Is it permissible to pay half the value of the expiation for an oath in cash, at less than its market price, if that is more beneficial?

The obligatory method, according to the majority of scholars, is to dispense expiation (kaffarah) in the form of food, and this is the fatwa we adhere to. However, if its monetary value is given, following the opinion of those who permitted it—such as the Hanafis or Sheikh Al-Islam Ibn Taymiyyah—there is no harm, provided that any deficiency in the amount is made up.

The method for calculating this according to the Hanafis is to determine the amount of food to be given (half a sa' of wheat or a sa' of dates/barley), then estimate its value multiplied by ten for a single expiation. If the full value is given, then there is no issue. If there is a shortfall, it must be completed for the same poor individuals who previously received it. If that is not possible, the expiation must be reinitiated.

As for Sheikh Al-Islam Ibn Taymiyyah, he does not specify a fixed amount for the expiation. Rather, its value is determined by custom, based on the average food one feeds their own family. So, if the value of a satisfying meal of the staple food is given, that suffices.