Is it permissible to purchase a villa owned by one's brother, in which the questioner has a share, using a loan from the electricity company, in order to build a separate villa, with a subsequent settlement between them, given that the value of the villa is equal to or greater than the loan amount?

For a loan to be permissible, it must be free from usurious interest. If it involves any increase or benefit for the lender, it is prohibited, even if a company pays the interest. Murabaha to the one who promises to purchase does not permit you to sell a villa that you and your brother own to the bank and then buy it back from them; because this scenario falls under the forbidden 'inah (buy-back) sale.