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$sp$ = sell price

$cp$ = cost price

$p$ = profit

$m$ = margin

So to get $p,$ we do:

$$sp - {sp\over6} - 0.08sp - 0.024sp - cp$$

or, with figures:

$$12.99 - {12.99 \over6} - 12.99 \times0.08 - 12.99 \times0.024 - 8.63$$

This gives $0.84$ profit.

To get margin, we do:

$0.84 / (12.99 / 1.2)$

This gives: $7.8\%$ margin

What would the formula be if we wanted to get the sell price / price to sell at, with a margin of $5\%$?

Apologies for the formatting, I'm new here.

lotmids
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  • There is a MathJax tutorial at https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – saulspatz May 23 '19 at 13:25
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    Why are you dividing by 1.2 to calculate margin? – Vizag May 23 '19 at 13:30
  • Shouldn't it just be profit/sp – Vizag May 23 '19 at 13:30
  • @Vizag divided by 1.2 to take off VAT tax at 20% – lotmids May 23 '19 at 13:33
  • I tried to format your post, but there seems to be a conflict. In the general equation, you multiply $.08sp$ by $.24sp$ but when you substitute numbers, you add them. I assumed that the latter is what was intended. Please check that I haven't changed what you meant to say. – saulspatz May 23 '19 at 13:34
  • Thank you @saulspatz, I tweaked the figures to make it clearer as I made an error in my original posting – lotmids May 23 '19 at 13:39

2 Answers2

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You want:

$$\frac{p}{sp/1.2} = 0.05 \quad (1)$$

$$p= sp - {sp\over6} - 0.08sp - 0.024sp - cp \quad (2)$$

$$cp = 8.63$$

Substitute $p$ as in $(2)$ to $(1)$ and solve for $sp$

Vizag
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You say profit

$$p = s_p - \frac{s_p}{6} - 0.08s_p - 0.024s_p - c_p$$

and margin is

$$m = \frac{p}{s_p / 1.2} $$

We can simplify these two expressions to give

$$ p = \frac{547}{750}s_p - c_p \quad \text{ and } \quad m = \frac{6p}{5s_p} $$

We then substitute:

$$ m = \frac{\frac{547}{125}s_p - 6c_p}{5s_p} = \frac{547}{625} - \frac{6c_p}{5s_p} $$

Rearranging:

$$ s_p = \frac{6c_p}{\frac{547}{125} - 5m} = \frac{750c_p}{547 - 625m} $$

If margin is $5\%$ and $c_p = 8.63$ then $s_p = 12.55$.

Infiaria
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  • Thank you so much for your answer! You are correct that 12.55 would give 5% margin, thank you! But I am confused about your formula. When I try to use your formula using a cost price of 7.39, I am getting negative numbers? – lotmids May 23 '19 at 13:53
  • @lotmids Are you sure? Taking $c_p = 7.39$ and $m = 5%$ gives $s_p = 10.75$. – Infiaria May 23 '19 at 13:54
  • Oh sorry, I see what I was doing wrong! You're a genius. Thank you so much! – lotmids May 23 '19 at 13:56