A firm had a net income of $100 per share last year, with a retention rate of 10%. In the first day of the current year, this firm is considering increasing its retention rate to 20%. This would reduce dividends in the short run and increase dividends in the longer run. How long would it take for dividends to be higher under a 20% retention rate instead of a 10% retention rate?

The answer is T > 11.95. I need to know to get to that. Thanks