The company buys back shares at its own discretion. They are not...

The company buys back shares at its own discretion. They are not obliged to buy and they will determine what price they want to buy at and how many on a day by day basis. Companies have a view as to what constitutes an under-valued share price and will buy at or below that. My observation from other such schemes is that it usually results in supporting a limit at the the low end rather than raising the price. As Dewey has indicated, market forces can over-ride such a limit and company performance has a stronger impact. Sometimes companies indicate that they will intervene on the market if the share price falls a certain percentage below a valuation measure, such as Price to NTA, PE etc. That means there is no fixed price that they will buy at but it will move as the company value moves.
I do not know how IPH will approach its buy-back plan but you will always be told when they have bought and how much, on a daily basis.