# Adjusting Valuation Multiples and the China Price (Part 1)

** **Size is often a major problem faced by valuation experts using the guideline public company multiples method under the market approach to value. The issue arises when you are valuing a small company (under $214 million in capitalization puts you in Ibbotson’s 10

^{th}decile) and all the comparable guideline public companies have equity market capitalizations in the hundreds of millions, billions or even greater. This raises the question of whether unadjusted pricing multiples derived from multibillion dollar companies are relevant to valuing a small company, even if the business descriptions are similar.

Fortunately, the valuation profession has developed a methodology to address the size problem.[1] [1] Start out by multiplying the share price by the number of common shares outstanding to develop the market value of equity ("MVE") for each of the guideline companies. Add interest-bearing debt and preferred stock to determine the market value of invested capital ("MVIC") for each company. Next develop sales and income measures for each company for the last 12 months prior to the valuation date. Remove items not related to the ongoing operations of the business, such as income from discontinued operations and goodwill impairment charges.

With this data one can easily calculate the following pricing multiples:

¨ MVE / Net Income (commonly referred to as the P/E ratio)

¨ MVIC / After-tax EBIT (defined as earnings before interest, less income taxes)

¨ MVIC / EBIT

¨ MVIC / EBITDA

Historical returns on marketable securities derived from common sources such as Ibbotson or Duff & Phelps indicate that small companies are riskier than larger companies, so the unadjusted guideline company multiples can be adjusted for the risks associated with the smaller subject company of the valuation.

The MVE/Net Income (P/E) multiple for the guideline companies can be adjusted using the formula:

Adjusted multiple = 1 / [ (1 / multiple) + X ]

Where:

X = The difference in the discount rate due to size.

The adjustment formula is based on the assumption that the inverse of a company's P/E ratio, the E/P ratio, is the capitalization rate for the company's equity. X, the size adjustment, is calculated as the difference in the total return of the guideline company’s stock decile (per Ibbotson) less the Ibbotson 10^{th} decile return (in which the subject company being valued would lie).

To show how this works in action, let’s take a guideline company whose MVE of $5 billion places it in Ibbotson’s 3^{rd} decile. The unadjusted P/E (MVE/Net Income) was 14.9. X, the difference in the return of the 3^{rd} decile versus the 10^{th} decile was 7.07%. Using the adjustment formula produces an adjusted P/E multiple of 7.3, a significant difference from the unadjusted multiple.

Just as the P/E ratio represents the ratio of a company's equity value to the income the equity investors receive, the company's MVIC/After-tax EBIT ratio represents the ratio of a company's invested capital (debt and equity) to the return that holders of a company's debt and equity receive. Consequently, the After-tax EBIT/MVIC ratio represents the capitalization rate for the Company's invested capital. The invested capital capitalization rate equals the Company's weighted average cost of capital ("WACC") less its growth rate.

The MVIC/After-tax EBIT adjustment is made using the following formula:

Adjusted multiple = 1 / [ (1 / multiple) + e X ]

e = The ratio of the equity value to the total

invested capital of the guideline company.

X = The difference in the discount rate due to size.

The WACC is affected by risk adjustments to the equity discount rate proportionately to the extent that equity contributes to the total invested capital of the company. This is why the "e" factor is used to adjust the size discount "X."

__ __Other MVIC multiples can be adjusted using a similar methodology. The adjustments are made using the following formula:

Adjusted multiple = 1 / [ (1 / multiple) + a e X ]

Where:

a = The scale factor, which converts the base measure of the benefits to an alternative measure of the benefits for the guideline company.

e = The ratio of the equity value to the total invested capital of the guideline company.

X = The difference in the discount rate due to size.

The "a" factor is the ratio of one MVIC multiple to MVIC/After-tax EBIT. For example, to adjust multiples of MVIC/EBIT, a commonly used valuation multiple, one would calculate "a" = EBIT/After-tax EBIT.

So now we have a quantitative methodology for adjusting multiples to fit the small privately-held company. But wouldn’t it be easier if we could find appropriate 10^{th} decile guideline companies to begin with? Then no adjustment would be necessary.

Unfortunately many American industries are either so large or so consolidated that no small public companies remain. This is often true in older, established industries. The microcap area of the *the 10 ^{th} decile guideline public company!*

(In part 2 next week, we will discuss the perspective that

[1] [2] Hitchner, __Financial Valuation - Applications and Models__, Second Edition, p. 311. Wiley Finance