Question: What is the evidence that it is allowed to pay zakaat by value, and not only by the specified types of property mentioned in hadith, such as wheat or sheep?
Answer: Paying by value is allowed according to the Hanafis, and also according to Al-Bukhari (the hadith collector). Some evidences are:
1. Mu3aath, when sent by the Prophet (may Allah raise his rank) to Yemen to collect zakaat, ordered the people to give him clothing instead of wheat and barley because it would be easier for them and better for the people in Madinah.
2. When Abu Bakr and Uthman distributed donations (3ataa', this is distributed to support teachers and scholars and other people that benefit society), they would ask if the receiver had any zakaat due. They would then subtract the value from the donation, without asking whether it was an silver, gold or goods.
3. The Prophet ordered those who had a 4 year old camel due, could pay a 3 year old plus two sheep (if easy) or 20 dirham. This shows that zakaat is by value, because two sheep could be more worth than a 4 year old weak camel.
4. The Prophet (may Allah raise his rank,) when he saw an exceptionally nice camel among those collected for zakaat, asked the collector "what is this?" (because only medium quality animals should be taken) The collector answered that he had traded it for two lesser animals. The Prophet approved this, and that shows that it is not the particular animal of a particular age that is due, but the value of it.
5. The obvious purpose of zakaat is to provide livelyhood for the poor. Do you not see that Allah ordered us to give zakaat, and also promised all creatures rizq? And that he gave some of them through by working on reasons and others through zakaat? Their livelyhood needs many different things, and they are not all covered by giving them animals. In fact, giving wheat or sheep may force them to go and sell these things at a discounted price -- if what they need at the moment is something else.
6. Whether you give a person wheat or the money to buy it, it serves the same purpose. The only difference is that money is better, because it give the poor the flexibility to choose what the need. The Prophet said that zakaat of fitr is a "tu3mah" for the poor, which means something like "a source of income". Zakaat was not prescribed to honor wheat!
... and Allah knows best.