Find eventual value after adding two percentage figures

A

andytrfs

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Hi

I have a problem which is pickling my brain and I'm not sure what phrase I should be Googl'ing for. I have a horrible feeling the answer is obvious and/or there's a standard formula that is applied in this scenario, so at risk of embarrassing myself ...

I sell items online, so buy at X price, sell at Y and have to pay Z in VAT and fees. I want to add a standard percentage profit margin of 5% of the cost price, then add the VAT and fees to get a selling price, but my problem is that both 20% VAT and 15% fees are removed from the total selling price, i.e. the fees are taken from the price including VAT.

If I add 20% VAT to my initial cost+5%, then add 15% fees, the VAT increases proportionately and vice versa. This leaves me with a net profit below the 5% I started with.

This is the best formula I can come up with (which is clearly wrong):

(((cost price) x 1.05) / 0.85) * 1.2

As an example, assuming my cost price is £10, meaning I want to be left with a net value of £10.50, my formula gives me a selling price of £14.82, but after deducting 15% fees and 20% VAT I'm left with £10.13.

Is anybody able to tell me how I handle this double percentage issue, please?
 
I shall try to answer this, but in the US we do not have VAT so the mechanics are quite hazy to me. I am guessing that the VAT is 20% of the difference between sales price and the sum of fees and cost. I am also guessing that fees are 15% of sales price. Is that correct? If so

s = 1.05c + 0.2(s - c - 0.15s) + 0.15s

s = 1.05c - 0.2c + 0.17s + 0.15s

s = 0.85c + 0.32s

s = 85c/68

So, if I understand how this all works, if the cost is 10 pounds, you want a profit of 0.5 pounds after VAT and fees.

The formula says the sales price would be 12.5 pound. Fees at 15% of sales price would be 1.875 pounds so fees plus cost would be 11.875. That leaves 12.5 - 11.875 = 0.625 for you and the tax extractor to deal with. 20% of 0.625 is
0.125. Paying that to HRH leaves you 0.5.

Now if I do not understand how VAT works, this is utter twaddle.
 
Hi Jeff - thanks for the reply!

Apologies, I should have clarified the VAT, which is 20% of the sale's total amount, not a portion such as the profit margin.

Obviously this means the formula you've kindly given will not give the correct value, but I may be able to work this out myself... if I can fully understand the equation. This is a format I've not come across before, so would I be right in saying...

1.05c = 5% of the cost price.
0.15s = 15% of selling price

If this is correct, how would I know what the selling price is within the formula on the first line? I assume if line 1 is to work out the value of 's', then I can't know what 's' is within the equation itself.

Sorry - this is my total lack of algebra knowledge, although I am a software developer, so I understand variables to a degree.

Thanks

Andy
 
Sorry that I do not have more time today. I am taking my wife to the surgeon.

1.05c is the cost plus 5 percent. That is, to get a profit of 5% of cost you must charge more than the cost. You have to get that cost back before you have a prayer.

Yes, 0.15s is 15% of the sales price. I was not sure why fees would be related to sales price, but that is how I understood what you said.

I'd not worry much about the previous formula if I misunderstand VAT. I thought VAT was not charged on the cost of goods sold, just on the excess. Ignorance. I shall try to work on this during the evening, but that will be late at night for you.
 
Thassa real headspinner, Andy !

I think we can look at it this way (using cost = 10000 to keep it clearer...)
c = 10000 (COST)
p = 500 (5% PROFIT)
-----------------------
k = 10500 (so "receipt" customer gets will "start" with 10500)
v = 2100 (VAT, 20% of k)
-----------------------------
w = 12600 (amount used to calculate fees)
f = 1890 (FEES, 15% of w)
------------------------------
t = 14490 (total collected from customer)

So customer gets this simple receipt:
Purchase: 10500
VAT..........: 2100
FEES.........: 1890
TOTAL.....: 14490

Is that CORRECT?
 
Not a problem at all! I hope your wife is ok!

I initially thought the solution to this was going to be something simple that I was missing, but I assume from your first formula that its more complex than I had envisaged. I've got an algebra knowledge gap I need to fill in order to get to the solution, so any help at all is very much appreciated.

To give a basic example, which hopefully will clarify any murky points I've not explained very well:

(s) Retail selling price: 10.00 GBP
(v) VAT @ 20% of selling price: 2.00 GBP
(f) Fees @ 15% of selling price: 1.50 GBP
(c) Cost price: 6.00 GBP
(p) Net profit: 0.50 GBP

At present, I start with (c) at 6.00 and I know that (f) and (v) are percentages of (s) to be deducted, but I don't have a formula that can tell me that (s) needs to be 10.00 in order to achieve (p) @ 5%.

I have to repeatedly guess what (s) might be and do each of the above calculations until (p) equals 5% of (c). As you can imagine, this is time consuming and highly inefficient when I've got 250 different products and have to price up potential new items to sell on a regular basis.
 
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Hi Denis - thanks for stepping in to help too! I only saw your response after I posted my last reply to Jeff.

I'm actually quite relieved that this is proving to be difficult, as I thought it was me being daft, not being able to see the obvious solution.

To use your example of cost = 10000, the correct selling price would be 16154, as per below:

(s) Retail selling price: 16154.00 GBP
(f) Fees @ 15% of selling price: 2423.10 GBP
(v) VAT @ 20% of selling price: 3230.80 GBP
(c) Cost price: 10000 GBP
(p) Net profit: 500.10 GBP

As you can see, its the selling price (s) of 16154 I need to discover, while starting with (c), wanting to achieve (p) and knowing the constants of (f) and (v).

I hope this is a good challenge and not one that's going to frustrate you (as it has done me for quite some time) !
 
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Let's see if I can help.
Suppose you charge £ 100
You have 15% fees = £ 15
The VAT fees is on £ 100 = £ 20
Now you will receive £ 100-15-20 = £ 65
Let x = the price you paid. Now you want to receive 1.05x which includes your 5% profit.

So you want 1.05x=65, ie x= £ 65/1.05 = £ 61.9047619048
So for every $61.9047619048 you want to receive (which includes your 5% profit) you charge $100

Using your example of wanting to get £ 10.50 you should charge £ (10)(100/61.9047619048)=£ 16.1538461538

Let's see if this works:
Charge £ 16.1538461538
fees= 2.42307692308
VAT fees= 3.23076923077
Now £ 16.1538461538 - 2.42307692308 - 3.23076923077 = £10.50 !!!!!

So simply multiply your cost by (100/61.9047619048) and sell at that price and enjoy your 5% profit.

Note to Denis: HaHa
 
andytrfs said:
(v) VAT @ 20% of selling price: 2.00 GBP
(f) Fees @ 15% of selling price: 1.50 GBP
Click to expand...
Ohhhhhhh: both are calculated from selling price...
So same as one charge @ 35%...

This appeared in your 1st post:
" i.e. the fees are taken from the price including VAT"
I took that as meaning "VAT added to price, then fees calculated...".
So you meant:
" i.e. the fees are taken from the price, so is the VAT"; right?

Well, my 1st mistake this year :(
You're now in Jomo's hands: good luck!
He'll probably charge you 35%!
I would have charged only a Yorkshire pudding :)
 
Wow - thanks !

I take full responsibility for the poor explanation at the start! A simple example is obviously much better than a wordy description. Sorry for leading everyone up the wrong path! Looking back, I've even made a mistake in one of my examples! Doh!

So, to simplify this formula a little further, using my previous example:

(s) Selling price = ?
(c) Cost price = 6.00
(p) 5% profit increase = 1.05
(f) Deductions of 20% VAT + 15% fees = 0.65

(c * p) / f = s

(6.00 * 1.05) / 0.65 = 9.69

... which would result in a selling price that leaves me with cost price + 5%.

Oh my word, do I feel stupid now.

Many, many thanks to you all. You've ended my pain and suffering!
 
andytrfs said:
(s) Selling price = ?
(c) Cost price = 6.00
(p) 5% profit increase = 1.05
(f) Deductions of 20% VAT + 15% fees = 0.65

(c * p) / f = s

(6.00 * 1.05) / 0.65 = 9.69
Click to expand...
Would be clearer if stated this way:

s = Selling price = ?
c = Cost price = 6.00
p = Profit = .05
d = Deductions (.20 VAT + .15 fees) = 0.35

s = c * (1 + p) / (1 - d)
s = 6 * 1.05 / .65 = 9.6923...

And the "receipt" you'd give your customer would look like:
Purchases : 6.30
Taxes..........: 3.39
Total...........: 9.69
 
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