Cost functions

Question 1

Cost function shapes

Answer 1

1) Linear : proportional cost increase to the level of activity (e.g.: operating variable costs)
2) Convex : higher than proportional cost increase to the level of activity (e.g.: paying for overtime)
3) Concave : lower than proportional cost increase to the level of activity (e.g.: depreciation per unit produced)

Question 2

Combinations of elementary cost functions

Answer 2

1) Semi-proportional : fixed costs + linear (variable) costs (e.g.: data bundles)
2) Upper and/or lower limit : constant costs up to a certain value + linear costs
3) Step fixed : increases by proportional leaps and bounds (e.g.: increase in machinery)
4) S shaped : mixture of fixed + proportional costs (e.g.: low machine utilisation -> concave, high utilisation -> convex)

Question 3

Cost Drivers

Answer 3

1) Cost drivers : are the explanatory variables of the cost function
- Input oriented : manufacturing/machine hours (q), direct labour/material costs (value)
- Output oriented : products manufactured (q), manufacturing costs/revenues (value)
2) Time horizon : cost functions are time dependent -> short-term fixed costs can be variable in the long run

Question 4

Learning and Experience curves

Answer 4

1) Learning curves : average working time decreases with number of products manufactured
- Concave function for direct labour costs (decrease per unit when output increases)
2) Experience curves : per unit costs decrease with increased output
- Concave function for manufacturing costs (decrease of material consumption when output increases)

Question 5

Determining cost functions : methods

Answer 5

1) Analytical : analyse cause and effect relationship between input and output in terms of quantity and time
- Resources : material bills, work schedules, legal regulations, etc
2) Statistical : use past costs to estimate cost functions and forecast future costs. 3 methods:
- Account analysis : classify cost of each category as fixed/proportional/mixed, then provides a subjective cost function
- High-low : considers only the highest and lowest past observations, then provides and objective estimate for the linear cost function
- Uni/multivariate : uses all available observations to conduct a linear/multiple regression analysis (line of best fit)

Question 6

Documenting cost forecast

Answer 6

1) Differentiated approach : cost functions are determined and documented separately for each OVC
- Recorded in cost-center summary sheets
2) Step-by-step plans : show the different levels of costs that could occur for different levels of capacity utilisation for each cost center (different columns show different percentages)