Summary
Application: New Energies
States :
Energies Nouveaux, a company specializing in renewable energy solutions, is looking to improve its sales margins. The company wants to determine the optimal selling price excluding tax for its new solar batteries. The available data are as follows: purchase price excluding tax of €120 per unit, desired margin rate of 40% and the applicable VAT is 20%.
Work to do :
- Calculate the selling price excluding VAT using the desired margin rate.
- Determine the selling price including tax of the solar batteries.
- Estimate the unit margin for a sale.
- Calculate the overall margin if 300 units of solar batteries are sold.
- Analyze the business implications if the purchase price increases to €130 per unit while keeping the same margin rate.
Proposed correction:
-
To calculate the selling price excluding tax using the margin rate, we use the formula: PV excluding tax = PA excluding tax x (1 + Margin rate).
By replacing, €120 x (1 + 0,40) = €168.
The selling price excluding tax of the solar batteries will be €168 to achieve the desired margin rate. -
The sales price including tax is calculated by adding VAT to the sales price excluding tax: PV including tax = PV excluding tax x (1 + VAT rate).
By replacing, €168 x (1 + 0,20) = €201,60.
The sales price including tax for solar batteries is €201,60. -
The unit margin is calculated as follows: Unit margin = PV HT – PA HT.
As a replacement, €168 – €120 = €48.
The unit margin per solar battery sold is €48.
-
The overall margin is calculated by multiplying the unit margin by the quantity sold: Overall margin = Unit margin x Quantity sold.
Replacing, €48 x 300 = €14.
The overall margin for 300 solar batteries sold is €14. -
If the purchase price increases to €130, let's recalculate the selling price excluding tax: PV excluding tax = €130 x (1 + 0,40) = €182.
The new selling price excluding VAT is €182.
Implication: To maintain the 40% margin rate, the selling price must increase, which may influence competitiveness compared to the current market.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax according to the margin rate | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: Daily Treats
States :
Gourmandises Quotidiennes, a family-run artisanal confectionery business, wants to optimize its prices for the end-of-year holidays. It produces boxes of chocolates. The purchase cost excluding tax per box is €15, and the company is aiming for a brand rate of 30%. The applicable VAT is 5,5%.
Work to do :
- Determine the selling price excluding tax to achieve the targeted markup rate.
- Calculate the selling price including tax of a box of chocolates.
- What is the share of VAT in the sales price including VAT?
- Calculate the unit margin made on each box sold.
- Develop a strategy if the competition offers a sales price including tax of €19 per box.
Proposed correction:
-
To calculate the selling price excluding tax with the markup rate, we use: PV excluding tax = PA excluding tax ÷ (1 – Markup rate).
Substituting, €15 ÷ (1 – 0,30) = €21,43.
The selling price excluding VAT to reach a markup rate of 30% is €21,43. -
The sales price including tax is calculated as follows: VAT inclusive price = VAT excluding tax x (1 + VAT rate).
By replacing, €21,43 x (1 + 0,055) = €22,61.
The retail price including tax for a box of chocolates is €22,61. -
The share of VAT in the sales price including tax: VAT = PV including tax – PV excluding tax.
As a replacement, €22,61 – €21,43 = €1,18.
The VAT share is €1,18.
-
The unit margin corresponds to: Unit margin = PV HT – PA HT.
As a replacement, €21,43 – €15 = €6,43.
The unit margin on each box sold is €6,43. -
If the competition offers €19 including tax per box, let's recalculate the margin by adapting the selling price excluding tax:
Competitor's VAT inclusive price = €19, or competitor's VAT exclusive price = €19 ÷ 1,055 = €18,01.
New unit margin = €18,01 – €15 = €3,01.
Implication: Maintaining the margin rate is difficult, diversifying the offers can be an alternative.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding VAT according to the markup rate | PV HT = PA HT ÷ (1 – Mark rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| VAT share | VAT = PV including VAT – PV excluding VAT |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
Application: Tech'Innov
States :
Tech'Innov, a start-up specializing in technological gadgets, plans to launch a new connected bracelet. The production cost of the bracelet is €50 excluding VAT per unit, and the company wants to achieve a margin rate of 25%. The applicable VAT is 20%.
Work to do :
- Calculate the selling price excluding tax that allows you to achieve the desired margin rate.
- What is the selling price including tax of the bracelet?
- Analyze the impact of a 10% reduction in the sales price including tax on the unit margin.
- Calculate the overall margin if 500 bracelets are sold at the original price.
- Propose an elasticity analysis if a price decrease increases sales by 20%.
Proposed correction:
-
To find the selling price excluding tax: PV excluding tax = PA excluding tax x (1 + Margin rate).
By replacing, €50 x (1 + 0,25) = €62,50.
The selling price excluding tax which allows the margin rate of 25% to be reached is €62,50. -
The sales price including tax is calculated by adding VAT: VAT inclusive = VAT excluding tax x (1 + VAT rate).
By replacing, €62,50 x (1 + 0,20) = €75.
The retail price of the bracelet including tax is €75. -
With a 10% discount, NV incl. VAT = €75 x (1 – 0,10) = €67,50.
NV excluding tax = €67,50 ÷ 1,20 = €56,25.
New unit margin = €56,25 – €50 = €6,25.
10% margin reduction impacts unit profitability significantly.
-
The overall margin with 500 units: Unit margin = €62,50 – €50 = €12,50.
Overall margin = €12,50 x 500 = €6.
The overall margin for 500 units sold is €6. -
Elasticity: NV excluding tax for increased sales = €56,25.
If sales increase to 600 (500 + 20%), increased overall margin = €6,25 x 600 = €3.
Strategic result: Favorable price elasticity, optimizes volumes with sustainable margin.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax according to the margin rate | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Impact on unit margin after reduction | NV HT = NV TTC ÷ (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Price-volume elasticity | NV TTC = PV TTC x (1 – Reduction) |
Application: FashionLuxe
States :
The haute couture house FashionLuxe wants to introduce its new collection of jackets. The purchase cost excluding VAT per jacket is €200, and the company plans to apply a markup rate of 45%. The VAT rate is 20%.
Work to do :
- Find the selling price excluding VAT to obtain the fixed markup rate.
- Determine the selling price including tax of a jacket.
- Calculate the unit margin obtained on each jacket sold.
- If 150 jackets are sold, what is the total margin generated?
- Discuss the consequences if the purchase cost is reduced by €10 per jacket.
Proposed correction:
-
Let's use the formula for the markup rate: PV HT = PA HT ÷ (1 – Markup rate).
Substituting, €200 ÷ (1 – 0,45) = €363,64.
The selling price excluding VAT to reach a markup rate of 45% is €363,64. -
Calculation to obtain the sales price including tax: VAT inclusive = VAT excluding tax x (1 + VAT rate).
By replacing, €363,64 x (1 + 0,20) = €436,37.
The selling price including tax for a jacket is €436,37. -
Let’s calculate the unit margin: Unit margin = PV HT – PA HT.
As a replacement, €363,64 – €200 = €163,64.
The unit margin per jacket is €163,64.
-
Calculation of overall margin: Overall margin = Unit margin x Quantity sold.
Replacing, €163,64 x 150 = €24.
The total margin for 150 jackets sold is €24. -
If the purchase cost drops by €10: New PA excluding tax = €190.
New unit margin = €363,64 – €190 = €173,64.
Cost reduction improves margin by €10/jacket, boosting profitability.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding VAT according to the markup rate | PV HT = PA HT ÷ (1 – Mark rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Total margin | Total Margin = Unit Margin x Quantity Sold |
Application: Artisanal Treats
States :
Artisanal Treats, an organic bakery, is trying to set a selling price for its new lemon tarts. The purchase cost excluding VAT for each tart is €5. The company wants to apply a margin rate of 50% with a VAT rate of 5,5%.
Work to do :
- What should the selling price excluding tax be to achieve the desired margin rate?
- Calculate the selling price including tax of a lemon tart.
- Determine the unit margin made on each pie sold.
- If 1000 pies are sold, what will be the overall margin accumulated?
- Evaluate the impact of an increase in purchasing costs to €5,50 on the pricing policy.
Proposed correction:
-
Let’s determine the selling price excluding tax using the margin rate: PV excluding tax = PA excluding tax x (1 + Margin rate).
By replacing, €5 x (1 + 0,50) = €7,50.
The selling price excluding tax required for the 50% margin rate is €7,50. -
Let’s calculate the sales price including VAT: VAT inclusive = VAT excluding VAT x (1 + VAT rate).
By replacing, €7,50 x (1 + 0,055) = €7,91.
The selling price including tax for a lemon tart is €7,91. -
The unit margin is obtained as follows: Unit margin = PV HT – PA HT.
As a replacement, €7,50 – €5 = €2,50.
The unit margin is €2,50 per tart sold.
-
Overall margin per 1000 sales: Overall margin = Unit margin x Quantity sold.
Replacing, €2,50 x 1000 = €2.
The total margin for 1000 pies sold is €2. -
With an increase to €5,50: New unit margin = €7,50 – €5,50 = €2.
Impact: Reduction of the margin by €0,50, reactivity required on the offer.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax according to the margin rate | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: GreenTech Motors
States :
GreenTech Motors, an innovative company in the automotive sector, wants to introduce a new range of eco-friendly cars. The cost of manufacturing a car is €18 excluding VAT. They are aiming for a 000% brand rate with a 20% VAT rate.
Work to do :
- Calculate the selling price excluding tax required to comply with the markup rate.
- Determine the selling price including tax of a car.
- Identify what the unit sales margin is.
- What will be the total margin if the company sells 50 cars?
- Analyze the effect of reducing production costs to €17 on profits.
Proposed correction:
-
To find the selling price excluding tax: PV excluding tax = PA excluding tax ÷ (1 – Markup rate).
Substituting, €18 ÷ (000 – 1) = €0,20.
The selling price excluding tax envisaged to obtain the markup rate is €22. -
The sales price including tax is therefore: VAT inclusive price = VAT excluding tax x (1 + VAT rate).
Substituting, €22 x (500 + 1) = €0,20.
The selling price including tax for a car is €27. -
Regarding the unit margin: Unit margin = PV HT – PA HT.
Replacing, €22 – €500 = €18.
The unit margin obtained on each sale is €4.
-
For a sale of 50 cars: Overall margin = Unit margin x Quantity sold.
Replacing, €4 x 500 = €50.
The total margin for 50 cars sold is €225. -
If the production cost decreases to €17, revaluation of the unit margin:
New Unit Margin = €22 – €500 = €17.
Conclusion: Lower costs increase margin per unit, optimizing overall profit.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding VAT according to the markup rate | PV HT = PA HT ÷ (1 – Mark rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Total margin | Total Margin = Unit Margin x Quantity Sold |
Application: HighTech Audio
States :
HighTech Audio, specializing in high-end audio equipment, offers a new audio amplifier. The purchase cost excluding tax of each amplifier is €400, with a desired margin rate of 35%. VAT is set at 20%.
Work to do :
- Find the selling price excluding tax that allows you to achieve the margin rate.
- Add VAT to get the VAT-inclusive selling price of an amp.
- What is the margin obtained for a unit?
- If promotions lower the price including tax to €600, what is the new unit margin?
- Suggest a strategic consideration if price variation also affected sales volumes.
Proposed correction:
-
The selling price excluding tax is obtained by: PV excluding tax = PA excluding tax x (1 + Margin rate).
By replacing, €400 x (1 + 0,35) = €540.
The selling price excluding VAT is €540. -
The price including tax is deducted from: VAT inclusive price = VAT excluding tax x (1 + VAT rate).
By replacing, €540 x (1 + 0,20) = €648.
The sales price including tax is therefore €648. -
The margin for each amplifier is: Unit margin = PV HT – PA HT.
540 € – 400 € = 140 €.
The unit margin is therefore €140 per amplifier.
-
With a promotion at €600 including tax, NV excluding tax = €600 ÷ 1,20 = €500.
New margin = €500 – €400 = €100.
The unit margin is reduced to €100 in this case. -
Reflection: Adjusting volumes to lower prices can balance the reduced margin and increase market share.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax according to the margin rate | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Price after promotion | NV HT = NV TTC ÷ (1 + VAT rate) |
Application: FitWell Apparel
States :
FitWell Apparel, a sportswear designer, plans to launch a new series of technical jerseys. The cost per jersey is €30 excluding VAT. The goal is to achieve a margin rate of 60%. The VAT rate is 20%.
Work to do :
- Calculate the selling price excluding tax to achieve the desired margin rate.
- Determine the selling price including tax.
- What is the margin made on each jersey sale?
- If the company sells 1 jerseys, what will be the gross profit?
- Analyze the potential impact if VAT increased by 2 percentage points.
Proposed correction:
-
The price excluding tax is calculated as follows: PV excluding tax = PA excluding tax x (1 + Margin rate).
€30 x (1 + 0,60) = €48.
Therefore, the selling price excluding VAT is set at €48. -
Applying VAT: VAT inclusive = VAT excluding VAT x (1 + VAT rate).
€48 x (1 + 0,20) = €57,60.
The sales price including tax of a discounted jersey is €57,60. -
For the margin: Unit margin = PV HT – PA HT.
48 € – 30 € = 18 €.
The margin made per jersey is €18.
-
By selling 1 jerseys, the total margin achieved is:
€18 x €1 = €000.
The gross profit for 1 jerseys is €000. -
If VAT rises to 22%, let's recalculate the price including VAT:
NV including tax = €48 x 1,22 = €58,56.
Strategic impact: adjust prices to preserve competitiveness.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax according to the margin rate | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Total margin | Total Margin = Unit Margin x Quantity Sold |
Application: Nature's Essence Skincare
States :
Nature's Essence Skincare, a company committed to natural beauty products, introduces a new anti-aging serum. The manufacturing cost excluding VAT per bottle is €12, with a desired markup rate of 50%. The applicable VAT is 20%.
Work to do :
- What should the selling price excluding tax be to reach the set markup rate?
- Get the sales price including VAT for a bottle.
- Calculate the unit gross operating surplus.
- Deduct the total margin if 10 bottles are sold.
- Analyze what an increase in costs to €13 would represent, hoping for other margins.
Proposed correction:
-
To obtain the markup rate, calculate: PV HT = PA HT ÷ (1 – Markup rate).
€12 ÷ (1 – 0,50) = €24.
The selling price excluding VAT for a markup rate of 50% is €24. -
The price including tax is obtained by: PV including tax = PV excluding tax x (1 + VAT rate).
€24 x (1 + 0,20) = €28,80.
Per bottle, the price including tax should be €28,80. -
Unit margin: Unit margin = PV HT – PA HT.
24 € – 12 € = 12 €.
The gross surplus per bottle is €12.
-
Total margin for 10 units is:
€12 x €10 = €000.
The cumulative margins reach €120. -
With purchase costs at €13, the new calculation:
New Unit Margin = €24 – €13 = €11.
Impact: Gross margin decrease of €1/unit, assessment required to maintain profitability.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding VAT according to the markup rate | PV HT = PA HT ÷ (1 – Mark rate) |
| Sales price including tax | PV including VAT = PV excluding VAT x (1 + VAT rate) |
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Total margin | Total Margin = Unit Margin x Quantity Sold |