Assuming a tax of 3%, if introduced how much sales must be made to earn a profit after tax equal to the current profit?

Here are the calculations for the questions.

4. Assuming a tax of 3% is introduced, how much sales must be made to earn a profit after tax equal to the current profit?

Step 1: Identify the target profit after tax and the tax rate.

• Target Profit After Tax = Current Net Profit = $\text{N}312,500$ (from previous calculations)
• Tax Rate = $3\% = 0.03$

Step 2: Calculate the required Profit Before Tax (PBT).
Let PBT be the Profit Before Tax.

$$\text{Profit After Tax} = \text{PBT} \times (1 - \text{Tax Rate})$$ $$\text{N}312,500 = \text{PBT} \times (1 - 0.03)$$ $$\text{N}312,500 = \text{PBT} \times 0.97$$ $$\text{PBT} = \frac{\text{N}312,500}{0.97}$$ $$\text{PBT} \approx \text{N}322,164.95$$

Step 3: Identify the fixed costs and contribution margin per unit from previous calculations.

• Total Fixed Costs (FC) = $\text{N}250,000$
• Contribution Margin per unit (CM per unit) = $\text{N}22.50/\text{unit}$

Step 4: Calculate the number of units that must be sold to achieve the target PBT.

$$\text{Units to be sold} = \frac{\text{Total Fixed Costs} + \text{Target PBT}}{\text{Contribution Margin per unit}}$$ $$\text{Units to be sold} = \frac{\text{N}250,000 + \text{N}322,164.95}{\text{N}22.50/\text{unit}}$$ $$\text{Units to be sold} = \frac{\text{N}572,164.95}{\text{N}22.50/\text{unit}}$$ $$\text{Units to be sold} \approx 25,429.55 \text{ units}$$

Since units must be whole numbers, we round up.

$$\text{Units to be sold} = 25,430 \text{ units}$$

Step 5: Calculate the total sales revenue required.

• Selling Price per unit (SP) = $\text{N}40/\text{unit}$

$$\text{Total Sales Revenue} = \text{Units to be sold} \times \text{SP}$$ $$\text{Total Sales Revenue} = 25,430 \text{ units} \times \text{N}40/\text{unit}$$ $$\text{Total Sales Revenue} = \text{N}1,017,200$$

The company must make sales of $\boxed{\text{N}1,017,200}$ to earn a profit after tax equal to the current profit.

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3. A break down of maintenance costing department of ABC Limited shows that there is a fixed element of $\text{N}5,000$ per month and a variable element related to hours per machine hour, with a rate of $\text{N}600$ per machine hour. What is the expected cost per month when the plan activity level is:

Step 1: Identify the fixed and variable cost components.

• Fixed Maintenance Cost = $\text{N}5,000$ per month
• Variable Maintenance Cost Rate = $\text{N}600$ per machine hour

The total maintenance cost formula is:

$$\text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost Rate} \times \text{Machine Hours})$$