AFAIK, borrowing money does not change Equity, because it increases Assets (more money in the bank) and Liabilities (more debt) by the same amount so Equity stays the same.
1. Profit/loss measures changes in equity resulting from operating activity, as opposed to financing activities (which just rearrange how the company is financed).
2. Examples of financing activities are taking out (or paying back) loans, issuing (or buying back) shares, and issuing dividends.
3. Some (not all, as you point out!) of those financing activities will increase or decrease equity. So, when thinking about profit as the rate of change of book value, you should be careful add back any changes that are the result of financing activities. (specifically: ignore changes in equity due to money going to, or coming from, shareholders)
- Your bank account (an asset) goes up by $1MM
- Your loan account (a liability) goes up by $1MM
So equity is unchanged at that point.
But every month after that, you'll be charged interest:
- Loan account (liability) increases (CR)
- P+L account (equity) decreases (DR)
Can you in fact do that? It's possible with a residential mortgage in the US, because there are laws prohibiting prepayment penalties. And I think even those don't apply to refinanced mortgages?
In reality, increasing debt to a certain point also increases risk, which in turn increases return on equity.
When a company takes a loan, even if that loan is so large as to make insolvency almost inevitable, there is no impact on equity (book value).