My understanding is that’s only a way to present things : looking back at the 2 examples given, I could say that if I look at it in a customer point of view (in net prices including taxes), I get a 11.9€ discount in the first case, and I get 10€ discount in the second case.
And looking at it in a professional manner I get 10€ discount in the first case (and a professional is not interested in the second case).
So at the end of the day it all depends on who your are sending invoices to. My 200+ clients using an ERP (mostly small businesses) are mainly dealing with professionals so they are happy with a discount before taxes. For the businesses dealing with end customers, most of them are also happy with discounts before taxes as this is the way it is done in France, even in big shops (like DIY shops). However, some customers in a highly competitive area, wanted to make it clear to their customers, what was the final discount (including taxes) for the customer. Also they wanted to be able to type a round net discount (e.g. 10€) so the customer could see the discount clearly.
However, in France (and I suspect it’s the same in any other country), you can not apply a discount on the amount including the taxes (as the taxes go to the government). So you need to apply the discount before tax, and in that case, recalculate the amount to make sure you get the result you want (a 10€ net discount) … but again it is not allowed to discount taxes.
So the example is (100-8.4) + ((100-8.4)/100 *19) = 109€ (compare to 119€ catalogue price)
.In this example, the IP user would type in 10€ and then IP would calculate the discount before tax 100-(100-(10/1.19)) = 8.403…
On the invoice, you could show a 10€ discount after taxes (or more likely on the quote to get the customer interested), but you will have to word it properly to avoid confusing an accountant who won’t be happy with a discount after taxes. If you display on the invoice (which I never did, I always displayed only the discount before taxes on the quote), you might want to display both discounts (before taxes and after taxes), but then again, that might confusing as this can be taken that you are applying both discounts.
To sum up, in France (and I assume in most-all ?- countries) you can not apply a discount after taxes, but you may type in a round amount of net discount that will recalculated as discount before taxes. Then you can create a nice quote with net prices and a tag like “you save X€” (where X is the net discount that has been typed in -10€ in our example), but as an accountant point of view the discount is 8.403… and that should be displayed on the invoice (then again you could have the same tag “you save X€” with the net price as long as you don’t write discount).
Sorry for the long post, but this is quite important to get it right. Still I don’t pretend that this could satisfy everybody, as the one thing I know for sure is that every body need is different (but then again, for the most part it is identical).