Selling price to get 5% profit after TAX

[Mohd_KB]

Dear all,

Knowing my cost of production, and my target Profit, i need to sell my product for X USD. Assuming that the tax % is applied after sale and it equals = T. how much should i put on the price tag Y so that after i pay my tax i would still get X exactly.

Thanks in advance,

 

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Is this homework?

?

 

[Mohd_KB]

No, Its a real life example!
I posted in correct forum "Finance/Business Math", right?

 

[Mohd_KB]

I think I figured it out yesterday

Price Tag * TAX% = Price Tag - (Production cost + (production cost * profit %))
Price Tag = (Production cost + (production cost * profit %)) / ( 1 - TAX%)

Is the answer correct?

 

[JeffM]

$$s = \text {sales price per item, } c = \text {cost per item,}\\ t = \text {tax rate, and } p = \text {profit percentage.}$$
$$p = \dfrac{s - st - c}{c} \implies cp = s(1 - t) - c \implies s(1 - t) = c + cp \implies\\ s = \dfrac{c(1 + p)}{1 - t}.$$
Let’s if that works.

Item costs 180. Desired profit rate is 10%. Tax rate is 4%.

Indicated sales price is $$\dfrac{180(1 + 0.1)}{1 - 0.04} = 206.25.$$
So the tax would be $$0.04 * 206.25 = 8.25.$$
$$206.25 - 8.25 = 198.00$$
$$198.00 - 180.00 = 18.00.$$
$$\dfrac{18.00}{180.00} = 10\%.$$
Your answer is correct.