So there are 2 ways to find growth rate.
P = D/ (r-g)
solve for g
g = b* ROE
If you are given data for both formulas, what is the tipoff that you would use one over the other?
Well the bottom formula is the sustainable growth rate, the top formula is just the growth rate, and the concepts are slightly different.
If you have a question which has, the price of a stock is $100, D1 is $4 and the required return is 15% based on the CAPM, then what is the implied growth rate, you clearly use the above formula, because it isn’t asking about the sustainable growth rate (even if the vignette has information about ROE retention rate, dividend payouts, etc).
You would just go: P/D1= 1/(r-g)
D1/P = r - g
g = r - D1/P
Or however you want to manipulate it algebraically. Just remember that there is a difference between the implied growth rate (when you have 3 of the 4 variables necessary) and the sustainable growth rate, so look for the words implied and sustainable.
While I would use the same tip-offs mentioned to choose between formula 1 and 2 I have to disagree slightly. Formula 1 also implies a sustainable growth rate, as this values a perpetuity which grows at g forever (so g better be sustainable or the formula should not be applied).
Formula 1 doesn’t imply a sustainable growth rate simply because the growth rate implied by the market can be unsustainable.
Unsustainable growth rates are a subset of all possible growth rates. Simply plug in an unsustainable growth rate into the formula, and solve for price; the formula will work fine. Or simply choose a price which implies an unsustainable growth rate for the company in question, the formula will still work fine. Does this mean the company can sustain that growth rate in perpetuity based on current information? No, because the growth rate is unsustainable. Nevertheless, that is what the implied growth rate is at the discount rate, price, and D1 in question.