Explain break-even analysis and its significance

Break-even analysis finds the level of output (or sales) at which total revenue equals total cost, so that there is neither profit nor loss.

Basic relations

• Total cost TC = Fixed cost (FC) + Variable cost per unit (v) × Q
• Revenue TR = Selling price per unit (p) × Q
• Break-even quantity: *Q = FC / (p − v)**, where (p − v) is the contribution per unit
• Break-even sales value = FC / (1 − v/p)
• Below Q* the project makes a loss; above Q* it makes a profit.

 Rs
  |                      TR
  |                    /
  |                  /      ...... TC
  |                /......
  |          ... *
  |  .......   / |
  |----------/---|--------------------- FC
  |        /     |
  |      /       |   * = break-even point
  |    /         |
  |  /           |
  |/_____________|_________________________ Q
                Q*

Break-even value and its significance

The break-even value (Q* or break-even sales) is the minimum volume the project must reach to recover all its costs. Its significance in project selection:

• A lower break-even point means lower risk, since the project becomes profitable sooner.
• It gives the margin of safety = (expected sales − break-even sales) / expected sales.
• For two alternatives with different cost structures (e.g. machine A: high FC, low v; machine B: low FC, high v), the volume at which their total costs are equal shows which one to choose: below that volume pick the option with the lower fixed cost, above it pick the option with the lower variable cost.
• It helps in pricing and cost-control decisions.

Example

A factory has FC = Rs 100,000 per year, v = Rs 30 per unit and p = Rs 50 per unit.

• Q* = 100,000 / (50 − 30) = 5,000 units
• Break-even sales = 5,000 × 50 = Rs 250,000
• If expected sales are 8,000 units, margin of safety = (8,000 − 5,000)/8,000 = 37.5%, and profit = 8,000 × 20 − 100,000 = Rs 60,000.

Since the expected output exceeds the break-even output, the project is acceptable.