Revise Cost-volume-profit analysis for Cambridge 9706 (2.2.4)

Contribution is a crucial concept in marginal costing and CVP analysis. It represents the amount of revenue from each unit sold that is available to cover fixed costs and then to generate profit. Unlike profit, contribution ignores fixed costs, making it ideal for short-term decision-making where fixed costs are often unavoidable. The break-even point (BEP) is the level of activity (in units or sales revenue) at which a business makes neither a profit nor a loss. At this point, total revenue exactly equals total costs, which also means total contribution equals total fixed costs. Any sales beyond the BEP will generate profit.

Contribution per unit = Selling price − Variable cost per unit

Break-even (units) = $\frac{\text{Fixed costs}}{\text{Contribution per unit}}$

Break-even (revenue) = $\frac{\text{Fixed costs}}{\text{C/S ratio}}$ where C/S = contribution ÷ selling price

The Contribution to Sales (C/S) ratio is a vital tool, expressing contribution as a percentage of sales revenue. A C/S ratio of 0.40 or 40% means that for every $1 of sales, $0.40 is generated as contribution. This ratio is particularly useful for calculating the break-even point in revenue terms and for analysing the profitability of different products or departments. It is calculated as: (Contribution per unit / Selling price per unit) or (Total Contribution / Total Sales Revenue).

The Margin of Safety (MoS) is a measure of risk. It quantifies the cushion between the current or budgeted sales level and the break-even point. A high margin of safety indicates that sales can fall by a significant amount before the business starts making a loss, suggesting a lower level of risk. Conversely, a low margin of safety signals higher risk. The target profit calculation is a simple extension of the break-even formula. To find the sales required to achieve a certain profit, the target profit amount is added to the fixed costs in the numerator. This treats the desired profit as an additional 'cost' that must be covered by the total contribution earned.

Margin of safety (units) = Budgeted sales − Break-even sales

Margin of safety (%) = $\frac{\text{MoS units}}{\text{Budgeted sales}} \times 100$

Sales for target profit = $\frac{\text{FC} + \text{Target profit}}{\text{Contribution per unit}}$

A CVP chart, or break-even chart, provides a visual representation of the relationship between costs, volume, and profit. To construct one, you draw two axes: the horizontal axis for activity level (units) and the vertical axis for costs and revenue ($). You then plot three key lines:

1. The Fixed Cost (FC) line, which is horizontal as it remains constant regardless of output.
2. The Total Cost (TC) line, which starts from the fixed cost point on the vertical axis and slopes upwards.
3. The Total Revenue (TR) line, which starts from the origin (0,0) and slopes upwards. The point where the TR and TC lines intersect is the break-even point. The area between the TR and TC lines to the right of the BEP represents profit, while the area to the left represents loss.

CVP analysis relies on several key assumptions to simplify the model. It's important to be aware of these as they define the limitations of the analysis. The main assumptions are:

1. All costs can be clearly classified into fixed and variable components.
2. The selling price per unit is constant and does not change with the level of sales (e.g., no bulk discounts).
3. The variable cost per unit is constant (e.g., no economies of scale).
4. Total fixed costs remain constant over the relevant range of activity.
5. For multi-product companies, the sales mix is assumed to be constant.
6. It is assumed that everything produced is sold, meaning there are no changes in inventory levels.

Most businesses sell more than one product. Standard CVP analysis, which focuses on a single product, is not directly applicable. To perform CVP analysis for a multi-product firm, we must calculate a weighted average contribution per unit, based on a constant sales mix. The sales mix is the relative proportion in which a company's products are sold. By calculating a weighted average contribution, we can treat the 'mix' of products as a single composite unit and apply the standard break-even formula.

Weighted Average Contribution per unit = $\sum (\text{Contribution per unit}_i \times \text{Sales mix ratio}_i)$

Multi-product BEP (units) = $\frac{\text{Total Fixed Costs}}{\text{Weighted Average Contribution per unit}}$