# help on Justified P/S

So my understnading is that P/S = [(E/S) (1-b)(1+g)]/(r-g) where (1-b) is the Retition Rate correct? and B being the payout ratio?

I ask because i am thinking my thinking is backwards per Schweser Exam booklet 2 Morning exam question 38. They say that the equation is [(profit margin) (payout ratio)(1+g)] /(r-g)

B = retention ratio. (1-B) is the payout ratio, or the dividends being paid out. So price to sales is basically the net profit margin * payout ratio * (1+g) / (r-g)

thats the same things e/s is the profit margin, 1-b (b =rentention ratio) is the payout ratio.

The second is quite easier to rememebr.

b is the retention ratio. 1-b is the payout ratio. Formula’s correct.

To remember that b is the retention ratio, know that g = b x ROE, the company can only grow if it retains earnings (retains b) and invests them in highest possible NPV projects.

Thanks

Everyone

to save me from digging through my notes JL P/E is always smaller than JT P/E right? and differs by multiplying 1+G to the DPR in the Numerator?

JL P/E {justified leading} must be smaller than JT P/E {justified trading} since in the latter case you use P/E at time zero and have to grow that first dividend by (1+g) before you plug in the price P into the P/E formula. Remember that: P = D (1+g) / (r-g) where D are dividends at time zero. The justified leading uses P/E where E are estimated earnings at time “1”. They sort of already include the “1+g” factor, E(1) = E(0)(1+g) so the term (1+g) cancels out for the leading. Leading: (1-b)/(r-g) Trailing: (1-b)(1+g)/(r-g)

As for the P/S, replace P with the Gordon formula above. Then you get E/S times those multiples. Hope this helps!

I used to always mix up ‘b’ as the payout ratio instead of the retention ratio as well. An alliterative mnemonic device that’s helped me is ‘b’ is what you ‘bring back,’ aka keep/retain.

b = plow B ack ratio; that’s how I’ve always remembered the term.

I would forget about the letters and think payout and retention.

So Justified P/S = trailing P/E * Profit margin, since trailing P/E = (1-b)(1+g)/(r-g).

Why does multipling P/E by PM produce P/S?

Derivation:

Start w/ regular dividend discount model:

Po=Do(1+g)/(k-g)

Note that Do=(Eo*(1-b)) where this just says our dividend equals our earnings times our payout ratio.

Rewrite Po as:

Po=Eo*(1-b)*(1+g)/(k-g)

Divide by So

Po/So=NPM*(1-b)(1+g)/(k-g) since NPM equals Eo/So

(price/sales) = (price/earnings)(net income / sales)

*divide both sides by net profit margin*

(price / sales) (sales / net income) = (price / earnings)

*elminate sales*

(price / net income) = (price / earnings)

The formula uses E/S as a proxy for NPM

Helps if you remember P/S as = Profit Margin * Trailing P/B