Help rearranging formula m=(s-c-svr)/s to have s=(something) please

[LostMagician]

Hello. I hope someone can help.

I'm trying to rearrange a formula but I'm struggling. It relates to selling products online.

S is the selling price (ex VAT)
C is cost of products (ex VAT)
V is VAT multiplier - i e. V = 1.2 at current 20% rate for UK tax
R is the rate charged by the online marketplace as a cost of sale. This is a percentage that's applied to the selling price (Inc VAT) to determine the fee amount paid
SVR is therefore the amount of fees to pay

M is my desired net margin

I know that:
m = (s - c - svr) / s

I'm trying to rearrange this to have a formula for s = something. This will then allow me to enter m to find s. For example, if I want to hit a margin of 12% then I can enter that (along with the costs, VAT rate and fee rate) to find what selling price I need to hit that margin level. I just can't isolate s as my algebra is rusty to say the least.

I'm ultimately trying to get to a formula I can use in a Google Sheet document, which spits out a suggested selling price after I enter my costs and desired margin.

Any help would be much appreciated.

Thanks in advance

 

[LostMagician]

My failed working goes like this:

ms = s - c - svr
c = s - ms - svr
c = s (1 - m - vr)
s = c / (1 - m - vr)

Is this correct working? When I try putting my figures back into this it doesn't stack up so I must be going wrong somewhere. I think it's around the fees that I have something wrong but not sure.

 

[LostMagician]

Sorry - I think I've solved this. I think my working was correct, but it was my spreadsheet working that was incorrect! I've focused so much on the formula I didn't realise some of the number formatting was wrong in my spreadsheet! ?‍

 

[Steven G]

Which step do you think is wrong?

For completion I will point something out.

If you picked values for m, s, c, v and r so m = (s - c - svr)/s you can then check each line to find out which is wrong.

For example s=5, c=10, v=1, r=1 and m= -2 (so -2 = (5-10 - 5*1*1)/5)
Then ms=(s - c - svr) is true since (-2)*5 = (5 - 10 - 5*1*1) or -10 = (5-10-5)

Now we say (incorrectly) ms/s = -c -svr or m = -c-svr which becomes -2 = -10 -5*1*1 = -10-5=-15 AND -2 = 15 is wrong! This means that when we went from ms=(s - c - svr) to m = -c-svr we must have made a mistake--so go and find it.