Business calculations corrected exercises | 9 Exercises

Application: The Delights of Provence

States :

Les Délices de Provence is a company specializing in the sale of local gourmet products. It wants to analyze the profitability of its artisanal jams. To do this, the company has the following data for a particular jam: the purchase price excluding tax (PA HT) is €3,50, and the sale price excluding tax (PV HT) is €5,00. The quantities sold over the year are 2 jars. Les Délices de Provence applies a VAT rate of 000%.

Work to do :

1. Calculate the unit margin made per jar of jam.
2. Determine the annual turnover excluding tax for this jam.
3. Calculate the margin rate for this product.
4. Find the markup rate of this product.
5. Analyze how the company could improve its profitability by changing the selling price and discuss the strategic implications.

Proposed correction:

1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT.
   Unit margin = PV excluding tax – PA excluding tax = €5,00 – €3,50 = €1,50.
   Each jar of jam generates a unit margin of €1,50.

2. The annual turnover excluding tax is calculated by multiplying the quantity sold by the selling price excluding tax.
   Annual turnover excluding tax = PV excluding tax x Quantity sold = €5,00 x 2 = €000.
   Sales of this jam generated a turnover of €10.

3. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((5,00 – 3,50) ÷ 3,50) x 100 = 42,86%.
The margin rate of jam is 42,86%.

4. The markup rate is given by: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((5,00 – 3,50) ÷ 5,00) x 100 = 30%.
   The markup rate is 30%.

5. To improve profitability, Les Délices de Provence could increase the selling price. By increasing the PV HT, the company must ensure that the increase does not affect sales. Changing the price could reduce competitiveness or customer loyalty, so it is essential to anticipate market reactions. A cost adjustment strategy could also be considered.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Annual turnover excluding tax	PV HT x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: TechnoGadget

States :

TechnoGadget is an innovative company specializing in electronic accessories. It wants to determine the financial viability of a new solar charger. The projected costs and revenues are as follows: purchase price excluding VAT per unit (PA excluding VAT) of €8, sale price excluding VAT (PV excluding VAT) of €20, and the company plans to sell 500 units in the year. A VAT of 20% is applied.

Work to do :

1. Calculate the overall annual margin made on this product.
2. Determine the turnover including tax achieved with these solar chargers.
3. Evaluate the margin rate of each solar charger.
4. Find the markup rate on this product.
5. Discuss the strategic implications if TechnoGadget considers price reduction to boost sales.

Proposed correction:

1. The overall margin is equal to the unit margin multiplied by the quantity sold.
   Unit margin = PV excluding tax – PA excluding tax = €20 – €8 = €12.
   Overall margin = Unit margin x Quantity sold = €12 x 500 = €6.
   The annual overall margin generated is €6.

2. The turnover including tax is calculated with PV excluding tax x Quantity sold x (1 + VAT rate).
   Turnover including tax = €20 x 500 x 1,20 = €12.
   The turnover including tax generated by sales of solar chargers is €12.

3. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((20 – 8) ÷ 8) x 100 = 150%.
The margin rate of solar chargers is 150%.

4. The markup rate is obtained by: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((20 – 8) ÷ 20) x 100 = 60%.
   The product's markup rate is 60%.

5. If TechnoGadget is considering lowering the price to increase sales, it must estimate the price elasticity of demand. Reducing the price could significantly increase sales if the product is elastic. However, lowering the price can also lead to a decrease in the unit margin, which could hurt overall profitability if the increase in sales is not sufficient.

Formulas Used:

Title	Formulas
Overall margin	Unit margin x Quantity sold
Turnover including tax	PV HT x Quantity sold x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: Eco Clothing

States :

Eco Vêtements, an eco-friendly company, focuses on selling textiles made from recycled materials. It analyzes the profitability of its bamboo t-shirts. Here is the available data: AP HT at €7, PV HT at €15, and annual sales of 3 units. The applicable VAT is 000%.

Work to do :

1. Calculate the unit margin for each t-shirt sold.
2. Determine the annual turnover excluding tax from the sale of these t-shirts.
3. Evaluate the margin rate achieved for each t-shirt.
4. Find the markup rate offered by this product.
5. Suggest strategies to increase profitability and discuss what this would mean for Eco Clothing.

Proposed correction:

1. To calculate the unit margin, we subtract the PA HT from the PV HT.
   Unit margin = PV excluding tax – PA excluding tax = €15 – €7 = €8.
   Each t-shirt sold generates a unit margin of €8.

2. The annual turnover excluding tax is obtained by multiplying the PV excluding tax by the annual sales.
   Annual turnover excluding tax = PV excluding tax x Annual sales = €15 x €3 = €000.
   The annual turnover excluding tax from t-shirts is €45.

3. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((15 – 7) ÷ 7) x 100 = 114,29%.
The margin rate for each t-shirt is 114,29%.

4. For the markup rate, we use: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((15 – 7) ÷ 15) x 100 = 53,33%.
   The markup rate of t-shirts is 53,33%.

5. To improve its profitability, Eco Vêtements could explore increasing prices while maintaining the perception of eco-responsible quality. In addition, reducing production costs without compromising quality could be considered. These actions help increase margins, but be careful to maintain the commitment to the brand's ethics and ecological values.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Annual turnover excluding tax	PV HT x Annual sales
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: Bio Beauty

States :

Bio Beauté is a company specializing in organic cosmetic products. It wants to analyze the profitability of its lavender essential oil. The data are as follows: the AP excluding tax is €12 per bottle, the PV excluding tax is €25, and they plan to sell 600 bottles this year. The applicable VAT rate is 20%.

Work to do :

1. Calculate the unit margin on each bottle of essential oil sold.
2. Determine the total turnover excluding tax expected for the year for this product.
3. Calculate the essential oil margin rate.
4. Find the corresponding markup rate.
5. Discuss the implications if Bio Beauté wishes to enter the international market with this product.

Proposed correction:

1. The unit margin is the difference between the PV HT and the PA HT.
   Unit margin = PV excluding tax – PA excluding tax = €25 – €12 = €13.
   The unit margin per bottle is €13.

2. The total turnover excluding tax is calculated by multiplying the PV excluding tax by the number of bottles sold.
   Total turnover excluding tax = PV excluding tax x Number of bottles = €25 x 600 = €15.
   The total expected turnover excluding tax is €15.

3. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((25 – 12) ÷ 12) x 100 = 108,33%.
The margin rate for essential oils is 108,33%.

4. For the markup rate, we apply: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((25 – 12) ÷ 25) x 100 = 52%.
   The associated mark rate is 52%.

5. When entering the international market, Bio Beauté will have to consider distribution costs, customs duties, and other fees that will impact the margin and sales price. Adjusting price positioning according to target markets while maintaining profitability is key to the international expansion strategy.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Total turnover excluding VAT	PV HT x Number of bottles
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: Silver Wheels

States :

Silver Wheels is an electric bike rental company. To assess performance, they look at the numbers associated with a particular model. Purchase price excluding VAT per bike (PA excluding VAT) of €800, rental price per day excluding VAT (PV excluding VAT) of €30, with an annual rental forecast of 4 days. A VAT of 000% is applied.

Work to do :

1. Calculate the projected annual turnover excluding tax for this bicycle model.
2. Evaluate profitability in terms of annual overall margin.
3. Find the margin rate on daily rental.
4. Calculate the markup rate applied to each rental.
5. Suggest ways to increase annual rental days, explaining the consequences.

Proposed correction:

1. The annual turnover excluding tax is obtained by multiplying the PV excluding tax by the number of rental days.
   Annual turnover excluding tax = PV excluding tax x Number of rental days = €30 x 4 = €000.
   The expected annual turnover excluding tax is €120.

2. To obtain the overall margin, we calculate the daily unit margin multiplied by the number of rental days.
   Daily unit margin = PV HT – PA HT x Cost/day = €30 – (€800 ÷ average number of expected annual uses) = depends on the precise economic yield.
   Overall Margin = Daily Unit Margin x 4.
   Exact margin details require further clarification on usage and additional costs.

3. The margin rate is obtained by the calculation: Margin rate = ((PV HT – (PA HT ÷ average number of uses)) ÷ (PA HT ÷ average number of uses)) x 100.

This is a rental model which varies depending on usage.

4. Markup Rate: Similar to traditional sales formula, highly dependent on accurate economic assessment over time.

5. To increase rental days, Silver Wheels could expand its marketing, offer promotions, or target special groups such as tourists or businesses. These actions could hopefully increase rentals but would involve changes in terms of management of the resources providing this increase.

Formulas Used:

Title	Formulas
Annual turnover excluding tax	PV HT x Number of rental days
Overall margin	Daily unit margin x Number of rental days
Margin rate	((PV HT – (PA HT ÷ average number of uses)) ÷ (PA HT ÷ average number of uses)) x 100
Brand taxes	(Margin x 100) ÷ PV HT

Application: RestauBio

States :

RestauBio is a local restaurant committed to sustainable development and organic catering. They want to analyze the success of a special vegan weekend menu. The cost per unit is €12, the selling price excluding VAT is €25, for an expected sale of 200 menus each weekend. VAT is set at 5,5%.

Work to do :

1. Determine the unit margin per menu sold.
2. Calculate the net turnover for a weekend.
3. Evaluate the margin rate for this menu.
4. Find the markup rate.
5. Analyze the implications and strategies if RestauBio wants to increase the number of menus sold each weekend.

Proposed correction:

1. Unit margin = PV excluding tax – Unit cost = €25 – €12 = €13.
   Each menu sold generates a unit margin of €13.

2. The net turnover for a weekend is PV HT x Number of planned menus.
   Turnover excluding tax = €25 x 200 = €5.
   The turnover for a weekend is €5.

3. Margin rate = ((PV HT – Unit cost) ÷ Unit cost) x 100 = ((25 – 12) ÷ 12) x 100 = 108,33%.

The margin rate for this menu is 108,33%.

4. Markup rate = ((PV HT – Unit cost) ÷ PV HT) x 100 = ((25 – 12) ÷ 25) x 100 = 52%.
   The menu markup rate is 52%.

5. RestauBio could boost sales by strengthening marketing, for example, by adjusting promotional campaigns or including a special offer. Increased sales would lead to more revenue and could allow for economies of scale, although the significant increase in menus implies rigorous supply management.

Formulas Used:

Title	Formulas
Unit margin	PV HT – Unit cost
Turnover excluding tax	PV HT x Number of menus planned
Margin rate	((PV HT – Unit cost) ÷ Unit cost) x 100
Brand taxes	((PV HT – Unit cost) ÷ PV HT) x 100

Application: StudioFit

States :

StudioFit is a fitness club that offers monthly subscriptions. They want to evaluate the profitability of a new premium subscription. Purchase price of monthly services for the club (PA HT) of €40, sale price of the subscription HT (PV HT) of €80, for a sales target of 150 subscriptions per month. VAT of 20%.

Work to do :

1. What is the unit margin on each premium subscription sold?
2. Determine the monthly net turnover of these subscriptions.
3. Evaluate the margin rate for this subscription.
4. Identify the subscription markup rate.
5. Provide strategic recommendations to increase sales.

Proposed correction:

1. Unit margin = PV excluding tax – PA excluding tax = €80 – €40 = €40.
   The unit margin per subscription is €40.

2. Monthly turnover excluding tax = PV excluding tax x Number of subscriptions sold = €80 x 150 = €12.
   The expected monthly turnover is €12.

3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((80 – 40) ÷ 40) x 100 = 100%.

The premium subscription margin rate is 100%.

4. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((80 – 40) ÷ 80) x 100 = 50%.
   The markup rate for this subscription is 50%.

5. StudioFit could consider family discounts or create free events to entice new memberships. They could also increase their online presence through social media marketing. These actions would potentially incur costs that must be offset by new memberships.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Monthly turnover excluding tax	PV HT x Number of subscriptions sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: GadgetPlanet

States :

GadgetPlanet is a retail company selling electronic gadgets. It wants to evaluate the potential of its new LED lamps. With a purchase cost excluding VAT (PA excluding VAT) of €10 and a sale price excluding VAT (SVP excluding VAT) of €25, the company plans to sell 1 lamps in the first quarter. The applicable VAT rate is 200%.

Work to do :

1. Calculate the overall margin achieved at the end of the quarter.
2. What would be the value of sales including VAT for this quarter?
3. Determine the margin rate for LED lamps.
4. Rate the markup rate for this product.
5. Discuss possible marketing actions to increase the distribution of these lamps.

Proposed correction:

1. Overall margin = (PV HT – PA HT) x Number of lamps sold = (€25 – €10) x 1 = €200.
   The overall margin at the end of the quarter is €18.

2. Value of sales including tax = PV excluding tax x Number of lamps sold x (1 + VAT rate) = €25 x 1 x 200 = €1,20.
   The value of sales including VAT for this quarter is €36.

3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((25 – 10) ÷ 10) x 100 = 150%.

The margin rate of LED lamps is 150%.

4. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((25 – 10) ÷ 25) x 100 = 60%.
   The markup rate for lamps is 60%.

5. GadgetPlanet could consider targeted online advertising campaigns, discounts on group purchases, or launching a communication on the energy savings achieved thanks to these lamps. These initiatives will boost sales, but will involve marketing expenses that must be planned correctly.

Formulas Used:

Title	Formulas
Overall margin	(PV HT – PA HT) x Number of lamps sold
Value of sales including VAT	PV HT x Number of lamps sold x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: EasyClean

States :

EasyClean is an eco-friendly cleaning company. In order to grow its business, it is looking at data related to its residential cleaning services. The cost per intervention (PA excluding VAT) is €30, the price charged excluding VAT is €65, with 400 services planned monthly. VAT is 20%.

Work to do :

1. Find the unit margin per intervention.
2. Calculate the anticipated monthly income excluding tax.
3. Evaluate the margin rate per intervention.
4. Calculate the markup rate for this service.
5. Suggest ways to improve margins while expanding the customer portfolio.

Proposed correction:

1. Unit margin = PV excluding tax – PA excluding tax = €65 – €30 = €35.
   Each intervention generates a unit margin of €35.

2. Monthly income excluding tax = PV excluding tax x Number of services = €65 x 400 = €26.
   The anticipated monthly income excluding tax is €26.

3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((65 – 30) ÷ 30) x 100 = 116,67%.

The margin rate of interventions is 116,67%.

4. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((65 – 30) ÷ 65) x 100 = 53,85%.
   The markup rate for the service is 53,85%.

5. To improve margins, EasyClean could offer a loyalty program for their regular customers, reducing some prospecting costs and facilitating additional sales. Ensuring a sustainable quality service, while optimizing agent routes and equipment maintenance costs, will help maximize profitability.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Monthly income excluding tax	PV HT x Number of services
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100