An apparatus and method are provided for using predicted result values. The apparatus has a processing unit that comprises processing circuitry for executing a sequence of instructions, and value prediction circuitry for identifying a predicted result value for at least one instruction. A result producing structure is provided that is responsive to a request issued from the processing unit when the processing circuitry is executing a first instruction, to produce a result value for the first instruction and return that result value to the processing unit. While waiting for the result value from the result producing structure, the processing circuitry can be arranged to speculatively execute at least one dependent instruction using a predicted result value for the first instruction as obtained from the value prediction circuitry. The request issued from the processing unit includes a signature value indicative of the predicted result value, and the result producing structure references the signature value in order to detect whether a mispredict condition exists indicating that the predicted result value differs from the result value. The apparatus further provides a mispredict signal transmission path via which the result producing structure, when the mispredict condition is detected, can assert a mispredict signal for receipt by the processing unit prior to the result value being available to the processing unit. Such an approach can reduce the misprediction penalty associated with using a mispredicted result value.