Question

1. “The Manager has projected the following costs corresponding to sales of 14,000 and 16,000 for the next month’s operation.

Cost Items	Number of Units
	14,000	16,000
Materials	£7,000	£8,000
Labour	£16,800	£19,200
Electricity	£11,580	£12,520
Rent	£8,900	£8,900
Advertising	£14,920	£16,480
Depreciation	£60,000	£60,000

Required:

Identify if the costs are fixed, variable or semi-variable. Provide mathematical proof to justify your answers.”

Answer 1

Before we bifurcate fixed, variable and semi variable costs, let us first briefly try to understand what each of the cost really mean.

Fixed costs: These costs do not change with change in production. Ex: Rent, etc

Variable costs: These costs change proportionately with change in production. If production is zero then variable costs are also zero. Ex: Direct material, Direct labour, etc.

Semi-variable costs: These costs are partly fixed and partly variable. Ex: Electricity charges,etc

Solution:

1) Material: Due to increase of 2000 units of production, material cost increased by 8000-7000=1000 pounds

Increase in material cost per unit=1000 pounds/2000 units= 0.5 pounds

At 14000 units of production, material cost = 14000 units*0.5pounds=7000 pounds

At 16000 units of production, material cost = 16000 units*0.5pounds=8000 pounds

We can observe that cost per unit is same at different production capacities.

If cost per unit remains the same at different production capacities, then it is a variable cost.

2) Labour: Due to increase of 2000 units of production, labour cost increased by 19200-16800=2400 pounds

Increase in labour cost per unit= 2400 pounds/2000 units= 1.2 pounds

At 14000 units of production, labour cost = 14000 units*1.2pounds=16800 pounds

At 16000 units of production, labour cost = 16000 units*1.2pounds=19200 pounds

Since cost per unit is same at different production capacities, it is a variable cost.

3) Electricity: Due to increase of 2000 units of production, electricity cost increased by 12520-11580=940 pounds

Increase in electricity cost per unit= 940 pounds/2000 units= 0.47 pounds

At 14000 units of production, electricity cost should be= 14000 units*0.47pounds=6580 pounds

But actually electricity charges at 14000 units of production are 11580 pounds.

Difference = 11580-6580= 5000 pounds

Cost per unit at 14000 units of production=11580/14000=0.827 pounds

Cost per unit at 16000 units of production=12520/16000=0.783 pounds

Cost per unit is not same at different production capacities.

By this we can understand that electricity is neither fixed nor variable. It is semi-variable.

Fixed part is 5000 pounds. Variable part is 0.47 pounds per unit.

4) Rent: Due to increase of 2000 units of production, rent increased by 0.

Cost per unit at 14000 units of production=8900/14000=0.636 pounds

Cost per unit at 16000 units of production=8900/16000=0.556 pounds

Cost per unit is not same at different production capacities.

Hence it is not a variable cost.It is not a semi varaible cost either because increase in cost due to increase in production is zero. It is a fixed cost.

(Note: Cost per unit for fixed costs always decrease with increase in production)

5) Advertising: Due to increase of 2000 units of production, advertising cost increased by 16480-14920=1560 pounds

Increase in advertising cost per unit= 1560 pounds/2000 units= 0.78 pounds

At 14000 units of production, advertising cost should be= 14000 units*0.78pounds=10920 pounds

But actually advertising charges at 14000 units of production are 14920 pounds.

Difference = 14920-10920= 4000 pounds

Cost per unit at 14000 units of production=14920/14000=1.066 pounds

Cost per unit at 16000 units of production=16480/16000=1.03 pounds

Cost per unit is not same at different production capacities.

By this we can understand that advertising charges are neither fixed nor variable. It is semi-variable.

Fixed part is 4000 pounds. Variable part is 0.78 pounds per unit.

6) Depreciation: Due to increase of 2000 units of production, depreciation increased by 0.

Cost per unit at 14000 units of production=60000/14000=4.286 pounds

Cost per unit at 16000 units of production=60000/16000=3.75 pounds

Cost per unit is not same at different production capacities.

Hence it is not a variable cost.It is not a semi varaible cost either because increase in cost due to increase in production is zero. It is a fixed cost.

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