Unit costs are computed by dividing some amount of total costs (the numerator) by the related number of units (the denominator).
In many cases, the numerator will include a fixed cost that will not change despite changes in the denominator. It is erroneous in those cases to multiply the unit cost by activity or volume change to predict changes in total costs at different activity or volume levels.
For example: In the production process the cost of materials is $10 per unit, the cost of labour is $6 per unit and overheads cost $4 per unit. The sum of the per-unit cost will be $10+$6+$4 = $20.
Normally we are not given individual costs per unit. We are given total costs at some production level, say at 1000 units of production level the total material cost is $10000, the total labour cost is $6000 and total overheads are $4000. Compute the per-unit cost. The solution will be as follows:
Total Cost of Production/Total number of units
= $10,000+$6,000+$4,000 / 1000 units
= $20,000/1000 units
= $20 unit