FE Home→Engineering Economics→Break-Even Analysis Example

Break-Even Analysis Example

Medium DifficultyFE Engineering Economics

Find the break-even quantity at which total revenue equals total cost (no profit, no loss).

Concept

Break-even occurs when total revenue T R = p \times Q equals total cost T C = F C + (V C) Q . Solving for Q gives the break-even quantity Q^{*} . The denominator p - V C is the contribution margin per unit; it must be positive for a finite break-even. T R = T C \Rightarrow pQ = F C + (V C) Q Q (p - V C) = F C \Rightarrow Q^{*} = \frac{F C}{p - V C} Notation: p = price per unit, Q = quantity sold, Q^{*} = break-even quantity, T R = total revenue, T C = total cost, F C = fixed cost, V C = variable cost per unit.

A product sells for p = $50 per unit. Fixed cost is F C = $12, 000 and variable cost is V C = $26 per unit. Find: The break-even quantity Q^{*} Verify that at Q^{*}, T R = T C

p = $50 per unit F C = $12, 000 V C = $26 per unit

T R = p \times Q T C = F C + (V C \times Q) T R = T C \Rightarrow pQ = F C + (V C) Q Q (p - V C) = F C \Rightarrow Q^{*} = \frac{F C}{p - V C} Q^{*} = \frac{12 , 000}{50 - 26} = \frac{12 , 000}{24} = 500 units

T R = 50 (500) = 25, 000, T C = 12, 000 + 26 (500) = 25, 000 ✓

Break-even quantity: Q^{*} = 500 units. At 500 units, total revenue and total cost both equal $25, 000 .

Break-even: Q^{*} = \frac{F C}{p - V C} (p > V C required) Notation: Q^{*} = break-even quantity, p = price per unit, V C = variable cost per unit, F C = fixed cost. Profit = T R - T C = (p - V C) Q - F C . Break-even is where profit = 0.