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): $SP = \frac{Total Sales}{Number of units sold} = \frac{N1,000,000}{25,000 units} = N40/unit$

• Variable Costs per unit (VC per unit):

  • Direct materials per unit = $\frac{N250,000}{25,000 units} = N10/\text{unit}$
  • Direct labor per unit = $\frac{N125,000}{25,000 units} = N5/\text{unit}$
  • Variable overhead per unit = $\frac{N62,500}{25,000 units} = N2.50/\text{unit}$ $VC per unit = N10 + N5 + N2.50 = N17.50/unit$

• Total Fixed Costs (FC): $FC = Fixed Admin expenses + Fixed miscellaneous expenses$ $FC = N180,000 + N70,000 = N250,000$

• Contribution Margin per unit (CM per unit): $CM per unit = SP - VC per unit = N40 - N17.50 = N22.50/unit$

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

Step 1: Identify the formula for break-even point in units. $Break-even point in units = \frac{Total Fixed Costs}{Contribution Margin per unit}$

Step 2: Substitute the calculated values into the formula. $Break-even point in units = \frac{N250,000}{N22.50/unit}$

Step 3: Calculate the break-even point. $Break-even point in units = 11,111.11 units$ Since units must be whole numbers, we round up to the next whole unit to ensure breaking even. $Break-even point in units = 11,112 units$ The company must sell $\boxed{11,112 units}$ to break even.

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

Step 2: Calculate the new total sales revenue. $New total sales revenue = 32,500 units \times N40/unit = N1,300,000$

Step 3: Calculate the new total variable costs. $New total variable costs = 32,500 units \times N17.50/unit = N568,750$

Step 4: Calculate the new total contribution margin. $New total contribution margin = N1,300,000 - N568,750 = N731,250$

Step 5: Calculate the new Net Profit. $New Net Profit = New total contribution margin - Total Fixed Costs$ $New Net Profit = N731,250 - N250,000 = N481,250$ The Net profit if sales increase by 30% will be $\boxed{N481,250}$.

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.