Difference quotient method

The difference quotient method is one of several methods for cost resolution that is used in the context of cost and performance accounting.

definition

The difference quotient method separates a company's total costs into fixed and variable costs by forming two differences (cost difference and output difference), which are then put in relation to each other.

example

A company produces 10,000 output units in period 1 (e.g. January) and 15,000 output units in period 2 (e.g. February) . In period 1 the total cost of the company is € 100,000 and in period 2 the total cost is € 120,000.

The increase in the quantity produced by 5,000 product units has therefore increased the total costs by € 20,000. From this it is concluded that each individual output unit increases the costs by 20,000 / 5,000 = € 4. The variable unit costs must therefore be € 4.

If an output unit causes variable unit costs of € 4, then 10,000 output units cause variable costs totaling 4 * 10,000 = € 40,000. If the total costs for 10,000 output units are € 100,000 and of which € 40,000 are variable, then the remaining € 60,000 must be fixed costs.

The cost function of the production process can be derived from this:

K = 60,000 + 4x

With the help of this cost function, the total costs (K) can be determined for any output quantity x.

formula

${\ displaystyle k _ {\ mathrm {v}} = {\ frac {K _ {\ mathrm {2}} -K _ {\ mathrm {1}}} {x _ {\ mathrm {2}} -x _ {\ mathrm {1 }}}}}$

${\ displaystyle k _ {\ mathrm {v}}}$ = variable unit costs

${\ displaystyle K _ {\ mathrm {1}}}$ = Total costs for period 1

${\ displaystyle K _ {\ mathrm {2}}}$ = Total costs for period 2

${\ displaystyle x _ {\ mathrm {1}}}$ = Output quantity of period 1

${\ displaystyle x _ {\ mathrm {2}}}$ = Output quantity of period 2

Criticism of the difference quotient method

• The method assumes a linear cost function. It leads to incorrect results for non-linear cost functions.
• If step- fixed costs occur when increasing the output quantities , the method also leads to incorrect results
• If the output differences on which the calculations are based are too small, the process becomes very imprecise
• Coincidences in cost fluctuations affect the outcome of the procedure