In this section:
Application: Pizzeria Le Gourmet
States :
Pizzeria Le Gourmet, located in the heart of Lyon, offers a wide range of takeaway pizzas. Given the constant influx of customers, the manager wants to ensure that he maintains adequate profit margins. He has set the sales price excluding tax (PV HT) of a pizza at €15,00 and the purchase price excluding tax (PA HT) of the necessary ingredients at €6,00.
Work to do :
- Calculate the margin rate for a pizza from Pizzeria Le Gourmet.
- What would be the selling price excluding tax for a desired margin rate of 50%?
- Determine the markup rate of the pizza currently on sale.
- If the purchase price increases by 10%, how will this affect the margin rate?
- Analyze the strategic implications if the margin rate suddenly drops to 10%.
Proposed correction:
Calculate the margin rate for a pizza from Pizzeria Le Gourmet.
To calculate the margin rate, use the formula:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
Replacing the values, we find:
[
((15,00 – 6,00) ÷ 6,00) x 100 = 150%
]
The margin rate is therefore 150%, which indicates good profitability compared to the cost of ingredients.What would be the selling price excluding tax for a desired margin rate of 50%?
The reverse formula guides us:
[
\text{PV HT} = \text{PA HT} + (\text{PA HT} x \text{Desired margin rate} ÷ 100)
]
With a desired margin rate of 50%, this gives:
[
\text{PV excluding tax} = 6,00 + (6,00 x 50 ÷ 100) = €9,00
]
The selling price excluding tax must therefore be €9,00 for a margin rate of 50%.Determine the markup rate of the pizza currently on sale.
Use the following formula:
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
By integrating current values:
[
((15,00 – 6,00) ÷ 15,00) x 100 = 60%
]
The current markup rate is 60%, which means that 60% of the selling price is the margin.
If the purchase price increases by 10%, how will this affect the margin rate?
With a revised HT PA:
[
\text{PA HT revised} = 6,00 x 1,10 = €6,60
]
The margin rate becomes:
[
((15,00 – 6,60) ÷ 6,60) x 100 = 127,27%
]
Rising costs lower the margin rate to 127,27%, potentially affecting profitability.Analyze the strategic implications if the margin rate suddenly drops to 10%.
A margin rate of only 10% means a much smaller gross margin. Pizzeria Le Gourmet should reevaluate its pricing strategies or cut its purchasing costs to maintain profitability. This could include negotiations with suppliers or adjusting the menu to appeal to a broader customer base while maintaining acceptable margins.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT + (PA HT x Desired margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
Application: Innovative Gadget
States :
Gadget Innovant is a start-up specializing in the sale of multifunctional gadgets. It offers a high-tech pen with a purchase price excluding tax (PA HT) of €8,00, and a sales price excluding tax (PV HT) of €20,00. The company wants to evaluate its pricing strategy.
Work to do :
- Calculate the margin rate for the high-tech pen sold by Gadget Innovant.
- What would be the markup rate for the aforementioned gadget currently on sale?
- Estimate the effect on the margin rate if the selling price is reduced by 15%.
- Calculate the gross margin in euros for 100 pens sold.
- Discuss the financial implications if the purchase price increases by 25%.
Proposed correction:
Calculate the margin rate for the high-tech pen sold by Gadget Innovant.
Using the formula:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
Let's substitute with the given values:
[
((20,00 – 8,00) ÷ 8,00) x 100 = 150%
]
A margin rate of 150% means that the selling price is 2,5 times the purchase price.What would be the markup rate for the aforementioned gadget currently on sale?
Apply the following formula:
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
Which give :
[
((20,00 – 8,00) ÷ 20,00) x 100 = 60%
]
Innovative Gadget thus achieves a margin of 60% on the sale price.Estimate the effect on the margin rate if the selling price is reduced by 15%.
New PV HT is:
[
\text{New PV HT} = 20,00 – (20,00 x 0,15) = €17,00
]
Let's calculate the new margin rate:
[
((17,00 – 8,00) ÷ 8,00) x 100 = 112,5%
]
With the reduction, the margin rate drops to 112,5%, reducing the margin.
Calculate the gross margin in euros for 100 pens sold.
Unit margin captured by:
[
\text{Unit margin} = \text{PV HT} – \text{PA HT} = 20,00 – 8,00 = 12,00 €
]
For 100 pens, it extends:
[
\text{Gross Margin} = 12,00 x 100 = €1
]
The gross margin is €1 for 200 pens sold.Discuss the financial implications if the purchase price increases by 25%.
Increase the HT PA by:
[
\text{PA HT increased} = 8,00 x 1,25 = 10,00 €
]
Margin rate then:
[
((20,00 – 10,00) ÷ 10,00) x 100 = 100%
]
An increase in the purchase price has a strong impact on the margin, reduced to 100%, which could require a re-evaluation of sales prices or reductions in operational costs.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Gross Margin | Unit margin x quantity sold |
Application: Fashion Chic Boutique
States :
Mode Chic Boutique is a renowned fashion store located in Paris. The store has recently introduced a new collection of blouses. The purchase price excluding tax (PA HT) per blouse is €50,00, and the sale price excluding tax (PV HT) is set at €90,00. The management wants to analyze the profitability of this new product line.
Work to do :
- Determine the margin rate applied to each blouse sold.
- Offer a selling price excluding VAT to achieve a margin rate of 100%.
- Calculate the current markup rate for the blouse on sale.
- Estimate the total gross margin if 200 blouses are sold.
- Consider the strategic impacts if the competing market results in a drop in the selling price to €75,00 per blouse.
Proposed correction:
Determine the margin rate applied to each blouse sold.
The margin rate is calculated as follows:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
By inserting the amounts:
[
((90,00 – 50,00) ÷ 50,00) x 100 = 80%
]
The margin rate for each blouse sold is 80%.Offer a selling price excluding VAT to achieve a margin rate of 100%.
Let's use the formula:
[
\text{PV HT} = \text{PA HT} + (\text{PA HT} x \text{Desired margin rate} ÷ 100)
]
Wanting a margin of 100%, let's calculate:
[
\text{PV excluding tax} = 50,00 + (50,00 x 100 ÷ 100) = €100,00
]
To achieve a margin rate of 100%, the selling price excluding tax must be €100,00 per blouse.Calculate the current markup rate for the blouse on sale.
With the appropriate formula:
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
We obtain :
[
((90,00 – 50,00) ÷ 90,00) x 100 = 44,44%
]
The current markup rate is 44,44%.
Estimate the total gross margin if 200 blouses are sold.
Calculated unit margin:
[
\text{Unit margin} = 90,00 – 50,00 = €40,00
]
So, for 200 blouses:
[
\text{Total gross margin} = 40,00 x 200 = €8
]
The total gross margin is €8 for these sales.Consider the strategic impacts if the competing market results in a drop in the selling price to €75,00 per blouse.
With a reduced PV HT:
[
\text{PV HT reduced} = €75,00
]
The adjusted margin rate becomes:
[
((75,00 – 50,00) ÷ 50,00) x 100 = 50%
]
This reduction in the selling price reduces the margin rate to 50%, which may force Mode Chic Boutique to reconsider its cost structures or marketing adjustments to maintain its obtained market share.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT + (PA HT x Desired margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Gross Margin | Unit margin x quantity sold |
Application: Futuristic Electronics
States :
Futuristic Electronics is a major player in the sale of digital gadgets. The company offers an innovative wireless charger at a purchase price excluding tax (PA HT) of €15,00, and the sales price excluding tax (PV HT) is set at €35,00. The marketing department wants to better understand the profitability of this product.
Work to do :
- Calculate the margin rate for the wireless charger.
- What should the selling price be excluding tax to obtain a margin rate of 120%?
- Find out the markup rate based on the current sale price.
- What is the overall margin for the first 50 chargers sold?
- Analyze the impact on profitability if manufacturing cost increases by 20%.
Proposed correction:
Calculate the margin rate for the wireless charger.
The formula is expressed as:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
By replacing, we obtain:
[
((35,00 – 15,00) ÷ 15,00) x 100 = 133,33%
]
The displayed margin rate is 133,33%.What should the selling price be excluding tax to obtain a margin rate of 120%?
Let's determine the PV HT with:
[
\text{PV HT} = \text{PA HT} + (\text{PA HT} x \text{Desired margin rate} ÷ 100)
]
For a margin rate of 120%, this comes to:
[
\text{PV excluding tax} = 15,00 + (15,00 x 120 ÷ 100) = €33,00
]
So the selling price excluding tax must be €33,00.Find out the markup rate based on the current sale price.
Using our equation:
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
Let's do the math:
[
((35,00 – 15,00) ÷ 35,00) x 100 = 57,14%
]
The markup rate soars to 57,14% for sales.
What is the overall margin for the first 50 chargers sold?
Unit margin translates to:
[
\text{Unit margin} = 35,00 – 15,00 = €20,00
]
For 50 pieces sold:
[
\text{Total margin} = 20,00 x 50 = €1
]
The overall margin taken into effect is €1.Analyze the impact on profitability if manufacturing cost increases by 20%.
Let’s interpret the increased PA HT:
[
\text{PA HT increased} = 15,00 x 1,20 = 18,00 €
]
New margin rate will be:
[
((35,00 – 18,00) ÷ 18,00) x 100 = 94,44%
]
Rising manufacturing costs are leading to a contraction in margin rates, which could call for strategic comparisons on preserving healthy profit margins and reducing costs.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT + (PA HT x Desired margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall margin | Unit margin x quantity sold |
Application: Fashionable Cuisine
States :
Cuisine à la Mode is a company that sells luxury kitchen equipment. One of their flagship products is a copper pan sold for €250,00 excluding VAT, purchased for €120,00 excluding VAT. The finance department wants to carry out a detailed analysis on the positioning of this product.
Work to do :
- Calculate the margin rate for the displayed copper pan.
- Determine the selling price excluding VAT if the company wants a markup rate of 65%.
- Estimate the profitability in terms of gross margin if 80 stoves are sold.
- Estimate the margin rate after a 30% increase in the purchase price.
- Discuss the business implications if the selling price has to be reduced by 20% to remain competitive.
Proposed correction:
Calculate the margin rate for the displayed copper pan.
The formula :
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
Given :
[
((250,00 – 120,00) ÷ 120,00) x 100 = 108,33%
]
A margin rate of 108,33% is thus obtained for each stove sold.Determine the selling price excluding VAT if the company wants a markup rate of 65%.
The associated formula is:
[
\text{PV HT} = \text{PA HT} ÷ (1 – (\text{Desired markup rate} ÷ 100))
]
For a 65%, this generates:
[
\text{PV excluding tax} = 120,00 ÷ (1 – (65 ÷ 100)) = €342,86
]
A sales price excluding VAT of €342,86 is essential to obtain this markup rate.Estimate the profitability in terms of gross margin if 80 stoves are sold.
Unit margin:
[
\text{Unit margin} = 250,00 – 120,00 = €130,00
]
For 80 units:
[
\text{Gross margin} = 130,00 x 80 = €10
]
The gross margin reached €10.
Estimate the margin rate after a 30% increase in the purchase price.
New PA HT:
[
\text{PA HT increased} = 120,00 x 1,30 = 156,00 €
]
Recalculated margin rate:
[
((250,00 – 156,00) ÷ 156,00) x 100 = 60,26%
]
Thus, the increase lowers the margin rate to 60,26%.Discuss the business implications if the selling price has to be reduced by 20% to remain competitive.
Let's recalculate the PV HT:
[
\text{PV HT reduced} = 250,00 – (250,00 x 0,20) = 200,00 €
]
The margin rate becomes:
[
((200,00 – 120,00) ÷ 120,00) x 100 = 66,67%
]
A reduction to €200,00 lowers the margin rate, requiring Cuisine à la Mode to cross-check its explanations to have a good price/volume balance by favoring its stocks and its talent promotions.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT ÷ (1 – (Desired markup rate ÷ 100)) |
| Gross margin | Unit margin x quantity sold |
Application: Development Innovation
States :
Aménagement Innovation is a company specializing in interior furnishings. It sells a set of contemporary furniture at a price of €500,00 excluding VAT, while the purchase cost excluding VAT is €300,00. The company is considering reviewing its pricing to improve its profit margin.
Work to do :
- Calculate the margin rate for the furniture set.
- Establish the selling price excluding tax to obtain a margin rate of 80%.
- Set the current markup rate of this furniture.
- What would be the gross margin if Aménagement Innovation sells 60 sets?
- Discuss the opportunities and obstacles the company might encounter if it increases the selling price by 10%.
Proposed correction:
Calculate the margin rate for the furniture set.
Use the formula:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
Knowing:
[
((500,00 – 300,00) ÷ 300,00) x 100 = 66,67%
]
The margin rate for all furniture is 66,67%.Establish the selling price excluding tax to obtain a margin rate of 80%.
Apply:
[
\text{PV HT} = \text{PA HT} + (\text{PA HT} x \text{Liked margin rate} ÷ 100)
]
Leads to:
[
\text{PV excluding tax} = 300,00 + (300,00 x 80 ÷ 100) = €540,00
]
This selling price excluding tax of €540,00 aims for a margin of 80%.Set the current markup rate of this furniture.
By the formula:
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
Replace:
[
((500,00 – 300,00) ÷ 500,00) x 100 = 40%
]
A markup rate of 40% is observed on this sale.
What would be the gross margin if Aménagement Innovation sells 60 sets?
Crucial unit margin:
[
\text{Unit margin} = 500,00 – 300,00 = €200,00
]
Multiply:
[
\text{Gross margin} = 200,00 x 60 = €12
]
The gross margin amounts to €12.Discuss the opportunities and obstacles the company might encounter if it increases the selling price by 10%.
New PV HT:
[
\text{New PV HT} = 500,00 x 1,10 = €550,00
]
Renewed margin rate:
[
((550,00 – 300,00) ÷ 300,00) x 100 = 83,33%
]
A 10% increase increases the margin rate, potentially increasing profitability, but could create resistance with loyal customers perceiving a perceived loss of value.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT + (PA HT x Liked margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Gross margin | Unit margin x quantity sold |
Application: Health Ô natural
States :
Santé Ô naturel is a pharmacy chain that is introducing an organic face cream. The purchase price excluding tax (PA HT) is €30,00, while the sales price excluding tax (PV HT) is €70,00. The sales department wants to examine the current margins.
Work to do :
- Determine the margin rate based on the current selling price.
- At what selling price excluding tax should we sell for a margin of 200%?
- Evaluate the current markup rate for these creams.
- What would be the total margin generated by 150 creams sold?
- Consider the viability of the pricing strategy if the purchase price increases by €15 per unit.
Proposed correction:
Determine the margin rate based on the current selling price.
Proceed as follows:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
Let us establish:
[
((70,00 – 30,00) ÷ 30,00) x 100 = 133,33%
]
The current margin rate is 133,33%.At what selling price excluding tax should we sell for a margin of 200%?
Use the following equivalent:
[
\text{PV HT} = \text{PA HT} + (\text{PA HT} x \text{Desired rate} ÷ 100)
]
For 200%, we extract:
[
\text{PV excluding tax} = 30,00 + (30,00 x 200 ÷ 100) = €90,00
]
A margin of 200% requires a selling price excluding tax of €90,00.Evaluate the current markup rate for these creams.
To follow :
[
\text{Brand rate} = ((\text{PV excluding tax} – \text{PA excluding tax}) ÷ \text{PV excluding tax}) x 100
]
Which completes:
[
((70,00 – 30,00) ÷ 70,00) x 100 = 57,14%
]
The mark rate results in 57,14%.
What would be the total margin generated by 150 creams sold?
Unit margin seen:
[
\text{Unit margin} = 70,00 – 30,00 = €40,00
]
So :
[
\text{Total margin} = 40,00 x 150 = €6
]
The margin reaches €6 for the 000 creams.Consider the viability of the pricing strategy if the purchase price increases by €15 per unit.
Basic calculation:
[
\text{New PA HT} = 30,00 + 15,00 = 45,00 €
]
Hence the modified margin rate:
[
((70,00 – 45,00) ÷ 45,00) x 100 = 55,56%
]
The increase in purchasing costs reduces the margin to 55,56%. To maintain profitability, a revision of prices will be necessary, as well as the evaluation of competitiveness and commercial positioning.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT + (PA HT x Desired rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total margin | Unit margin x quantity sold |
Application: Easy DIY
States :
Bricoler Facile is a leading company in tools and building materials. It sells a DIY tool kit for €150,00 excluding VAT, buying it for €75,00 excluding VAT. Due to increasing competition, it is essential to assess the attractiveness of current margins.
Work to do :
- Estimate the current margin rate of the toolkit.
- What PV HT should be set for a markup rate of 50%?
- Analyze the gross margin if 120 kits are sold.
- Should the economic impact of a 12% reduction in the sale price be a cause for concern?
- Calculate the new margin rate if costs drop by €10 per kit.
Proposed correction:
Estimate the current margin rate of the toolkit.
The formula :
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
For a margin rate:
[
((150,00 – 75,00) ÷ 75,00) x 100 = 100%
]
Currently, the margin rate is therefore 100%.What PV HT should be set for a markup rate of 50%?
Let's do the math with:
[
\text{PV HT} = \text{PA HT} ÷ (1 – (\text{Desired rate} ÷ 100))
]
For 50%, we obtain:
[
\text{PV excluding tax} = 75,00 ÷ (1 – (50 ÷ 100)) = €150,00
]
A PV excluding tax of €150,00 ensures a markup rate of 50%.Analyze the gross margin if 120 kits are sold.
Unit margin is:
[
\text{Unit margin} = 150,00 – 75,00 = €75,00
]
So :
[
\text{Gross margin} = 75,00 x 120 = €9
]
The total gross margin will reach €9.
Should the economic impact of a 12% reduction in the sale price be a cause for concern?
Let's calculate the new PV HT:
[
\text{Reduced PV HT} = 150,00 – (150,00 x 0,12) = 132,00 €
]
Corrected margin rate:
[
((132,00 – 75,00) ÷ 75,00) x 100 = 76,00%
]
The drop in the margin rate to 76% could impact sustainability in terms of profit loss. Such a reduction should be considered with caution.Calculate the new margin rate if costs drop by €10 per kit.
Newly adjusted HT PA:
[
\text{PA excluding tax} = 75,00 – 10,00 = €65,00
]
Transformed margin rate:
[
((150,00 – 65,00) ÷ 65,00) x 100 = 130,77%
]
A decrease in purchasing cost increases the margin rate to 130,77%. This provides a strategic opportunity to invest in other aspects of product or service improvement.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT ÷ (1 – (Desired rate ÷ 100)) |
| Gross margin | Unit margin x quantity sold |
Application: Tech Visions
States :
Tech Visions, a leading company in the technology industry, is marketing a virtual reality headset. The purchase price excluding VAT is €120,00, and the sale price excluding VAT is €300,00. The management team wants to know the profits generated from current sales.
Work to do :
- Determine the margin rate on the virtual reality headset.
- Establish the sales price excluding tax which would ensure a markup rate of 70%.
- What is the total expected profit if 500 helmets are sold?
- Consider the potential impact of a 25% increase in the purchase price.
- Explain the possible competitive advantages if the selling price is reduced by €50.
Proposed correction:
Determine the margin rate on the virtual reality headset.
When calculating, let's base ourselves on:
[
\text{Margin rate} = ((\text{PV HT} – \text{PA HT}) ÷ \text{PA HT}) x 100
]
with:
[
((300,00 – 120,00) ÷ 120,00) x 100 = 150%
]
The margin rate is 150%.Establish the sales price excluding tax which would ensure a markup rate of 70%.
Apply the formula:
[
\text{PV HT} = \text{PA HT} ÷ (1 – (Preferred brand rate ÷ 100))
]
Calculation for 70%:
[
\text{PV excluding tax} = 120,00 ÷ (1 – (70 ÷ 100)) = €400,00
]
A selling price excluding tax of €400,00 would allow for a markup rate of 70%.What is the total expected profit if 500 helmets are sold?
Unit margin follows:
[
\text{Unit margin} = 300,00 – 120,00 = €180,00
]
Cumulative for 500 helmets:
[
\text{Total profit} = 180,00 x 500 = €90
]
The expected profit is €90 for these sales.
Consider the potential impact of a 25% increase in the purchase price.
Let's look at the new HT PA:
[
\text{PA HT increased} = 120,00 x 1,25 = 150,00 €
]
The recalculated margin rate would be:
[
((300,00 – 150,00) ÷ 150,00) x 100 = 100%
]
The effect is clear: the margin rate falls to 100%, which requires a reconsideration of profitability and cost structure to maintain a competitive position.Explain the possible competitive advantages if the selling price is reduced by €50.
New PV HT:
[
\text{PV HT reduced} = 300,00 – 50,00 = 250,00 €
]
Margin rate adjustment:
[
((250,00 – 120,00) ÷ 120,00) x 100 = 108,33%
]
This reduced price, while lowering the margin rate, could potentially improve market share and generate more sales, thereby increasing brand awareness and creating a lasting footprint.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Selling price excluding tax | PA HT ÷ (1 – (Preferred brand rate ÷ 100)) |
| Total Profit | Unit margin x quantity sold |