EPS up, when ROE goes down

CFA Level II
#1

I’m not sure if I have an error in my notes, so I wanted to run it by you folks.

The question is: How can EPS go up, when ROE is going down?

EPS = ROE * Book Value Per Share

EPS = (Net Income / # Common Shares Outstanding)

ROE = (NI / Equity), and

BVPS = (Equity / # Common Shares Outstanding)

In my notes, I have two possible answers.

  1. Issue more shares continuously at higher prices, which makes #CSO go up, but Equity goes up a by lot more. So, BVPS goes up, and ROE goes down.

  2. Reduce the dividend payout ratio.

What I want to understand is how it happens through reducing the dividend payout ratio. My guess is that you increase the retention ratio, which increases ending retained earnings, adding to equity - and you have the same effect, where BVPS goes up, and ROE goes down.

I’m not sure if that’s right. Can anyone else shed light on how reducing the dividend payout ratio can increase EPS, while ROE goes down?

#2

Seems correct, mathmatically at least. Not sure what it’s applicable to though for practical purposes.