business-calculations-management

Business Calculations Management | 9 Exercises

by

Application: The Delights of the Orchard

States :

Les Délices du Verger is a food store dedicated to fruits and fruit-based products. Its growing success requires rigorous management of prices and costs. The company is currently looking at its flagship product, raspberry jam, to analyze its margins and set a competitive selling price.

Work to do :

  1. Calculate the margin rate for raspberry jam if the purchase price excluding tax is €4 and the sale price excluding tax is €5,60.

  2. If the store wants to achieve a markup rate of 30%, what should be the selling price excluding tax for a jam purchased for €4 excluding tax?

  3. For a quantity sold of 500 pots, calculate the overall margin if the unit margin is €1,60.

  1. Assuming that the cost of storing jam jars is €0,20 per jar per year and that the ordering cost is €5, calculate the QEPC (Economic Production Quantity) knowing that the annual demand is 2 jars.

  2. Discuss the impact of the increase in the cost of purchasing raw materials on the gross margin of Délices du Verger.

Proposed correction:

  1. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Let's replace: ((€5,60 – €4) ÷ €4) x 100 = 40%.
    The jam achieves a margin rate of 40%.

  2. To obtain a markup rate of 30%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, €4 ÷ (1 – 0,30) = €5,71.
    The selling price excluding VAT should be €5,71 to achieve a mark-up rate of 30%.

  3. The overall margin is calculated by the formula: Overall margin = Unit margin x quantity sold.

Replacing: €1,60 x 500 = €800.
The overall margin for 500 pots is €800.

  1. The QEC is calculated by the formula: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    By replacing: QEC = ?((2 x 2 x 000) ÷ 5) = ?((0,20) ÷ 20) = ?000 = 0,20.
    The QEC is 316 jars of jam.

  2. An increase in the cost of purchasing raw materials will decrease the gross margin if the selling prices excluding VAT are not adjusted accordingly. This could affect the overall profitability of the company if new customers are not attracted to compensate.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
Overall margin Unit margin x quantity sold
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: TechnoMobil

States :

TechnoMobil, a company specializing in the sale of mobile phone accessories, wants to optimize its pricing policy. It wants to estimate the profits from the sale of phone cases by comparing different brand rates and evaluating the costs associated with its annual operations.

Work to do :

  1. Determine the purchase price excluding VAT of a hull if the margin rate is 25% and the sale price excluding VAT is €15.

  2. What selling price excluding tax would allow a markup rate of 35% to be achieved for a hull purchased at €8 excluding tax?

  3. Calculate the overall margin if TechnoMobil sells 800 hulls with a unit margin of €2.

  1. If the annual storage cost is €0,50 per shell, the ordering cost is €12 and the annual demand is 5 shells, find the QEC.

  2. Analyze the potential effects on the markup rate if the company decides to lower prices by 10% to compete with rivals.

Proposed correction:

  1. The margin rate is given by the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    So, 25 = ((15 – PA HT) ÷ PA HT) x 100.
    We obtain: PA HT = €12.
    The purchase price excluding VAT of a hull is €12.

  2. To obtain a markup rate of 35%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
    Let's replace: €8 ÷ (1 – 0,35) = €12,31.
    The selling price excluding VAT should be €12,31 to achieve a mark-up rate of 35%.

  3. Calculation of overall margin: Overall margin = Unit margin x quantity sold.

Let's replace: €2 x 800 = €1.
The overall margin is €1.

  1. Calculation of QEC: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    Let's replace: QEC = ?((2 x 5 x 000) ÷ 12) = ?(0,50 ÷ 120) = ?000 = 0,50.
    The QEC is 490 hulls.

  2. By lowering prices by 10%, the PV_HT decreases, which could reduce the markup rate if purchase prices remain constant. The challenge could be to compensate by increasing sales volumes.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
Overall margin Unit margin x quantity sold
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Fashion & Chic

States :

Mode & Chic is a high-end clothing store that is looking to adjust its prices and margins to maximize profits. Currently, it wants to review the financial results of a winter sweater collection to determine what pricing adjustments are needed.

Work to do :

  1. Find the purchase price excluding tax of a sweater if the margin rate is 40% for a sale price of €140 excluding tax.

  2. What would be the selling price excluding tax to obtain a markup rate of 20% knowing that the purchase price excluding tax of the sweater is €100?

  3. If Mode & Chic sells 1 sweaters with a unit margin of €000, calculate the overall margin.

  1. Calculate the QEC for these sweaters, with a storage cost of €1 per sweater per year, an ordering cost of €25, and an annual demand of 3 sweaters.

  2. Evaluate the potential impact of a 15% increase in purchasing costs on the company's prices and margin rate.

Proposed correction:

  1. For the margin rate, we use: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    So, 40 = ((140 – PA HT) ÷ PA HT) x 100.
    Solving, PA HT = €100.
    The purchase price excluding VAT is €100.

  2. For a markup rate of 20%, the formula is: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, €100 ÷ (1 – 0,20) = €125.
    The selling price excluding tax must be €125 for a markup rate of 20%.

  3. Overall margin: Overall margin = Unit margin x quantity sold.

Replacing: €50 x €1 = €000.
The overall margin is €50.

  1. The QEC: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    By replacing: QEC = ?((2 x 3 x 000) ÷ 25) = ?(1) = 150.
    The QEC is 387 sweaters.

  2. The 15% increase in purchasing costs will reduce the gross margin unless the selling prices excluding VAT are adjusted accordingly. Mode & Chic will have to assess whether the price increase could affect demand and thus adjust its strategy.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
Overall margin Unit margin x quantity sold
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Gourmet Bio

States :

Gourmet Bio is a delicatessen that is committed to offering organic and quality products. In full expansion, it wants to recheck its economic model, particularly for its olive oils which are a flagship product.

Work to do :

  1. Calculate the margin rate if the olive oil is purchased at €10 excluding VAT and sold at €14 excluding VAT.

  2. What selling price would be necessary to achieve a markup rate of 40%, if the purchase price excluding tax is €9 for a bottle of olive oil?

  3. Gourmet Bio sells 300 bottles with a unit margin of €4. Find the overall margin.

  1. Evaluate the QEC if the storage cost is €0,30 per unit per year, the ordering cost is €3 and the annual demand is 6 bottles.

  2. Discuss the impact of strong competition on the need to reconsider pricing strategy to defend Gourmet Bio's margins.

Proposed correction:

  1. Using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Let's replace: ((€14 – €10) ÷ €10) x 100 = 40%.
    The margin rate is 40%.

  2. For a markup rate of 40%, we have: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, €9 ÷ (1 – 0,40) = €15.
    The selling price excluding tax must be €15 for a markup rate of 40%.

  3. Overall margin: Overall margin = Unit margin x quantity sold.

Let's replace: €4 x 300 = €1.
The overall margin reaches €1.

  1. Calculation of QEC: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    Substitute: ?((2 x 6 x 000) ÷ 3) = ?0,30 = 120.
    The QEC is 346 bottles.

  2. Increased competition may require a re-evaluation of prices to maintain or increase market share while ensuring that margins are protected. Gourmet Bio may need to review costs and adjust its offerings.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
Overall margin Unit margin x quantity sold
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: GreenTech Solutions

States :

GreenTech Solutions, a leader in the sale of ecological solar panels, seeks to optimize its profitability by carrying out a strategic analysis of the costs related to its main products. The company is specifically interested in its new generation models.

Work to do :

  1. What is the total margin achieved if 400 panels are sold with a unit margin of €150?

  2. Calculate the margin rate for a solar panel purchased for €500 excluding tax and sold for €650 excluding tax.

  3. What selling price excluding tax should be set for a panel purchased for €550 in order to obtain a mark-up rate of 25%?

  1. Find the QEC if storage costs are €5 per panel per year, ordering costs are €50 and annual demand is 2 panels.

  2. Examine the potential impact of new regulations on production costs and, therefore, on GreenTech Solutions' future pricing strategies.

Proposed correction:

  1. Total margin: Overall margin = Unit margin x quantity sold.
    Let's replace: €150 x 400 = €60.
    The total margin achieved amounts to €60.

  2. Calculation of the margin rate: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Let's replace: ((€650 – €500) ÷ €500) x 100 = 30%.
    The margin rate is 30%.

  3. To obtain a markup rate of 25%, we use: PV HT = PA HT ÷ (1 – Markup rate).

Substituting, €550 ÷ (1 – 0,25) = €733,33.
The selling price excluding tax must be €733,33 for a markup rate of 25%.

  1. Calculation of QEC: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    Replacing: ?((2 x 2000 x 50) ÷ 5) = ?40000 = 200.
    The QEC is 200 panels.

  2. New regulations could increase production costs by forcing GreenTech to invest in new, more expensive technologies. This could require price adjustments to maintain margins.

Formulas Used:

Title Formulas
Overall margin Unit margin x quantity sold
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Artisans of Taste

States :

Artisans du Goût, a luxury catering company, is considering reviewing its pricing strategies for its new meal trays aimed at a business clientele. The goal is to maximize profits and consolidate its position in this market segment.

Work to do :

  1. Determine the overall margin if Artisans du Goût sells 200 meal trays with a unit margin of €15.

  2. What is the margin rate if a tray is purchased at €18 excluding VAT and resold at €25 excluding VAT?

  3. What selling price is required for a tray purchased for €20 excluding VAT in order to achieve a markup rate of 30%?

  1. If the storage cost is around €0,70 per tray per year, the ordering cost is €10, and the annual demand is 1 trays, calculate the QEC.

  2. Analyze how the introduction of a new tax could influence the pricing strategy and profitability of Artisans du Goût.

Proposed correction:

  1. Overall margin: Unit margin x quantity sold.
    €15 x 200 = €3.
    The overall margin is €3.

  2. Margin rate: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€25 – €18) ÷ €18) x 100 = 38,89%.
    The margin rate is 38,89%.

  3. PV HT for a markup rate of 30%: PA HT ÷ (1 – Markup rate).

€20 ÷ (1 – 0,30) = €28,57.
The selling price excluding VAT must be €28,57 to reach a mark-up rate of 30%.

  1. QEC: ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    ?((2 x 1 x 000) ÷ 10) = ?0,70 ? 28571,43.
    The QEC is 169 plateaus.

  2. The introduction of a new tax could reduce gross margin and force Artisans du Goût to review its prices. The ability to pass on this additional cost to customers without harming demand will be crucial.

Formulas Used:

Title Formulas
Overall margin Unit margin x quantity sold
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Medical Innovation

States :

Medical equipment supplier Innovation Médicale is reviewing its pricing strategy to adapt to a rapidly changing market. It wants to reassess the cost and profitability of its diagnostic devices in order to remain competitive.

Work to do :

  1. Calculate the margin rate for a device purchased for €2 excluding VAT and sold for €000 excluding VAT.

  2. If a 20% increase in the mark-up rate is desired, what should be the new selling price excluding tax of a device purchased for €2?

  3. Determine the overall margin if the organization sells 300 devices with a unit margin of €600.

  1. Evaluate the QEC if the storage cost is €30 per device per year, ordering cost is €150 and annual demand is 600 devices.

  2. Discuss possible strategies to manage the impact of a sharply rising dollar on the import costs of these medical devices.

Proposed correction:

  1. Margin rate: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€2 – €500) ÷ €2) x 000 = 2%.
    The margin rate is 25%.

  2. PV HT for a 20% increase in the mark rate: PA HT ÷ (1 – Mark rate + 0,20).
    €2 ÷ (200 – 1) = €0,20.
    The selling price excluding tax must increase to €2 for this increase.

  3. Overall margin: Unit margin x quantity sold.

€600 x 300 = €180.
The overall margin is €180.

  1. QEC: ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    ?((2 x 600 x 150) ÷ 30) = ?6000 = 77,46.
    The QEC is 78 devices.

  2. The rise of the dollar would require assessing the supply chain and possibly diversifying sources to mitigate the impacts. Setting up forward contracts for the purchase of foreign currency could also be considered.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV with mark increase PA HT ÷ (1 – Mark rate + 0,20)
Overall margin Unit margin x quantity sold
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: EcoMobility

States :

EcoMobility, a company specializing in the sale of electric bicycles, seeks to analyze the profitability of its new bicycle model while adapting to market fluctuations. The company must take into account various economic aspects while seeking to maximize its revenues.

Work to do :

  1. What is the overall margin if EcoMobility sells 250 bikes with a unit margin of €280?

  2. Calculate the margin rate for a bicycle purchased for €900 excluding VAT and sold for €1 excluding VAT.

  3. What would be the selling price excluding tax required to obtain a 15% markup rate on a bike purchased for €1 excluding tax?

  1. Evaluate the QEC if the storage cost is €10 per bike per year, ordering cost is €50 and annual demand is 1 bikes.

  2. Discuss the potential implications for pricing strategy if subsidies for e-bikes are significantly reduced.

Proposed correction:

  1. Overall margin: Unit margin x quantity sold.
    €280 x 250 = €70.
    The overall margin is €70.

  2. Margin rate: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€1 – €200) ÷ €900) x 900 = 100%.
    The margin rate is 33,33%.

  3. PV HT for a markup rate of 15%: PA HT ÷ (1 – Markup rate).

€1 ÷ (000 – 1) = €0,15.
The selling price excluding VAT should be €1 to obtain this markup rate.

  1. QEC: ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    ?((2 x 1 x 200) ÷ 50) = ?10 = 12000.
    The QEC is 110 bikes.

  2. A reduction in subsidies would force EcoMobility to review its sales prices and perhaps focus more on added values ​​for customers to maintain stable demand.

Formulas Used:

Title Formulas
Overall margin Unit margin x quantity sold
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Application: Well-being and Health

States :

Wellness and Health, a company engaged in the sale of wellness products, is exploring new strategies to maximize its market opportunities. The sector is experiencing rapid growth, requiring strategic thinking on pricing and profitability.

Work to do :

  1. Calculate the total margin if Wellness and Health sells 500 yoga mats with a unit margin of €20.

  2. If the margin rate is 25%, what is the purchase price excluding tax of a carpet sold at €50 excluding tax?

  3. Determine the selling price excluding tax to achieve a markup rate of 25% if the purchase price excluding tax of the carpet is €30.

  1. Evaluate the QEC if there is a storage cost of €2 per mat per year, an ordering cost of €15, with an annual demand of 1 mats.

  2. Consider the necessary adjustments in Wellness and Health's pricing policy in the event of new trends favoring alternative and less expensive products.

Proposed correction:

  1. Total margin: Unit margin x quantity sold.
    €20 x 500 = €10.
    The total margin is €10.

  2. Margin rate: ((PV HT – PA HT) ÷ PA HT) x 100 with 25 = ((50 – PA HT) ÷ PA HT) x 100.
    PA HT = €40.
    The purchase price excluding VAT is €40.

  3. PV HT for a markup rate of 25%: PA HT ÷ (1 – Markup rate).

€30 ÷ (1 – 0,25) = €40.
The selling price excluding tax must be €40 to obtain a markup rate of 25%.

  1. QEC: ?((2 x Annual demand x Ordering cost) ÷ Storage cost).
    ?((2 x 1 x 500) ÷ 15) = ?2 = 45000.
    The QEC is 212 mats.

  2. The emergence of new alternative products is forcing Well-being and Health to adapt its pricing strategy, perhaps by retaining its current customers or by justifying its prices by improved service or quality.

Formulas Used:

Title Formulas
Overall margin Unit margin x quantity sold
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV for Mark Rate PA HT ÷ (1 – Mark rate)
QEC ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)

Leave comments