Do justified P/B and justified P/S have same numerator?

i’m confused by these two ratio since the formula seem to indicate they have different numerator §

P/B = (ROE - g) / (r - g) dervied from P/B = (D / (r-g)) / B

P/S = SM * (1 - b) × (1 + g) / (r-g) derived from P/S = (D (1 + g) / (r-g)) / B

Do these indicate D in the first equation is D_1 and D in the second equation is D_0?

If yes, these two would have same numerators. Then can we always use justified P/B to back out justified P/S by

justified PS = justified PB * B / S

In this case, there should have no difference when we use these two to evaulate a stock vs market price since the implied P are same. It is difference only when we use them to compare with industry avg or other company.

oops, wrong subject. it should be “numerator” not “denomiantor”


Never thought about it. I just know that justified P/S has profit margin times growth times payout ratio divided by r minus g. Justified p/B uses what you have. What is SM?