adjustments are not entirely accepted by the court of law.

Interactions between Cost of capital and Size adjustments

The subject company might have a much higher cost of capital than guideline public companies, mainly due to the existence of size premium; in that case, it may not be relevant to use unadjusted value multiples derived from guideline companies for valuing the subject. Value multiples should be adjusted for size disparity before using them to determine the fair value of the subject—higher cost of capital for the subject results in larger size adjustment in public company multiples.

Conclusion

Publicly traded companies are usually much larger than most private companies, and the valuation multiple derived from these companies may not be the appropriate benchmark for the valuation of relatively smaller private companies. However, we do have some valuation multiple size adjustment techniques, but they come with their own set of problems. So, should we use these size-adjusted value multiples in business valuation, or should we prefer other valuation methods such as DCF, etc.?

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