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7.2. Production

Syllabus
0264–2027–2028
Topic
7.2
Level
—

Learning objectives

7.2.1Labour productivity• Labour productivity = Output per period (units) / Number of employees = units per employee.7.2.2Total variable cost• Total variable cost = Variable cost per unit × number of units.7.2.3Variable cost per unit• Variable cost per unit = Total variable cost / Number of units.7.2.4Total cost• Total cost = Total fixed costs + total variable costs.7.2.5Average cost• Average cost = Total cost / Number of units.7.2.6Break-even output• Break-even output = Fixed costs / Contribution per unit.7.2.7Contribution per unit• Contribution per unit = Selling price per unit - variable cost per unit.7.2.8Margin of safety• Margin of safety = Actual number of sales - break-even number of sales.

Calculate labour productivity

labour productivity=output per periodnumber of employeeslabour\ productivity=\frac{output\ per\ period}{number\ of\ employees}

If 24 employees produce 9,600 units in a month, labour productivity is 400 units per employee per month. Always state both the output unit and the time period.

Compare like with like. Higher productivity can lower labour cost per unit and increase capacity, but may reflect machinery, product mix or working hours as well as employee effort.

Productivity is output per worker, not total output and not profit. Do not call a workforce less productive merely because it is smaller.

Calculate total variable cost

total variable cost=variable cost per unit×number of unitstotal\ variable\ cost=variable\ cost\ per\ unit\times number\ of\ units

At 6variablecostperunitandoutputof2,500units,totalvariablecostis6 variable cost per unit and output of 2,500 units, total variable cost is15,000. If output doubles and unit variable cost is unchanged, total variable cost doubles.

Use units produced when the cost is incurred in production. Total variable cost is not total cost because fixed costs have not yet been added.

Find variable cost per unit

variable cost per unit=total variable costnumber of unitsvariable\ cost\ per\ unit=\frac{total\ variable\ cost}{number\ of\ units}

If total variable cost is 18,000for3,000units,variablecostperunitis18,000 for 3,000 units, variable cost per unit is6. This reverses the total-variable-cost calculation and gives a cost for one unit.

The result helps calculate contribution, forecast cost at another output level and compare production choices, provided the variable cost per unit is expected to remain stable.

Do not divide total cost by units: that gives average cost and includes fixed cost. Match the total variable cost and output to the same period.

Build total cost

total cost=total fixed costs+total variable coststotal\ cost=total\ fixed\ costs+total\ variable\ costs

With fixed costs of 40,000andtotalvariablecostsof40,000 and total variable costs of30,000, total cost is $70,000. As output changes, the variable part changes while fixed costs normally stay unchanged within the relevant range.

Add totals to totals. Do not add fixed cost to variable cost per unit unless both have first been expressed on the same per-unit basis.

Calculate average cost

average cost=total costnumber of unitsaverage\ cost=\frac{total\ cost}{number\ of\ units}

A total cost of 72,000for6,000unitsgivesanaveragecostof72,000 for 6,000 units gives an average cost of12 per unit. If output rises while fixed cost is spread over more units, average cost may fall.

Compare average cost with selling price to understand the cost margin per unit, and compare periods only after checking changes in scale, product mix and input prices.

Average cost includes both fixed and variable cost. It is not the same as variable cost per unit and it does not by itself give profit per unit.

Calculate break-even output

break ⁣− ⁣even output=fixed costscontribution per unitbreak\! -\! even\ output=\frac{fixed\ costs}{contribution\ per\ unit}

With fixed costs of 48,000andcontributionof48,000 and contribution of12 per unit, break-even output is 4,000 units. At that output, total revenue equals total cost and profit is zero.

A higher selling price or lower variable cost raises contribution and lowers break-even output; higher fixed cost raises it. Use the result to test whether forecast demand is sufficient.

Break-even output is not a sales target that guarantees success. The model assumes stable price, unit variable cost and fixed cost, and that sales equal output.

Find contribution per unit

contribution per unit=selling price per unit−variable cost per unitcontribution\ per\ unit=selling\ price\ per\ unit-variable\ cost\ per\ unit

A product sold for 25withvariablecostof25 with variable cost of15 contributes $10 per unit. Each unit first contributes toward fixed costs; after total contribution covers fixed costs, further contribution becomes profit.

Contribution supports break-even calculations and short-run product decisions. Compare contribution with any capacity constraint and with the effect on demand, quality and longer-term positioning.

Contribution is not profit because fixed costs still have to be paid. A positive contribution does not automatically mean the whole business is profitable.

Calculate the margin of safety

margin of safety=actual sales−break ⁣− ⁣even salesmargin\ of\ safety=actual\ sales-break\! -\! even\ sales

If actual sales are 5,600 units and break-even sales are 4,000, the margin of safety is 1,600 units. Sales could fall by 1,600 units before the business begins making a loss, under the model’s assumptions.

A larger positive margin provides more protection against a demand fall. A zero margin means break-even; a negative result means current sales are below break-even.

Use the same unit and period for actual and break-even sales. Margin of safety is a volume difference, not profit and not automatically a percentage.