Exercises: Business costs, revenue, and profit

The coffee shop "The Corner Cup" has the following costs: premises rent, coffee beans, fixed salary of the waiter, cardboard cups, monthly fee for the card payment terminal, and napkins. Classify them into fixed costs (they exist even if no one comes) and variable costs (they increase with every coffee sold), and explain what happens to each group in August when the neighbourhood is quiet because many locals are away on holidays.

Define total revenue, total cost, and profit, and calculate them in this case: at the market, Julia sells $40$ bracelets at $\text{€}\ 3$ each; the materials for each bracelet cost her $\text{€}\ 0.50$ and the stall cost $\text{€}\ 20$. How much revenue does she take in, how much does she spend, and how much profit does she make?

The figure shows the total revenue (green line) and total costs (red line) of Nayara's group's T-shirt stall, based on the number of T-shirts sold. Each T-shirt is sold for $\text{€}\ 3$, the materials for each cost $\text{€}\ 1$, and the fixed costs of the stall are $\text{€}\ 60$.

1. a) Do the calculations to find how many T-shirts must be sold for total revenue and total costs to be equal, and explain what the point marked with the question mark represents.
2. b) Explain what happens on the graph to the left and to the right of that point (where there are losses and where there are profits) and what would happen to the point if fixed costs increased.

The 'Rizos' hairdresser's pays: the rent of the premises, the dyes and shampoos it uses with each customer, the hairdresser's fixed wage, the water and electricity (which rise with every wash), the insurance premium and the disposable towels.

1. a) Classify each cost as fixed or variable.
2. b) Explain what happens to profits in a quiet January, when fixed costs are still there but variable ones fall.

At the neighbourhood fete, Kim's lemonade stall sells $80$ cups at $\text{€}\ 1.50$; the lemons, sugar and cups cost him $\text{€}\ 0.40$ per cup, and the awning and posters, $\text{€}\ 15$.

1. a) Calculate his total revenue.
2. b) Calculate his total costs (fixed plus variable).
3. c) Calculate his profit for the day.

The price of a product doesn't come out of nowhere: the shop adds up its costs and adds a margin. At the bookshop, a notebook costs $\text{€}\ 4$ to buy in and sells at $\text{€}\ 6$.

1. a) Calculate the margin per notebook and explain what that margin is for (paying the fixed costs and, if anything is left, making a profit).
2. b) Explain two reasons why the same notebook can have different prices in two shops.

A gym has fixed costs of $\text{€}\ 2,400$ a month and $120$ members paying a $\text{€}\ 25$ fee; each new member barely adds costs.

1. a) Calculate its revenue and its monthly profit.
2. b) Calculate the fixed cost each member 'carries' (the $\text{€}\ 2,400$ split among the $120$) and explain why the gym is so keen to sign up new members.

Explain the difference between high turnover and high profit with this case: shop A sells $\text{€}\ 10,000$ a month with costs of $\text{€}\ 9,500$; shop B sells $\text{€}\ 4,000$ with costs of $\text{€}\ 3,000$.

1. a) Calculate each one's monthly profit.
2. b) Which one 'moves' more money and which one is more profitable? Say which you would rather own and justify it.

The bicycle repair shop "La Rueda" pays $\text{€}\ 900$ per month in rent and utilities, regardless of how many repairs it carries out. It charges $\text{€}\ 30$ per repair and parts cost an average of $\text{€}\ 10$.

1. a) Calculate the margin left by each repair and how many repairs are needed per month to cover fixed costs.
2. b) If it carried out $60$ repairs this month, calculate its profit.
3. c) Explain what would happen to these figures if the landlord raised the rent.

The food truck "El Perrito Viajero" sells each hot dog for $\text{€}\ 5$; the roll, sausage, and ingredients cost $\text{€}\ 2$ per hot dog, and the monthly fixed costs (insurance, permits, fuel) are $\text{€}\ 600$.

1. a) Calculate the profit if it sells $250$ hot dogs.
2. b) Calculate how many hot dogs it needs to sell per month to avoid losing money.
3. c) To attract customers, it is considering lowering the price to $\text{€}\ 4$: calculate the new break-even point and advise whether this move could work out well or badly.

The bakery "Dulce Vera" sells each cake for $\text{€}\ 18$. Until now, the ingredients for each cake cost $\text{€}\ 6$, but chocolate prices have gone up and they now cost $\text{€}\ 8$. The bakery's fixed costs are $\text{€}\ 480$ per month.

1. a) Calculate how many cakes it had to sell per month to cover costs before the price increase.
2. b) Calculate how many it needs now.
3. c) Propose two decisions to return to the previous figure without reducing quality, and verify them with numbers.

The fair's churro stall sells each portion at $\text{€}\ 4$; the ingredients cost $\text{€}\ 1.20$ per portion and the fixed expenses (booth rental, electricity, permit) are $\text{€}\ 420$ per fair.

1. a) Calculate the margin each portion leaves.
2. b) Calculate how many portions it needs to sell to cover costs.
3. c) If the fair lasts $4$ days and it sells $90$ portions a day, calculate the profit for the fair.

At the 'Trigo y Miel' bakery, each loaf sells at $\text{€}\ 1.30$ and the ingredients cost $\text{€}\ 0.50$; fixed expenses are $\text{€}\ 1,600$ a month.

1. a) Calculate how many loaves must be sold a month to cover costs.
2. b) The price of flour rises and the cost per loaf goes up to $\text{€}\ 0.60$: calculate the new break-even point.
3. c) Explain why a small rise in the variable cost moves the number of loaves needed so much.

The neighbourhood print shop can only accept one of these two jobs this month: (A) $2,000$ posters at $\text{€}\ 0.50$ with a material cost of $\text{€}\ 0.20$ each; (B) $300$ banners at $\text{€}\ 8$ with a cost of $\text{€}\ 3$ each.

1. a) Calculate the total margin of each job.
2. b) Say which you would choose if both take the same time and what else you would ask before deciding (whether the customer is trustworthy, whether they will come back, whether a new machine is needed).

The internet café buys a $\text{€}\ 600$ 3D printer to print parts to order; each part leaves a margin of $\text{€}\ 3$ after paying for the material.

1. a) Calculate how many parts it needs to print to pay off the printer (recover what was paid for it).
2. b) If it prints about $25$ parts a month, calculate in how many months it recovers it and explain why an investment must be 'paid off' before it yields profits.

The artisan bakery buys flour in sacks at $\text{€}\ 0.80$ a kilo; if it buys a whole pallet, the kilo drops to $\text{€}\ 0.60$. Each loaf takes $0.3$ kg of flour and it produces $3,000$ loaves a month.

1. a) Calculate how much flour it uses a month and how much it would save by buying the pallet.
2. b) Explain why producing on a large scale usually cheapens the cost per unit (economies of scale) and give another example from your neighbourhood.

The local delivery app "RepartoSur" charges $\text{€}\ 3$ per order and pays $\text{€}\ 2$ to the delivery driver who carries it out. Its fixed costs (office, licences, advertising) are $\text{€}\ 2,000$ per month.

1. a) Calculate how many orders it needs per month to cover costs.
2. b) Last month it fulfilled $1,700$ orders: calculate the result and reason whether the business should close now or hold on, taking into account that its orders are growing every month.
3. c) Propose two measures (increasing the price to $\text{€}\ 3.50$, charging restaurants a fixed monthly fee) and analyse a risk associated with each.

The stationer's "El Tintero" sells $100$ backpacks a month for $\text{€}\ 25$ each; each backpack costs $\text{€}\ 12$ from the supplier, and its fixed costs are $\text{€}\ 1,040$ per month. The owner is considering lowering the price to $\text{€}\ 22$ and believes that doing so would increase sales to $150$.

1. a) Calculate the current profit.
2. b) Calculate the expected profit with the discount and decide whether it is worthwhile.
3. c) Calculate how many backpacks it would need to sell at $\text{€}\ 22$ to make exactly the same profit as now, and assess the risk of the discount if sales do not rise as much as expected.

"As long as I sell, the business is going well." Bruno sells customised T-shirts for $\text{€}\ 10$ each; each one costs him $\text{€}\ 9$ in total for the T-shirt and ink, and he pays $\text{€}\ 150$ per month for his workshop-storage unit. This month he has sold $100$.

1. a) Calculate his financial result for the month and explain why selling a lot is not enough: use the margin per T-shirt and fixed costs.
2. b) Calculate how many T-shirts he needs to sell per month just to cover costs.
3. c) Propose two solutions (raising the price to $\text{€}\ 12$, sharing the workshop with another craftsperson) and verify with numbers that they work.

The 'Kronos' gym has fixed costs of $\text{€}\ 3,600$ a month and almost no variable cost; each member pays a $\text{€}\ 30$ fee.

1. a) Calculate how many members it needs to cover costs.
2. b) Today it has $100$ members: calculate its monthly result and explain the risk of a business with so many fixed costs if it suddenly loses $30$ members (for example, if another gym opens opposite).
3. c) Propose two strategies to keep members loyal (annual fee with a discount, classes included) and analyse what effect each one has on revenue.

'If I lower the price, I'll sell more, so lowering it always pays off.' Answer with numbers: a shop sells $200$ phone cases at $\text{€}\ 10$ with a cost of $\text{€}\ 4$ per case, and is considering lowering the price to $\text{€}\ 8$.

1. a) Calculate the current margin and how many cases it would have to sell at $\text{€}\ 8$ to earn the same.
2. b) Explain why the statement fails almost always and say in which two specific cases lowering the price could pay off (stock that expires, entering a new market).

The 'Volcán' pizzeria sells $1,500$ pizzas a month at $€9$; each one costs it $€3.50$ and its fixed expenses are $€5,000$. Deliveries are done by a rider it pays $€1$ per pizza delivered, and $60\ \%$ of the pizzas are home deliveries.

1. a) Calculate the current monthly profit.
2. b) It is considering charging home-delivery customers a $€1.50$ delivery fee: calculate the new profit if sales don't change.
3. c) Assess the risk of the measure (fewer delivery orders or customers going to the competition) and propose an alternative.

The 'Babel' bookshop has been selling $\text{€}\ 2,800$ a month for three months. Its fixed costs are $\text{€}\ 2,000$ and its variable ones, $40\ \%$ of sales.

1. a) Calculate its total costs and its monthly result.
2. b) Calculate what sales it would need to cover all its costs.
3. c) The owner is torn between closing or holding out for six more months with a campaign: explain what data would help her decide (whether sales at least cover the variable costs, whether the campaign can raise them, whether she has savings to hold out) and argue what you would do.

Your class is setting up the end-of-year party stall. Design the viability plan:

1. a) Estimate the fixed costs (permit, awning, posters) and the variable costs of your product with real prices you find out.
2. b) Set a selling price and calculate the break-even point.
3. c) Write a paragraph assessing whether the number of units needed is realistic for a four-hour party and what you would do if it were not.

Topic Challenge. Test the viability of your very own microenterprise! Design a project to market an artisanal product (such as baked goods, soaps, or printed T-shirts) in your local area.

1. Factors and sectors: Classify your activity into the corresponding economic sector and draw up a table detailing the required productive factors: natural resources/land (raw materials), labour (time spent), and capital (tools or machinery).

2. Collection of real costs: Go to the website of a real supermarket or distributor and record the actual prices of the ingredients or materials to calculate the unit variable cost ($CV_u$, for example, $1.35$ € per unit). Also estimate reasonable monthly fixed costs ($CF$, such as electricity or minimum utility fees).

3. Breakeven and profits: Set a retail selling price ($P$). Apply the breakeven point formula, $Q^* = \frac{CF}{P - CV_u}$, to find out how many units you need to sell to avoid losses. Write a brief one-page report with a table calculating total revenue ($IT$), total costs ($CT$), and profit ($B = IT - CT$) for three different sales levels.

Evaluation criteria:

• Thoroughness in the classification of productive factors and definition of the economic sector.

• Realism of the collected cost data and mathematical accuracy in calculating the breakeven point ($Q^*$) and profits.

• Economic coherence and clarity of presentation in the submitted final report.