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( + ke,hg) J + (EPS0 )* (Payout Ration )(l + g) (l + gn)

where, g = Growth rate in the first n years ke,hg = Cost of equity in high growth Payout = Payout ratio in the first n years gn = Growth rate after n years forever (Stable growth rate) ke,hg = Cost of equity in stable growth Payoutn = Payout ratio after n years for the stable firm Rewriting EPS0 in terms of the profit margin, EPS0 = (Sales0) (Profit Margin) and bringing Sales0 to the left hand side of the equation, you get:

Price Sales

The left hand side of the equation is the price-sales ratio. It is determined by--

(a) Net Profit Margin: Net Income / Revenues. The price-sales ratio is an increasing function of the net profit margin. Firms with higher net margins, other things remaining equal, should trade at higher price to sales ratios.

(b) Payout ratio during the high growth period and in the stable period: The PS ratio increases as the payout ratio increases, for any given growth rate.

(c) Riskiness (through the discount rate ke,hg in the high growth period and ke,st in the stable period): The PS ratio becomes lower as riskiness increases, since higher risk translates into a higher cost of equity.

(d) Expected growth rate in Earnings, in both the high growth and stable phases: The PS increases as the growth rate increases, in both the high growth and stable growth period.

You can apply this equation to estimate the price to sales ratio, even for a firm that is not paying dividends currently. As with the price to book ratio, you can substitute in the free cash flows to equity for the dividends in making this estimate. Doing so will yield a more reasonable estimate of the price to sales ratio for firms that pay out dividends that are far lower than what they can afford to pay out.

Price Sales

FCFE

Earnings^

Illustration 20.1: Estimating the PS ratio for a high growth firm in the two-stage model

Assume that you have been asked to estimate the PS ratio for a firm that is expected to be in high growth for the next 5 years. The following is a summary of the inputs for the valuation.

Growth rate in first five years = 25% Payout ratio in first five years = 20%

Growth rate after five years = 8% Beta = 1.0

Net Profit Margin = 10%

This firm's price to sales ratio can be estimated as follows:

Payout ratio after five years = 50% Riskfree rate = T.Bond Rate = 6%

PS=0.10

0.115-0.25

(0.115-0.08)(1.115)5 l 0 Based upon this firm's fundamentals, you would expect its equity to trade at 2.87 times revenues.

Illustration 20.2: Estimating the price to sales ratio for Unilever

Unilever is a U.K. based company that sells consumer products globally. To estimate the price to sales ratio for Unilever, we used the following inputs for the high growth and stable growth periods. The costs of equity and growth rates are estimated in British pounds. Table 20.2 summarizes the inputs used in the valuation.

Table 20.2: Inputs for Estimating Price to Sales: Unilever

High Growth Period |
Stable Growth Period | |

Length |
5 years |
Forever after year 5 |

Growth Rate |
8.67% |
5% |

Net Profit Margin |
5.82% |
5.82% |

Beta |
1.10 |
1.10 |

Cost of Equity |
10.5% |
9.4% |

Payout Ratio |
51.17% |
66.67% |

The riskfree rate used in the analysis is 5% (long term British government bond rate) and the risk premium is 5% in the high growth period (due to Unilever's exposure in emerging markets) and 4% in stable growth.

The riskfree rate used in the analysis is 5% (long term British government bond rate) and the risk premium is 5% in the high growth period (due to Unilever's exposure in emerging markets) and 4% in stable growth.

0.1050-0.0867

è (1.1050)5 0 + (0.6667)(1.0867) 5(1.05) (0.094-0.05)(1.1050)5

Based upon its fundamentals, you would expect Unilever to trade at 0.99 times revenues. The stock was trading at 1.15 times revenues in May 2001.

Value to Sales Ratio

To analyze the relationship between value and sales, consider the value of a stable growth firm:

_ , EBIT (1 -1)(1 - Reinvestment Rate) Firm Value0 =-—-—--

Cost of Capital - gn Dividing both sides by the revenue, you get

Firm Value0 _ (EBITj(1 - t)/Sales)(1 - Reinvestment Rate)

Sales

Cost of Capital - gn

Firm Value0 = (After - tax Operating Margin)! - Reinvestment Rate)

Sales

### Cost of Capital - gn

Just as the price to sales ratio is determined by net profit margins, payout ratios and costs of equity, the value to sales ratio is determined by after-tax operating margins, reinvestment rates and the cost of capital. Firms with higher operating margins, lower reinvestment rates (for any given growth rate) and lower costs of capital will trade at higher value to sales multiples.

This equation can be expanded to cover a firm in high growth by using a two-stage firm valuation model.

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