Is the father obligated to pay for the sacrificial animal that his son gave him from his livestock?

If the father owns the sacrificial animal through a valid ownership, whether by gift or purchase, it is permissible for him to offer it as a sacrifice. It is not a condition for the permissibility of the sacrifice to pay its value. Rather, he may sacrifice it even if he acquired its ownership through a donation, such as charity or a gift, so he is not obliged to pay its price.