LBO exercise question

Well, I have got a question. I dont know if this the right place to ask so dont be angry at me if it isn't. I have been training LBO models lately, so easter holidays have been a real blast ahaha. I am currently doing a carlyle lbo exercise and there's something that I am not sure about it.

My question is about Equity Value and Goodwill:

1) Carlyle will buy a publicly traded firm with a 25 % premium. Imagine Stock Price = 10$ and 50 Basic Shares Out. and 10 stock options at 5$. Using the Treasury Stock Method, new shares issued is 5 (using the 10$) and so fully diluted shares outstanding = 15. Equity value would be 10$ * (1+25%) *15. But I have seen other people's solutions where they completely ignore the stock options, while others use the 10$ * (1+%premium = 25%) as the repurchase price, which hecking baffles me. How would you tackle it?

2) Now about Goodwill = Equity Value - Total Assets + Liabilities + (Existing Goodwill?), so does Goodwill accumulate? It is the only way my BS balances after 2 hours looking at what the heck was wrong on the model.

Bonus Question: They also mention that this is a stock deal so "no step-ups in the basis of the assets". So we don't do anything to PP&E, Intangible assets, and other L.T assets, right?

I'm happy to share the Carlyle exercise and my model as soon as I have finished (although I am still a rookie on this). I am in a recruitment process of a small PE firm so any help would be appreciated! Thank you!