How do you derive P/B and P/S?

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iregula

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Schweser doesn’t do a good job in deriving these two ratios. It just says
P/B = (ROE - g)/(r-g)
and P/S = (E/S)*(1-b)*(1+g)/(r-g)
Can someone explain how these were derived using the gordon growth model?
 
1. P/S ratio: (since this is easier)
P = D1/ (r-g)
D1 = E1 * (1-b)
so P = E1 * (1-b) / (r-g)
P = E0 * (1-b) * (1+g) / (r - g)
Divide by S on both side
P/S = E/S * (1-b) * (1+g) / (r - g)
E/S = Net Profit Margin.
So P/S = Net Profit Margin * (1-b) * (1+g) / (r - g)
P/B Ratio
=============
Earnings Next year / Book Value previous year= ROE (does that make sense)
Or ROE = E1/B0
P/E1 = (1-b)/(r-g)
So
P/B0 = E1/B0 * (1-b) / (r-g)
= ROE * (1-b) / (r-g)
= (ROE * b.ROE) / (r-g)
= (ROE - g) / (r-g)
 
Last part, is this an error CP?
= ROE*(1-b)/(r-g)
= (ROE-ROE*b)/ (r-g)
Remember, b = retention rate and ROE*b = growth rate (the earnings retained in business not paid out as dividends)
= (ROE - g)/(r-g)
 
Glad to know I’m not the only geek who derived the formulas for himself in the margins of Schweser :)
It really helped cement it in my memory.
 
= ROE * (1-b) / (r-g)
= (ROE * b.ROE) / (r-g)
This is a typo by cpk above (as already mentioned by AliMan)
= ROE * (1-b) / (r-g)
= (ROE - b.ROE) / (r-g)
= (ROE - g)/(r - g)
 
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