CVP Analysis Practice Questions: Break-Even, Contribution Ratio, Margin of Safety & More

(i) To calculate the break-even point, we need to determine the level of sales (in tonnes) at which the company neither makes a profit nor incurs a loss.

Break-even point (in tonnes) = Fixed overheads / Contribution margin per tonne

Contribution margin per tonne = Selling price per tonne - Total variable cost per tonne = $100 - ($30 + $20 + $10) = $100 - $60 = $40

Break-even point (in tonnes) = $20,000 (Fixed overheads) / $40 (Contribution margin per tonne) = 500 tonnes

Therefore, the break-even point is 500 tonnes.

(ii) Contribution to sales ratio is the percentage of each sales dollar that contributes to covering fixed costs and generating profit.

Contribution to sales ratio = Contribution margin per tonne / Selling price per tonne

Contribution to sales ratio = $40 (Contribution margin per tonne) / $100 (Selling price per tonne) = 0.4 or 40%

(iii) Margin of safety is the difference between actual sales and the break-even point, expressed as a percentage of actual sales.

Margin of safety = (Actual sales - Break-even point) / Actual sales

(iv) To calculate the percentage increase in profit if sales volume is increased by 10%, we need to calculate the new profit and compare it to the original profit.

Original profit = (Selling price per tonne - Total cost per tonne) * Sales volume

New profit = (Selling price per tonne - Total cost per tonne) * (Sales volume + 10%)

Percentage increase in profit = (New profit - Original profit) / Original profit * 100%

(v) To calculate the extra tonnes that need to be sold in order to maintain the existing profit level if the selling price is reduced by 8%, we need to determine the change in contribution margin per tonne and divide it by the original contribution margin per tonne.

Change in contribution margin per tonne = Selling price reduction per tonne - Variable cost reduction per tonne = $100 * 8% - ($30 + $20 + $10) = $8 - $60 = -$52

Extra tonnes to be sold = Fixed overheads / |Change in contribution margin per tonne|

Note: Absolute value is used to ensure a positive result.

Please provide the actual sales volume in order to calculate the margin of safety and the percentage increase in profit accurately.