4.2 Calculation & Pricing

Introduction

In costing, the costs are determined in order to determine a sales price. In a company, all costs must be included in the calculation (full cost accounting). The calculation serves in particular to determine the price, because the sales price of a product or service must cover all the company's costs.

The calculation is used in the business plan to calculate the price. To calculate means to approach the selling price step by step. That means: 

• The market price is the price achieved by competitors in the market. This price must be researched in the market and among the competitors.
• The cost price (also called full cost price) is the price that includes the total costs of the enterprise. This is to be calculated.
• The selling price (also called the offer price) is the price at which the goods are to be offered on the market. This must be determined by weighing up the market price and the cost price. 

4.2.1 Market price, cost price, selling price

In pricing, the market price, the cost price and the sales price play the decisive role. Calculating the price of an offer requires knowledge of the market price and the cost price. Only then can the decision be made for the sales price.

• The determination of the market price can be done through a targeted market investigation. The market prices are to be determined for the products and services offered. For this purpose, the sales prices of competitors should be closely examined. The better the market research, the more accurate the basis for your own calculation.
• The cost price must first be determined on a full cost basis. In full cost accounting, all operating expenses are included and allocated to the individual offer. The cost price must include both direct and indirect costs. The cost price does not guarantee that this price can also be achieved as a sales price in the market.
• The costs of an individual company are not the only decisive factor for the sales price. The customer decides on the sales price in competition with the other competitors. The customer decides what, where and at what price he buys something.
•  In the long run, the relationship between supply and demand determines the market price. The individual company will align its sales prices with the market price. The sales price can deviate upwards, deviate downwards or be equal to the market price. The decoupling from the market price - the sales price is far above or below the market price - must be justified by special conditions in the market or by operational conditions.  

When determining the sales price, the business plan must also take into account price fixing: e.g. official maximum or minimum prices, as in the case of agricultural products; e.g. horizontal price fixing through cartel-like agreements by competing companies; e.g. vertical price fixing through "recommended retail prices".

Regulations for price labelling must also be observed: e.g. in the retail trade, in the hospitality industry, in offers, at petrol stations, in the banking industry.

If the sales price to be achieved is above the calculated cost price, the entrepreneur's profit increases. If the sales price to be achieved is below the calculated cost price, there is a reduction in profit. If the cost price is permanently undercut, the enterprise will make losses.

4.2.2 Calculations

There are different methods and areas of application for calculating the costs and price of a service. Calculations in commercial enterprises, in craft or industrial enterprises, in service and consulting companies or those of a freelancer differ significantly from each other.

Costing can take the form of preliminary, intermediate or final costing. As a preliminary costing or quotation costing, it serves to prepare decisions or the acceptance or rejection of projects and orders. Intermediate costing is carried out during the creation of products in order to control the adherence to cost budgets at the same time. In a final costing, the actual costs incurred can be compared to the cost targets. The final costing is a component of controlling.

Costing procedure

Different procedures can be distinguished.

• Full cost accounting
• Overhead calculation, division method, equivalence method
• Industry-specific calculations

Full cost accounting

In full cost accounting, all costs of the enterprise are allocated to the individual products and services. Full costs include all costs incurred in the manufacture of a product or service (full manufacturing costs) or all costs incurred for the products sold in a period (full cost of goods sold).

The calculation of full costs in larger companies is only possible with the help of an allocation of overhead costs, since not all costs incurred in a company have a direct causal relationship with the products manufactured or sold. This results in a fuzziness in the determination of the costs of an individual service. This fuzziness should be included in the decision on the cost price.

If costs and activities can be recorded exactly for each production order, it can be recalculated on an ongoing basis. The choice of the lowest hierarchical level in cost unit accounting (usually the order) determines the possible level of detail of the calculation. Full cost accounting ensures that all costs are covered by the unit price of a quotation.

 

Example: Full cost accounting

A start-up wants to sell something. His monthly fixed costs amount to: 

Monthly fixed costs
Entrepreneurial wages	2.000,00 €	65%
+ Share of social security (approx. 25%)	500,00 €	16%
= Total personnel costs	2.500,00 €	81%
+ room costs	300,00 €	10%
+ Overhead costs (general costs)	300,00 €	10%
= Total fixed costs	3.100,00 €	100%
+ variable cost share per order	Amount x €
= Total costs or full costs	Sum x €

Table 7: Full cost accounting

If the entrepreneur were to carry out only one order per month, he would have to calculate at least € 3,100 fixed costs for it, plus the variable costs for carrying out the order. If he could do two orders or a multiple thereof, the proportionate fixed costs of each order are reduced by the number of units.

Cost shares per unit of output	Units	Fixed costs
1st order	1	3.100,00 €
2nd order	2	1.550,00 €
3rd order	10	310,00 €
4. order	50	62,00 €

 

The variable cost share per unit of output must be added to the fixed cost share. The profit mark-up must not be missing from this, provided it can be achieved on the market.

Example calculation: Break-even

Break-even is the profit threshold. If goods or services are sold, the break-even determines the intersection point from which profit can be made.

 

Graphical representation

 

An example from the conference sector:

For conferences, seminars or events, it must be decided with how many customers an event can be carried out to cover costs. Break-even is the point at which the break-even point is reached. 

A calculation makes assumptions:

-       Turnover: The fee for the conference should be € 250 per day and client plus € 35 for catering and hospitality. This means a total of € 285 per client. While the sales price is fixed, the number of clients who accept the offer is variable.

-       Expenses/costs: The fixed costs of holding the conference include: Speaker fees, conference rooms, advertising, administrative costs, costs of running the business including management; these should total € 5,100. These expenses are incurred regardless of the number of participants. The variable costs are dependent on the number of participants, such as catering (35 €) or working materials amounting to 50,- €, which are only claimed if the client actually participates.

The break-even rquestion is: With how many participants can a seminar calculated in this way break even? This is shown in the following break-even table. It shows how income and expenses change in relation to the number of participants. It is only with 22 participants that the income exceeds the expenses. However, the profit or loss threshold then rises progressively with each additional participant.

Tabular calculation of the break-even point

Participant	Remuneration variable Proceeds	Remuneration variable Proceeds	Fixed costs	Variable costs	Revenue	Expenditure	P&L
	250 €/TN	35 €/TN	5.100 €	50 €/ TN	total	Total	€
... 9	2250	315	5100	450	2565	5550	-2985
10	2500	350	5100	500	2850	5600	-2750
11	2750	385	5100	550	3135	5650	-2515
12	3000	420	5100	600	3420	5700	-2280
13	3250	455	5100	650	3705	5750	-2045
14	3500	490	5100	700	3990	5800	-1810
15	3750	525	5100	750	4275	5850	-1575
16	4000	560	5100	800	4560	5900	-1340
17	4250	595	5100	850	4845	5950	-1105
18	4500	630	5100	900	5130	6000	-870
19	4750	665	5100	950	5415	6050	-635
20	5000	700	5100	1000	5700	6100	-400
21	5250	735	5100	1050	5985	6150	-165
22	5500	770	5100	1100	6270	6200	70 €	Break-even point
23	5750	805	5100	1150	6555	6250	305
24	6000	840	5100	1200	6840	6300	540
25	6250	875	5100	1250	7125	6350	775
26	6500	910	5100	1300	7410	6400	1010
27	6750	945	5100	1350	7695	6450	1245

Table 8: Break Even Point

 

The decision as to whether and under what conditions the event should be held is an entrepreneurial one.

Surcharge calculation

In overhead costing, the unit costs or cost price of a unit of output are calculated. With the help of overhead rates, which can be determined for example in a cost accounting sheet (BAB), an overhead rate is added to the direct costs in order to determine the cost of goods sold by way of a summary or step-by-step procedure.

 

Overhead calculation I

Scheme

+	Direct material costs	MEK
+	Material overheads	MGK
=	Material costs or cost price	MK
+	Profit mark-up in %	G
=	Selling price	VP

 

1. calculate material costs	Direct material costs + material overheads= total material costs
2. calculate production costs or also creation costs	+ direct production costs+ production overheads + special production costs + total production costs= production costs (= material costs + manufacturing costs)
3. calculate overheads	+ administrative overheads (overhead) + sales overheads (marketing) + other special direct costs+ total administrative + sales overheads = Cost of goods sold (= manufacturing costs + (administrative and/or sales overheads)) (V+V)
4. calculate profit and surcharges	+ profit surcharge (17 %)    Cash selling price+ discount (x= 3%) + agent commission = target sales price 100% + discount (z= 10%) = list sales price (= net offer price) + sales tax (19%) = Gross sales price (= Gross offer price)

(cf. cost accounting for start-ups)

Table 9: Surcharge calculation

 

 

Overhead calculation II

An example in a company could look as follows: A gross sales price of € 34,652.11 is calculated from € 19,400.00 production costs.

Cost type	Subsidiary account	Amount in €
Direct material costs		10 500
+ Material overheads		500
=Material costs		11 000
+ Direct production costs		6 000
+ Production overheads		400
+ special costs. Manufacturing		2 000
+ Manufacturing costs		8 400
= Production costs		19 400
+ Administrative overheads		750
+ Sales overheads		1 300
+ Special direct costs		380
+ V u. V*		2 430
= Cost price		21 830
+ profit surcharge 17 %	100 % = 21830	3 711
	17 % = x
= cash selling price	x = 3711	25 541
+ discount 2 %	100%-3%-2%=95%	1 344,26
+ commission 3 %	95% = 25 541
	5% = x
= Target selling price	x = 1 344,26	26 885,26
+ discount 10 %	100 %-10%=90%	2 987,25
	90% = 26 885,26
= List sales price	10% = x
(net offer)	x = 2987,25	29 872,51
+ VAT (19%)		5 675,77
= gross sales price		35 548,28

(cf. cost accounting for start-ups)

Table 10: Example: Surcharge calculation

 

 

Pre- and post-calculation

In any case, the sales price must first be calculated, that is a preliminary calculation. If it is reviewed after some time, a post-calculation is made. In principle, this applies to all services that a company produces and sells.

In production, pre- and post-calculation is of particular importance because direct material costs and overhead costs cannot yet be determined exactly, especially during the introductory phase. The deviations must be determined and taken into account for future orders.

The following table shows exemplary values that can illustrate deviations.

• For example, the post-calculation shows a cost of goods sold of € 23,230. The difference of € 1,400 to the preliminary costing of € 21,830 represents a cost under-recovery.

 

(cf. cost accounting for start-ups)

Table 11: Pre- and post-calculation

 

In simple overhead costing, the total overhead costs of a business are added to the total direct costs for materials and wages and then divided by the sum of the output quantity produced.

In differentiated overhead costing, costs are determined step by step for the areas of materials, production, sales, administration, personnel, etc.

 

 

 

 

Example: Percentages of an overhead calculation

 

Cost unit accounting
Production quantity in pieces	10,000 piece	Cost price per piece	Percentage of cost price
Production material	100.000 €	10 €	18,5%
+ Production wages	200.000 €	20 €	37%
= Total direct costs	300.000 €	30 €	55,5%
+ Overheads	240.000 €	24 €	44%
= Cost price	540.000 €	54 €	100 %

 

Table 12: Percentages of an overhead calculation

Division procedure

The division method is suitable for calculating unit or direct costs. The method is generally applicable. To determine the cost of a unit, the total cost is divided by the quantity produced.

 

Example: Simple division calculation

 

Equivalence procedure

Equivalence costing is used when a company produces "several similar" products, e.g. bricks, drinks, dairy products, which go through the same production process but differ in shape, size, colour, etc. in the final stage. These differences are tried to be determined with the help of valuation or ratio figures. The unit costs of the different, similar products are determined with the aim of identifying the relationship between them. With the help of the equivalence number, the calculation can be considerably simplified.

 

 

 

Example: Scheme of an equivalence calculation

Table 13: Equivalence calculation

The ratio is calculated by dividing the unit of output by the amount of output: 1000:1250 = 0.8, etc. The unit of output relates to the total cost as 1:1.5 (13,500: 9000= 1.5). Thus, the ratio of the output quantity to the output unit is 0.8 * 1.5 = 1.20 Euros.

In all cases, the business needs information regarding material costs, production costs, manufacturing costs, personnel costs and total cost of goods sold to make decisions.

4.2.3 Industry-specific calculations

Calculation in the trading company

A trading company is characterised by the fact that it sells goods in different quantities and sales forms, such as retail, wholesale, mail order. The goods to be sold have to be obtained, possibly stored, offered in a salesroom or catalogue and finally sold in a sales talk. The goods are usually not changed by the trader.

In trade, therefore, the goods must first be purchased by the entrepreneur himself before they can be resold. A distinction is made between a purchase calculation and a sales calculation.

• The purchase price calculation determines the purchase price of the goods. The starting point is the invoice price (net) or the list price. After deducting discounts and rebates, the purchase price remains. Delivery costs may also have to be added.
• The sales calculation takes the purchase price as a starting point and adds the business costs incurred in the business as prime costs. In addition, a provisional profit share is added until the final sales price (net) is found. The sales price (net) plus turnover tax results in the sales price (gross).

 

Scheme: Overhead calculation trade
- +	Gross purchase price Invoice deductions (reseller discount, cash discount Procurement costs
=	Purchase price, cost price or net purchase price
+ + +	Business expenses Profit Sales surcharge
=	Effective or gross sales price

 

 

	Reference price calculation				Sales price calculation
	Invoice price	240,00 €			Subscription price	250,00 €
-	Discount	7,20 €		+	Action costs 25 %	62,50 €
=	Target purchase price	232,80 €		=	Cost price	312,50 €
-	Cash discount	4,66 €		+	Profit 12 %	37,50 €
=	Cash purchase price	228,14 €		=	Cash selling price	350,00 €
+	Procurement costs	21,86 €		+	Discount 2 % (in hundred)	7,14 €
	Subscription price	250,00 €		=	Target selling price	357,14 €
				+	Discount 5 % i. H.	18,80 €
				=	Final sales price (net)	375,94 €
				+	Value added tax 19 % (resp. 7 %)	71,42 €
				=	Selling price (gross)	447,36 €

 

Table 14: Relationship between reference pricing and sales pricing

 

In the sales talk, the trader often has to grant a discount or cash discount for cash payment; these are added as sales surcharges in the calculation beforehand.

• The gross profit, expressed as a percentage of the reference price, is called the calculation mark-up.
• The gross profit, expressed as a percentage of the selling price, is called the trading margin.
• The net profit (in the sense of income tax) is calculated as a percentage of the cost price and added to it. Example: Turnover at cost = 122,000 €; net profit: 15,000 €; net profit as a percentage of turnover = 15 T€:122T€ *100 = 12.2 %.
• The net profit includes the entrepreneur's salary as remuneration for his activity, the interest on the equity invested in the business and the actual entrepreneurial profit, which also serves to cover the general, incalculable entrepreneurial risk.
• The calculation can be determined in a simplified way with the help of a calculation factor, which can be formed when some experience is available.

Calculation in the manufacturing plant

A manufacturing company is characterised by the fact that it produces goods and products itself or processes them further. The costing in a company that produces goods must first buy them as preliminary products, then process them and finally sell them. This also applies to many craft enterprises.

 

Example: Quotation calculation in the manufacturing industry in euros

The offer at which a certain product is to be sold to a customer is to be determined:

Designation	Values
Product designation		Screws
Quantity required		10.000
Machine designation		CNC machine
Machine hour charge rate		50,00 €
Max. Production quantity per hour (in pieces)		1000
Proportionate machine costs per unit		0,05 €
+ material costs per piece		0,10 €
+ External power per piece		0,10 €
= Cost price per piece		0,25 €
+ Profit per unit	50%	0,125€
= Selling price net piece		0,375 €
* Supply quantity to be produced		10.000
Net bid amount	%	3.750 €
* VAT in %	19%	712,50 €
Gross bid amount		4.462,50 €

Table 15: Offer calculation

 

A trader needs 10,000 screws. They can be produced with a CNC machine. The production hour of the machine should cost 50 €. The machine can produce 1,000 screws per hour. The proportional machine cost per screw is 50 €:1000= 0,05 €. The material costs amount to 0.10 €. External services, such as galvanising, amount to another 0.10 €. The cost price is therefore 0.25 € per piece. The company wants to realise a profit of 50 %. The sales price is therefore 0.375 € per piece. With 10,000 pieces, this results in a gross offer amount of 4,350 €.

Calculation of services

The calculation of a service is determined by the type of service provision and the know-how required for this. The selling price is based on the individual hourly rates of the person offering the service. 

 

Example: Quotation calculation for services in euros

The service offer can be calculated on an hourly basis. A total service is assumed for which a definable number of hours can be charged. External services (from third parties), for example, are required to create the service and must be included accordingly.

 

Costing levels		Amount
Wage costs per chargeable working hour		20,47 €
+ variable overheads		4,47 €
+ fixed overheads per chargeable working hour		12,85 €
= Hourly rate (cost-covering)	100 %	37,79 €
+ Profit share per working hour	15 %	5,66 €
= Hourly billing rate		43,45 €
* Number of working hours required	10
= Offer sum for own services		434,50€
+ External services	100,00€	100,00€
+ external service surcharge	10%	10,00€
= Offer sum (net)	100%	544,50€
+ VAT in %	19 %	103,45€
= bid amount (gross)	116%	647,95€

Table 16: Costing levels

 

Fixed price calculation for services in euros

The fixed price calculation is based on the fact that a fixed hourly rate is determined as a starting point. The order volume is to be estimated in work units or time units.

 

Costing levels	Amount
Labour costs per hour worked	50%	25,00 €
+ variable overheads	20%	5,00 €
+ fixed overheads per chargeable working hour	30%	7,50 €
= Hourly rate (cost-covering)	100%	37,50 €
+ Profit share per working hour	10%	3,75 €
= Hourly billing rate according to operating data		41,25 €
Shortage or surplus per working hour		8,75 €
= Hourly rate offered		50,00 €
* Number of working hours required	15
= Offer sum for own services		750,00 €
+ External services		1.400,00 €
+ Third-party surcharge in %	0%	-   €
= Offer sum (net)	100%	750,00 €
+ VAT in %	19%	142,50 €
= total amount offered (gross) specified	116%	892,50 €

Table 17: Fixed price calculation

 

Calculation of freelance activities

Cost calculation in the liberal professions is based on the type of business. Only when the type of service is defined and the type of income, a calculation scheme for the calculation of the respective services is possible. The activity of a freelance commercial agent is completely different from that of a freelance lawyer, doctor or psychological practitioner. Neither in the case of a commercial agent are the revenues defined by sales figures and corresponding commissions, whereas the revenues of lawyers or doctors are defined by fee schedules - partly on a statutory basis. If, for example, flat rates per case are paid for medical services, a price calculation of an individual service is hardly possible. Instead, the doctor must try to adjust the service to the price. This also happens when services are budgeted. In any case, a calculation must refer to the overall performance of the enterprise and the total costs.

If a freelance management consultant sells his consulting services on his own, he has to take into account not only material and office costs, but above all the "time spent". It makes a big difference whether a consultancy hour costs € 25, € 50 or even € 200.

Model calculation of a consultant, trainer, lecturer

Consultants, trainers, course instructors, lecturers are usually paid on an hourly basis. In the case of a consultancy assignment or a seminar, only a certain fee can be achieved:

 

Table 18: Calculation of freelance work

 

Possible income: The income range for the same working hours is therefore very different.

Necessary working time: From the point of view of the self-employed entrepreneur, the question is how great the effort must be in order to achieve a certain income. The basis for this is at least the entrepreneur's wage - after deduction of all costs.

 

 

 

 

Table 19: Calculation working time

To achieve an income of 1,500 €, 100 working hours must be spent at an hourly fee of 15 €. With a fee of 200 €/hour, on the other hand, only 7.5 hours.

The valuation of the hourly fee must be based on the market price at which the freelancer can sell his service. The hourly fee must cover the costs in total.

As a freelancer, the fee (gross) is taxable in full within the scope of income tax after deduction of business and deductible costs. Pension expenses and the costs of running a business should also be paid from the gross; the net income is therefore correspondingly lower.

The calculation for freelancers depends on the type of business. Another possibility is the sale of advisory services at a fixed cost rate. The determination of service packages or of contracts for work, where not the individual hour or day is sold, but a service product at a calculated price, is another way of calculating sales prices.

4.2.4 Contribution margin accounting

In order to place an offer in the market, it may be necessary not to determine the price on a full cost basis, but to calculate the contribution margin. This means giving up part of the fixed costs or part of the administrative costs or profit.

Contribution margin accounting provides answers to the following questions:

• Which products are uneconomical and should not be offered any longer?
• From which number of units does the company reach the break-even point (break-even analysis)?
• Where is the absolute lower price limit of a product?
• What is more cost-effective: to manufacture a product yourself or to buy it?

 

Calculation scheme

Sales revenue ./. total variable costs= total contribution margin

Sales price per unit ./. variable costs per unit= contribution margin per unit

 

For one product, the list sales price in the sales calculation is € 436.70, with a profit of € 83.21 included. In order to check whether the costs are covered by this price, the variable costs must be determined. These amounted to € 410 in the calculation:

 

The production of the product makes sense because the positive contribution margin of each unit reduces the burden of fixed costs. The operating result is improved by each additional unit sold - in our example by € 26.70.

In contribution margin accounting, only the variable costs are charged to a product. If the achievable sales price exceeds the variable costs, a contribution margin is generated.

By back-calculating, it is possible to see which product revenues cover the fixed costs and which products generate profits. It is also possible to see which product groups should be discontinued or reduced in production because they generate too low or negative contribution margins. In practice, direct costing systems are designed as contribution margin accounting.

Example of a contribution margin calculation in euros

The contribution margin calculation indicates how high the contribution margin is to cover the fixed costs and to cover the profit.

 

Designation	Std. rate	Order 1	Order 2	Order 3
Order total = sales price		30.000 €	10.000 €	64.000 €
Fixed: Number of working hours		100	100	100
Fixed: Material costs		23.000 €	9.000 €	43.000 €
Variable: Wage cost share	25 €	2.500 €	2.500 €	2.500 €
Contribution margin		4.500 €	-1.500 €	18.500 €
Contribution margin per working hour		45 €	-15 €	185 €
- Fixed costs per working hour	20 €	20 €	20 €	20 €
Variable: profit per working hour		25 €	-35 €	165 €
Profit / loss total order		2.500 €	-3.500 €	16.500 €

Table 20: Contribution margin calculation

• Order 1 has a contract sum of 30,000 € with 100 working hours. After deducting the material costs, a sum of 7,500 € remains. This sum includes a profit mark-up of 2,500 € as well as a labour cost share of 4,500 €. Knowing the internal cost structure, the fixed costs of working time amount to 2,000 € and the variable wage costs to 2,500 €. The possible contribution margin is € 4,500, i.e. the variable cost shares.
• Order 2 has a contract sum of 10,000 € with 100 hours. This includes 9,000 € in material costs. The variable wage cost share is 100 *25 € = 2,500 €. This results in a negative contribution margin of 1,500 €. With this loss, the contribution margin per hour is 15 €. The total loss is 3,500 €.
• Order 3 has a total of € 64,000. With material costs of € 43,000 and a variable wage cost share of € 2,500, the contribution margin is € 18,500 and the profit is € 16,500.

4.2.5 Criteria for the price decision

The calculation has to calculate the cost prices on the basis of operational reality. However, the decision of the sales price must also include aspects of the marketing strategy. The price sends a message. The price conveys a feeling of value to the customer: Thus, a high price can mean for one customer an expression of "luxury", for another an expression of "too expensive!", for a third "reasonably priced!" and for the fourth customer: "fits!

The following considerations are helpful in justifying the selling price:

• What is the relationship between the sales price and the market price and cost price of the company? Maximum price, high price, normal price, low price, dumping price?
• Sales price in customer evaluation: How do customers rate the offer? What is the customer benefit? Unit price and individual price?
• Price sensitivity of customers: How do different customers react to the sales price.
• Optimal price structure: What is the optimal price structure for the company's services? Which price variants and target groups should be distinguished in the sales price?
• Competitor reactions: What prices are the competition taking? How will you react to the new offer and the new selling price?
• The prices actually achieved must be determined: What is left after deducting discounts and rebates? What prices are actually achieved in reality? What does the final costing look like?
• Selling price and market price: How do the two relate to each other in concrete terms? Is the sales price in line with the market?

Pricing decisions have a strategic significance. They have a communicative effect for the company.