When a company knows its overall result goal and fixed costs in percentage, it can determine the desired profit margin percentage for single products. For example in big superstores, the single products are priced by multiplying variable costs with a constant:[br][br] [math]\Large \textcolor{blue}{\begin{eqnarray}\text{contribution price}&=&\text{pricing multiplier}\cdot \text{variable costs}\\[br]\text{pricing multiplier}&=&\frac{\text{contribution price}}{\text{variable costs}}[br]\end{eqnarray}}[/math][br][br]Usually, the variable costs are the same as purchase price.[br][br]For a single product, sales proceeds and selling price are the same. If overall desired profit margin in percentage (pm%) is known, the part of variable costs in percentage form the selling price can be determined:[br][br][table] [tr][br] [td]sales procees in % [/td][br] [td]100%[/td][br] [td][br][/td][br][/tr][br] [tr][br] [td]variable costs in %[/td][br] [td]100% - pm%[br][/td][br] [td][br][/td][br][/tr][br] [tr][br] [td]profit margin[/td][br] [td]pm%[/td][br] [td][br][/td][br][/tr][br][/table][br]Thus, the multiplier used with all products can be determined from [br][br]  [math]\Large \textcolor{blue}{\text{pricing multiplier}=\frac{100}{100-\text{pm}}.}[/math]

A batch of chain saws arrived into a hardware store. The profit margin goal is 41%. What should the contribution price be, if the purchase prices were 135 euros for model 1 and 99 euros for model 2?[br][br]As a desired profit margin is 41%, the variable costs should cover 59% of the contribution price. Thus, the pricing multiplier is[br][br]   [math]\Large \frac{100}{59}=1.6949[/math][br][br]Thus, the contribution price for the model 1 should be [math]\Large 135\cdot \frac{100}{59}(=135\cdot 1.6949)=228.81 \approx 229[/math] euros and for the model 2 [math]\Large 99\cdot \frac{100}{59}(=99\cdot 1.6949)=167.80 \approx 168[/math] euros.

When pricing the products, it should be taken into account that part of the products may go off, be stolen, or are sold at discount. [br][br]A shopkeeper bought 400 kg of grapes for 4.46 euros per kilo. The profit margin goal is 25%. A shopkeeper knows from the past, that about 20% of grapes will go off and cannot be sold. What should be price per kilo in the ticket label?[br][br]Only [math]\Large 0.8\cdot 400\text{ kg}=320\text{ kg}[/math] of grapes is expected to be sold. As a desired profit margin is 25%, when variables costs should cover 75% of the sales proceeds. It gives us the table:[br][br][table][tr][td]sales proceeds [/td][td][math]\Large 320\text{kg}\cdot x[/math][/td][td]100%[/td][/tr][tr][td]variable costs [/td][td][math]\Large 400\text{ kg}\cdot 4.46\text{ €/kg}=1784€[/math] [/td][td]75%[/td][/tr][tr][td]profit margin[/td][td][/td][td]25%[/td][/tr][/table][br]We get the selling price with direct variation.[br][br]  [math]\Large\begin{eqnarray} \frac{320\text{ kg}\cdot x}{1784€}&=&\frac{100\%}{75\%}\\[br]x&=&\frac{1784€\cdot 100\%}{320\text{ kg}\cdot 75\%}=7.43\text{€/kg}[br]\end{eqnarray}[/math][br][br]As the price in the ticket label includes also VAT (14% for food), this price must be multiplied with 1.14. Thus, the price in the ticket label is 8.47 /kg.

A gift shop buys some Easter decorations from a store at 4.12€ per piece. A seller thinks, that 30% of decorations may be sold after Easter at 60% discount. What should the price in the ticket label be, if the desired profit margin is 35%?[br][br]Variable costs are 60%, so the sales proceeds for one product should be[br][br]  [math]\Large\begin{eqnarray} \frac{x}{4.12€}&=&\frac{100\%}{65\%}\\[br]x&=&\frac{4.12€\cdot 100\%}{65\%}=6.34€[br]\end{eqnarray}[/math][br][br]This sales proceeds must be covered, although 70% of the products are sold at normal price and 30% at reduced price. Let us mark the original price at [i]x[/i]:[br][br][math]\Large \begin{eqnarray} &&&0.7x+0.3\cdot 0.4x&=&6.34 \\[br]&\Leftrightarrow &&0.82x&=&6.34\\[br]&\Leftrightarrow&& x&=&7.73\end{eqnarray}[/math][br][br]Thus, the price in the ticket label is [math]\Large 1.24\cdot 7.73€=9.59€.[/math]