The company will give him a loan equal to the price of what he wants to buy; can he tell them a figure greater than the real price, so that he may take a bigger loan?

Praise be to Allah.

What you must do is fulfil the conditions stipulated by the company from which you are borrowing the money, and you should spend the entire amount that you borrow on purchasing the land. As for purchasing the land with some of that money, as mentioned in the question, then writing in the contract that you bought it for more than it really cost, this is not permissible, because it comes under the heading of deceit, cheating and lying, and it is breaking the condition that was stipulated. The basic principle is that you must fulfil the conditions that are stipulated between you and the company. It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “The Muslims are bound by their conditions.” Narrated by Abu Dawood (3594); classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

In al-Mawsoo‘ah al-Fiqhiyyah (35/238) it says: A person may commit himself to something, so that becomes binding upon him in shar‘i terms, so long as it is not contrary to Islamic teachings. In other words, Islam regards his committing himself to it as binding. That includes contracts; if two people make a contract between themselves, the rulings thereon become binding on them, as in the case of a sales contract, for example. It makes it binding upon them to transfer ownership of the sold item to the purchaser, and to transfer ownership of the price to the seller. Another example is an employment contract, which makes it binding upon the hired worker to do the work, and it makes it binding upon the one who hired him to pay him his wages. This also applies to any valid condition that the person who enters into the contract takes upon himself; it becomes binding upon him. That is because Allah, may He be exalted, says (interpretation of the meaning): “O you who believe! Fulfill (your) obligations” [al-Maa’idah 5:1]. And the Prophet (blessings and peace of Allah be upon him) said: “The Muslims are bound by their conditions.” End quote. 

And Allah knows best.