How to Calculate Overall Gross Margin | 9 Exercises

Application: The Market Fine Grocery

States :

L'Épicerie Fine du Marché is a store located in a dynamic city and offers local and artisanal food products. For the year 2023, it wants to carry out an in-depth analysis of its overall gross margin. The store's flagship products are artisanal matured cheeses, sold at a price of €25 each, and organic wines, sold at an average price of €18 per bottle. The grocery store sold 1 cheeses and 200 bottles of wine last year. The purchase cost of cheeses is €800 per unit, and that of wines is €15 per unit.

Work to do :

1. Calculate the unit gross margin for cheeses and wines sold by L'Épicerie Fine du Marché.
2. Calculate the overall gross margin for each product.
3. Determine the margin rate for cheeses and wines.
4. The Grocery Store wants to increase its overall gross margin by 10%. What should the new selling price of cheese be to achieve this goal, assuming that the purchase cost remains constant?
5. Analyze the strategic implications of increasing gross margin for L'Épicerie Fine du Marché.

Proposed correction:

1. Calculation of unit gross margin:

   • For cheeses:

     Gross margin per unit = PV – PA = €25 – €15 = €10

   • For wines:

     Gross margin per unit = PV – PA = €18 – €10 = €8

   The gross margin per unit is respectively €10 for cheeses and €8 for wines.

2. Calculation of the overall gross margin:

   • Cheeses: Overall margin = Unit margin x Quantity sold = €10 x 1 = €200

   • Wines: Overall margin = Unit margin x Quantity sold = €8 x 800 = €6

   The overall gross margin is €12 for cheeses and €000 for wines.

3. Determination of the margin rate:

• For cheeses:

  Margin rate = ((PV – PA) ÷ PA) x 100 = ((€25 – €15) ÷ €15) x 100 = 66,67%

• For wines:

  Margin rate = ((PV – PA) ÷ PA) x 100 = ((€18 – €10) ÷ €10) x 100 = 80%

The margin rate is 66,67% for cheeses and 80% for wines.

4. Increase overall gross margin by 10%:

   Current overall margin target = €12 + €000 = €6

   Increased gross margin target = €18 x 400 = €1,10

   To increase only the price of cheese, the margin on the latter must increase to:

   New margin requirement on cheeses = €20 – €240 = €6

   New sales price: (New margin ÷ Quantity) + CA = 13 ÷ 840 + 1 = 200 + 15 = €11,53

   The new selling price of cheese must be €26,53 to reach the increase target.

5. Analysis of strategic implications:

   Increasing the selling price of cheese may attract fewer customers, but provide greater profitability for the product. It is essential for L'Épicerie Fine du Marché to analyze the price sensitivity of its customers to ensure that this price increase does not decrease overall sales.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Margin rate	((PV – PA) ÷ PA) x 100
Increase in margin	Old margin x percentage increase
New sale price	(New Margin ÷ Quantity) + CA

Application: The Innovative Startup TechGo

States :

TechGo is a startup specializing in innovative tech gadgets, mainly smartwatches and wireless earphones. In 2023, the company sold 3 smartwatches at a unit price of €000 and 150 pairs of earphones at a unit price of €5. The purchase cost of a watch is €000, while that of the earphones is €80. TechGo wants to calculate its overall gross margin for these products and consider optimization strategies.

Work to do :

1. Calculate gross margin per unit for smartwatches and wireless headphones.
2. Evaluate the overall gross margin obtained for the two products sold by TechGo.
3. Find out the markup rate for each type of product.
4. Offer the new markup rate hoped for if TechGo offers a promotional discount of €10 on watches to boost sales.
5. Examine the potential impact of adding new features to watches on overall gross margin.

Proposed correction:

1. Calculation of unit gross margin:

   For smartwatches:

   Gross margin per unit = PV – PA = €150 – €90 = €60

   For wireless headphones:

   Gross margin per unit = PV – PA = €80 – €50 = €30

   The gross margin per unit is €60 for watches and €30 for headphones.

2. Overall gross margin assessment:

   Watches: Overall margin = Unit margin x Quantity = €60 x 3 = €000

   Headphones: Overall margin = Unit margin x Quantity = €30 x €5 = €000

   The overall gross margin is €180 for watches and €000 for headphones.

3. Markup rate for each product:

• For smartwatches:

  Markup rate = ((PV – PA) ÷ PV) x 100 = ((€150 – €90) ÷ €150) x 100 = 40%

• For headphones:

  Markup rate = ((PV – PA) ÷ PV) x 100 = ((€80 – €50) ÷ €80) x 100 = 37,5%

The markup rate is 40% for watches and 37,5% for headphones.

4. New brand rate with discount:

   New watch sale price = €150 – €10 = €140

   New markup rate = ((€140 – €90) ÷ €140) x 100 = 35,71%

   With a €10 discount, the new brand rate for watches would be 35,71%.

5. Consequences of new features:

   Adding features can increase perceived value and potentially justify a higher selling price, which could maintain gross margin levels or even increase them if price increases more than costs. However, the impact on sales volume and market competitiveness must be monitored.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV – PA) ÷ PV) x 100
New sale price with discount	Old PV – Reduction
New mark rate	((New HP – AP) ÷ New HP) x 100

Application: The Golden Malt Craft Brewery

States :

Brasserie Artisanale Le Malt d'Or produces and sells local craft beers. This year, it produced three types of beers: Blonde, Ambrée, and Brune. The average selling price of the Blonde is €5, the Ambrée is €6, and the Brune is €7. The respective production costs are €3, €3,5, and €4. Demand has been strong with 10 bottles of Blonde, 000 bottles of Ambrée, and 8 bottles of Brune sold. The brewery is looking to understand and optimize its overall gross margin.

Work to do :

1. Calculate the unit gross margin for each type of beer.
2. Determine the overall gross margin generated by each type of beer and the total.
3. Evaluate the margin rate for each type of beer.
4. If Le Malt d'Or wanted to increase the margin rate by 5% for Blonde beer, what would be the new selling price required?
5. Analyze how increasing production costs could affect the company's margin strategy.

Proposed correction:

1. Calculation of unit gross margin:

   • Blonde: Gross unit margin = PV – PA = €5 – €3 = €2

   • Amber: Gross unit margin = PV – PA = €6 – €3,5 = €2,5

   • Brown: Gross unit margin = PV – PA = €7 – €4 = €3

   Thus, the gross unit margin is €2 for the Blonde, €2,5 for the Ambrée, and €3 for the Brune.

2. Overall gross margin:

   • Blonde: Overall margin = €2 x 10 = €000

   • Amber: Overall margin = €2,5 x €8 = €000

   • Brown: Overall margin = €3 x €6 = €000

   The total overall gross margin is €58.

3. Margin rate:

• Blonde: Margin rate = ((€5 – €3) ÷ €3) x 100 = 66,67%

• Amber: Margin rate = ((€6 – €3,5) ÷ €3,5) x 100 = 71,43%

• Brown: Margin rate = ((€7 – €4) ÷ €4) x 100 = 75%

The margin rates are 66,67% for Blonde, 71,43% for Amber, and 75% for Brown.

4. Increase the Blonde's margin rate by 5%:

   New margin rate target = 66,67% + 5% = 71,67%

   New sale price = ((€3 × (1 + (71,67 ÷ 100))) = €5,15

   To achieve a margin rate of 71,67%, the price of the Blonde must be €5,15.

5. Analysis of the impact of increased production costs:

   An increase in production costs could reduce margins if sales prices remain constant. This could force the company to increase its sales prices or look for ways to reduce costs to maintain its margins.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Margin rate	((PV – PA) ÷ PA) x 100
New target margin rate	Old margin rate + Desired increase
New selling price for margin	PA × (1 + (New Margin Rate ÷ 100))

Application: Camille's Jewelry

States :

Camille's Jewelry is a craft business that produces handmade jewelry. Camille sold 400 necklaces, 600 rings, and 500 bracelets last year. Each necklace sold for €90, each ring for €60, and each bracelet for €50. Production costs are €45 for the necklaces, €30 for the rings, and €25 for the bracelets. Camille wants to do a detailed analysis of her overall gross margin.

Work to do :

1. Calculate the unit gross margin for each type of jewelry manufactured by Camille.
2. Determine the overall gross margin for each type of jewelry.
3. Evaluate the markup rate applied to each piece of jewelry.
4. Suggest a potential selling price for the necklaces to achieve a 60% markup rate.
5. What are the risks and benefits of increasing the markup rate for Les Bijoux de Camille?

Proposed correction:

1. Calculation of unit gross margin:

   • Necklaces: Gross unit margin = PV – PA = €90 – €45 = €45

   • Rings: Gross unit margin = PV – PA = €60 – €30 = €30

   • Bracelets: Gross margin per unit = PV – PA = €50 – €25 = €25

   The gross margins per unit are €45 for necklaces, €30 for rings and €25 for bracelets.

2. Overall gross margin:

   • Necklaces: Total margin = €45 x 400 = €18

   • Rings: Total margin = €30 x €600 = €18

   • Bracelets: Overall margin = €25 x 500 = €12

   The overall gross margin is a total of €48.

3. Mark rate:

• Necklaces: Markup rate = ((€90 – €45) ÷ €90) x 100 = 50%

• Rings: Markup rate = ((€60 – €30) ÷ €60) x 100 = 50%

• Bracelets: Markdown rate = ((€50 – €25) ÷ €50) x 100 = 50%

Markdown rates are uniformly 50% for all jewelry.

4. Selling price for 60% markup rate:

   For necklaces with a 60% markup rate:

   Selling price = PA ÷ (1 – Markup rate) = €45 ÷ (1 – 0,60) = €112,50

   To achieve a 60% markup, the necklaces must be sold at €112,50.

5. Risks and benefits of increasing the markup rate:

   Increasing the markup rate increases profitability per piece sold, but can make products less competitive and decrease sales volume if customers are price sensitive. This requires good market and customer knowledge.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV – PA) ÷ PV) x 100
Price for a new brand rate	PA ÷ (1 – Desired markup rate)

Application: Gastronomic Restaurant La Fourchette d'Or

States :

The gourmet restaurant La Fourchette d'Or offers tasting menus to its customers. Each menu is priced at €120, and the ingredients cost an average of €50 per menu. The restaurant served 1 menus last year. The chef wants to analyze the gross margin in order to improve his pricing and cost strategy.

Work to do :

1. Calculate the unit gross margin for each tasting menu.
2. Evaluate the overall gross margin for the past year.
3. Calculate the margin rate of the proposed menu.
4. Suppose costs increase by 10%. What should the new selling price be to maintain the same margin rate?
5. Discuss the strategic implications of raising prices on the restaurant's exclusive clientele.

Proposed correction:

1. Calculation of unit gross margin:

   Gross margin per unit = PV – PA = €120 – €50 = €70

   Each tasting menu generates a gross unit margin of €70.

2. Overall gross margin:

   Overall margin = Unit margin x Quantity = €70 x 1 = €500

   The overall gross margin for the past year is €105.

3. Margin rate:

Margin rate = ((PV – PA) ÷ PA) x 100 = ((€120 – €50) ÷ €50) x 100 = 140%

The menu margin rate is 140%.

4. New selling price to maintain the margin rate:

   New PA = PA x 1,10 = €50 x 1,10 = €55

   New PV to maintain the margin rate:

   = New PA x (1 + (Margin rate ÷ 100)) = €55 x (1 + 1,40) = €132

   To maintain a margin rate of 140%, the restaurant must sell the menu at €132.

5. Strategic impact of price increases:

   Raising the price may reduce demand but still maintain the same profitability per customer if the clientele is less price sensitive. A balance must be found so as not to harm the restaurant's traffic.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Margin rate	((PV – PA) ÷ PA) x 100
New PA with increase	Old PA x (1 + Increase Rate)
New PV to keep same margin rate	New PA x (1 + (Margin Rate ÷ 100))

Application: Luxury Hotel Le Grand Palace

States :

The Grand Palace is a luxury hotel offering premium suites at €400 per night, with an operating cost per night of €150. In 2023, the hotel recorded 2 overnight stays. The manager wants to analyze the overall gross margin to assess the profitability of the establishment.

Work to do :

1. Calculate the gross margin per unit for each night in a premium suite.
2. Estimate the overall gross margin for the year.
3. Calculate the markup rate of the hotel proposal.
4. The hotel needs to renovate the suites, which will increase the cost by 20%. What will be the selling price needed to maintain the same markup?
5. Analyze the potential implications of the price increase due to renovations on the hotel's loyal customer base.

Proposed correction:

1. Calculation of unit gross margin:

   Gross margin per unit = PV – PA = €400 – €150 = €250

   Each night in a premium suite generates a gross margin of €250.

2. Overall gross margin:

   Overall margin = Unit margin x Quantity = €250 x 2 = €000

   The overall gross margin for the year is €500.

3. Mark rate:

Markup rate = ((PV – PA) ÷ PV) x 100 = ((€400 – €150) ÷ €400) x 100 = 62,5%

The markup rate for suites is 62,5%.

4. Selling price to maintain the mark rate with renovation:

   Cost increase: €150 x 1,20 = €180

   New PV to maintain the mark rate:

   = PA ÷ (1 – Markup rate) = €180 ÷ (1 – 0,625) = €480

   The price per night should be €480 to maintain the markup rate at 62,5%.

5. Implications of the price increase:

   Raising prices can help offset increased costs without affecting profitability. However, it may affect affordability for some guests. The hotel must ensure that the perceived value of the renovations justifies the rate increase.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV – PA) ÷ PV) x 100
New PA after renovation	Former PA x (1 + Renovation rate)
New PV to keep same brand rate	PA ÷ (1 – Mark rate)

Application: The Enchanted Bookstore

States :

Librairie Enchantée is an independent store selling new and used books. Over the past year, it has sold 5 new books at an average price of €000 and 20 used books at an average price of €8. The purchasing costs are €000 for a new book and €5 for a used book. The bookstore is looking to determine its overall gross margin and consider restructuring its prices.

Work to do :

1. Calculate the gross margin per unit for new and used books.
2. Determine the overall gross margin achieved by the bookstore.
3. Analyze the margin rate for each book category.
4. Evaluate the impact of a 10% reduction in the selling price of new books on the overall margin.
5. What would be the potential effects of such a price reduction on customers and on the company's strategy?

Proposed correction:

1. Calculation of unit gross margin:

   • New books: Gross unit margin = PV – PA = €20 – €12 = €8

   • Used books: Gross margin per unit = PV – PA = €5 – €2 = €3

   The gross margin per unit is €8 for new books and €3 for used books.

2. Overall gross margin:

   • New books: Total margin = €8 x €5 = €000

   • Used books: Total margin = €3 x €8 = €000

   The overall gross margin is €64.

3. Margin rate:

• New books: Margin rate = ((€20 – €12) ÷ €12) x 100 = 66,67%

• Used books: Margin rate = ((€5 – €2) ÷ €2) x 100 = 150%

The margin rate is 66,67% for new books and 150% for used books.

4. Impact of a 10% price reduction:

   New PV for new books = €20 x (1 – 0,10) = €18

   New gross margin per unit = €18 – €12 = €6

   New overall margin = €6 x €5 = €000

   The new overall margin is €30 for new books, reducing the total gross margin to €000.

5. Effects of price reduction:

   A price cut might expand the customer base and boost sales, but it reduces unit margin. So the strategy should focus on increasing sales volume to compensate for the lower unit margins.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Margin rate	((PV – PA) ÷ PA) x 100
New price after discount	Old PV x (1 – Reduction Rate)
New gross margin per unit	New PV – PA

Application: The Leonard Couture Workshop

States :

Atelier de Couture Léonard is a company that makes custom clothing. It offers three types of services: dress making, suits, and shirts. The average prices are €200, €300, and €120 respectively. The production costs for each service are €80, €140, and €60. During the year, Léonard made 200 dresses, 150 suits, and 400 shirts. The workshop wants to calculate its overall gross margin and explore possible price adjustments.

Work to do :

1. Calculate the gross margin per unit for each type of service offered by Atelier Léonard.
2. Determine the overall gross margin obtained for each service and the total.
3. Find out the markup rate for each type of product.
4. Leonardo plans to increase the profit margin on suits by 10%. What would the new selling price be?
5. Analyze the implications of this price adjustment on competitiveness and customer satisfaction.

Proposed correction:

1. Calculation of unit gross margin:

   • Dresses: Gross unit margin = PV – PA = €200 – €80 = €120

   • Costumes: Gross unit margin = PV – PA = €300 – €140 = €160

   • Shirts: Gross margin per unit = PV – PA = €120 – €60 = €60

   The gross margins per unit are €120 for dresses, €160 for suits, and €60 for shirts.

2. Overall gross margin:

   • Dresses: Total margin = €120 x 200 = €24

   • Costumes: Total margin = €160 x 150 = €24

   • Shirts: Total margin = €60 x 400 = €24

   The total overall gross margin is €72.

3. Mark rate:

• Dresses: Markdown rate = ((€200 – €80) ÷ €200) x 100 = 60%

• Costumes: Markup rate = ((€300 – €140) ÷ €300) x 100 = 53,33%

• Shirts: Markup rate = ((€120 – €60) ÷ €120) x 100 = 50%

The markup rates are 60% for dresses, 53,33% for suits, and 50% for shirts.

4. New selling price for suits with increased margin of 10%:

   Desired margin rate = 53,33% + 10% = 63,33%

   New PV = PA ÷ (1 – Markup rate) = €140 ÷ (1 – 0,6333) = €382,35

   Leonardo needs to sell the suits for around €382,35 to reach the markup rate of 63,33%.

5. Implications of the price adjustment:

   Price adjustment could increase gross margin but risks making the suits less attractive to competitors. It is essential to understand the price sensitivity of the customer before changing prices.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV – PA) ÷ PV) x 100
New PV for target mark rate	PA ÷ (1 – Desired markup rate)

Application: The Exquisite Chocolatier

States :

Le Chocolatier Exquis makes artisanal chocolates for the holidays. The flagship products are boxes of truffles, pralines, and ganaches. The prices of the boxes are set at €30, €25, and €35 ​​respectively. The production costs are €15, €10, and €20. During the holiday season, 700 boxes of truffles, 500 pralines, and 600 ganaches were sold. The chocolatier wants to optimize its overall gross margin.

Work to do :

1. Calculate the unit gross margin for each product type.
2. Evaluate the overall gross margin for each product and the total margin.
3. Calculate the margin rate for each type of chocolate.
4. If the chocolatier wants to achieve an overall margin of €50, what should be the new selling price for truffles exclusively?
5. Discuss the risks associated with increasing selling prices in the luxury market.

Proposed correction:

1. Calculation of unit gross margin:

   • Truffles: Gross unit margin = PV – PA = €30 – €15 = €15

   • Pralines: Gross unit margin = PV – PA = €25 – €10 = €15

   • Ganaches: Gross unit margin = PV – PA = €35 – €20 = €15

   The gross margin per unit is €15 for each type of chocolate.

2. Overall gross margin:

   • Truffles: Total margin = €15 x 700 = €10

   • Pralines: Total margin = €15 x 500 = €7

   • Ganaches: Total margin = €15 x 600 = €9

   The total gross margin is €27.

3. Margin rate:

• Truffles: Margin rate = ((€30 – €15) ÷ €15) x 100 = 100%

• Pralines: Margin rate = ((€25 – €10) ÷ €10) x 100 = 150%

• Ganaches: Margin rate = ((€35 – €20) ÷ €20) x 100 = 75%

The margin rates are 100% for truffles, 150% for pralines, and 75% for ganaches.

4. Truffle prices for a total margin of €50:

   Additional margin target = €50 – €000 = €27

   New unit margin requirement: €23 ÷ €000 = €700

   New PV for truffles = Cost + New unit margin = €15 + €32,86 = €47,86

   The price of truffles should be €47,86 to reach the target margin.

5. Risks of price increase:

   Price increases in the luxury segment could be perceived positively if they reinforce the perception of quality. However, too high increases can exceed the market's tolerance and decrease demand.

Formulas Used:

Title	Formulas
Unit gross margin	PV – PA
Overall margin	Unit margin x Quantity sold
Margin rate	((PV – PA) ÷ PA) x 100
New overall margin target	Old Margin + Additional Objective
New PV for truffles	Cost + New Unit Margin