The cost volume formula

The cost volume formula is used to derive the total cost that will be incurred at certain production volumes. The formula is useful for deriving total costs for budgeting purposes, or to identify the approximate profit or loss levels likely to be achieved at certain sales volumes. The cost volume formula is:

Y = a + bx

Y = Total cost
a = Total fixed cost (that is, a cost that does not vary in proportion to activity)
b = Variable cost per unit of activity; this is a cost that does vary in proportion to activity
x = Number of units of activity

For example, a company has fixed production costs of $1,000,000 per month, and sells a single product that costs $50 to build. If the company produces 10,000 units during a month, the cost volume formula shows that the total cost that will be incurred at this volume level will be:

$1,000,000 Fixed cost + ($50/unit x 10,000 units) = $1,500,000 Total cost

The primary failing of the cost volume formula is that it only works within a relevant range of unit volumes. Outside of that range, both the fixed and variable cost components of the formula are likely to change. For example:

  • A higher volume level may require expenditures for more fixed costs to increase the capacity of the production line or to expand the production space.
  • A higher volume level may result in bulk-purchasing discounts that reduce the variable cost per unit.

Thus, the relevant range of activity must be carefully analyzed when using the cost volume formula, to see if the outcome of the calculation will be valid.

Another issue with the formula is that it is overly simplistic. In reality, there will be a number of mixed costs containing both fixed and variable elements, costs that vary with different cost drivers, and a broad range of products, rather than just one product type. Given these complexities, the formula may require considerable adjustment to properly reflect the costing environment of a business.

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