A small boy plc manufactures and sells a product called mummy. The following reports were extracted from its records: Sales (2500 units @ N40 each): N 1,000,000. Expenses: Direct materials: N 250,000, Direct labour: N 125,000, Variable overhead: N 62,500, Fixed admin expenses: N 180,000, Fixed miscellaneous expenses: N 70,000. Total expenses: N 687,500. Net profit: N 312,500. Required: 1. How many units must be sold before the company can break even? 2. What will be the Net profit if sales increase by 30% assuming no increase in selling price? 3. If selling price is reduced by 5% how many units must be sold in order to maintain a net profit equal to the current profit?

Here are the calculations for the required questions.

First, let's extract the necessary information and calculate the per-unit costs and total fixed costs.

Given Data:

• Sales: 25,000 units @ $\text{N}40$ each = $\text{N}1,000,000$
• Direct materials = $\text{N}250,000$
• Direct labor = $\text{N}125,000$
• Variable overhead = $\text{N}62,500$
• Fixed Admin expenses = $\text{N}180,000$
• Fixed miscellaneous expenses = $\text{N}70,000$
• Current Net profit = $\text{N}312,500$

Step 1: Calculate per-unit and total fixed costs.

• Selling Price per unit (SP):

  $$\text{SP} = \frac{\text{Total Sales}}{\text{Number of units sold}} = \frac{\text{N}1,000,000}{25,000 \text{ units}} = \text{N}40/\text{unit}$$

• Variable Costs per unit (VC per unit):

  • Direct materials per unit = $\frac{\text{N}250,000}{25,000 \text{ units}} = \text{N}10/\text{unit}$
  • Direct labor per unit = $\frac{\text{N}125,000}{25,000 \text{ units}} = \text{N}5/\text{unit}$
  • Variable overhead per unit = $\frac{\text{N}62,500}{25,000 \text{ units}} = \text{N}2.50/\text{unit}$
  $$\text{VC per unit} = \text{N}10 + \text{N}5 + \text{N}2.50 = \text{N}17.50/\text{unit}$$

• Total Fixed Costs (FC):

  $$\text{FC} = \text{Fixed Admin expenses} + \text{Fixed miscellaneous expenses}$$ $$\text{FC} = \text{N}180,000 + \text{N}70,000 = \text{N}250,000$$

• Contribution Margin per unit (CM per unit):

  $$\text{CM per unit} = \text{SP} - \text{VC per unit} = \text{N}40 - \text{N}17.50 = \text{N}22.50/\text{unit}$$

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1. How many units must be sold before the company can break even?

Step 1: Identify the formula for break-even point in units.

$$\text{Break-even point in units} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin per unit}}$$

Step 2: Substitute the calculated values into the formula.

$$\text{Break-even point in units} = \frac{\text{N}250,000}{\text{N}22.50/\text{unit}}$$

Step 3: Calculate the break-even point.

$$\text{Break-even point in units} = 11,111.11 \text{ units}$$

Since units must be whole numbers, we round up to the next whole unit to ensure breaking even.

$$\text{Break-even point in units} = 11,112 \text{ units}$$

The company must sell $\boxed{11,112 \text{ units}}$ to break even.

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2. What will be the Net profit if sales increase by 30% assuming no increase in selling price?

Step 1: Calculate the new number of units sold.

$$\text{New units sold} = 25,000 \text{ units} \times (1 + 0.30) = 25,000 \text{ units} \times 1.30 = 32,500 \text{ units}$$

Step 2: Calculate the new total sales revenue.

$$\text{New total sales revenue} = 32,500 \text{ units} \times \text{N}40/\text{unit} = \text{N}1,300,000$$

Step 3: Calculate the new total variable costs.

$$\text{New total variable costs} = 32,500 \text{ units} \times \text{N}17.50/\text{unit} = \text{N}568,750$$

Step 4: Calculate the new total contribution margin.

$$\text{New total contribution margin} = \text{N}1,300,000 - \text{N}568,750 = \text{N}731,250$$

Step 5: Calculate the new Net Profit.

$$\text{New Net Profit} = \text{New total contribution margin} - \text{Total Fixed Costs}$$ $$\text{New Net Profit} = \text{N}731,250 - \text{N}250,000 = \text{N}481,250$$

The Net profit if sales increase by 30% will be $\boxed{\text{N}481,250}$.

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3. If selling price is reduced by 5%, how many units must be sold in order to maintain a net profit equal to the current profit?

Step 1: Identify the target profit.
Target Net Profit = Current Net Profit = $\text{N}312,500$

Step 2: Calculate the new selling price per unit.

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