couple of thoughts...
1. I don't think we're considering only insurance companies here - if Company A is a car manufacturer and Company B is a tire maker 'admissable assets' and 'statutory solvency purposes' will be alien concepts. Important to consider all possibilities if the question is not specific.
2. Acquisitions can be structured in a number of ways - a the main ones are:
a) Company A pays cash to Company B's shareholders in return for Company B's shares (called a 'share deal'), and Company A acquires control of a % of Company B's business (could be 100%)
b) Company A pays cash to Company B to acquire a specific part of Company B's business ('asset deal') - Company B may be selling off a part of the business that isn't making money or doesn't fit well with the rest of its business. Think about a bank selling off it's life assurance book.
In both cases the bank balance reduces (assets down) but this is offset against increase in assets as Company A now own a) shares which will have a market value, or b) a bunch of assets less related liabilities.
3. In practice few companies have the level of cash in their bank accounts to perform this kind of transaction, and have to raise capital through issuing debt or equity to do it:
- issuing its own shares / bonds to current owner of Company B
- issuing shares through a rights offer to raise capital for the acquisition
- issue debt to the market / banks to raise the necessary capital.
4. The real balance sheet impact is the combination of:
a) The value of the acquisition over the price Company A paid for it, and
b) Impact of new capital raised to effect the acquisition
Hope this helps clear things up and good luck for the exam!
