91Ó°ÊÓ

The break-even point is when the total revenue earned by the business entity equals the total expenditure incurred, indicating that the firm has no loss or gain.

$$\begin{gathered} \text{Required} \text{sales} \text{in} \text{units} \text{=} \frac{\text{Fixed} \text{cost}+\text{Target} \text{profit} }{\text{Contribution} \text{margin} \text{per} \text{unit}} \\ = \frac{\$156000+\$0 }{\$750-\$450} \\ =\frac{\$156000}{\$300} \\ = 520 \text{Units} \end{gathered}$$

The company must sell 520 units each month to reach the breakeven point.

$$\begin{gathered} \text{Calculationofmarginofsafetyinunits} \\ \text{Margin} \text{of} \text{safety} \text{in} \text{units =} \left(\text{currently sells} \text{units per month}-\text{Break} \text{even} \text{sales} \text{units}\right) \\ \text{=} \left(\text{945}-\text{520}\right) \\ =425 \text{Units} \\ \text{Calculationofmarginofsafetyindollars} \\ \text{Margin} \text{of} \text{safety} \text{in} \text{dollars =} \left(\text{Total} \text{sales}-\text{Breakeven} \text{sales}\right) \\ = \left(945× \$750 - 520×\$750\right) \\ =\$708,750×\$390,000 \\ = \$318,750 \end{gathered}$$

$$\begin{gathered} \text{Required} \text{units} \text{=} \frac{\text{Fixed} \text{cost} \text{+} \text{Target} \text{profit}}{\text{Contribution} \text{margin} \text{per} \text{unit}} \\ = \frac{\$156,000 + \$15,000}{\$750-\$450} \\ =\frac{\$171,000}{\$300} \\ = 570 \text{Units} \end{gathered}$$

To make a profit of $15,000 per month, the company must sell 570 units.

$$\begin{gathered} \text{Breakeven} \text{units} \text{=} \frac{\text{Fixed} \text{cost}+\text{Target} \text{profit}}{\text{Contribution margin per} \text{unit}} \\ = \frac{\$90,000+\$0}{\$750-\$525} \\ = \frac{\$90,000}{\$225} \\ =400 \text{Units} \end{gathered}$$

Calculation of new margin of safety

$$\begin{gathered} \text{Margin} \text{of} \text{safety} \text{=}\left( \text{Unit} \text{sells}-\text{Breakeven} \text{units}\right) \\ = \left(945-400\right) \\ = 545 \text{Units} \end{gathered}$$

When the breakeven unit decreases,the margin of safety unit increases because the earning or net profit increases.