# Equities: Justified PE, P/B, P/S, dvd yield

Can anyone explain what is going on with the “justifying” of the multiples? PE: [(1 - b) x (1 + g)]/(r - g) P/B: (ROE - g)/(r - g) P/S: [(E/S) x (1 - b) x (1 + g)]/(r - g) Dividend Yield: (r - g)/(1 + g) I don’t understand the logic of these formulas

As you know, what we calculate as intrinsic value by using different metholodigies (DDM, FCFE etc.) is not equal to the security’s price most of the time. Those “justified” formulas give you what the ratios would be if the price equaled the intrinsic value. So, if you find that the justified P/E is 10 while the P/E calculated with the market price is 8, you should infer that the stock is overpriced.

They’re mathematical derivations of gordons growth model, according to fundamentals. GGM: P0= D1/r-g For PE, divide both sides by E: P0/E1= (D1/E1)/r-g = 1-b/r-g P0/E0= (D0(1+g)/E0)/r-g = (1-b)(1+g)/r-g For PB, start with leading PE ratio. Remeber E1= ROE x B0 P0/E1 = 1-b/r-g P0/ROExB0= 1-b/r-g Therefore… P0/B0 = ROE(1-b)/r-g = ROE-g/r-g For PS, remember D0= Sales x Profit Margin x payout ratio = S x (E0/S0) x (1-b). To get D1, multiply it by (1+g). Therefore, just rearranging GGM: P = D1/r-g = (S(E0/S0)(1-b)(1+g))/r-g To get PS, divide both sides by S: P0/S0 = (E0/S0)(1-b)(1+g)/r-g Yay? This way, you also know what driver the various ratios. Hope that helps.

Oh, and dividend yield is D0/P0… P0 = D1/r-g = D0(1+g)/r-g P0/D0 = 1+g/r-g Invert them… D0/P0 = r-g/1+g

revisor Wrote: ------------------------------------------------------- > So, if you find that the justified P/E is > 10 while the P/E calculated with the market price > is 8, you should infer that the stock is > overpriced. Just a slight correction. Stock would be underpriced in this case. Just a typing error, i guess.

Wow…thanks so much.

Thank you rus1bus for the correction… This is another issue in the CFA process; being aware of what your are dealing with, P/E or E/P (earning yield) etc…

Question: Is the statement below correct? For P/E and P/S, we include (1+g) in the numerator ONLY IF we are looking for trailing justified multiples. If we want leading multiples, DO NOT multiply by (1+G) in the numerator. That is my understanding…