- How are fractional shares handled?
- How many shares of each company are there?
- Are the shares of XYZ to pay for ABC added before or after the price is set at $16?
For the first and last questions, I can do this multiple ways. For the middle question, I'll just make up values. If you want different ones, you will have to redo the math.
I am going to assume that you participate in the merger exchange, swapping your share for their offer.
If you own one share, it depends how they handle fractional shares. Your original one share of ABC can be worth either one share of XYZ or 1.05 shares of XYZ. If you get one share, you typically get an additional $.80 cash to make up for the fractional share.
You might ask why you don't just get $20 cash and one share of XYZ. Consider the case where you own twenty shares of ABC. Then you'd own twenty-one shares of XYZ and $384. No need for fractional shares.
Beyond all this though, the share value of XYZ is not set autocratically. The shares might be worth $16, $40, or $2 after the merger. If both stocks are perfectly valued and the market is aware of that value, then it will depend partially on the number of shares of each.
For example, if we assume there are 10,000 shares of ABC and 50,000 shares of XYZ (including the shares paid for ABC), then their initial market values are $320,000 for ABC and $800,000 for XYZ. XYZ is paying $360,000, so its value drops to $440,000. But it is gaining ABC, which is worth $320,000. Net value now is $760,000 or $15.20 per share.
This has assumed that the shares transferred from XYZ to the shareholders of ABC were already included in the market value. This may mean that the stock price was previously $20 or so with almost 40,000 shares in circulation. Then they issued new shares, diluting the value down to $16. We could start at 50,000 shares at $16 and end up with 60,000 to 60,050 shares at $13.332 to $13.333 per share. Then XYZ is really only paying $326,658.31 for ABC. That's a premium of only $6,658.31 for ABC and gives a final stock value of $13.222 per share.
The problem though is that in reality, there is no equivalent of perfect value. So I say again that the market value might be $15.20 (the theoretic answer that best fits the question given the example quantities of shares), $13, $20, or something else. It will depend on how the market perceives the deal. Is the combined company worth more or less than the sum of its parts?
And beyond this, you will have $19.20 to $20 in cash in addition to your XYZ share (or 1.05 shares). Assuming 1.05 shares, that would be $15.96 plus the $19.20--that's $35.16 total in theory or anything from $19.20 up in practice. With the givens, the only thing of which you can be sure is the $19.20 cash. The value of the stock is up in the air.
If XYZ is only privately traded, this is still true. The stock is worth the price that someone will pay for it. The "someone" is just more limited with privately traded stocks.