The private sector uses accrual accounting and has for decades. The difference, of course, with the private sector is that it doesn't have appropriations. So that's a major difference between it and the government and parliamentary sector.
The private sector will have budgets that will be on an accrual basis, but will also have things like cashflow statements, so they will be doing tracking. They will have several different tools available to them, which will give them a full base, so the cashflow, for example, is very important in the private sector.