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. $Profit After Tax = PBT \times (1 - Tax Rate)$ $N312,500 = PBT \times (1 - 0.03)$ $N312,500 = PBT \times 0.97$ $PBT = \frac{N312,500}{0.97}$ $PBT \approx N322,164.95$

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. $Units to be sold = \frac{Total Fixed Costs + Target PBT}{Contribution Margin per unit}$ $Units to be sold = \frac{N250,000 + N322,164.95}{N22.50/unit}$ $Units to be sold = \frac{N572,164.95}{N22.50/unit}$ $Units to be sold \approx 25,429.55 units$ Since units must be whole numbers, we round up. $Units to be sold = 25,430 units$

Step 5: Calculate the total sales revenue required.

• Selling Price per unit (SP) = $\text{N}40/\text{unit}$ $Total Sales Revenue = Units to be sold \times SP$ $Total Sales Revenue = 25,430 units \times N40/unit$ $Total Sales Revenue = N1,017,200$ The company must make sales of $\boxed{N1,017,200}$ to earn a profit after tax equal to the current profit.

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: $Total Cost = Fixed Cost + (Variable Cost Rate \times Machine Hours)$

i) $2,500$ machine hours

Step 2: Calculate the total maintenance cost for $2,500$ machine hours. $Total Cost = N5,000 + (N600/machine hour \times 2,500 machine hours)$ $Total Cost = N5,000 + N1,500,000$ $Total Cost = N1,505,000$ The expected cost per month for $2,500$ machine hours is $\boxed{N1,505,000}$.

ii) $3,000$ machine hours

Step 3: Calculate the total maintenance cost for $3,000$ machine hours. $Total Cost = N5,000 + (N600/machine hour \times 3,000 machine hours)$ $Total Cost = N5,000 + N1,800,000$ $Total Cost = N1,805,000$ The expected cost per month for $3,000$ machine hours is $\boxed{N1,805,000}$.