Share buy back effects on share price

I wanted to start a thread on share buy backs and how they effect the share price. Here is my basic understanding. When a company repurchases shares they are decreasing their equity value and also decreasing their number of shares outstanding. By decreasing their equity value, they theoretically also should be lowering their stock price. But if the number of shares outstanding is also decreasing, why wouldn't their share price remain the same?

DISCLAIMER: I understand that there is a difference between book value of equity and that share buy backs are usually a positive sign for market value of equity for shareholders because it increases EPS numbers and also gives equity holders greater value for the positions they hold. I am just asking this question for the purpose of going through the theory behind how someone would answer this in an interview question.