Magento 1.9 Cart Tax Vat

I have a client who wants to show the products without VAT, but the prices are charged with VAT in the administrator. he requires something like this: Price: $ 1000 calculates TAX VAT backwards so then show price: $ 840 tax vat: $ 160 (19%) total: $ 1000

Is this posible only working with magento configuration values? PS: the price in administrator is set in $ 1000 and includes tax vat. The versión of magento is 1.9.3 Thank you