Exercises: Cost structure: classification and calculation

Classify these bakery costs as fixed or variable: premises rent, flour and sugar, the manager's fixed salary, oven electricity (which increases with production), card transaction fees, and depreciation of the bakery equipment.

A business has monthly fixed costs of $3.000\ \text{€}$ and a variable cost per unit of $2\ \text{€}$. If it produces 1 000 units, calculate: a) total variable cost; b) total cost: $CT = CF + CV_u \cdot q$; c) average or unit cost: $CMe = \frac{CT}{q}$.

The figure shows a business's costs against production volume: fixed costs (FC), variable costs (VC) and total costs (TC). Explain what the point marked with "?" represents where the TC line intersects the vertical axis, and why the total cost line starts at that point even when production is zero.

Classify these costs of a bicycle repair workshop as fixed or variable: premises insurance, the brakes and tyres it fits in each repair, the salary of the full-time mechanic, the fee the payment platform charges for each card payment, the annual social media advertising and the workshop's water and electricity, which barely change whether it produces a lot or a little.

A carpentry workshop has fixed costs of $5.000\ \text{€}$ a month and a variable cost per unit of $30\ \text{€}$ per piece of furniture. If it makes 200 pieces of furniture a month, calculate: a) total variable cost; b) total cost: $CT = CF + CV_u \cdot q$; c) the average cost of each piece of furniture: $CMe = \frac{CT}{q}$.

A candle factory produces 500 units a month with a total variable cost of $1.500\ \text{€}$ and fixed costs of $2.000\ \text{€}$. a) Calculate the average variable cost: $CVMe = \frac{CV}{q}$. b) Calculate the total average cost. c) Explain in your own words the difference between the two indicators.

A shop sells 300 backpacks a month at $40\ \text{€}$ each. Its monthly fixed costs are $4.000\ \text{€}$ and the variable cost per unit is $22\ \text{€}$. a) Calculate the total revenue and the total cost for the month. b) Calculate the profit: $B = IT - CT$.

A car park closed for a month due to works and did not have a single car, but its owner kept paying the rent, the insurance and the loan instalment. a) Explain why those costs are called fixed and what other costs disappeared with there being no activity. b) Reason what happened to the car park's profit that month.

A factory has monthly fixed costs of $12.000\ \text{€}$ and a variable cost per unit of $8\ \text{€}$. For a production of 2 000 units, calculate: a) total variable cost; b) total cost; c) average cost. d) Repeat the average cost calculation for 4 000 units and comment on what happened to it.

Explain with a simple numerical example why average cost decreases as production increases even if fixed costs do not change (they are spread over more units), and how this phenomenon relates to economies of scale.

A business can manufacture a part with a variable cost per unit of $5\ \text{€}$ by incurring fixed costs of $20.000\ \text{€}$ per year, or buy it from a supplier at $7\ \text{€}$ per unit. a) Calculate the annual cost of each option if 5 000 parts are needed. b) What if 15 000 parts are needed? c) Comment on the conclusion the business draws from the comparison.

A ceramics factory has fixed costs of $20.000\ \text{€}$ a month and a variable cost per unit of $6\ \text{€}$. a) Calculate the total cost and the average cost if it produces 5 000 pieces a month. b) Repeat the calculations for 10 000 pieces. c) Explain why the average cost changes even though the fixed costs and the variable cost per unit do not vary.

A business sells its product at $50\ \text{€}$, with fixed costs of $30.000\ \text{€}$ a month and a variable cost per unit of $30\ \text{€}$. a) Calculate the monthly profit if it sells 1 000 units. b) Calculate the profit if it sells 2 000 units. c) Comment on how the profit has changed when sales doubled and explain why it has not exactly doubled.

A business has fixed costs of $9.000\ \text{€}$ and a variable cost per unit of $3\ \text{€}$. a) Build a table with the total variable cost, total cost, average cost and average variable cost for production levels of 0, 1,000, 2 000 and 3 000 units. b) Comment on which columns stay constant and which one falls as production increases, and explain why.

You can do it on paper and send a photo with your answer.

A patisserie produces 1 000 cakes a month at a total cost of $8.000\ \text{€}$; producing 1 001 cakes would raise the total cost to $8.006\ \text{€}$. a) Calculate the marginal cost of the additional cake. b) Calculate the average cost of the 1 000 cakes. c) Reason which of the two figures the patisserie should look at to decide whether to accept an extra order at $6,5\ \text{€}$ per cake.

A removals company has these monthly costs: warehouse rent $3.000\ \text{€}$, fixed salaries $9.000\ \text{€}$, fuel $80\ \text{€}$ per removal, hourly loaders $120\ \text{€}$ per removal and advertising $500\ \text{€}$. It carries out 100 removals a month at an average price of $450\ \text{€}$. a) Classify the costs as fixed and variable and calculate the total fixed cost and the variable cost per unit. b) Calculate the total cost and the average cost. c) Calculate the monthly profit.

Compare the cost structure of a highly automated printing house (high fixed costs, very low variable cost per unit) with that of a craft workshop (low fixed costs, high variable cost). a) Which handles a sharp drop in sales better? b) Which earns more when sales skyrocket? Reason your answers using total cost and revenue lines.

A canning factory with annual fixed costs of $200.000\ \text{€}$ and a unit variable cost of $3\ \text{€}$ produces and sells 100.000 cans at a price of $6\ \text{€}$ (its maximum capacity is 140.000 cans). A foreign chain offers to buy a special order of 20.000 cans at $4,20\ \text{€}$ per unit. The commercial director strongly opposes it, stating: "Our current average unit cost is $5\ \text{€}$, so selling at $4,20\ \text{€}$ would mean losing $0,80\ \text{€}$ per can and destroying value." a) Refute the commercial director's position by calculating the average cost before and after the order, as well as the real impact of the offer on the company's annual profit. b) Determine the minimum short-term price that the cannery could accept for that batch of 20.000 cans without incurring losses and justify why it does not coincide with the average cost. c) Identify two strategic or commercial risks that would justify rejecting the proposal even though the short-term numbers are positive.

A restaurant offers two options on its menu: Daily Menu (selling price $12\ \text{€}$, direct ingredients $3\ \text{€}$) and Tasting Menu (price $32\ \text{€}$, direct ingredients $12\ \text{€}$). Each month, it sells 1.800 daily menus and 200 tasting menus. Its monthly indirect costs (rent, premises energy, and fixed kitchen salaries) amount to $9.000\ \text{€}$. Management decides to allocate these indirect costs equally among the total number of meals served ($4,50\ \text{€}$ per menu) and, observing that the Daily Menu only leaves an apparent net margin of $4,50\ \text{€}$ ($12 - 3 - 4,50$), proposes eliminating it to focus only on the Tasting Menu. a) Numerically demonstrate how the restaurant's overall profit would change if it eliminates the Daily Menu, assuming that sales of the Tasting Menu do not increase. b) Justify why the allocation criterion used by management distorts the real profitability of each product (cross-subsidisation). c) Propose an alternative criterion for allocating indirect costs and explain what effect it would have on decision-making.

A snacks brand produces with fixed costs of $120.000\ \text{€}$ a year and a variable cost per unit of $2,5\ \text{€}$, and sells 60 000 packets. A co-packer offers to produce everything for it at $4\ \text{€}$ per packet, with which the brand would eliminate its fixed costs. a) Calculate the annual total cost of producing and of outsourcing. b) Calculate the annual volume above which it would be worthwhile to go back to producing in-house. c) Comment on what non-monetary factors the brand should consider (quality, delivery times, dependence on the supplier).

A board game company sells its product for $35\ \text{€}$ per unit, with annual fixed costs of $50.000\ \text{€}$ and a unit variable cost of $15\ \text{€}$. Given the economic uncertainty, the company estimates that demand next year will range between 2.000 units (pessimistic scenario) and 4.000 units (optimistic scenario). To reduce risks, it considers a change in technology: outsourcing part of the process, which would reduce fixed costs to $20.000\ \text{€}$ but increase the unit variable cost to $22,5\ \text{€}$. a) Calculate the break-even point for the original structure and for the flexible structure. b) Determine the profit of both structures in the pessimistic scenario (2.000 units) and in the optimistic scenario (4.000 units). c) Calculate the sales volume that makes both structures indifferent and justify which of the two options management should choose based on its demand expectations and its risk aversion.

A group has two workshops. Workshop A has fixed costs of $8.000\ \text{€}$ and a variable cost per unit of $12\ \text{€}$; workshop B, fixed costs of $20.000\ \text{€}$ and a variable cost per unit of $7\ \text{€}$. a) Calculate the total cost of producing 1 000 units in each workshop. b) Repeat the calculation for 3 000 units. c) Calculate at what volume both workshops cost the same and reason how the group should split production according to expected demand.

A company has capacity for 5 000 units a month with fixed costs of $40.000\ \text{€}$ and a variable cost per unit of $8\ \text{€}$, and sells all its production at $20\ \text{€}$. It receives an order for 1 000 extra units that it could only fulfil by subcontracting them at $15\ \text{€}$ per unit. a) Calculate the average cost of the 5 000 own units and the profit from selling them. b) Calculate how much it would earn with the 1 000 subcontracted units. c) Reason whether it is worth accepting the extra order and what condition the subcontracting price must meet.

An office furniture company produces 500 desks per month and sells them for $150\ \text{€}$ each. Its monthly costs are: factory premises rent ($4.000\ \text{€}$), machinery depreciation ($1.500\ \text{€}$), fixed salaries ($14.000\ \text{€}$), administration ($2.000\ \text{€}$), wood and fittings ($45\ \text{€}$ per desk), and factory energy ($5\ \text{€}$ per desk). The sales director proposes increasing production and sales by $40\ \%$ (up to 700 desks) and claims: "By producing $40\ \%$ more, our total costs will increase by exactly $40\ \%$, so the profit margin per desk will remain the same." a) Classify the costs into fixed and variable and refute the director's statement by calculating the total cost, average cost, and monthly profit for both 500 and 700 desks. b) Explain the economic reason why the average cost changes when changing the scale of production and identify the associated economic concept. c) If, in order to sell the 700 desks on the market, the company had to apply a discount, calculate the minimum unit price at which it could sell them to maintain exactly the same absolute profit it obtained with 500 units.