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lindon company is the exclusive distributor for an automotive product selling for $30.00 per unit with a cm ratio of 30%. the companys fixed expenses are $162,000 per year and it plans to sell 20,200 units this year.
required:

1. what are the variable expenses per unit?

note: round your \per unit\ answer to 2 decimal places.

1. what is the break-even point in unit sales and in dollar sales?
2. what amount of unit sales and dollar sales is required to attain a target profit of $72,000 per year?
3. assume by using a more efficient shipper, the company can reduce its variable expenses by $3.00 per unit. what is the companys new break-even point in unit sales and dollar sales? what dollar sales are required to attain a target profit of $72,000?
4. variable expense per unit
5. break-even point in units
6. break-even point in dollar sales
7. unit sales needed to attain target profit
8. dollar sales needed to attain target profit
9. new break-even point in unit sales
10. new break-even point in dollar sales
11. dollar sales needed to attain target profit

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Explanation:

Step1: Find variable expense per unit

Contribution margin (CM) per unit = $30.00 \times 30\% = \$9.00$
Variable expense per unit = $30.00 - 9.00 = \$21.00$

Step2: Break-even in unit sales

Break-even units = $\frac{\text{Fixed Expenses}}{\text{CM per unit}} = \frac{162000}{9} = 18000$ units

Step3: Break-even in dollar sales

Break-even dollars = $\frac{\text{Fixed Expenses}}{\text{CM Ratio}} = \frac{162000}{0.30} = \$540000$

Step4: Unit sales for target profit

Target unit sales = $\frac{\text{Fixed Expenses + Target Profit}}{\text{CM per unit}} = \frac{162000 + 72000}{9} = 26000$ units

Step5: Dollar sales for target profit

Target dollar sales = $\frac{\text{Fixed Expenses + Target Profit}}{\text{CM Ratio}} = \frac{162000 + 72000}{0.30} = \$780000$

Step6: New variable expense & CM per unit

New variable expense = $21.00 - 3.00 = \$18.00$
New CM per unit = $30.00 - 18.00 = \$12.00$
New CM ratio = $\frac{12}{30} = 0.40$

Step7: New break-even unit sales

New break-even units = $\frac{162000}{12} = 13500$ units

Step8: New break-even dollar sales

New break-even dollars = $\frac{162000}{0.40} = \$405000$

Step9: New target dollar sales

New target dollars = $\frac{162000 + 72000}{0.40} = \$585000$

Answer:

1. Variable expense per unit: $\$21.00$
2. Break-even point in units: 18,000 units
3. Break-even point in dollar sales: $\$540,000$
4. Unit sales needed to attain target profit: 26,000 units
5. Dollar sales needed to attain target profit: $\$780,000$
6. New break-even point in unit sales: 13,500 units
7. New break-even point in dollar sales: $\$405,000$
8. New dollar sales needed to attain target profit: $\$585,000$