How much should you pay?

Here is part of a write-up I gave my management explaining the use of P/E based valuation of ABC Company we were looking to acquire.

A Note on the profit based valuation process of ABC
"The basic objective of the valuation was to determine what we can pay for a company that can generate about 25% return on equity.

In trying to determine a multiple of profits we can pay for such a company, we would need to find out the organic (meaning, without additional infusion of capital) growth potential that it has. The metric to determine this growth is a function of current ROE and percentage of the retained current earnings. To explain this concept, intuitively, a company with a zero ROE would have no growth since it is not generating any capital for redeployment in the business and would work with same capital as it had in the beginning of a given period. Either the ROE has to turn positive or there has to be additional capital infusion for it to have any growth. For a company generating positive return on capital, the organic growth would, hence be a product of the capital it retains and the ROE. This is the first of the bases of valuation.
Arguably, either of these variables can change – ROE due to change in product profitability or similar and capital due to additional infusion/withdrawal. However, this is a decision down the line that we (as a controlling stakeholder) will make and hence, should not pay the current owners of ABC for. Hence, this metric of organic growth has no subjectivity involved."

Continuing on the above part of my note:-
ROE is the net profit available to shareholders divided by Shareholder's Equity (Book Value). This can be easily found by dividing EPS by Book Value Per Share.