## Cl

Revenue Multiple

There are two things worth noting in this distribution. The first is that revenue multiples are even more skewed towards positive values than earnings multiples. The second is that the price to sales ratio is generally lower than the value to sales ratio, which should not be surprising since the former includes only equity while the latter considers firm value.

Table 20.1 provides summary statistics on both the price to sales and the value to sales ratios.

Table 20.1:Summary Statistics on Revenue Multiples: July 2000

 Price to Sales Ratio Value to Sales Ratio Number of firms 4940 4940 Average 13.22 13.89 Median 1.06 1.32
 Standard Deviation 131.32 127.26 10th percentile 0.15 0.27 90th percentile 13.25 12.89

The average values for both multiples are much higher than the median values, largely as the result of outliers - there are firms that trade at multiples that exceed 100 or more. The price to sales ratio is slightly lower than the value to sales ratio but that is not surprising since the former uses only the value of equity in the numerator whereas the latter looks at firm value.

psdata.xls: There is a dataset on the web that summarizes price to sales and value to sales ratios and fundamentals by industry group in the United States for the most recent year.

### Analysis of Revenue Multiples

The variables that determine the revenue multiples can be extracted by going back to the appropriate discounted cash flow models - dividend discount model (or a FCFE valuation model) for price to sales and a firm valuation model for value to sales ratios.

Price to Sales Ratios

The price to sales ratio for a stable firm can be extracted from a stable growth dividend discount model.

P0 = Value of equity

DPSi = Expected dividends per share next year r = Required rate of return on equity gn = Growth rate in dividends (forever) Substituting in for DPSi = EPS0 (1+gn) (Payout ratio), the value of the equity can be written as:

Defining the Net Profit Margin _-0-, the value of equity can be written as:

Sales per share p _ (Sales0)(Net Margin)(Payout Ratio)(l + gn) P0

Rewriting in terms of the Price/Sales ratio,

The PS ratio is an increasing function of the profit margin, the payout ratio and the growth rate and a decreasing function of the riskiness of the firm.

The price-sales ratio for a high growth firm can also be related to fundamentals. In the special case of the two-stage dividend discount model, this relationship can be made explicit fairly simply. With two stages of growth, a high growth stage and a stable growth phase, the dividend discount model can be written as follows:

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