How to calculate a discount - monbtsmco.com

How to calculate a discount

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Welcome to this article on exercises on business calculations and more specifically on how to calculate a discount. Here you will find questions and answers related to the subject. But also no less than 11 detailed corrected management exercises on business calculations for Operational Management.

At the end of this article, you will know how to calculate a discount in business calculations without any worries.

The Beautiful Star App

price comparison before discount - monbtsmco.com

States :

Mrs. Dupont is the manager of the boutique "La Belle Étoile", which sells women's clothing. She wants to set up a promotion on summer dresses. The initial sale price of a dress is €120 including tax. Mrs. Dupont is considering offering a 15% discount to increase sales.

Work to do :

  1. How to calculate the amount of the discount in euros?
  2. What will be the new sales price including tax after discount?
  3. What is the VAT rate applied to dresses?
  4. What would be the selling price excluding tax after discount?
  5. How to calculate the new margin rate after discount, knowing that the purchase price excluding tax of the dress is €50?

Proposed correction:

  1. To calculate the amount of the discount in euros, we use the following formula:

    ( \text{Discount Amount} = \text{Initial Price} \times \frac{\text{Discount Rate}}{100} ).

    ( \text{Discount amount} = €120 \times \frac{15}{100} = €18 )

  2. The new sales price including tax after discount is calculated by subtracting the discount amount from the initial price. ( \text{New price including tax} = \text{Initial price} - \text{Discount amount} )

    ( \text{New price including tax} = €120 - €18 = €102 )

  3. The VAT rate on dresses is 20%.

  4. To calculate the selling price excluding VAT after discount, we use the following formula: ( \text{Price excluding VAT} = \frac{\text{Price including VAT}}{1 + \frac{\text{VAT rate}}{100}} ).

    ( \text{Price excluding VAT after discount} = \frac{102 €}{1 + \frac{20}{100}} = 85 € )

  5. To calculate the new margin rate after discount, we use the formula:

    ( \text{Margin rate} = \left( \frac{\text{PV HT} - \text{PA HT}}{\text{PA HT}} \right) \times 100 ).

    ( \text{Margin rate after discount} = \left( \frac{85 € - 50 €}{50 €} \right) \times 100 = 70% )

List of formulas used:

FormulasDescription
( \text{Discount Amount} = \text{Initial Price} \times \frac{\text{Discount Rate}}{100} )Calculation of the amount of the discount in euros
( \text{New price including tax} = \text{Initial price} - \text{Discount amount} )Calculation of the new sales price including tax after discount
( \text{Price excluding VAT} = \frac{\text{Price including VAT}}{1 + \frac{\text{VAT rate}}{100}} )Calculation of the selling price excluding tax after discount
( \text{Margin rate} = \left( \frac{\text{PV HT} - \text{PA HT}}{\text{PA HT}} \right) \times 100 )Calculation of the margin rate after discount

BioHealth Application

States :

Mrs. Leclerc runs “BioSanté”, a grocery store that sells organic products. She offers a basket of fruits and vegetables for €35 including tax. To build customer loyalty, she plans to offer a 5% discount for regular customers and an additional 3% discount for those who buy more than 3 baskets in a week.

Work to do :

  1. How much is the discount in euros for a regular customer who buys a basket?
  2. What is the total amount of the discount in euros for a customer who buys more than 3 baskets and is also a regular customer?
  3. What will be the sales price including tax of the basket for a customer who benefits from both discounts?
  4. Is the VAT rate on these baskets 20% or 5%?
  5. If the purchase price excluding VAT of the basket is €25, what will be the new margin rate for a basket sold with both discounts?

Proposed correction:

  1. For a regular customer, the discount amount is calculated as follows:

    ( \text{Discount Amount} = \text{Initial Price} \times \frac{\text{Discount Rate}}{100} ).

    ( \text{Discount amount} = €35 \times \frac{5}{100} = €1,75 )

  2. For a customer who purchases more than 3 baskets and is also a regular customer, the total discount amount is the sum of the two individual discounts:

    ( \text{Total discount amount} = €35 \times \frac{5 + 3}{100} )

    ( \text{Total discount amount} = €35 \times \frac{8}{100} = €2,80 )

  3. The new sales price including tax for a customer who benefits from both discounts is obtained by subtracting the total amount of the discount from the initial price:

    ( \text{New price including tax} = €35 - €2,80 = €32,20 )

  4. The VAT rate on these fruit and vegetable baskets is generally 5%.

  5. To calculate the new margin rate, we use the formula:

    ( \text{Margin rate} = \left( \frac{\text{PV HT} - \text{PA HT}}{\text{PA HT}} \right) \times 100 ).

    First, let's find the selling price excluding VAT after discount:

    ( \text{Price excluding VAT after discount} = \frac{32,20 €}{1 + \frac{5}{100}} = 30,67 € )

    Next, let's calculate the margin rate:

    ( \text{Margin rate after discount} = \left( \frac{30,67 € - 25 €}{25 €} \right) \times 100 = 22,68% )

List of formulas used:

FormulasDescription
( \text{Discount Amount} = \text{Initial Price} \times \frac{\text{Discount Rate}}{100} )Calculation of the amount of the discount in euros
( \text{New price including VAT} = \text{Initial price} - \text{Total discount amount} )Calculation of the new sales price including tax after discount(s)
( \text{Price excluding VAT} = \frac{\text{Price including VAT}}{1 + \frac{\text{VAT rate}}{100}} )Calculation of the selling price excluding tax after discount(s)
( \text{Margin rate} = \left( \frac{\text{PV HT} - \text{PA HT}}{\text{PA HT}} \right) \times 100 )Calculation of the margin rate after discount(s)

Discount on bundled products – SpotFit

total cost distribution - monbtsmco.com

States :

The company "SportFit" sells dumbbells. The sales price including VAT of a dumbbell is €150. The company offers a 10% discount for purchases in sets of 5 dumbbells or more. A customer wants to buy 7 dumbbells.

Work to do :

  1. How much is the unit discount in euros on a dumbbell?
  2. What is the total discount amount for 7 dumbbells?
  3. What will be the total cost of the purchase for the customer?
  4. If the VAT rate is 20%, what will be the selling price excluding VAT of a dumbbell after discount?
  5. If the purchase price excluding VAT of a dumbbell is €100, what will the new margin rate be after discount?

Proposed correction:

  1. The amount of the unit discount is: (150 € \times \frac{10}{100} = 15 €)

  2. The total discount amount for 7 dumbbells is: (15 € \times 7 = 105 €)

  3. The total cost of the purchase for the customer will be: ((€150 - €15) \times 7 = €945)

  4. The selling price excluding VAT after discount is: ( \frac{135 €}{1 + \frac{20}{100}} = 112,50 €)

  5. The new margin rate is: ( \left( \frac{€112,50 - €100}{€100} \right) \times 100 = 12,50% )

Successive discounts – Read More

purchase cost breakdown - monbtsmco.com

States :

The bookstore "LirePlus" sells a cookbook for €40 including tax. It offers a 20% discount for the first month and an additional 10% discount for members of the "LirePlus" club.

Work to do :

  1. What is the total discount amount for a member of the “LirePlus” club?
  2. What is the new sales price including tax for a club member?
  3. If the VAT rate is 5%, what will the selling price excluding VAT be after the two discounts?
  4. If the purchase price excluding VAT is €30, what is the new margin rate?
  5. What would the sales price including tax be if the bookstore decided to offer only one 28% discount instead of two successive discounts?

Proposed correction:

  1. The total amount of the discount is: (40 € \times \left(1 - \left(1 - \frac{20}{100}\right) \times \left(1 - \frac{10}{100}\right)\right) = 40 € \times (1 - 0,8 \times 0,9) = €40 \times 0,28 = €11,20 )

  2. The new sales price including VAT is: (€40 – €11,20 = €28,80)

  3. The selling price excluding VAT after discount is: (\frac{€28,80}{1 + \frac{5}{100}} = €27,43)

  4. The new margin rate is: ( \left( \frac{€27,43 - €30}{€30} \right) \times 100 = -8,57% )

  5. The sales price including tax with a single discount of 28% would be:

    (€40 \times \left(1 - \frac{28}{100}\right) = €28,80)
old and new margin rate - monbtsmco.com

Discount on the second item – Golden Sparkle

States :

In the “Éclat d'Or” jewelry store, the purchase of a necklace for €200 including tax gives you a 50% discount on a bracelet priced at €150 including tax.

Work to do :

  1. How much is the discount in euros on the bracelet?
  2. What will be the total cost of the purchase for the customer?
  3. If the VAT rate is 20%, what will be the selling price excluding VAT of the bracelet after discount?
  4. If the purchase price excluding VAT of the bracelet is €100, what will the new margin rate be?
  5. What would be the average discount rate on the entire purchase?

Proposed correction:

  1. The amount of the discount on the bracelet is (150 € \times \frac{50}{100} = 75 €).

  2. The total cost of the purchase for the customer is (€200 + (€150 – €75) = €275).

  3. The selling price excluding VAT of the bracelet after discount is (\frac{75 €}{1 + \frac{20}{100}} = 62,50 €).

  4. The new margin rate on the bracelet is (\left(\frac{€62,50 - €100}{€100}\right) \times 100 = -37,50%).

  5. The average discount rate on the entire purchase is (\frac{€200 + €150 - €275}{€200 + €150} \times 100 = \frac{75}{350} \times 100 \approx 21,43%).

Volume purchase discount – ElectroShop

cost allocation - monbtsmco.com

States :

ElectroShop sells vacuum cleaners for €250 including VAT. For purchases of more than 10 units, a 12% discount is applied to the entire order. A hotel wants to buy 15 vacuum cleaners.

Work to do :

  1. What is the total discount for 15 vacuum cleaners?
  2. What will be the total cost of purchase for the hotel?
  3. If the VAT rate is 20%, what will be the selling price excluding VAT for a vacuum cleaner after discount?
  4. If the purchase price excluding tax is €180, what will be the new margin rate for the hotel?
  5. How much do you save per vacuum cleaner with the discount?

Proposed correction:

  1. The total discount amount for 15 vacuum cleaners is (15 \times €250 \times \frac{12}{100} = €450).

  2. The total cost of purchase for the hotel is ((15 \times €250) - €450 = €3).

  3. The selling price excluding VAT of a vacuum cleaner after discount is (\frac{220 €}{1 + \frac{20}{100}} = 183,33 €).

  4. The new margin rate for the hotel is (\left(\frac{€183,33 - €180}{€180}\right) \times 100 = 1,85%).

  5. The amount saved per vacuum cleaner thanks to the discount is (\frac{450 €}{15} = 30 €).

Cascade Discount – Chic Fashion

States :

The clothing store Mode Chic is offering a 10% discount on the first item, 20% on the second and 30% on the third. The items cost €50, €80 and €100 respectively, including tax.

Work to do :

  1. What is the total amount of rebates in euros?
  2. What is the total cost of purchase for the customer?
  3. If the VAT rate is 20%, what will be the total cost excluding VAT for the customer?
  4. What is the average discount rate on the entire purchase?
  5. If the total purchase cost excluding tax for the store is €150, what will the new margin rate be?

Proposed correction:

  1. The total amount of discounts is (50 € \times \frac{10}{100} + 80 € \times \frac{20}{100} + 100 € \times \frac{30}{100} = 5 € + 16 € + 30 € = 51 €).

  2. The total cost of the purchase for the customer is ((€50 + €80 + €100) – €51 = €179).

  3. The total cost excluding tax for the customer is (\frac{179 €}{1 + \frac{20}{100}} = 149,17 €).

  4. The average discount rate on the entire purchase is (\frac{51 €}{50 € + 80 € + 100 €} \times 100 = \frac{51}{230} \times 100 \approx 22,17%).

  5. The new margin rate is (\left(\frac{€149,17 - €150}{€150}\right) \times 100 = -0,55%).

TechNovation Application

Technovision cost allocation - monbtsmco.com

States :

You are currently working as a financial management expert in a company called "TechNovation". The latter specializes in the sale of electronic products. The company often offers discounts to its customers in order to increase its sales volume and stand out from the competition.

A new customer wants to buy a computer with a retail price (RP) of €1 excluding VAT. TechNovation is offering a 200% discount on this item. The VAT applied is 10%.

Work to do :

1. How much is the discount in euros?
2. What is the sales price excluding tax (PV HT) after the discount?
3. What is the total amount of VAT?
4. What is the sales price including all taxes (TTC) after the discount?
5. If the company wants to maintain a margin rate of 30%, what should be the purchase price excluding tax (PA HT) of the computer?

Proposed correction:

1. The amount of the discount is calculated using the formula: (Discount in % x Sale price excluding VAT) / 100. Here, this gives: (10 x €1 excluding VAT) / 200 = €100.

2. The sales price excluding tax after the discount is obtained by subtracting the amount of the discount from the initial sales price: €1 excluding tax – €200 = €120 excluding tax.

3. The amount of VAT is calculated using the formula: (VAT rate x Sales price excluding VAT after discount) / 100. Here, this gives: (20 x €1 excluding VAT) / 080 = €100.

4. To obtain the price including tax after discount, add the amount of VAT to the price excluding tax after discount: €1 excluding tax + €080 = €216 including tax.

5. If the company wants to maintain a margin rate of 30%, it must apply the formula: Selling price excluding VAT after discount / (1 + Margin rate / 100). This gives: €1 / (080 + 1 / 30) = €100 excluding VAT.

Summary of Formulas Used:

– Discount amount = (Discount in % x Sales price excluding VAT) / 100.
– Selling price excluding VAT after discount = Selling price excluding VAT – discount amount.
– VAT amount = (VAT rate x Sales price excluding VAT after discount) / 100.
– Sales price including tax after discount = Sales price excluding tax after discount + VAT amount.
– Purchase price excluding VAT with a desired margin rate = Sale price excluding VAT after discount / (1 + Margin rate / 100).

TechMaster Application

States :

The company "TechMaster" specializes in selling high-tech equipment and you are in charge of the sales department. You are planning to launch a series of discounts to boost sales during the holiday period.

Product A, which usually costs €1200, is marked with a 20% discount. Product B has a regular price of €2000 with a 15% discount offered. Product C is sold at a price of €700 with a special discount that means it is sold at €570.

Work to do :

1. What is the new price (after discount) of product A?
2. How much money will customers save on product B with the proposed discount?
3. What is the discount rate applied to product C?
4. If the company plans to sell 500 units of product A, 400 units of product B, and 300 units of product C with these discounts, what will be the total expected revenue?
5. If the company decides to remove all discounts and return to original prices, how much will total revenue increase for the same quantities sold?

Proposed correction:

1. The new price of product A will be: Original price – (Original price x Discount rate) => €1200 – (€1200 x 20 ÷ 100) = €960

2. Customers will save on product B: Original price x Discount rate => €2000 x 15 ÷ 100 = €300

3. The discount rate applied to product C is: ((Original price – Discounted price) ÷ Original price) x 100 => ((€700 – €570) ÷ €700) x 100 = 18,57%

4. With discounts, the total revenue for these quantities will be:

(500 x 960 € (product A)) + (400 x (2000 € – 300 €) (product B)) + (300 x 570 € (product C)) = 480000 € + 680000 € + 171000 € (product C) = 1331000 €

5. Without discounts, total revenue would increase by:

(500 x 1200 € (product A)) + (400 x 2000 € (product B)) + (300 x 700 € (product C)) – 1331000 € = 600000 € + 800000 € + 210000 € – 1331000 € = 1610000 € – 1331000 € = 279000 €

Summary of Formulas Used:

– New price after discount = Original price – (Original price x Discount rate)
– Discounted Savings = Original Price x Discount Rate
– Discount rate = ((Original price – Discounted price) ÷ Original price) x 100
– Total revenue = sum (quantity sold x Price after discount) for all products
– Total revenue increase without discounts = sum (quantity sold x Original price) for all products – Total revenue with discounts.

Fashion Forward App

cost allocation and discounts - monbtsmco.com

States :

The high fashion clothing company "Fashion Forward" has decided to hold an end-of-season sale to clear out its clothing inventory from the previous year. The managers have decided to apply discounts ranging from 10% to 50% on various items. They have turned to you as a financial manager to help calculate the net prices after discounts and to assess the financial implications of this sale.

Work to do :

1. If a dress that costs €200 is discounted by 15%, what would its new price be?
2. If a pair of pants costing €80 has a 30% discount, what is the net price after the discount?
3. How does the discount rate affect the overall margin of a product?
4. If a €50 shirt was sold with a 20% discount and the acquisition cost of the shirt was €25, what is the margin rate after this discount?
5. If “Fashion Forward” decides to apply an additional 5% discount on all items already on sale, how would this affect financial returns?

Proposed correction:

1. The price of the dress after a 15% discount is calculated as follows: €200 – €200 x 15/100
Which gives: €200 – €30 = €170.

2. The price of the pants after the 30% discount will be as follows: 80€ – 80€ x 30/100
Which gives: €80 – €24 = €56.

3. The discount rate has a direct impact on the overall margin of the product. The higher the discount rate, the lower the overall margin. This is because the net selling price (after discount) is brought closer to the purchase price, thus reducing the difference (the margin).

4. The margin rate is calculated using the formula: ((PV HT – PA HT) / PA HT) * 100
For this shirt, it would be: ((€50 x (1 – 20/100) – €25) / €25) x 100. Which gives: ((€50 – €10 – €25) / €25) x 100 = 60%.

5. If "Fashion Forward" applies an additional 5% discount, this will further reduce the company's revenue and therefore net profit. The analysis of the financial consequences requires a more in-depth assessment.

Summary of Formulas Used:

– Price after discount = Base price – Base price x Discount rate / 100
– Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) / Purchase price excluding VAT) x 100

Home Decor App

States :

A furniture store, “Deco Maison”, recently received a new shipment of sofas.

The unit purchase excluding tax of the sofa is €400.
The margin rate desired by “Deco Maison” is 50%.
The company applies a 20% VAT on its products.
"Deco Maison" wants to offer a 10% discount on this sofa for the first month in order to attract customers.

Work to do :

1. What is the selling price excluding VAT of the sofa before the discount?
2. What is the selling price including tax of the sofa before the discount?
3. What is the monetary value of the discount?
4. What is the selling price excluding VAT of the sofa after the discount?
5. What is the selling price including tax of the sofa after the discount?

Proposed correction:

1. To calculate the selling price excluding tax before the discount, we use the formula: PA excluding tax x (1 + Margin rate). That is: €400 x (1 + 0,5) = €600.

2. The sales price including tax before the discount is calculated using the formula: Sales price excluding tax x (1 + VAT rate). That is: €600 x (1 + 0,2) = €720.

3. The discount is obtained by calculating: Sales price excluding tax x Discount rate. That is: €600 x 0,1 = €60.

4. The selling price excluding VAT after the discount is given by: Selling price excluding VAT – Discount. That is: €600 – €60 = €540.

5. Finally, to obtain the sales price including VAT after the discount, we use the formula: Sales price excluding VAT after the discount x (1 + VAT rate). Therefore: €540 x (1 + 0,2) = €648.

Summary of Formulas Used:

– Selling price excluding tax = PA excluding tax x (1 + Margin rate)
– Sales price including tax = Sales price excluding tax x (1 + VAT rate)
– Discount = Selling price excluding VAT x Discount rate
– Selling price excluding VAT after discount = Selling price excluding VAT – Discount
– Sales price including tax after discount = Sales price excluding tax after discount x (1 + VAT rate)

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