Ravin T. Bright
MCE’s Financial Analyst
Answering the question when sales would start to generate profits is especially important in managing an enterprise. Sales not always generate profits. As costs precede revenues, sales of products up to a certain value would not generate profits, and would only cover costs incurred previously. A profit can be achieved not before exceeding a certain level of sales.
Due to that reason, it is important for financial analysts from Meridian Capital Enterprises Ltd. to obtain the information on conditions of coverage total costs of the company and profits achieved as a result of projects implemented. To this end, the analysts use the break even point and break even analysis.
The break even points means the number of products sold, at which sales revenues match costs of the products.
To determine the break even point, financial analysts from Meridian Capital Enterprises Ltd. use different methods. The presentation of the break even analysis should start from an enterprise manufacturing homogenous products. In such case, the break even point is determined by:
1. number of finished products sold
2. unit sale price
3. unit variable costs
4. total fixed costs
Taking into account the assumptions accepted by financial analysts from Meridian Capital Enterprises Ltd. total own costs are calculated with the use of the following formula:
where:
Tc – total costs
Tfc – total fixed costs
Tvc – total variable costs
Total variable costs are calculated as the following product:
where:
Tvc – total variable costs
Vcup – unit variable costs
Pv – production volume
Financial analysts from Meridian Capital Enterprises Ltd. assume that the value of sales is a product of the production volume and sale price, and sales revenues can be calculated with the use of the following formula:
where:
Sr – sales revenues
p – sale price
Sv – sales volume
The break even point is the level at which sales revenues match total own costs, namely:
In long form it is presented as follows:
Mathematical transformations of the aforementioned equation allow determining the production volume at which the financial result equals zero:
where:
Pv – production volume
Tfc – total fixed costs
p – sale price
vcup – unit variable costs
This production volume is referred to as the break even point of a finished product BEPvo namely Pv = BEPvo. The break even point expressed in such a way is a volume critical point, as it reflects the number of products that should be sold by the enterprise in order to cover fixed and variable costs incurred.
The formula (p - vcup)included in the numerator is a gross unit surplus, often referred to as unit gross profit margin. The unit gross profit margin is a difference between the sale price of a finished product and unit variable cost. In global values, the gross surplus is expressed as follows:
where:
Mgp – gross profit margin
Sr – revenues from sales of finished products
Tvc – total variable costs
Deducting total variable costs from sales revenues gives fixed costs and profit if sales are profitable. Consequently, the gross profit margin covers fixed costs and ensures a profit. Therefore, the gross profit margin is often referred to as the coverage margin.
In addition to absolute values, the gross profit margin is expressed in relative values:
where:
Mpgr – gross profit margin ratio
Mgp – gross profit margin
Sr – revenues from sales of finished products
The gross profit margin ratio is a percentage share of the gross profit margin in sales and reflects the profitability of sales calculated on the basis of the gross profit margin.
The safety margin is another type of margin. The safety margin is a difference between the revenue obtained from actual sales (planned sales revenues can also be used) and the revenue at the break even point. Financial analysts from Meridian Capital Enterprises Ltd. present it as the following formula:
where:
Ms – safety margin
Sra – actual sales revenue
BEPsr – sales revenue at the break even point
The safety margin notifies analysts from Meridian Capital Enterprises Ltd. of the level by which sales may drop to a degree not exposing the enterprise to losses. This margin is also expressed by the following ratio:
In addition to the volume break even point, financial analysts from Meridian Capital Enterprises Ltd. often use the value break even point, which shows the value of sales revenues covering total costs. The value break even point is obtained by multiplying the volume break even point by the price of a product:
namely:
or applied by analysts:
where:
BEPva – value break even point
BEPvo – volume break even point
Tfc – total fixed costs
p – sale price
vcup – unit variable costs
Financial analysts from Meridian Capital Enterprises Ltd. use the break even point formula and calculate the production volume, which would guarantee the planned level of the profit on sales. This value is calculated with the use of the following formula:
where:
Pv – production volume
Tfc – total fixed costs
Pps – planned profit on sales
p – sale price
vcup – unit variable costs
If the production volume ensuring the planned level of the profit on sales is multiplied by the sale price, the analysts would obtain the sales value, which the enterprise must achieve to generate the planned amount of the profit on sales. Financial analysts from Meridian Capital Enterprises Ltd. present it using the following formulas:
or
where:
Sv – sales value
p – sale price
Svo – sales volume
Tfc – total fixed costs
Pps – planned profit on sales
vcup – unit variable costs
The break even point helps the analysts in the evaluation of risk of decisions made in respect to the production volume and the price of the product. For instance analysts consider the following situation:
The enterprise would like to enter new sales market, drive out competitors or strengthen its position on the market, and considers reducing the sale price of the finished product to p2. At the same time, the management board of the enterprise is interested in achieving the profit from the previous period, equal Pps1. Consequently, the analysts need to identify the level of sales (its growth) to cover the planned price reduction.
As the price of the finished product would change, the production break even point would also change. The volume break even point would equal:
where:
BEPvo2 – volume break even point of production
Tfc1 – total fixed costs from the previous period
p2 – sale price from the period after its reduction
vcup1 – unit variable costs from the previous period
The value break even point will change in the similar way and will equal:
where:
Tfc1 – total fixed costs from the previous period
vcup1 – unit costs from the previous period
p2 - sale price from the period after its reduction
According to the aforementioned equations:
and thus the break even for the second period is higher than the break even in the previous period – taking into account volume, as well as value. Financial analysts from Meridian Capital Enterprises Ltd. assume that making such decisions bears significant risk. Obviously, in this case shifting the break even point would automatically result in an increase of the production volume, ensuring a specific level of the profit on sales.
The production volume ensuring achieving the hitherto profit on sales after making the decision on reducing the sale price of the finished product would equal:
This production volume corresponds to the following sales value:
where:
Tfc1 – total fixed costs from the previous period
Pps1 – profit on sales from the previous period
p2 – sale price from the period after its reduction
vcup1 – unit variable cost from the previous period
Svo2 – sales volume from the period after changing the sale price
The break even point in case of complex (multi-product) production is determined in a slightly different way. In this case, the break even point is determined using different methods. They depend on numerical information provided by the accounting, in particular cost accounting. It should be emphasised that identifying the break even point for the enterprise manufacturing different products is more difficult, and thus analysis potential is limited.
The mathematical equation describing the break even point for complex production has the following form:
where: Tfc – total fixed costs
vcupi – unit variable cost of product i
Svoi – sales volume of product i
pi – unit sale price of product i
Basing on the equation presented, analysts from Meridian Capital Enterprises Ltd. are able to determine that the enterprise achieves the break even when costs for the period become equal to the revenues from sales of individual products.
The so-called break even analysis by segment is one of the methods of analysing the break even point for complex production. When applying it, analysts divide fixed costs into two parts: fixed costs related to individual products and fixed costs of the enterprise. This last group is assigned by analysts from Meridian Capital Enterprises Ltd. to individual products proportionally to the gross profit margin assumed. The aforementioned method can be applied only in the multi-level variable cost accounting.
Determining the minimum sales level using the compound gross profit margin is another method of determining the break even point. However, it is possible only when unit sale prices and unit variable costs of every product, fixed costs of the enterprise as a whole and sales volume of each product type are known. In this case, the break even point can be expressed using the following formula:
where:
BEPva – value break even point
TFC – total fixed costs
Sr – sales revenues
If the percentage share of individual products in the production volume is known, the break even can be determined with the use of the following formula:
where:
BEPvo – volume break even point
TFC – total fixed costs
pi – sale price of product i
vcupi – unit variable cost of product i
Shi – percentage share of product i in the production volume
In the summary of the presented theories it should be emphasised that in practice the break even point and its analysis are of great importance in making short-term decisions in respect to the following issues:
MCE’s Financial Analyst
Answering the question when sales would start to generate profits is especially important in managing an enterprise. Sales not always generate profits. As costs precede revenues, sales of products up to a certain value would not generate profits, and would only cover costs incurred previously. A profit can be achieved not before exceeding a certain level of sales.
Due to that reason, it is important for financial analysts from Meridian Capital Enterprises Ltd. to obtain the information on conditions of coverage total costs of the company and profits achieved as a result of projects implemented. To this end, the analysts use the break even point and break even analysis.
The break even points means the number of products sold, at which sales revenues match costs of the products.
To determine the break even point, financial analysts from Meridian Capital Enterprises Ltd. use different methods. The presentation of the break even analysis should start from an enterprise manufacturing homogenous products. In such case, the break even point is determined by:
1. number of finished products sold
2. unit sale price
3. unit variable costs
4. total fixed costs
Taking into account the assumptions accepted by financial analysts from Meridian Capital Enterprises Ltd. total own costs are calculated with the use of the following formula:
Tc = Tfc + Tvc
where:
Tc – total costs
Tfc – total fixed costs
Tvc – total variable costs
Total variable costs are calculated as the following product:
Tvc = Vcup • Pv
where:
Tvc – total variable costs
Vcup – unit variable costs
Pv – production volume
Financial analysts from Meridian Capital Enterprises Ltd. assume that the value of sales is a product of the production volume and sale price, and sales revenues can be calculated with the use of the following formula:
Sr = p • Sv
where:
Sr – sales revenues
p – sale price
Sv – sales volume
The break even point is the level at which sales revenues match total own costs, namely:
Sr = Tc
In long form it is presented as follows:
p • Sv = Tfc + Vcup • Sv
Mathematical transformations of the aforementioned equation allow determining the production volume at which the financial result equals zero:
where:
Pv – production volume
Tfc – total fixed costs
p – sale price
vcup – unit variable costs
This production volume is referred to as the break even point of a finished product BEPvo namely Pv = BEPvo. The break even point expressed in such a way is a volume critical point, as it reflects the number of products that should be sold by the enterprise in order to cover fixed and variable costs incurred.
The formula (p - vcup)included in the numerator is a gross unit surplus, often referred to as unit gross profit margin. The unit gross profit margin is a difference between the sale price of a finished product and unit variable cost. In global values, the gross surplus is expressed as follows:
Mgp = Sr – Tvc
where:
Mgp – gross profit margin
Sr – revenues from sales of finished products
Tvc – total variable costs
Deducting total variable costs from sales revenues gives fixed costs and profit if sales are profitable. Consequently, the gross profit margin covers fixed costs and ensures a profit. Therefore, the gross profit margin is often referred to as the coverage margin.
In addition to absolute values, the gross profit margin is expressed in relative values:
where:
Mpgr – gross profit margin ratio
Mgp – gross profit margin
Sr – revenues from sales of finished products
The gross profit margin ratio is a percentage share of the gross profit margin in sales and reflects the profitability of sales calculated on the basis of the gross profit margin.
The safety margin is another type of margin. The safety margin is a difference between the revenue obtained from actual sales (planned sales revenues can also be used) and the revenue at the break even point. Financial analysts from Meridian Capital Enterprises Ltd. present it as the following formula:
Ms = Sra - BEPsr
where:
Ms – safety margin
Sra – actual sales revenue
BEPsr – sales revenue at the break even point
The safety margin notifies analysts from Meridian Capital Enterprises Ltd. of the level by which sales may drop to a degree not exposing the enterprise to losses. This margin is also expressed by the following ratio:
Mpgr = Sra-BEPsr / Sra x 100
In addition to the volume break even point, financial analysts from Meridian Capital Enterprises Ltd. often use the value break even point, which shows the value of sales revenues covering total costs. The value break even point is obtained by multiplying the volume break even point by the price of a product:
BEPva = BEPvo * p
namely:
or applied by analysts:
where:
BEPva – value break even point
BEPvo – volume break even point
Tfc – total fixed costs
p – sale price
vcup – unit variable costs
Financial analysts from Meridian Capital Enterprises Ltd. use the break even point formula and calculate the production volume, which would guarantee the planned level of the profit on sales. This value is calculated with the use of the following formula:
where:
Pv – production volume
Tfc – total fixed costs
Pps – planned profit on sales
p – sale price
vcup – unit variable costs
If the production volume ensuring the planned level of the profit on sales is multiplied by the sale price, the analysts would obtain the sales value, which the enterprise must achieve to generate the planned amount of the profit on sales. Financial analysts from Meridian Capital Enterprises Ltd. present it using the following formulas:
Sv = p • Svo
or
where:
Sv – sales value
p – sale price
Svo – sales volume
Tfc – total fixed costs
Pps – planned profit on sales
vcup – unit variable costs
The break even point helps the analysts in the evaluation of risk of decisions made in respect to the production volume and the price of the product. For instance analysts consider the following situation:
The enterprise would like to enter new sales market, drive out competitors or strengthen its position on the market, and considers reducing the sale price of the finished product to p2. At the same time, the management board of the enterprise is interested in achieving the profit from the previous period, equal Pps1. Consequently, the analysts need to identify the level of sales (its growth) to cover the planned price reduction.
As the price of the finished product would change, the production break even point would also change. The volume break even point would equal:
where:
BEPvo2 – volume break even point of production
Tfc1 – total fixed costs from the previous period
p2 – sale price from the period after its reduction
vcup1 – unit variable costs from the previous period
The value break even point will change in the similar way and will equal:
where:
Tfc1 – total fixed costs from the previous period
vcup1 – unit costs from the previous period
p2 - sale price from the period after its reduction
According to the aforementioned equations:
BEPvo2 > BEPvo1
BEPva2> BEPva1
and thus the break even for the second period is higher than the break even in the previous period – taking into account volume, as well as value. Financial analysts from Meridian Capital Enterprises Ltd. assume that making such decisions bears significant risk. Obviously, in this case shifting the break even point would automatically result in an increase of the production volume, ensuring a specific level of the profit on sales.
The production volume ensuring achieving the hitherto profit on sales after making the decision on reducing the sale price of the finished product would equal:
This production volume corresponds to the following sales value:
Sr2 = Svo2 • p2
where:
Tfc1 – total fixed costs from the previous period
Pps1 – profit on sales from the previous period
p2 – sale price from the period after its reduction
vcup1 – unit variable cost from the previous period
Svo2 – sales volume from the period after changing the sale price
The break even point in case of complex (multi-product) production is determined in a slightly different way. In this case, the break even point is determined using different methods. They depend on numerical information provided by the accounting, in particular cost accounting. It should be emphasised that identifying the break even point for the enterprise manufacturing different products is more difficult, and thus analysis potential is limited.
The mathematical equation describing the break even point for complex production has the following form:
where: Tfc – total fixed costs
vcupi – unit variable cost of product i
Svoi – sales volume of product i
pi – unit sale price of product i
Basing on the equation presented, analysts from Meridian Capital Enterprises Ltd. are able to determine that the enterprise achieves the break even when costs for the period become equal to the revenues from sales of individual products.
The so-called break even analysis by segment is one of the methods of analysing the break even point for complex production. When applying it, analysts divide fixed costs into two parts: fixed costs related to individual products and fixed costs of the enterprise. This last group is assigned by analysts from Meridian Capital Enterprises Ltd. to individual products proportionally to the gross profit margin assumed. The aforementioned method can be applied only in the multi-level variable cost accounting.
Determining the minimum sales level using the compound gross profit margin is another method of determining the break even point. However, it is possible only when unit sale prices and unit variable costs of every product, fixed costs of the enterprise as a whole and sales volume of each product type are known. In this case, the break even point can be expressed using the following formula:
where:
BEPva – value break even point
TFC – total fixed costs
Sr – sales revenues
If the percentage share of individual products in the production volume is known, the break even can be determined with the use of the following formula:
where:
BEPvo – volume break even point
TFC – total fixed costs
pi – sale price of product i
vcupi – unit variable cost of product i
Shi – percentage share of product i in the production volume
In the summary of the presented theories it should be emphasised that in practice the break even point and its analysis are of great importance in making short-term decisions in respect to the following issues:
- determining profit optimisation;
- setting prices of manufactured products;
- calculating the production volume ensuring the achievement of the assumed profit;
- determining the impact of changes in the production volume, price and costs on the result;
- determining profitability of decision options in different production techniques.
