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Q 2 Ltd is planning to sell 100000 units of product for ₹ 12 per unit. The fixed costs are ₹ 280000. In order to realize a profit of ₹ 20000, what would be the variable cost?

Answer :

To determine the variable cost per unit that allows Q 2 Ltd to sell 100,000 units at [tex]\text{₹} 12[/tex] per unit, while covering fixed costs of [tex]\text{₹} 280,000[/tex] and achieving a profit of [tex]\text{₹} 20,000[/tex], we follow these steps:

  1. Understanding Total Revenue:

    • The company plans to sell 100,000 units at [tex]\text{₹} 12[/tex] each.
    • Total Revenue (TR) is calculated as:
      [tex]\text{TR} = 100,000 \times 12 = \text{₹} 1,200,000[/tex]

  2. Understanding Total Costs and Desired Profit:

    • Fixed Costs (FC) are [tex]\text{₹} 280,000[/tex].
    • Desired Profit is [tex]\text{₹} 20,000[/tex].
    • Therefore, the Total Costs (TC) including the desired profit can be given by the equation:
      [tex]\text{TC} + \text{Desired Profit} = \text{TR}[/tex]
      [tex]\text{VC} \times 100,000 + 280,000 = 1,200,000 - 20,000[/tex]
      [tex]\text{VC} \times 100,000 + 280,000 = 1,180,000[/tex]

  3. Solving for Variable Cost (VC):

    • Rearranging the equation, we get:
      [tex]\text{VC} \times 100,000 = 1,180,000 - 280,000[/tex]
      [tex]\text{VC} \times 100,000 = 900,000[/tex]
      [tex]\text{VC} = \frac{900,000}{100,000}[/tex]
      [tex]\text{VC} = \text{₹} 9[/tex]

Thus, the variable cost per unit that allows the firm to reach its profit objectives is [tex]\text{₹} 9[/tex]. By ensuring variable costs are set at this level, the company can achieve the desired profit of [tex]\text{₹} 20,000[/tex] while covering its fixed costs.

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