What should have been the ticket price at least for not to make any loss in the previous example?[br][br]Total costs are 750€, as fixed costs are 550€ and variable costs [math]\Large 50\cdot 4€=200€[/math]. The ticket price must include also VAT but that is not used in sales proceeds. As the VAT for this kind of event is 10%, the ticket price must be [math]\Large x+10\text{\% of }x.[/math][br][br]We can solve [i]x[/i] from costs:[br][br]  [math]\Large\begin{eqnarray} 50x&=&750€\\[br]x&=&15€[br]\end{eqnarray}[/math][br][br]Actually, the ticket price should have been at least [math]\Large 1.1\cdot 15€=16.50€[/math]. It seems, that students forgot VAT in their calculations.

Profit margin calculation can also be used for fixing the price. Please remember, that the prices in margin profit are without VAT, so it must be added in the end.

The margin profit of a product is 30% and variable costs 28€ per one product. What should be the selling price (with VAT) for this product? VAT for the product is 24%.[br][br]Now, we can do the sales proceeds -table for one product. Variable costs must be 70%, as margin profit is 30%.[br][br]  [math]\Large\begin{eqnarray}[br]\text{Sales proceeds} &&\text{ x €} & 100\%\\[br]\underline{\text{Variable costs}} & &\underline{28€ }& \underline{70\% }\\[br]\text{Margin profit} && &30\%[br]\end{eqnarray}[/math][br][br]We have direct variation, where[br][br]  [math]\Large \begin{eqnarray}[br]\frac{\text{Sales proceeds in €}}{\text{Variable cost in €}}&=&\frac{\text{Sales proceed in \%}}{\text{Variable costs in \%}}\\[br]\vspace{12mm}[br]\frac{x}{28€}&=&\frac{100\%}{70\%}\\[br]\vspace{12mm}[br]x&=&\frac{100\%\cdot 28€}{70\%}=40€[br] \end{eqnarray}[/math][br][br]As this is the unit price without VAT (contribution price), we have to add VAT:[br][br]  [math]\Large 40€ + 24\%\text{ of }40€ =1.24\cdot 40€ = 49.60€[/math]

Ice cream is sold in waffle cone. Variable costs for one sold ice cream are 0.80€ and fixed costs 1200€ in a month. What should be the selling price, if the profit should be 10% and sales in a month is 1100 ice creams in average?[br][br]Sales proceeds table looks like[br][br][br]  [math]\Large\begin{eqnarray}[br]\text{Sales proceeds x €} && 100\%\\[br][br]\left .\begin{eqnarray}\text{Variable costs } 1100\cdot 0.80€ \\[br]\underline{\text{Fixed costs }} \underline{1200€ }\end{eqnarray}\big \right \} && \underline{90\% }\\[br]\text{Margin profit} && 10\%[br]\end{eqnarray}[/math][br][br]Based on the table, 90% of sales proceeds must equal to total costs: [math]\Large 1100\cdot 0.80€+1200€= 2080€[/math]. Thus,[br][br][br]  [math]\Large \begin{eqnarray}[br]\frac{x}{2080€}&=&\frac{100\%}{90\%}\\[br]\vspace{12mm}[br]x&=&\frac{100\%\cdot 2080€}{90\%}=2311.11€[br] \end{eqnarray}[/math][br][br]Now, [i]x[/i] is total sales proceeds, so [br][br][math]\Large\begin{eqnarray} 1100y&=&2311.11€\\[br]y&=&2.10€,[br]\end{eqnarray}[/math][br][br]where [i]y[/i] is the contribution price for a unit. The selling price must be [math]\Large 2.10e+0.14\cdot 2.10€ = 1.14\cdot 2.10€=2.40€[/math] at least. The VAT is assumed to be 14%, as for food usually. [br][br]You can also make an equation, where[br][br][math]\Large\begin{eqnarray}[br]\text{sales proceeds}&=&\text{ total costs + profit}\\[br]1100y &=& \overbrace{1100\cdot 0.8+1200€}^{\text{total costs}}+\overbrace{0.1\cdot 1100y}^{10\% \text{ of sales proceeds}}\\[br] 1100y&=&2080€+110y\\[br]990y&=&2080€\\[br]y&=&\frac{2080€}{990}=2.10€\end{eqnarray}[/math]