# Financial engineering : Question 7

What are the precise reasons why a share buyback results in an increase in EPS when inverse P/E is higher than the cost of debt after tax?

P/E is equal to the value of shares divided by net profits. Inverse P/E corresponds to an instantaneous book return on an investment. If a company is worth 100 with net profits of 5, its P/E is 20. The inverse of 20 is 5%, which is the dividen return you get when you pay 100 per share, while the net profit for the shareholder is 5.

If the company buys its own shares for 100, it gets an instantaneous book return on this investment of 5%, and if it can borrow at 3% after tax to do so, it makes a profit, which explains why in this situation EPS increases.

But this is purely arithmetic, and depends only on P/E and the after tax interest rate at which the company can borrow, which is not proof of the creation of value.

For more information, see chapter 38 of the Vernimmen.

If the company buys its own shares for 100, it gets an instantaneous book return on this investment of 5%, and if it can borrow at 3% after tax to do so, it makes a profit, which explains why in this situation EPS increases.

But this is purely arithmetic, and depends only on P/E and the after tax interest rate at which the company can borrow, which is not proof of the creation of value.

For more information, see chapter 38 of the Vernimmen.