Contribution analysis is a technique for decision making. Contribution (C) is the difference between the Sales revenue (S) of a project and a variable or extra cost (V) incurred by investing in that project. As long as S-V result in C being positive it means that something is left over to make a contribution to the remaining cost ( F) of the entity. If the fixed cost has already been covered by other projects, then the contribution increases the entities profit.
As I have been mentioning in my previous blogs "absorption costs" are the costs charged out to the individual unit of production. We identify the 'direct costs' and share of 'indirect costs;' to each unit per hour or machine hour. The 'absorption costs' are affected by the overhead rates. Costs can also change with activity and called 'variable costs'. The costing can be used to define the value of stock, but this method may not be appropriate for decision making as the 'fixed costs' may be affected by the decision.
Economists often use 'marginal costs' to describe extra cost for making additional unit. The concept of 'marginal costs' is known as 'contribution'.
'Contribution' can be calculated as:
Sales revenue - Total cost = Profit (or loss)
Total cost = Variable cost and fixed cost, so
Sales revenue - (Variable costs + Fixed costs) - Profit ( or loss), so
Sales revenue - Variable cost = Fixed cost + Profit (or loss)
It is called the 'marginal cost equation.
'Contribution' is the difference between the Sales revenue and the Variable cost, so
Contribution = Fixed Cost + Profit
If entity makes a contribution, it means that is has generated a certain amount of sales revenue and the variable cost of making those sales is less then the total sales revenue. If the 'contribution' is insufficient to cover the fixed cost, the business will make loss.
We need to remember that fixed costs can often be ignored when making decision, because these will not change. Managers can concentrate on decisions that will maximise the contribution.
There are certain assumptions made for the marginal cost technique:
* Total cost can be split between fixed cost and variable cost
* Fixed cost remains constant
* Fixed costs do not bear relation to specific unit
* Variable cost vary in proportion to activity
Therefore, we need to be able to distinguish between the fixed costs and variable costs. Some costs may be semi-variable but these would be easy to calculate.
Format
The basic format for 'contribution analysis' is presented in figure below:
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
It is called the 'marginal cost statement'.
Managers may then ask themselves some questions:
* What would be the profit if we increased the price for product A,B or C?
* What would be the effect if we reduced the price of product A,B or C?
* What would be the effect if we eliminated one of the products?
* What would be the effect if we changed quantity of any of the products so that the variable cost of each unit would increase or decrease?
* Would any of the decisions affect fixed costs?
Application
For change in variable costs - If, for example a selling price of an unit is £10, and the variable cost per unit is £5 ( 50% of the selling price) the contribution is £5 per unit. If 100 units are sold, the contribution is £500 as it remains at 50% of the selling price. The fixed costs are ignored.
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
For changes in profit at varying levels of activity - We may have different levels of activity, for example 1000 units, 2000 units, 3000 units, 4000 units and 5000 units. The variable cost would stay at 50% of the sales price and the contribution would also be 50%. The fixed cost would not change. The contribution needed to cover the fixed cost is £10,000. Because each unit makes a contribution of £5, the total number of units needed to be sold in order to break even will be 2000 units (£10,000 / £5). If more then 2000 units are sold, we make profit. The relationship between Sales revenue and contribution is known at the" Profit/volume' ratio as the contribution in relationship to sales. We can then quickly calculate the profit at any level of sales. We need to multiply the P/V ratio by the sales revenue and the deduct the fixed cost.
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
Graphs and charts
Contribution can be presented through 'break-even chart' as per figure below.
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
the total cost line is the combination of fixed costs and variable costs. It ranges depending on the quantity of units. The wider the 'angle of incidence', the greater the amount of profit. The margin of safety can be measured either by the number of units or revenue generated. Activity is measured either in units or sales revenue.
The contribution graph would be slightly different.
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
The contribution graph shows the variable cost line ranging from when there is no activity to 5000 units. The fixed cost is drawn in parallel to the variable costs. The fixed cost line also serves the total cost line.
The break even chart is more common but the contribution chart is generally more helpful as the fixed and variable costs are shown separately. The issue with both of them is that they do not show the amount of profit. A profit chart would need to be shown separately.
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
Reservations
There are certain reservations we need to consider with this technique:
Cost classification. Cost cannot be easily divided into fixed and variable categories.
Variable cost. It might not vary in direct proportion to sales revenue and the level of activity. costs of direct materials may change if goods are bought in bulk from suppliers.
Fixed costs. They are unlikely to remain constant over a wide range of activity.
Time period. In a short term a cost may be fixed and in a long-term variable.
Complementary products. A specific decision on one product may affect other products.
Cost recovery. Sometimes excluding fixed costs may be unwise because in a longer term the entity should recover all his costs.
Diagrammatic presentation. The charts are simplistic as the sale of all types of products is totalled and it assumption is there that change of one product will affect others.
Non-cost factors. Decisions can't only be taken on the basis of cost. comfort, loyalty, reliability cannot be quantified.
Behavioural factors. we cannot always decide of a particular behaviour.
Formulae
With the reservations in mind, we can still use the technique to be helpful for decision making. Even if the costs cannot be precisely calculated.
The main equations are summarised below:
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
Example
Source: Dyson J, 2010, "Accounting for Non-accounting students", Pearson Education UK
And another example for less happy entity.
The aim is to always increase contribution, because the greater the contribution the more chance of making a profit and of covering the fixed costs. We need to choose the work that provides the maximum contribution per unit of limiting factor employed.
Calculate contribution made by each product
Divide the contribution that each product makes by the number of the direct labour hours used in making each product
This gives the contribution per direct labour hour employed
Select the project that gives the highest contribution per unit of limiting factor
for example, if we are choosing between job A and job B. We could convert each job contribution into the amount of contribution earned for every direct labour hour worked on A and B respectively. We would then opt for the job that earn the most contribution per direct labour hour.
Example
In the example above, there is an assumption that there is only one limiting factor, but there could be many.
To summarise, the contribution analysis is particularly useful for short term decisions but it is of less value for longer term decisions.
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