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Accents Associates sells only one product,with a current selling price of $70 per unit.Variable costs are 40% of this selling price,and fixed costs are $12,000 per month.Management has decided to reduce the selling price to $65 per unit in an effort to increase sales.Assume that the cost of the product and fixed operating expenses are not changed by this reduction in selling price.
-At the current selling price of $70 per unit,what dollar volume of sales per month is required for Accents to earn a monthly operating income of $15,000?

Question

Quizplus · Accepted Answer

We can use the contribution margin ratio (CM ratio) to calculate the break-even point in dollars, and then add the desired operating income to find the required sales volume.

First, let's calculate the CM ratio:
CM ratio = (selling price - variable cost) / selling price
CM ratio = ($70 - 0.4*$70) / $70 = 0.6 or 60%

This means that for every dollar of sales, 60 cents are available to cover fixed costs and contribute to operating income.

To find the break-even point in dollars, we can use the following formula:
Break-even point ($) = fixed costs / CM ratio
Break-even point ($) = $12,000 / 0.6 = $20,000

This means that Accents needs to sell $20,000 worth of its product each month just to break even, i.e. to cover its fixed costs and variable costs.

To earn a monthly operating income of $15,000, Accents needs to sell:
Required sales volume = break-even point + desired operating income
Required sales volume = $20,000 + $15,000 = $35,000

At a selling price of $70 per unit, the required sales volume is:
$35,000 / $70 per unit = 500 units

Now let's check whether Accents can achieve the same operating income with the new selling price of $65 per unit. Since the cost structure and fixed expenses have not changed, we can still use the same CM ratio of 60%. However, the selling price and therefore the contribution margin per unit will be lower:
New CM per unit = $65 - 0.4*$65 = $39 per unit
New CM ratio = $39 / $65 = 60%

The required sales volume is now:
Required sales volume = ($12,000 + $15,000) / 0.6 / $39 per unit = 769.23 units

Round that up to the nearest whole number of units, the required sales volume is 770 units.

To find the dollar volume of sales, we can multiply the required sales volume by the selling price:
Required sales in dollars = 770 units * $65 per unit = $50,050

Therefore, the best choice is C) $45,000, which is the closest answer to the required sales volume of $50,050 at the new selling price of $65 per unit.

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