The break-even equation is ______.

The break-even equation is ______.

• A. P x Q = VC x Q - FC
• B. P x Q - FC = VC x Q
• C. P x Q = FC
• D. (P - VC) x Q = FC

Answer: (D)

Break-even happens when revenue just covers all costs. Revenue is price per unit times quantity (P × Q). Total costs are fixed costs plus variable costs (FC + VC × Q). Setting revenue equal to total costs gives P × Q = FC + VC × Q. Subtracting VC × Q from both sides isolates the contribution each unit adds: (P − VC) × Q = FC. This form highlights that the per-unit contribution margin (P − VC) times the number of units must equal fixed costs. It’s equivalent to the standard equation P × Q = VC × Q + FC, but the (P − VC) × Q = FC form makes the idea of contribution margin driving fixed costs clear. If you needed the break-even quantity, it would be FC divided by (P − VC).

Break-even happens when revenue just covers all costs. Revenue is price per unit times quantity (P × Q). Total costs are fixed costs plus variable costs (FC + VC × Q). Setting revenue equal to total costs gives P × Q = FC + VC × Q. Subtracting VC × Q from both sides isolates the contribution each unit adds: (P − VC) × Q = FC. This form highlights that the per-unit contribution margin (P − VC) times the number of units must equal fixed costs. It’s equivalent to the standard equation P × Q = VC × Q + FC, but the (P − VC) × Q = FC form makes the idea of contribution margin driving fixed costs clear. If you needed the break-even quantity, it would be FC divided by (P − VC).