A Little Puzzle?

In the UK under certain circumstances you can use the Retail Margin VAT Scheme. There are several ways to apply this scheme, the first, the VAT is calculated on your Gross Profit and you apply this rate as your effective rate of VAT. The second, and the one I use, is per transaction, the amount of VAT you pay depends on the amount of profit received for each sale that the Retail Margin Scheme is applicable. The difference between the UK and some EU countries is the sales tax on art is a fixed but substantially reduced rate.

This worked all very well until Artist Royalties (AR) came along. The wizards at DAC's decided to follow the EU model and use a banded scale based upon the Euro Day Rate which may impact on the bands to calculate Artist Royalty. It would be easy if the sales staff quoted a price plus AR, oh no, they give inclusive prices, this price is binding as it has been accepted.

To calculate the AR you need to know the Profit but to calculate the Profit you need to know the AR. Two unknowns!

The sale is £75,000 inclusive of both VAT and Artist Royalty
The cost is £50,000.

The Euro Rate is 1.3962 based on 16th November 2007
The AR bands are €50,000 @ 4% and €200,000 @ 3%
Vat 17.5% is calculated on the Profit element only
Atist Royalty is exempt from VAT

How much is the Profit?
What is the Vat Payable?
What is the Amount of Artist Royalty due?

This is the link to the AR Calculator.

http://http://resale.dacs.org.uk/ARRCalculator.aspx

I found a way in Excel to work this out but it is less than elegant and to me using Excel is like surrendering.

Simon