# Breakeven point analysis-mathematical approach

Breakeven point analysis is a mathematical model. It is that level of activity or operation whereby the total revenue is equal to total cost (ie TR=TC). Three questions arise from this mathematical model;

- Is there any correlation between breakeven point mathematical model and marginal costing?
- Is it possible to compute the activity level that represents breakeven point scenario using mathematical approach?
- How can this model be presented mathematically
- If breakeven point model represents zero profit scenario, is it possible as an entrepreneur to set the right level of production so as to realize a specific profitability level

The answer for (i) up to (iv) is **YES**

LETS Go….

## Correlation between breakeven point mathematical model and marginal costing

Before we demonstrate the association between the breakeven point model and marginal costing, the following definitions are paramount

**Definition: **

**Marginal costing** is a technique of presenting cost information to the management in a manner such that the variable and fixed cost are separated when determining the net profit of the firm or a department.

**Variable cost** is also referred to as **marginal cost** or relevant cost and it is the cost that varies with variance to the level of output. It is direct cost. As production level change, the level of variable cost also change. This implies that at zero level of production, variable cost is also zero.

**Fixed cost** is cost which is constant within a particular level of output or production. When production level is at zero level, the fixed cost already is at a particular level.

NB: In marginal costing, the fixed cost is written off against the contribution value

**Sales **is the product of selling price and the quantity sold within a particular period of time

**Contribution **is the difference between sales value and variable cost

The relationship between breakeven point model and marginal costing can be demonstrated using step by step procedure as follows;

*STEP ONE*

Contribution can be expressed as follows;

CONTRIBUTION=SALES-MARGINAL COST

Where;

Sales=selling price*units sold

Marginal cost=Direct Materials +Direct Labour +Direct Expenses +Variable Overheads

*STEP TWO*

Profit is the net of contribution where by fixed cost is netted from gross contribution as;

PROFIT=CONTRIBUTION-FIXED COST

*STEP THREE*

TOTAL COST=VARIABLE COST+FIXED COST

*STEP FOUR*

Logically, Total Revenue (TR) or sales is the total cost incurred in producing a good **PLUS** the desired profit. This can be expressed as follows;

*STEP FIVE*

Suppose the entrepreneur desires no profits at all, then it means that profits=0

*STEP SIX*

Divide Contribution on both sides of the equation

## Breakeven Point Model-Mathematical Approach

In **conclusion**, the breakeven point model is associated with marginal costing technique

## Setting of specific production level (units) to realize specific profitability level

If breakeven point model represents zero profit scenario, is it possible as an entrepreneur to set the right level of production so as to realize a specific profitability level. This question can be answered by using an example;

Example

FTZ co. ltd is a producer of medicinal juice for Covid-19 supplement purposes. The cost per unit data for the month of June 2020 was as follows;

Item **Amt. $**

Direct materials 16.00

Direct wage rate 8.00

Variable overhead 4.00

Fixed cost for the month of June was $72,000

Selling price per unit/litre was $48

In the month of June, the organization produced some units of juice in litres. The data was missing and the management need help from you as a consultant to determine the exact litres produced if the organization had reached breakeven point.

Required

- What was the breakeven point in units/litres
- Suppose the management felt that a profit of $7,500, how many units/litres should the business produce?

**Solution **

**Workings**

ii)Suppose the management felt that a profit of $7,500, how many units/litres should the business produce?

**Solution**