Calculating selling price with a certain percentage of profit

Question

I have a math problem and I hope somebody can help me out:

Example

I have a product that costs me 80 dollar to buy. I want to sell it with a 10% profit. The tax authorities will charge 21% tax over selling the product. Now comes the part that makes it difficult for me: Another company will charge me 15% of the selling price including tax.

How can I calculate my selling price to make sure I still have a 10% profit?

Thanks for your answer!

Update

Thanks for all the answers until so far! I hope by describing how far I got shows where I am struggling.

Buy in: 80 dollar

plus profit: 80 x 1.1 = 88

plus taxes: 88 x 1.21 = 106.48

for me: 106.48 x 0.85 = 90.508 for other company: 106.48 x 0.15 = 15.972

My check for the profit: (for me) / 121 x 100 - 80

My check seems to be right if I add 15.5 something to the profit with a selling price of about 125 dollar, but how do I get to that price?

Is the $21%$ tax really on the sales price? Not on the profit? In the United States at least, taxes would be charged on the excess, if any, of the sales price, after commission, over the original cost. That is the tax would be $$.21(.85P-80)$$ where $P$ is the sales price, if that is a positive number. Is this correct? — saulspatz, Aug 08 '18 at 20:03

Rushabh Mehta · Answer 1 · 2018-08-08T20:37:04.883

0

Let's label each important number in this problem. TC is total cost. SP is selling price.

Hence, $$TC = 80 + SP\cdot0.21 + SP\cdot(1+0.21)\cdot0.15$$

Why does this formula make sense? The tax is obviously $0.21$ of the Selling Price, but the company cut is $15\%$ of the SP with tax, which is why we multiply $0.15$ by $(1+0.21)\cdot SP$.

So, $$TC = 80 + 0.3915\cdot SP$$

We also know that we want there to be a 10% profit, so

$$TC\cdot(1+0.1) = SP$$

We substitute to get

$$TC = 80+0.43065\cdot TC$$ $$.56935\cdot TC = 80$$ $$TC = \$140.51$$ $$SP = 1.1\cdot TC = \$154.56$$

So, the selling price should be $154.56.

Edit

Under the assumption that @saulspatz is correct, the tax is slightly different, and takes the form $$0.21(0.85P−80)$$ since the tax is taken on the profit made. Make sure to adjust this process for this formula!

edited Aug 08 '18 at 20:37

answered Aug 08 '18 at 19:57

Rushabh Mehta

13,663

The formula doesn't make sense. The company is not going to charge a $15%$ commission on the tax, for example. – saulspatz Aug 08 '18 at 19:59
"Another company will charge me 15% of the selling price including tax." From his question. – Rushabh Mehta Aug 08 '18 at 19:59
The phrase "including tax" means that that the tax is not deducted from the sales price in determining the amount of the commission. It does not mean "plus tax." – saulspatz Aug 08 '18 at 20:04
I'm sorry, I don't understand, could you explain> – Rushabh Mehta Aug 08 '18 at 20:30
I'm sorry, I don't know what else to say. The OP simply means that the amount of commission charged takes no cognizance of the tax. – saulspatz Aug 08 '18 at 20:33
Huh, I guess I'll delete my answer cuz I'm still not getting it – Rushabh Mehta Aug 08 '18 at 20:33
Look at my comment under the original question – saulspatz Aug 08 '18 at 20:34
Let us continue this discussion in chat. – Rushabh Mehta Aug 08 '18 at 20:37

score 0 · Answer 2 · answered Aug 08 '18 at 21:04

Well, saying that you want to make $10\%$ profit means that you want to end up with $80+0.1\cdot80=\$88$ in your pocket after the sale.

Let's say the selling price is $X$ dollars. If I'm understanding your question correctly, you're going to lose $0.21X$ to tax and $0.15X$ to the other company. So all in all you'll have to pay out $0.21X+0.15X=0.36X$, and you'll get to keep $X-0.36X=0.64X$ in your pocket. So the equation to determine the selling price $X$ is $$0.64X=88.$$

NOTE: If I'm misinterpreting how the tax and the other company's charge are calculated, let me know in comments, and we can adjust the calculation.

Calculating selling price with a certain percentage of profit

2 Answers2

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