Don't mess with the second model--stick with the first one.
With the first model you only have to worry about Expected Earnings in the next period. In contrast, (as you indicated) the second model is trying to predict two random variables (or, to be more precise, the ratio of two random variables, which complicates your issue even further).
Besides converting your statistical analysis from a "Hard Problem" to an "Incredibly Hard Problem", there are a couple of things to keep in mind:
- This approach has the added benefit of separating issues related to Business Risk from those related to Financing.
- Whereas the level of earnings in a given year will be a function of many different random variables (depending on things like the current state of the economy, consumer preferences, etc.) shares outstanding will entirely depend on the decisions of the board of directors. Hence, it's probably best to analyze these two issues separately.
- Also, keep in mind that you're forecasting the lefthand side of the equation so that you can use it in some model you have today (in period t) . For many of these models, next-period earnings is the missing link (in fact, dividing by shares outstanding is merely a convenience in these models so that you're speaking in terms of share price and not the entire market value of the company's equity).
 Think of, for example, the Gordon Growth Model (Specifically, when deriving "Justified" Price Multiples).