Cost function
Cost function is the equation linking total cost to activity, y = a + bx, where a is fixed cost and b is variable cost per unit; high-low, scattergraph and regression all estimate it.
See it move
The high-low method estimates a cost function from two months of machine-hour data: 8,000 hours cost €62,000 and 3,000 hours cost €42,000. Variable cost per hour is (€62,000 − €42,000) ÷ (8,000 − 3,000) = €4.00, and fixed cost is €62,000 − (€4.00 × 8,000) = €30,000, giving y = €30,000 + €4.00x.
The formula
Variables
- Total cost (€)
- Fixed cost (€)
- Variable cost per unit of activity (€)
- Activity level (units or hours)
Models total cost as a straight line in activity; a is the fixed component and b is the variable cost per unit of the cost driver.
Check yourself
Using the high-low method: at 10,000 units, total cost was €150,000; at 4,000 units, total cost was €96,000. Using the resulting cost function, what is the estimated total cost at 7,000 units?