All perfect praise is due to Allah, The Lord of The Worlds; and may His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Udhiyah (sacrificial animal offered in E`ed Al-Addha) is a confirmed Sunnah according to the opinion of the majority of the Muslim scholars.
Al-Imam An-Nawawi (May Allah bless him) said: "According to our Madhab (Juristic school), Udhiyah is a confirmed Sunnah to the person who can afford it, and he isn`t obliged to offer it. In fact, this is the view of many Muslim scholars such as Abu Baker, Umar, Billal…..etc." {Al-Majmou`(8/385)}.
One who doesn`t have the price of that Udhiyah as a surplus to his expenses and those of his family isn`t considered among those who can afford it. Therefore, it is better that he doesn`t borrow money to buy it in order not to be burdened financially, and it is feared that he may not be able to pay off this debt in case he died or else.
Salama Bin Al-Akwa narrated: "A dead person was brought to the Prophet (PBUH) so that he might lead the funeral prayer for him. He asked, "Is he in debt?" When the people replied in the negative, he led the funeral prayer. Another dead person was brought and he asked, "Is he in debt?" They said, "Yes." He (refused to lead the prayer and) said, "Lead the prayer of your friend." Abu Qatada said, "O Allah's Messenger (PBUH)! I undertake to pay his debt." Allah's Messenger (PBUH) then led his funeral prayer.(Bukhari).
In any case, if he offered an Udhiyah, which meets the conditions stated in Sharia, from lawful money, then it is acceptable, God`s willing, even if he had borrowed money to buy it and burdened himself unnecessarily. And Allah knows best.