If you want to verify the program's answer the easiest way is to start with the gross that it came up with and work back down. Another thing to note is that there may be more than one Gross that comes back to the desired net, because of interaction between different deductions.
The general case of net->gross is distinctly non-trivial to approach analytically. Consider the case where there is a pension deduction that is itself a percentage of the gross and is tax deductible but does not gain NI relief, and a student loan deduction which kicks in at an entirely different threshold, and there is also a council tax attachment whose value depends on net pay before the attachment is considered! Furthermore many of the statutory deductions depend on step functions rather than being pure percentages. The only general solution involves trial and error.
-- Edited by Tom McClelland on Tuesday 24th of September 2013 01:55:55 PM
Can anyone point me towards where I can learn the procedure for "Grossing Up"?
I have a Director who wanted to receive £3000 pay for month 4, and my payroll program came up with a result and calculated the tax and NI applicable, but I want to understand how to do it "longhand".
You can only do it longhand by trial and error, in general (something that computers are very good and fast at). You guess at an answer and see what net comes back, then based on that you guess an adjustment to answer and try again, and repeat until you find a gross that comes back to the net you want.
You would need the taxable pay to date at the end of month 3, the tax paid to date at the end of month 3, the director's tax code for month 4. If you give me the answer your system gave you for the gross pay, tax and ni, I will stir the grey matter and see if I can calculate it and then show you the steps?
But learning the steps on this one calculation won't work for a different employee on a different tax code, earning a different amount and with different ytd figures, if I were you Andy I would be happy with whatever the software tells you!
Thank you all for those comments - all very interesting and useful to know. They confirm, more or less, the approach I had been left with when fuddling my way through the problem.
In this case there is a student loan repayment to consider as well, so I am taking Tom's advice and trusting to 12Pay.
I don't think it would be too difficult to do longhand and may be useful to learn for occassions when someone may ask for £x net.
You could use trial and error but would take too long. What would be better would be to set up some sinultaneous equation formulas in excel.
Jasp
I don't think it would be too difficult to do longhand and may be useful to learn for occassions when someone may ask for £x net. You could use trial and error but would take too long. What would be better would be to set up some sinultaneous equation formulas in excel. Jasp
The formulae aren't linear, they are step functions. You can get within a £ or 2 with a linear approximation, but you can then only find the correct answer with trial and error.
