Business · 4 Operations management

4.4.1 Identify and classify costs

Before you start

What output means: the number of units a business produces in a period, such as a month.
Revenue = Selling price per unit × number of units sold, and Profit = Total revenue – total costs.
Multiplying and dividing with a calculator, including amounts of money with cents.

Syllabus objectives covered (2)

classify and calculate costs using examples, e.g. fixed, variable, average and total
use cost data to help make simple decisions, e.g. which product to produce, whether to continue or stop production, what price to set, help choose suppliers

Part 1 of 4

Fixed or variable: the one question to ask

A cost is money a business spends to produce and sell its goods or services. Before you can calculate anything, you sort costs into two kinds, and one question does the sorting: does this cost change when the business makes more?
Fixed costs do not change when output changes. A bakery pays the same rent whether it bakes 100 cakes this month or 3,000. Examples: rent, insurance, managers' salaries, interest on a loan, a monthly website fee.
Variable costs change directly with output. Every extra cake needs more flour, more eggs and another box, so these costs rise as output rises — and fall to zero if nothing is made. Examples: raw materials, packaging, wages paid for each item produced.
The first trap: fixed does not mean the cost can never change. The landlord can put the rent up next year and it is still a fixed cost, because it does not change with output. Always test a cost against output, not against time.
The second trap is wages. A manager on a monthly salary is paid the same whatever the output, so her salary is a fixed cost. A worker paid for each item made costs more when more is made, so that is a variable cost. Read how the pay is described before you classify it.
Notice what this means at zero output: variable costs disappear, but fixed costs still have to be paid. That is why a business can make a loss even while it is selling, and it is the starting point for break-even analysis in 4.4.3.

Part 2 of 4

Calculating total cost and average cost

None of the cost formulas is printed on the exam paper, so you must recall them. Write the formula line first and the numbers second: if the calculator slips, the method is still on the page.
Total variable cost is the variable cost of one unit multiplied by the number of units.
$Total variable cost = Variable cost per unit \times number of units$
If you are given the total variable cost instead, divide to get back to one unit.
$Variable cost per unit = \frac{Total variable cost}{Number of units}$
Total cost adds the two kinds together.
$Total cost = Total fixed costs + total variable costs$
Average cost is the cost of producing each unit, on average: total cost shared equally across every unit made.
$Average cost = \frac{Total cost}{Number of units}$
Try it on Crumb & Co, a bakery. Its fixed costs are $$ 4,000$ a month: rent $$ 1,800$ , the manager's salary $$ 2,000$ and insurance $$ 200$ . Each cake uses $$ 3.00$ of ingredients and a $$ 0.50$ box, so the variable cost per cake is $$ 3.50$ .
At 1,000 cakes a month: total variable cost = $$ 3.50$ × 1,000 = $$ 3,500$ . Total cost = $$ 4,000$ + $$ 3,500$ = $$ 7,500$ . Average cost = $$ 7,500$ ÷ 1,000 = $$ 7.50$ per cake.
At 2,000 cakes a month: total variable cost = $$ 3.50$ × 2,000 = $$ 7,000$ . Total cost = $$ 4,000$ + $$ 7,000$ = $$ 11,000$ . Average cost = $$ 11,000$ ÷ 2,000 = $$ 5.50$ per cake.
Look at what happened. Total cost rose, from $$ 7,500$ to $$ 11,000$ . Average cost fell, from $$ 7.50$ to $$ 5.50$ . The reason is the fixed costs: $$ 4,000$ shared between 1,000 cakes is $$ 4.00$ a cake, but shared between 2,000 cakes it is only $$ 2.00$ a cake.
The trap here is dividing only the variable costs by output. $$ 3,500$ ÷ 1,000 = $$ 3.50$ is the variable cost per unit, not the average cost. Average cost includes the fixed costs, so always start from total cost.

Part 3 of 4

Decisions: what price to set, and which product to make

Cost figures matter because they change what a business does. The syllabus gives four examples of decisions they help with: which product to produce, whether to continue or stop production, what price to set, and which supplier to choose.
What price to set. If the price is below average cost, every unit sold loses money. At 1,000 cakes Crumb & Co's average cost is $$ 7.50$ , so a price of $$ 7.00$ loses money on every cake, while a price of $$ 9.00$ earns $$ 1.50$ profit on each one.
Be careful: average cost depends on how many units are made. A $$ 7.00$ price is above average cost at 2,000 cakes ( $$ 5.50$ ) but below it at 1,000 cakes ( $$ 7.50$ ). A price based on average cost is only safe if the business really will sell that many.
Which product to produce. Compare how much each product earns above its cost. If Crumb & Co's muffins sell for $$ 3.00$ and cost $$ 1.80$ each on average, it keeps $$ 1.20$ per muffin. If its cookies sell for $$ 2.00$ and cost $$ 1.60$ , it keeps only $$ 0.40$ per cookie.
So if the bakery has room in its ovens to make more of only one of them, muffins add more profit per unit. The cost data turns a guess into a comparison.

Part 4 of 4

Decisions: whether to stop production, and which supplier to use

Whether to continue or stop production. A product that shows a loss is not automatically worth stopping. Stopping it saves its variable costs, but fixed costs such as rent still have to be paid.
Suppose Crumb & Co sells 500 pies a month at $$ 5.00$ each. Each pie has a variable cost of $$ 3.00$ , and $$ 1,500$ of the bakery's rent is charged to the pies. Revenue is $$ 2,500$ and total cost is $$ 1,500$ + $$ 1,500$ = $$ 3,000$ , so the pies seem to make a $$ 500$ loss.
Now stop the pies. The $$ 1,500$ of variable costs disappears, but so does $$ 2,500$ of revenue, and the $$ 1,500$ of rent is still paid. The bakery is $$ 1,000$ worse off than before: each pie was bringing in $$ 2.00$ more than its variable cost, and that money was helping to pay the rent.
So ask: does the selling price cover the variable cost of each unit? If it does, the product is helping to pay the fixed costs, and stopping it lowers total profit. If it does not, every unit made adds to the loss, and stopping makes sense.
Which supplier to choose. Compare the total cost of the quantity you actually need from each supplier, including any fixed charge such as delivery. The lowest price per unit is not always the cheapest order — the third worked example shows why.
Cost is never the whole story. A cheaper supplier who delivers late, or a cheaper ingredient that customers notice, can lose the business sales and reputation. In a longer answer, weighing cost against reliability and quality is what turns a calculation into a justified decision.

Worked examples

Example 1. InkWave prints designs on T-shirts. Each month it pays rent of $$ 600$ , insurance of $$ 150$ and a website fee of $$ 50$ . For each T-shirt it pays $$ 4.00$ for the blank shirt and $$ 1.00$ for ink. In May it printed 400 T-shirts. Classify InkWave's costs, then calculate its total cost and average cost for May.

Show the working

Classify each cost by asking whether it changes when InkWave prints more shirts. Rent, insurance and the website fee stay the same, so they are fixed. Blank shirts and ink rise with every shirt, so they are variable.
Total fixed costs:
$$ 600 + $ 150 + $ 50 = $ 800$
Variable cost per unit is the materials for one shirt:
$$ 4.00 + $ 1.00 = $ 5.00$
Total variable cost — formula first, then numbers:
$Total variable cost = $ 5.00 \times 400 = $ 2,000$
Total cost:
$Total cost = $ 800 + $ 2,000 = $ 2,800$
Average cost divides total cost, not variable cost, by output:
$Average cost = \frac{$ 2,800}{400} = $ 7.00$
Check it is sensible. Average cost must be more than the $$ 5.00$ variable cost, because each shirt also carries a share of the fixed costs: $$ 800$ ÷ 400 = $$ 2.00$ , and $$ 5.00$ + $$ 2.00$ = $$ 7.00$ .

Answer: Fixed: rent, insurance and website fee ( $$ 800$ in total). Variable: blank shirts and ink ( $$ 5.00$ per shirt). Total cost $$ 2,800$ ; average cost $$ 7.00$ per T-shirt.

Example 2. InkWave sells its T-shirts for $$ 8.00$ each. In a quiet month it prints and sells only 200. Calculate the average cost at 200 T-shirts, and consider whether $$ 8.00$ is a sensible price at 200 and at 400 T-shirts.

Show the working

Total variable cost at 200 shirts:
$$ 5.00 \times 200 = $ 1,000$
Total cost — the fixed costs are still $$ 800$ , because they do not change with output:
$$ 800 + $ 1,000 = $ 1,800$
Average cost:
$\frac{$ 1,800}{200} = $ 9.00$
At 400 shirts average cost is $$ 7.00$ (from the first example). A price of $$ 8.00$ is $$ 1.00$ above that, so InkWave makes $$ 1.00$ profit per shirt: $$ 400$ for the month.
At 200 shirts average cost is $$ 9.00$ . The same $$ 8.00$ price is now $$ 1.00$ below average cost: a loss of $$ 1.00$ per shirt, $$ 200$ for the month.
Nothing changed in the price or in the cost of materials. What changed is how many shirts shared the $$ 800$ of fixed costs. That is why a price decision must be tied to a realistic sales figure.

Answer: Average cost at 200 T-shirts is $$ 9.00$ . A price of $$ 8.00$ makes a profit at 400 shirts ( $$ 400$ ) but a loss at 200 shirts ( $$ 200$ ), so it is only sensible if InkWave expects to sell well above 200.

Example 3. InkWave needs blank T-shirts. Supplier A charges $$ 4.20$ per shirt with free delivery. Supplier B charges $$ 3.80$ per shirt plus a delivery charge of $$ 100$ for each order. Calculate which supplier is cheaper for an order of 400 shirts, and for an order of 200 shirts.

Show the working

Compare the total cost of each whole order. Comparing only the price per shirt would ignore Supplier B's delivery charge.
400 shirts from Supplier A:
$$ 4.20 \times 400 = $ 1,680$
400 shirts from Supplier B. The delivery charge is paid once per order, so add it after multiplying:
$($ 3.80 \times 400) + $ 100 = $ 1,520 + $ 100 = $ 1,620$
For 400 shirts Supplier B is cheaper, by $$ 1,680$ − $$ 1,620$ = $$ 60$ .
200 shirts from Supplier A:
$$ 4.20 \times 200 = $ 840$
200 shirts from Supplier B:
$($ 3.80 \times 200) + $ 100 = $ 760 + $ 100 = $ 860$
For 200 shirts Supplier A is cheaper, by $$ 20$ . Supplier B saves $$ 0.40$ on each shirt, but on 200 shirts that is only $$ 80$ — not enough to cover the $$ 100$ delivery charge. On 400 shirts the saving is $$ 160$ , which is.
Before deciding, InkWave should also ask which supplier is more reliable and whose shirts are better quality. A cheap shirt that fades after one wash costs InkWave customers.

Answer: 400 shirts: Supplier B is cheaper ( $$ 1,620$ against $$ 1,680$ ). 200 shirts: Supplier A is cheaper ( $$ 840$ against $$ 860$ ).

Where people go wrong

Mistake: Calling rent a variable cost because the landlord put it up this year.

Instead: Rent is a fixed cost. Classify a cost by whether it changes with output.

Fixed costs can change over time. What makes them fixed is that making more units does not change them.

Mistake: Dividing total variable cost by output and calling the answer average cost.

Instead: Average cost = Total cost ÷ Number of units, and total cost includes the fixed costs.

Leaving out fixed costs gives the variable cost per unit. It understates what each unit really costs, and a price set from it can make a loss.

Mistake: Assuming average cost is the same whatever the level of output.

Instead: Recalculate average cost for the output in the question. With fixed costs of $$ 800$ , it was $$ 7.00$ per shirt at 400 shirts and $$ 9.00$ at 200.

The fixed costs are shared over however many units are made, so fewer units means each carries a bigger share.

Mistake: Deciding to stop any product that shows a loss.

Instead: First check whether its price covers its variable cost per unit.

The fixed costs charged to it are still paid after it stops. If the price is above variable cost, the product was helping to pay them, and stopping it lowers total profit.

Mistake: Choosing the supplier with the lowest price per unit without adding charges such as delivery.

Instead: Compare the total cost of the quantity actually needed.

A fixed charge per order matters most on small orders, so the cheaper supplier can change with the size of the order.

Check yourself

For a pizza restaurant, classify each cost as fixed or variable: cheese, rent of the building, the head chef's monthly salary, pizza boxes, insurance.
Answer
Fixed: rent, the head chef's monthly salary, insurance. Variable: cheese, pizza boxes.
A business has fixed costs of $$ 2,500$ a month and a variable cost per unit of $$ 6$ . Calculate the total cost of making 500 units.
Answer
Total variable cost = $$ 6$ × 500 = $$ 3,000$ . Total cost = $$ 2,500$ + $$ 3,000$ = $$ 5,500$ .
Calculate the average cost of those 500 units.
Answer
Average cost = Total cost ÷ Number of units = $$ 5,500$ ÷ 500 = $$ 11.00$ per unit.
Total variable cost is $$ 4,800$ for 1,200 units. Calculate the variable cost per unit.
Answer
Variable cost per unit = Total variable cost ÷ Number of units = $$ 4,800$ ÷ 1,200 = $$ 4.00$ .
When Crumb & Co doubled its output from 1,000 to 2,000 cakes, its total cost rose but its average cost fell. Explain why.
Answer
Total cost rose because variable costs rose with output. Average cost fell because the $$ 4,000$ of fixed costs was shared over twice as many cakes, so each cake carried $$ 2.00$ of fixed costs instead of $$ 4.00$ .
A product sells for $$ 10$ . Its variable cost per unit is $$ 7$ and its average cost is $$ 12$ , so it makes a loss. Explain why stopping it could lower the business's total profit.
Answer
Each unit sells for $$ 3$ more than its variable cost, and that $$ 3$ helps pay fixed costs that would still have to be paid if the product stopped. Stopping it loses $$ 3$ towards the fixed costs for every unit no longer sold.
Supplier X charges $$ 2.50$ per unit with no delivery charge. Supplier Y charges $$ 2.00$ per unit plus $$ 150$ delivery. Which is cheaper for an order of 250 units?
Answer
X: $$ 2.50$ × 250 = $$ 625$ . Y: ( $$ 2.00$ × 250) + $$ 150$ = $$ 650$ . Supplier X is cheaper, by $$ 25$ .
State four decisions that cost data can help a business make.
Answer
Which product to produce; whether to continue or stop production; what price to set; which supplier to choose.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. Sunita owns FreshPress, a small business that makes bottled fruit juice. FreshPress rents a unit on an industrial estate and pays two workers monthly salaries. Its fixed costs are $$ 3,000$ per month. Each bottle of juice uses $$ 0.90$ of fruit and $$ 0.30$ for the bottle and label. In June, FreshPress produced and sold 5,000 bottles at $$ 2.00$ each.

(a) Define 'variable costs'. 2 marks

Mark scheme

pt2 Award 2 marks for clear understanding, 1 mark for some understanding. Clear: costs that change directly with the level of output / rise as more units are produced (2). Some: costs that change (1). Do not award examples, such as fruit, as they do not define the term.

(b) Calculate the average cost of a bottle of juice in June. 2 marks

Mark scheme

pt1 Correct method: ( $$ 3,000$ + ( $$ 1.20$ × 5,000)) ÷ 5,000 / $$ 9,000$ ÷ 5,000. Do not award $$ 1.20$ × 5,000 ÷ 5,000, which leaves out fixed costs.
pt1 Correct answer: $$ 1.80$ per bottle. A correct answer with no working earns both marks.

(c) Outline two ways FreshPress could use its cost data to make decisions. 4 marks

Mark scheme

k1 First way identified, e.g. setting a price above average cost / deciding whether to continue or stop making a product / comparing suppliers / choosing which product to produce.
app1 Applied to FreshPress, e.g. a price above the $$ 1.80$ average cost of a bottle / comparing fruit suppliers against the $$ 0.90$ of fruit per bottle / choosing between its juices.
k1 Second, different way identified. Do not credit the same way twice.
app1 Applied to FreshPress, e.g. its fixed costs of $$ 3,000$ / 5,000 bottles / the $$ 2.00$ price. The reference must make sense for the point made.

(d) FreshPress also makes mango juice. It sells 1,000 bottles a month at $$ 1.50$ each. The variable cost of a bottle of mango juice is $$ 1.10$ , and $$ 600$ of the monthly fixed costs are charged to mango juice, so it appears to make a loss of $$ 200$ a month. Do you think Sunita should stop producing mango juice? Justify your answer. 8 marks

Mark scheme

k2 Identification of relevant points, e.g. fixed costs remain if a product is stopped / the price covers the variable cost per unit / other products would carry more of the fixed costs / the resources could make a more profitable product / customers may buy other juices because mango is offered.
app2 Relevant application, e.g. $$ 1.50$ price against $$ 1.10$ variable cost / $$ 0.40$ per bottle / $$ 400$ a month / $$ 600$ of fixed costs still paid / 1,000 bottles / fruit juice.
an2 Relevant development, e.g. the $$ 400$ a month helps pay the rent and salaries, so stopping would lower FreshPress's total profit by $$ 400$ / the $$ 600$ of fixed costs would move onto the other juices, raising their average cost / the freed capacity could make a juice that brings in more than $$ 400$ a month.
eval2 A justified decision, e.g. "Sunita should keep mango juice, because the $$ 600$ of fixed costs would be paid anyway, and each bottle brings in $$ 0.40$ more than it costs to make, so stopping would cut profit by $$ 400$ a month — unless the space and workers could be used for a juice that earns more." The justification should not repeat earlier points.

Question 2. FreshPress needs 4,000 kg of oranges each month. Supplier P charges $$ 0.60$ per kg with free delivery. Supplier Q charges $$ 0.55$ per kg plus a delivery charge of $$ 250$ per month. Supplier Q delivered late twice this year.

(a) Calculate the monthly cost of 4,000 kg of oranges from each supplier. 2 marks

Mark scheme

pt1 Supplier P: $$ 2,400$ ( $$ 0.60$ × 4,000).
pt1 Supplier Q: $$ 2,450$ (( $$ 0.55$ × 4,000) + $$ 250$ ).

(b) Explain one advantage and one disadvantage for FreshPress of choosing Supplier Q. 6 marks

Mark scheme

k1 Advantage identified, e.g. lower price per kg / cheaper on large orders.
app1 Applied, e.g. $$ 0.55$ per kg against $$ 0.60$ / Q becomes cheaper above 5,000 kg a month / oranges for its juice.
an1 Developed, e.g. if FreshPress grows and buys more oranges, its variable cost per bottle would fall, raising profit per bottle.
k1 Disadvantage identified, e.g. more expensive in total at the current quantity / unreliable deliveries.
app1 Applied, e.g. $$ 50$ a month more than Supplier P / delivered late twice this year / 4,000 kg.
an1 Developed, e.g. higher costs raise the average cost of each bottle and reduce profit / late fruit could stop production, so orders are missed and customers lost.

How this is examined

Weighing a cost-based decision, such as stopping a product or switching supplier: a final 8-mark part, "Do you think…? Justify your answer.", set around the business's own cost figures Points for both sides, each tied to the business's figures and developed into a consequence ("each bottle sells for $$ 0.40$ more than its variable cost, so stopping loses $$ 400$ a month towards the fixed costs"), then a decision that says why one side matters more for this business — without repeating the earlier points.
Explaining how cost data helps a business decide: an Explain part (6) or Outline part (4) about a named business Name the decision [k], use the business's product or numbers [app], and for Explain say what follows — higher profit per unit, avoiding a loss, a lower average cost [an].
Calculating total cost and average cost from given data: a short Calculate part, often worth 2 marks The formula line written first (Average cost = Total cost ÷ Number of units) shows a correct method even if the final figure slips. Total cost must include fixed costs; the correct final figure alone earns full marks.
Defining or classifying fixed and variable costs: a Define (2) or Identify part, or a step inside a calculation A definition that mentions output: "costs that do not change when output changes" / "costs that change directly with output". Examples on their own do not define the term.

Words to know

Fixed costs: Costs that do not change when output changes, such as rent and managers' salaries.
Variable costs: Costs that change directly with output, such as raw materials and packaging.
Total cost: Total fixed costs + total variable costs.
Average cost: The cost of producing each unit on average: Total cost ÷ Number of units.
Output: The number of units a business produces in a period of time.

All Business lessons Next: 4.4.2 Economies and diseconomies of scale