 # B2: Decision Making Techniques | Cost Volume Profit Analysis (ACCA F5)

Cost Volume Profit Analysis looks at the nature of CVP analysis, how to calculate the break even point and the margin of safety, the contribution to sales ratio, target profit, how to prepare and interpret break even and porofit volume charts and discusses the limitations of CVP.

## Cost Volume Profit Analysis

Cost volume profit analysis which is also known as breakeven analysis is the “study of the interrelationships between costs, volume and profit at various levels of activity.”

Formula: Contribution per unit = unit selling price – unit variable costs

Formula: Profit = (sales volume x contribution per unit) – fixed costs

Formula: Sales revenue at breakeven point = fixed costs ÷ C/S ratio

Formula: Sales volume to achieve a target profit = (fixed cost + target profit) ÷ contribution per unit

### a) Explain the nature of CVP analysis.

Cost-volume-profit analysis looks at how costs and profits fluctuate when volumes or the level of activities change.

CVP Assumptions

• CVP analysis can be applied to one product or to several products that are sold in fixed proportions.
• Fixed costs “per period are same in total” and unit variable costs are “a constant amount at all levels of output and sales.
• Sales prices are “constant at all levels of activity.”
• Production volume = sales volume

### b) Calculate and interpret the break-even point and margin of safety.

The breakeven point is the point where there is no profit and where the total contribution is equal to the total fixed costs.

Formula: Breakeven Point = total fixed costs ÷ contribution unit

Formula: Breakeven Point = contribution required to breakeven ÷ contribution per unit

The margin of safety measures the percentage fall in “budgeted sales that can be allowed before breakeven is reached.

Formula: Margin of safety = budgeted sales units – breakeven sales units

Formula: Margin of safety = (budgeted sales – breakeven sales) ÷ budgeted sales x 100%

Example: A company manufactures and sells widgets. The selling price of each widget is \$20. The variable cost of making and selling each widget is \$6 and the fixed costs per month are \$280,000. The company aims to sell 100,000 widgets a month.

1. Calculate the budgeted profit per month and the breakeven point in sales
• Contribution per unit = 20 – 6 = 14
• Contribution/ Sales ratio = 14 ÷ 20 = 0.7
• Budgeted profit = (100,000 x 14) – \$280,000 = \$1,120,000
• Breakeven point in units = 280,000 ÷ 14 = 20,000 per month
• Breakeven points in sales = 280,000 ÷ 0.7 = 400,000
2. Calculate the margin of safety
• Margin of safety = (100,000 – 20,000) ÷ 100,000 = 80%
3. Calculate the amount of sales required to achieve a profit of \$150,000
• Total contribution = 280,000 + 150,000 = 430,000.
• Therefore unit sales must be 430,000 ÷ 14 = 30,714 units
• And sales revenue = 430,000 ÷ 0.7 = 614,286 in sales revenue

### c) Calculate the contribution to sales ratio, in single and multi-product situations, and demonstrate an understanding of its use.

The contribution to sales ratio can be used to calculate the breakeven point for a standard sales mix of products.

Formula: Contribution/ Sales Ratio = profit/ volume ratio = (contribution ÷ sales) x 100%

Example: A company produces and sells two products A and B. A sells for \$8 and has a total variable cost of \$1.5o. B sells for \$15 and has a total variable cost of \$4.50. For every ten units of A sold, one unit of B will be sold. The company’s fixed costs for each period are \$155,000. Calculate the breakeven point for the company.

Step 1: Calculate the contribution per unit and the weighted average contribution per unit

• Product A
• Sales price = \$8
• Variable cost = \$1.50
• Contribution = \$6.50
• Product B
• Sales price = \$15
• Variable cost = \$4.50
• Contribution = \$10.50
• Contribution from sale of 10 units of A and 1 unit of B
• Contribution from sale of 10 units of A= 6.50 x 10 = 65.00
• Contribution from sale of 1 unit of B = 1 x 10.50 = 10.50
• Therefore contribution from sale of 11 units in sales mix = 65.00 +10.50 = 75.50
• Weighted average contribution per unit = 75.50 / 11 = \$6.86 per unit

Step 2: Calculate the breakeven points in units

• Breakeven point in units = 155,000 ÷ 6.86 = 22,595 units
• Breakeven point for A = 20,541
• Breakeven point for B = 2,054

Step 3: Calculate the breakeven point in sales revenue

• Breakeven point for A = 20,541 x 8 = 164,328
• Breakeven point for B = 2,041 x 15 = 30,615
• Total breakeven point in sales revenue = \$194,193

### d) Calculate target profit or revenue in single and multi-product situations, and demonstrate an understanding of its use.

Formula: Target profit = (Fixed costs + Profit) ÷ Weighted average contribution per unit

Please refer to BPP’s ACCA F5 Performance Management Study Text for examples on how to calculate target profit.

### e) Prepare break even charts and profit volume charts and interpret the information contained within each, including multi-product situations.

The breakeven chart shows “the approximate profit or loss at different levels of sales volume within a limited range.” It plots “total costs  and revenues at different levels of volume and shows the activity level at which breakeven is achieved.”

Note: on the breakeven chart the x axis (horizontal axis) shows the sales units and the y axis (vertical axis) shows the costs and revenues.

The profit volume chart shows “the net profit or loss at any level of activity.

Note: On the profit volume chart, the x axis (horizontal axis) shows the revenue and the y axis (vertical axis) shows the profit and loss.

### f) Discuss the limitations of CVP

Limitations of CVP are:

• It assumes that fixed costs are the same in total at all levels of output
• It assumes that variable costs are the same per unit at all levels of output
• It assumes that sales prices remain constant at all levels of activity
• It assumes that production and sales are the same
• It ignores uncertainty in the estimates of fixed costs and unit variable costs