Whether it be to take advantage of stock undervaluation or in order to distribute part of their profits to shareholders, firms may buy back their own shares. One of the ways they do this is by including accelerated share repurchases as part of their repurchase programs. We study the pricing and optimal execution strategy of an accelerated share repurchase contract with a fixed notional. In such a contract the firm pays a fixed notional F to the bank and receives in exchange a number of shares corresponding to the ratio of F to the average stock price over the purchase period (the duration of this period being decided upon by the bank). From a mathematical point of view, the problem is related to both optimal execution and exotic option pricing.