commercial calculation indicator | 9 Exercises

Application: The Delights of Mary

States :

Les Délices de Marie is an artisanal bakery and pastry shop located in the heart of Lyon. It wants to optimize its sales prices and inventory management. You have the following data: Unit purchase price of croissants: €0,80 excluding VAT, Unit sales price excluding VAT: €1,50, Quantity sold per week: 750, Annual storage cost: 25%, Order cost: €50.

Work to do :

1. Calculate the unit margin of the croissants.

2. Determine the margin rate for croissants.

3. Determine the markup rate of the croissants.

4. Calculate the overall weekly margin of croissants.

5. Use the QEC (Economic Order Quantity) formula to optimize weekly inventory.

Proposed correction:

1. The unit margin is calculated by subtracting the pre-tax purchase price from the pre-tax selling price.

   Unit margin = PV excluding tax – PA excluding tax = €1,50 – €0,80 = €0,70.

   Thus, the unit margin for croissants is €0,70.

2. The margin rate is given by the formula:

   ((PV HT – PA HT) ÷ PA HT) x 100.

   Replacing, ((€1,50 – €0,80) ÷ €0,80) x 100 = 87,50%.

   The margin rate for croissants is therefore 87,50%.

3. The markup rate is given by the formula:

((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€1,50 – €0,80) ÷ €1,50) x 100 = 46,67%.

Thus, the markup rate for croissants is 46,67%.

4. The overall weekly margin is calculated by multiplying the unit margin by the quantity sold.

   Overall margin = Unit margin x Quantity sold = €0,70 x 750 = €525.

   So the overall weekly margin is €525.

5. Let’s calculate the QEC to optimize stocks:

   QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).

   Assuming annual demand based on weekly sales (750 x 52 weeks), we have:

   QEC = ?((2 x 39 x 000) ÷ 50) = ?0,25 = 3 (approximately).

   Therefore, the economic order quantity is approximately 1 units.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Overall margin	Unit margin x Quantity sold
Economic Order Quantity (EOQ)	?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Tech Innovators

States :

Tech Innovators, a start-up specializing in online management software, wants to evaluate the profitability of its new software. The purchase price of the software is set at €10 excluding VAT. They plan to sell it at €000 excluding VAT. Their initial forecast is to sell 15 units per year. The annual promotion cost is €000, and the annual hosting rate on servers is €120.

Work to do :

1. Calculate the margin rate on the new software.

2. Determine the projected annual turnover.

3. Find the break-even point in number of software to sell to cover the fixed costs of promotion and hosting.

4. Estimate the total annual margin in euros.

5. What would be the profitability if the purchase cost was reduced by 10%?

Proposed correction:

1. The margin rate is given by the formula:

   ((PV HT – PA HT) ÷ PA HT) x 100.

   Substituting, ((€15 – €000) ÷ €10) x 000 = 10%.

   The software margin rate is therefore 50%.

2. The forecast annual turnover is calculated by:

   PV HT x Quantity sold = €15 x 000 = €120.

   So the forecast annual turnover is €1.

3. To find the break-even point, we must first add up the fixed costs (promotion + accommodation):

Fixed costs = €1 + €500 = €3.

Break-even point = Fixed costs ÷ Unit margin.

Unit margin = PV excluding tax – PA excluding tax = €15 – €000 = €10.

Break-even point = €4 ÷ €500 = 5.

Since the number of software must be an integer, the break-even point is 1 software to sell (rounding up).

4. The total annual margin is calculated by:

   Unit margin x Quantity sold = €5 x 000 = €120.

   The total annual margin is therefore €600.

5. If the purchase cost is reduced by 10%, it becomes:

   New PA excluding tax = €10 – (€000 x 10%) = €000.

   New unit margin = PV excluding tax – New PA excluding tax = €15 – €000 = €9.

   New total annual margin = €6 x 000 = €120.

   Thus, with the reduced purchase cost, profitability would increase considerably, reaching a total annual margin of €720.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Turnover	PV HT x Quantity sold
Break even	Fixed costs ÷ Unit margin
Total annual margin	Unit margin x Quantity sold

Application: Fashion Forward

States :

Fashion Forward, a fashion company in Paris, is in the middle of launching their new clothing collection. The purchase price of a dress is €40 excluding VAT, and the selling price excluding VAT is €80. They plan to sell 2000 dresses this season. The marketing cost for the season is €8, and the additional production costs amount to €000.

Work to do :

1. Calculate the markup rate for dresses.

2. Determine the total revenue for the season.

3. Estimate the break-even point in number of dresses.

4. Calculate the net margin for the season in euros.

5. Suggest an improvement strategy if the mark rate was 60%.

Proposed correction:

1. The markup rate is calculated using the formula:

   ((PV HT – PA HT) ÷ PV HT) x 100.

   Replacing, ((€80 – €40) ÷ €80) x 100 = 50%.

   So, the markup rate of dresses is 50%.

2. The total turnover for the season is calculated by:

   PV HT x Quantity sold = €80 x 2000 = €160.

   So the total turnover for the season is €160.

3. The break-even point is calculated to cover total fixed costs (marketing + production).

Fixed costs = €8 + €000 = €12.

Unit margin = PV excluding tax – PA excluding tax = €80 – €40 = €40.

Break-even point = Fixed costs ÷ Unit margin = €20 ÷ €000 = 40 dresses.

The break-even point is therefore 500 dresses.

4. The net margin for the season is calculated by considering the fixed costs:

   Total margin = Unit margin x Quantity sold = €40 x 2000 = €80.

   Net margin = Total margin – Fixed costs = €80 – €000 = €20.

   So the net margin for the season is €60.

5. To achieve a 60% markup rate, the formula is:

   PV HT = PA HT ÷ (1 – Mark rate).

   New PV HT target = €40 ÷ (1 – 0,60) = €100.

   To improve profitability, Fashion Forward could consider increasing the selling price to €100 to approach this markup rate, but should at the same time monitor the impact on demand.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Turnover	PV HT x Quantity sold
Break even	Fixed costs ÷ Unit margin
Net margin	Total Margin – Fixed Costs
PV HT adjustment	PA HT ÷ (1 – Mark rate)

Application: Green Garden Supplies

States :

Green Garden Supplies is a gardening company that sells electric lawnmowers. The purchase price of a lawnmower is €150 excluding VAT and the selling price excluding VAT is €250. They have sold 500 lawnmowers this year. The transport and logistics costs for the lawnmowers are €5 per year. The annual storage cost is 000% of the stock value.

Work to do :

1. Determine the margin rate for mowers.

2. Calculate the gross margin obtained on annual sales.

3. Estimate the total storage costs for the year.

4. Calculate the break-even point in number of mowers sold.

5. Provide an analysis of the impact of the 5% reduction in the selling price.

Proposed correction:

1. The margin rate is given by:

   ((PV HT – PA HT) ÷ PA HT) x 100.

   Replacing, ((€250 – €150) ÷ €150) x 100 = 66,67%.

   The margin rate for lawnmowers is therefore 66,67%.

2. Gross margin is calculated by multiplying the unit margin by the quantity sold:

   Unit margin = PV excluding tax – PA excluding tax = €250 – €150 = €100.

   Gross margin = Unit margin x Quantity sold = €100 x 500 = €50.

   The gross margin obtained on annual sales is €50.

3. Annual storage costs are calculated based on the total value of the stock purchased:

Stock value = PA HT x Quantity = €150 x 500 = €75.

Storage cost = 10% x Stock value = 0,10 x €75 = €000.

Total storage costs for the year amount to €7.

4. To calculate the break-even point, we need to cover the transportation and logistics costs with the unit margin.

   Logistics costs = €5.

   Break-even point = Logistics costs ÷ Unit margin = €5 ÷ €000 = 100 mowers.

   The break-even point is 50 mowers.

5. If a 5% discount is applied to the sale price, the new sale price becomes:

   New PV excluding tax = €250 – (€250 x 5%) = €237,50.

   New unit margin = New PV excluding tax – PA excluding tax = €237,50 – €150 = €87,50.

   New gross margin = New unit margin x Quantity sold = €87,50 x 500 = €43.

   This price reduction results in a decrease in gross margin of €6, which may affect the company's profitability.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Gross margin	Unit margin x Quantity sold
Storage cost	Annual storage cost x Stock value
Break even	Logistics costs ÷ Unit margin
Adjustment of the PV HT	PV HT – (PV HT x Reduction %)

Application: Wellness Wave

States :

Wellness Wave, a health product distribution company, sells massagers. The purchase price is €200 excluding VAT per unit, and the selling price is set at €350 excluding VAT. They anticipate selling 300 units during the year. Annual fixed expenses including trade shows and promotions amount to €10.

Work to do :

1. Calculate the margin rate of massage devices.

2. Estimate the expected annual turnover.

3. Determine the total gross margin for the year.

4. Calculate the break-even point in devices sold.

5. Discuss the impact of a 15% reduced purchase cost on margin.

Proposed correction:

1. The margin rate is calculated by:

   ((PV HT – PA HT) ÷ PA HT) x 100.

   Replacing, ((€350 – €200) ÷ €200) x 100 = 75%.

   The margin rate for massage devices is 75%.

2. The expected annual turnover is:

   PV HT x Quantity sold = €350 x 300 = €105.

   So the expected turnover for the year is €105.

3. The total gross margin is obtained by:

Unit margin = PV excluding tax – PA excluding tax = €350 – €200 = €150.

Total gross margin = Unit margin x Quantity sold = €150 x 300 = €45.

The total gross margin for the year is €45.

4. To cover fixed costs, the break-even point is calculated as follows:

   Break-even point = Fixed costs ÷ Unit margin = €10 ÷ €000 = 150 devices.

   The break-even point is therefore approximately 67 devices (rounded to the nearest whole number).

5. A purchase cost reduced by 15% would give a new PA excluding tax:

   New PA excluding tax = €200 – (€200 x 15%) = €170.

   New unit margin = PV excluding tax – New PA excluding tax = €350 – €170 = €180.

   This cost reduction would increase the unit margin to €180, thus improving total profitability.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Turnover	PV HT x Quantity sold
Total gross margin	Unit margin x Quantity sold
Break even	Fixed costs ÷ Unit margin
New PA HT	PA HT – (PA HT x Reduction %)

Application: Golbal Gourmet Goods

States :

Golbal Gourmet Goods is a company specializing in the distribution of high-end organic food products. One of their flagship products is an organic olive oil. They buy each bottle at €5 excluding VAT and resell it at €12 excluding VAT. The company sells an average of 20 bottles per quarter. The cost of storing the oil is estimated at 000% of the stock value.

Work to do :

1. Calculate the unit margin of olive oil.

2. How much do they make from quarterly sales?

3. Evaluate quarterly storage costs.

4. Calculate the markup rate of olive oil.

5. Provide recommendations on the impact of a sale price of €10 excluding VAT.

Proposed correction:

1. The unit margin is calculated by:

   PV excluding VAT – PA excluding VAT = €12 – €5 = €7.

   Thus, the unit margin of oil is €7.

2. Quarterly sales report:

   PV HT x Quantity sold = €12 x 20 = €000.

   So, quarterly sales are €240.

3. The storage cost is estimated as follows:

Stock value = PA HT x Quantity = €5 x 20 = €000.

Storage cost = 8% x Stock value = 0,08 x €100 = €000.

The quarterly storage costs are therefore €8.

4. The mark rate is given by:

   ((PV HT – PA HT) ÷ PV HT) x 100.

   Replacing, ((€12 – €5) ÷ €12) x 100 = 58,33%.

   Thus, the mark rate of olive oil is 58,33%.

5. If the sale price is adjusted to €10 excluding VAT:

   New unit margin = €10 – €5 = €5.

   New quarterly turnover = €10 x €20 = €000.

   Although revenue would reduce gross margins, a price decrease could increase sales volume. It is therefore crucial to examine the elasticity of demand before further price adjustments.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Quarterly sales	PV HT x Quantity sold
Storage cost	Annual storage cost x Stock value
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New turnover	New PV HT x Quantity sold

Application: Digital Den

States :

Digital Den is an electronics company that sells digital tablets. Currently, each tablet is purchased for €200 excluding VAT and sold for €350 excluding VAT. Their goal is to sell 1 units annually. The company faces variable costs of €500 per unit and fixed costs of €30 annually.

Work to do :

1. Evaluate the overall cost per tablet.

2. Calculate the total revenue targeted for the year.

3. Determine the variable cost margin for each tablet.

4. Calculate the break-even point in number of tablets.

5. Analyze the effect of a 20% increase in fixed costs on the break-even point.

Proposed correction:

1. The overall cost per tablet is the sum of the purchase price and variable costs:

   Cost price = PA excluding tax + Variable costs = €200 + €30 = €230.

   So the cost price per tablet is €230.

2. The total turnover targeted is given by:

   PV HT x Quantity targeted = €350 x 1 = €500.

   So the total turnover targeted is €525.

3. The variable cost margin per unit is calculated by:

PV HT – Variable cost = €350 – €30 = €320.

The margin on variable cost is €320 per tablet.

4. The break-even point is calculated by dividing fixed costs by the margin on variable cost:

   Break-even point = Fixed costs ÷ Variable cost margin = €25 ÷ €000 = 320.

   Rounded, the break-even point is 79 tablets.

5. If fixed costs increase by 20%, they become:

   New fixed costs = €25 + (000 x €0,20) = €25.

   New break-even point = New fixed costs ÷ Margin on variable cost = €30 ÷ €000 = 320.

   Rounded up, the new break-even point becomes 94 tablets. This means that the company will need to sell 15 additional tablets to reach the break-even point after increasing fixed costs.

Formulas Used:

Title	Formulas
Total cost price	PA HT + Variable costs
Total turnover	PV HT x Target quantity
Margin on variable cost	PV HT – Variable cost
Break even	Fixed costs ÷ Margin on variable cost
New fixed costs	Fixed costs + (Increase % x Fixed costs)

Application: EcoLight Solutions

States :

EcoLight Solutions is a company specializing in eco-friendly LED bulbs. It buys its bulbs at €3 excluding VAT per unit and resells them at €8 excluding VAT. The expected annual sale is 50 units. Transport costs amount to €000 per year, and the stocking rate is 7% of the stock value.

Work to do :

1. Calculate the unit margin on LED bulbs.

2. Estimate the expected annual turnover.

3. Determine the transportation costs per unit.

4. Calculate the break-even point in bulbs.

5. Discuss the potential impact of a 25% increase in transportation costs on the break-even point.

Proposed correction:

1. The unit margin on bulbs is calculated by:

   PV excluding VAT – PA excluding VAT = €8 – €3 = €5.

   So the unit margin is €5.

2. The expected annual turnover is given by:

   PV HT x Quantity sold = €8 x 50 = €000.

   So the expected annual turnover is €400.

3. The transport costs per unit are estimated as follows:

Transportation cost per unit = Transportation costs ÷ Quantity sold = €7 ÷ 000 = €50 per unit.

The cost of transport is €0,14 per bulb.

4. The break-even point is determined by dividing fixed costs by the unit margin:

   Break-even point = Transport costs ÷ Unit margin = €7 ÷ €000 = 5 bulbs.

   The break-even point is 1 bulbs.

5. If transportation costs increase by 25%, the new cost is:

   New transport costs = €7 + (000 x €0,25) = €7.

   New break-even point = New transport costs ÷ Unit margin = €8 ÷ €750 = 5 bulbs.

   Increasing transportation costs by 25% would bring the break-even point to 1 bulbs, requiring the sale of an additional 750 units to remain profitable.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Annual sales	PV HT x Quantity sold
Transportation cost per unit	Shipping costs ÷ Quantity sold
Break even	Transport costs ÷ Unit margin
New transport costs	Transportation costs + (Increase % x Transportation costs)

Application: SafeFoods Inc.

States :

SafeFoods Inc. is a company that produces and sells organic food products. The production cost of a pack of cereal is €2 excluding VAT, and the selling price is €5 excluding VAT. They sell 80 packs each month. The company also has a fixed monthly cost for energy and personnel of €000.

Work to do :

1. Calculate the gross margin per pack of cereal.

2. What is their total monthly margin?

3. Estimate the monthly break-even point in number of packages.

4. Calculate the total monthly turnover.

5. Analyze the effect of a 15% reduction in production cost on the margin.

Proposed correction:

1. Gross margin per pack is calculated by subtracting the cost of production from the selling price:

   Gross margin = PV excluding tax – Production cost = €5 – €2 = €3.

   The gross margin per pack is therefore €3.

2. The total monthly margin is given by:

   Gross margin x Monthly quantity = €3 x 80 = €000.

   The total monthly margin amounts to €240.

3. The monthly break-even point is calculated by:

Break-even point = Fixed costs ÷ Gross margin = €60 ÷ €000 = 3 packs.

This company needs to sell 20 packs to cover its fixed costs.

4. The total monthly turnover is:

   PV HT x Quantity sold = €5 x 80 = €000.

   So the monthly turnover is €400.

5. If the production cost is reduced by 15%, the new cost is:

   New production cost = €2 – (€2 x 0,15) = €1,70.

   New gross margin = PV excluding tax – New production cost = €5 – €1,70 = €3,30.

   Thus, the reduction in production cost would bring the margin to €3,30 per pack, increasing the overall profitability of SafeFoods Inc.

Formulas Used:

Title	Formulas
Gross margin	PV HT – Production cost
Total monthly margin	Gross Margin x Monthly Quantity
Break even	Fixed costs ÷ Gross margin
Monthly turnover	PV HT x Quantity sold
New production cost	Production Cost – (Production Cost x Reduction %)