formulas

Contribution Margin

Total CM:

Contribution Margin (CM)=Sales−Variable Costs\text{Contribution Margin (CM)} = \text{Sales} - \text{Variable Costs}Contribution Margin (CM)=Sales−Variable Costs

CM per Unit:

CM per Unit=Selling Price per Unit−Variable Cost per Unit\text{CM per Unit} = \text{Selling Price per Unit} - \text{Variable Cost per Unit}CM per Unit=Selling Price per Unit−Variable Cost per Unit

Contribution Margin Ratio

CM Ratio=CM per UnitSelling Price per Unit\text{CM Ratio} = \frac{\text{CM per Unit}}{\text{Selling Price per Unit}}CM Ratio=Selling Price per UnitCM per Unit​

Variable Cost Ratio:

Variable Cost Ratio=1−CM Ratio\text{Variable Cost Ratio} = 1 - \text{CM Ratio}Variable Cost Ratio=1−CM Ratio

Break-even Point

Formula Method (Units):

Break-even Units=Fixed CostsCM per Unit\text{Break-even Units} = \frac{\text{Fixed Costs}}{\text{CM per Unit}}Break-even Units=CM per UnitFixed Costs​

Formula Method (Sales Revenue):

Break-even Sales=Fixed CostsCM Ratio\text{Break-even Sales} = \frac{\text{Fixed Costs}}{\text{CM Ratio}}Break-even Sales=CM RatioFixed Costs​

Equation Method:

Sales=Fixed Costs+Variable Costs+Profit (Target Income)\text{Sales} = \text{Fixed Costs} + \text{Variable Costs} + \text{Profit (Target Income)}Sales=Fixed Costs+Variable Costs+Profit (Target Income)

Target Income (Units):

Units for Target Income=Fixed Costs+Target IncomeCM per Unit\text{Units for Target Income} = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{CM per Unit}}Units for Target Income=CM per UnitFixed Costs+Target Income​

Target Income (Sales):

Sales for Target Income=Fixed Costs+Target IncomeCM Ratio\text{Sales for Target Income} = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{CM Ratio}}Sales for Target Income=CM RatioFixed Costs+Target Income​

Effect of Changes on Break-even and Target Income

  • Selling Price ↑: Break-even decreases (CM per unit increases).

  • Variable Cost ↑: Break-even increases (CM per unit decreases).

  • Fixed Cost ↑: Break-even increases.

Break-even for Multiple Products

  1. Calculate Weighted Average CM Ratio:

Overall CM Ratio=Total CMTotal Sales\text{Overall CM Ratio} = \frac{\text{Total CM}}{\text{Total Sales}}Overall CM Ratio=Total SalesTotal CM​

  1. Use this ratio in break-even formulas.

Margin of Safety (MOS)

MOS=Actual Sales−Break-even Sales\text{MOS} = \text{Actual Sales} - \text{Break-even Sales}MOS=Actual Sales−Break-even Sales