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
