# Benham Grossing Up

I cannot find any ‘simple’ explanation for the formula for grossing up re: Benham.

I am dealing with an estate valued at £4.2m; no legacies; full NRB/TNRB; residue 51% to charity & 49% to nieces - IHT reduced to 36%.

The formula I seem to keep finding is:

(R + 2/3N) / (F + 2/3)

R = residue - fine
N = NRB - fine

2/3 = where does this fraction come from?

F = ‘reciprocal of the fraction of the residue which is chargeable - fraction turned upside down’ how is the fraction of the residue determined in order to turn it upside down?

Personally I find the best way to make the appropriate calculation is with a spreadsheet. Make a guess at the correct pre-tax allocation and see which way the post tax allocation falls, then adjust the pre-tax numbers up or down until you get the right post tax result. It should take about 10 minutes.

Paul Davies
Clarke Willmott

Thank you Paul - I’ve done a spreadsheet and calculated the pre-tax/post-tax allocations @ 51/49%.

I’ve deducted the charity’s difference from the charity’s pre-tax and added the nieces’ difference to the nieces’ pre-tax, which I thought would make sense following your post, but there is an anomaly of £25,560 (value of estate less total differences AND charity difference minus nieces difference pre/post allocations both give this figure).

Could you please consider how this anomaly arises - perhaps I’m not adjusting the pre-tax numbers up/down correctly as suggested?

If you have constructed the spreadsheet correctly then you should be able to adjust the pre tax numbers up and down and the post tax numbers are automatically calculated. You just adjust the numbers until the post tax proportions are correct. It should not take very long.

I suggest the following:
The inheritance tax chargeable is 36/64ths of 49% of (£4.2m-£650k) =‘£978,469
The estate after tax is £4.2m less £978,469 = £3,221,531.
The nieces’ share is 49% thereof £1,578,550
The charity’s share is 51% thereof £1,642,981.

According to my method the charities will be entitled to 43.4608% of the estate (=££1,825,354) before tax which gives them 51% after tax.
The nieces get £2,374646 before tax, deducting the £650K NRB means £1,724,646 subject to tax at 36%, tax = £620,873. £2,374646 minus £620,873 is £1,753,774 after tax.
£1,825,354 + £1,753,774 = £3,579,127
51% of £3,579,127 = £1,825,355
QED

NB the 2/3rds fraction only works if IHT is payable at 40% (it’s 40% / 60%), it won’t work if tax is at 36%.