Companies' main object is profitability, which is evaluated with profit margin. Profit margin is normally used for short-term analysis (e.g. a day, a week, a month, or a year). In profit margin calculations, total costs are shared to fixed and variable costs. Profit margin can be expressed either with currency or percentages. Percentages are better for comparing different companies or different products and services inside the company.[br][br]In profit margin calculation, it is always used [b]prices without value added tax (VAT)[/b]. Value added taxes just goes through the company from a customer to the government. They have no effect on company's profitability. Thus, this is valid also for costs. If a company pays some VAT when buying and gets some VAT when selling, it needs to pay only the difference for the government. [br][br]

[b]Sales proceeds (SP)= unit price [math]\cdot[/math] quantity.[/b] Sales proceeds tells, how much money flows in. [br][br][b]Variable costs (C[sub]v[/sub])[/b] changes in the same relation to the sales and production. Variable costs are, for example, material costs, cost prices of selling products etc. [br][br][b]Fixed costs (C[sub]f[/sub])[/b] do not change in the relation to the production or sales. They could be retail and /or equipment rent, fixed salaries, rates, marketing costs etc.[br][br][b]Profit margin (PM) = Sales proceeds - variable costs.[/b] If profit margin is expressed in per cents (=profit margin ratio, PMR), it will tell which proportion of the unit price stays in the company after variable costs. [br][br]  [math]\large \textcolor{blue}{PMR=\frac{\text{profit margin}}{\text{sales proceeds}} \cdot 100\%}[/math][br][br][b]Result (R)[/b] will tell, whether the company is profitable. If the result is negative, the company makes loss. If the result is expressed in per cents, the result is divided with sales proceeds:[br][br]  [math]\large \textcolor{blue}{\text{Result(\%)}=\frac{\text{result}}{\text{sales proceeds}} \cdot 100\%}[/math]

Selling price (p) of a product without VAT is 15€. If 3,900 items are sold, then the total return (= sales proceeds) is [math]15€\cdot 3900= 58500€.[/math][br][br]The fixed costs (rent, water. heat, etc.) were in the previous financial year C[sub]f[/sub] = 6 500 €. Variable costs (materials etc) of one product were C[sub]v [/sub][sub][/sub]= 9.50 € per item.[br][br]The cost function consists of fixed costs and variable costs. Fixed costs will be paid even if there is no sale. Each product sold increases costs in terms of variable costs. However, the margin calculation assumes that unit costs will remain constant even if the sales volume fluctuates.Total cost function C on[br][br][math]C(x)=6500€ + 9.50€\cdot x,[/math][br][br]where [i]x [/i] in number of items sold.[br][br]Thus, total costs are [math]C(3900)=6500€+9.50€\cdot 3900= 43550€.[/math][br][br]Unit costs, i.e. the costs per product, are obtained by dividing the fixed costs by the number of products sold and adding the variable unit costs. In this case[br][br][math]c=\frac{6500€}{3900}+9,5€=11.17€.[/math][br][br]The unit costs therefore change according to the volume of sales of the products. The more sold, the more fixed costs are distributed. [br][br]The result (R) of the sale of the product is the difference between profits and costs:[br][br][math]R=SP-C=58500€-43550€=14950€.[/math][br][br]The result can also be calculated based on unit data:[br][br][math]\begin{eqnarray} [br]R&=&\underbrace{px}_{SP}-\underbrace{(C_f+C_v x)}_C\\[br]&=&px-C_f-C_v x\\[br]&=&(p-C_v)x-C_f\\[br]&=&(15€-9.50€)\cdot 3900-6500€\\[br]&=&14950€\end{eqnarray}[/math]

Profit and loss account (PCA) based on profit margin is given as a table:[br][br]Sales Proceeds (SP)[br]- Variable costs (C[sub]v[/sub])[br]________________________________________[br][b]Profit margin (PM)[/b][br]- Fixed costs (C[sub]f[/sub])[br]________________________________________[br][b]Result (R)[/b][br][br][br]PCA for the example 1 would be[br][br][br][math]\begin{array}{lrcrr}[br]\textbf{ Sales Proceeds } & 3900\cdot 15€ &=&\textbf{58500€}& 100 \%\\[br]\text{-Variable costs } & 3900\cdot 9.50€ &=&37050 €&63.3 \%\\[br]\textbf{= Profit margin } & &&\textbf{21450€}&\textbf{36.7\%}\\[br]\text{- Fixed costs} &&&6500 €&11.1\%\\[br]\textbf{= Result}& & &\textbf{14950€}&\textbf{25.6\%} \\[br]\end{array}[/math][br][br]All percentages are given to sales proceeds.

A group of students arranged an event. Tickets were be sold at 15 euros/ticket. The retail rent was 250 euros and salaries for fellow students 300 euros in total. They also noticed, that they used 4 euros/customer for snacks and drinks. [br] [br]Value added tax for events in Finland is 10% . Thus, the unit price for tickets used in sales proceeds is [br][br][math]\begin{eqnarray}[br]x+0.1x&=&15€\\[br]1.1x&=&15€\\[br]x&=&13.64€[br]\end{eqnarray}[/math][br][br]Sold tickets: 50[br]Selling price: 15€ with VAT [br] 13.64€ without VAT[br]Salaries: 300€[br]Snacks and drinks: 4€/customer[br]Rent: 250€[br][br][math]\begin{array}{lrcll}[br]\textbf{ Sales proceeds} & 50\cdot 13.64€ &=&\textbf{682€}&\\[br]\text{- Variable costs} & 50\cdot 4€ &=& 200€&\\[br]\textbf{= Profit margin} & &&\textbf{482€}&\textbf{71\%}\\[br]\text{- Fixed costs} &&&550 €&\\[br]\textbf{= Result}& & &\textbf{-68€}&\textbf{-10\%} \\[br]\end{array}[/math][br][br]The profit margin in this example is quite good but fixed costs are too high for a small event.

Profit margin of a product is 30%. What is the new profit margin in percentages, if the price is reduced by 20%.[br][br]If profit margin is 30%, then variable costs are 70% of the price. The price reduce affects only to sales proceeds but not in variable costs. If the original price is [i]p[/i], then the new price is 80% of [i]p[/i] = 0.8[i]p[/i]. Now, we can write a direct variation to solve the new variable costs in percentage:[br][br]  [math]\begin{array}{rclcl}[br]\frac{\text{New sales proceeds}}{\text{Variable costs}}&=&\frac{100\%}{x}\\[br]\frac{0.8p}{0.7p}&=&\frac{100\%}{x}\\[br]\frac{0.8}{0.7}&=&\frac{100\%}{x}&&|\text{p is cancelled}\\[br]x&=&\frac{100\cdot 0.7 p}{0.8 p}&=&87.5\%[br]\end{array}[/math][br][br]Thus, the new profit margin is [math]SP - C_v= 100\% - 87.5\%=12.5\%[/math]