Question

Question: This problem continues the Piedmont Computer Company situation from Chapter 19. Piedmont Computer Company manufactures personal computers and tablets. Based on the latest information from the cost accountant, using the current sales mix, the weighted-average sales price per unit is \(750 and the weighed-average variable cost per unit is \)450. The company does not expect the sales mix to vary for the next year. Average fixed costs per month are \(156,000.

Requirements

1. What is the number of units that must be sold each month to reach the breakeven point?

2. If the company currently sells 945 units per month, what is the margin of safety in units and dollars?

3. If Piedmont Computer Company desires to make a profit of \)15,000 per month, how many units must be sold?

4. Piedmont Computer Company thinks it can restructure some costs so that fixed costs will be reduced to \(90,000 per month, but the weighted-average variable cost per unit will increase to \)525 per unit. What is the new breakeven point in units? Does this increase or decrease the margin of safety? Why or why not?

Short answer

Answer

1. The Break-even point is520 units
2. The margin of safety is425 units and$318,750
3. 570 must sell to earn a profit of$15,000
4. The new break-even point is400 units, and the margin of safety is545 units.

Step-by-step solution

Meaning of Break-even Point

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.

Calculation of break-even point in units 

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

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

Calculation of margin of safety

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

Calculation of the desired number of units sold to earn a profit of $15,000

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

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

Calculation of new break-even point

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

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.