Shares buy back: What's behind the pursue of a better EPS?

Shares buy back is when the company buys back part of its free float. This is a good strategy when shareholders are interested in EPS (earnings per share) indicator. But, does it really increases the company value? The answer for me is NO! Look at the example:

A company has annual earning of 6,000, a market cap of 50,000 and 1,000 shares, thus, its shares worth 50 per share.

Imagine the following balance sheet in market values:
TOTAL ASSETS 70,000
Extra cash 2,500
Other assets 67,500
TOTAL LIABILITIES 70,000
Liabilities 20,000
Equity 50,000

If the company buys back shares at market value, it can us its 2,500 extra cash to buy 50 shares. So, it spends 2,500 cash and replace it to 2,500 worthen assets (its own shares), and then, using an accountant measure zero its assets with 2,500 on its equity, reducing the outstanding shares to 1,000 - 50 = 950 shares. So its assets worth 50,000 - 2,500 = 67,500 and its equity worth 47,500.

It's price per share keeps with a value of 47,500 / 950 = 50, but its EPS now is 6,000 / 950 = 6.32.

So the EPS increased. But so does the value to the shareholder? Of course not and the price per share reflects that. Each shareholder will now receive a higher share of the earning, but the 2,500 extra cash that could be immediately distributed as dividends are not available anymore.

Imagine the company has to pay a premium for buying back the shares and make it a 52 per share.

With the same 2,500 extra cash, the company can only buy now 48 shares, reporting a loss of (52 - 50) * 48 = 96 on its equity. Automatically the company replaces 2,500 extra cash with assets worthing 50 x 48 = 2,404 and its equity value decreases from 50,000 to 49,904.

After zeroing the treasury shares, its total assets worth now 67,500 and its equity 49,904 - 2,404 = 47,500 . The outstanding shares now are only 1,000 - 48 = 952 shares, worthing 47,500 / 952 = 49.90 per share.

It's earning per share are now 6.30, but, again, it doesn't mean the company created value to the shareholder. Actually, as we can see through the share value, the company destroyed value to the shareholder buying shares over its market price.

To conclude, what we have to understand is that, in the very first moment, before buying back shares, the equity value was the expected earning discounted to present value (6,000/ 12.63%), plus the cash value of 2,500. The discount rate was obtained doing th reverse calculation : 6,000 / (50,000 - 2,500). If we make the calculation for all the examples before, we see that the discounted rate, that is the profitability expected by the shareholder and associated with the business risk, keeps the same in all the cases, 12.63%.

But if your bonuses are based on EPS indicator, don't try to explain this to your boss.