The CVP analysis functions as a tool for planning and decision making, as it points out the relation of costs, sales and price, also identifies the scope and magnitude of the economic problems faced by a company as well as its possible solution, It also allows to carry out a sensitivity analysis by examining the impact of various price or cost levels on the profits.

## Equilibrium Point in units

To define the point of equilibrium or the point of 0 utilities it is necessary To determine what is the unit (tangible or intangible), then the fixed and variable costs are separate. In The CVP analysis, the units sold, the fixed and variable components of the costs as well as the revenues with respect to the units shall be considered; In other words, it sees the company as a whole (production, marketing, administration).

### Operation Utility Focus

Concentrates your attention on the status of results

(Operating Profit = sales Revenue-variable Costs-fixed Costs)

Net income is the result of detracting taxes from the operating utility.

Focus of the contribution framework

At the point of equilibrium, the contribution margin is equal to the fixed costs, that is to say, it is equal to the sales revenues-total variable costs

If The unit contribution margin is replaced by the price minus the unit variable cost in the operating utility equation and the number of units is determined, the following expression of the equilibrium point is obtained:

Number of units = fixed Costs/contribution Margin per unit (total contribution margin/sold units)

Profit Goals

The Operating Utility goal can be expressed as an amount of money or as a percentage of sales income. It Is important to consider that the contribution margin per unit for each unit above the equilibrium point is equivalent to the per-unit utility.

The goal of profits does not consider income taxes, to consider them, they are calculated as a percentage of utility (Operating Income = net income/(1-tax rate)

-Variable cost ratio. It Is Simply the proportion of each monetary sales unit that should be used to cover the variable costs.

The ratio of contribution margin is the proportion of each available sales currency unit to cover fixed costs and to provide a utility.

Product line Analysis

When you have two models of a product you must separate the direct fixed costs (exclusive costs of that product) from the common fixed costs (those that would remain constant their one of the products will be eliminated). It Is necessary to calculate the equilibrium point for each one.

#### Sales Mix

It Is The relative combination of products that are being sold by a company, expressed in sold units (5:2 products sold-Product A and B) or in revenue ratios (62.5%: 37.5%) Although this percentage affects the prices of both products.

To be able to make decisions or perform a complete UVCS analysis, this mixture is considered as a package of 2 products and it is found in equilibrium point. However, the actions that change the prices of individual products can affect the sales mix because consumers can buy a relatively greater or lesser amount of the product. The complexity of the equilibrium point approach in units increases in transcendental form as the number of products increases.

Monetary Sales Amount Approach

The result statement Is used, the balance point expressed as sales revenue is also based on the expected sales mix.

Balance Point expressed in sales = fixed costs/contribution margin ratio

Graphical Representation of CVP relations

Utility Graph-Volume

It Presents the relationship between the profits and the sales volume, i.e. the equation of the operating utility. (Operation Utility = (price x Units) – (unit variable cost x units) – fixed costs). In This graph, the operating utility (the utility) is the dependent variable (vertical axis) and the units are the independent variable (horizontal axis).

Cost-volume-utility Graph

In This it is necessary to present in a graphic form two separate lines: the total income line and the total cost line. Are represented by the following equations:

Income = Price x units

Total Cost = (unit variable Cost x units) + Fixed Costs

The Vertical axis is money, the horizontal units.

UVCS Analysis Assumptions

The Utility graphs-volume and cost-volume-utility that have just been illustrated are Ba-san in some important assumptions like the following:

Represents a linear function of income and costs.

The UVCS Analysis is for SHORT term, therefore, the current operating range or relevant range, for which the linear cost and income ratios are valid

It Assumes that the price, total fixed costs and unit variables can be identified accurately and remain constant.

Assumes that what is produced is sold

In the case of product line analysis, the sales mix implies being known

Prices and costs are supposed to be known with certainty.

Changes in the CVP variables

In The analysis it is important to take into account and explain the effects of risk and uncertainty.

Units sold x Unit contribution margin = Total contribution margin – fixed costs = Utility

Introduction to risk and uncertainty

Risk and uncertainty are a part of the cisiones of business and must be treated in some way. The risk differs from the uncertainty that with the risk, the probability distributions of the variables are known and with the uncertainty they are not, although here they are used homogeneously.

To address the risk it is important to keep in mind where there could be cost variance, and so instead of handling exact data use ranges, for that purpose two concepts are handled: security margin and operational leverage.

Safety Margin

They Are The units sold or are expected to sell, income earned or expected to be won above the volume of the equilibrium point. It can be expressed in units sold or in sales revenue. It’S better to be tall.

Operational Leverage

It Is related to the relative mix of fixed costs and variable costs in an organization. When companies lower variable costs and increase fixed costs is reflected in greater profits, that is, fixed costs are being used as leverage to increase profits. Therefore, leverage is the use of fixed costs to draw higher percentage changes in profits as sales activity changes. The higher the degree of operational leverage, the more that changes in sales activities will affect utilities.

Degree of operational leverage = Margin of contribution/Utilities

Sensitivity and CVP Analysis

A technique of the type what would happen if…? Which examines the impact of changes in the fundamental assumptions on an answer. It Also provides administrators with an impression on the degree to which a poorly predicted variable will affect a response.

Activity-based CVP and costing Analysis

Conventional analysis CVP divides the costs into variables (sales volume) and fixed. In an activity-based costing system, the costs are divided into the non-unit-based and base-based categories. The activity-based costing admits that some costs are going to the units produced and that some costs do not. A cost equation ABC is expressed:

Total Cost = fixed costs + (unit variable costs x number of units) + (machine preparation cost x number of machine preparations) + (engineering cost x number of engineering hours)

A comparison of the ABC-based equilibrium point with the conventional equilibrium point reveals that fixed costs differ, as some fixed costs may vary with non-unitary cost generators (machine preparations and Engineering hours).

This is:

CVP: Units = (utility target + fixed costs)/(price – unit variable cost)

ABC: Units = (utility objective + fixed costs + preparation cost + engineering cost)/(Price – unit variable cost)

The CVP and ABC analysis are complemented to make decisions, as they provide greater discernment and therefore better design decisions can be made.

By adopting JIT, the variable cost per unit is reduced and the fixed costs are increased. Cost Equation for JIT: Total Cost = fixed costs + (unit variable cost x units) + (engineering cost x number of hours of engineering).

What elements are needed for UVCS analysis?

The prices, the volume, the costs, the profits and the sales mix. It Serves short-term planning and decision making and the result can be expressed in units or sales revenues.

What is the equilibrium point?

The Point of 0 utilities, i.e. the units or revenues needed to cover fixed and variable costs.

What is the reason for the contribution margin?

The contribution margin is equal to the fixed costs, a unitary contribution margin can be calculated, that is to say, per unit sold the percentage that is used to cover the fixed costs.

What is the reason for variable cost?

The variable cost ratio. It Is Simply the proportion of each monetary sales unit that should be used to cover the variable costs.

When is it advisable to make a sales mix?

When analyzing a product line, common and direct costs are calculated, then the sales revenue of each product is considered to be able to take a relationship, and to carry out a Cost-Volume-Utility analysis of both products as if it were a package .

What graphics does the Operation utility show?

The Utility-Volume graph presents the relationship between the profits and the volume in sales, that is, the equation of the operating utility.

What could be considered limiting the UVCS analysis?

It Assumes that the relationship between income and costs is linear, besides that it considers price and costs can be identified with accuracy and remain constant, also that what is produced is sold. Therefore, it serves short-term and as a decision-making tool.

What is the security margin?

What is sold or expected to be sold above the equilibrium point can be expressed in units or sales revenue.

What is operational leverage?

Is the use of fixed costs to extract higher percentage changes in profits as sales activity changes.

is The conventional UVCS analysis and the ABC analysis contradictory?

No, they are actually complemented to make decisions, because they provide greater discernment and therefore, better design decisions can be made.