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Fill in the Blank QuestionFill in the blank question.RST Company produces a product that has a variable cost of $6 per unit. The company's fixed costs are $30,000. The product sells for $10 per unit. The company is considering purchasing a new manufacturing machine which would improve efficiency. The new machine would decrease the variable cost to $4, but increase fixed costs by $15,000. The revised break-even point in dollars is $.

Question

Fill in the Blank QuestionFill in the blank question.RST Company produces a product that has a variable cost of 6perunit.Thecompany′sfixedcostsare6 per unit. The company's fixed costs are 30,000. The product sells for 10perunit.Thecompanyisconsideringpurchasinganewmanufacturingmachinewhichwouldimproveefficiency.Thenewmachinewoulddecreasethevariablecostto10 per unit. The company is considering purchasing a new manufacturing machine which would improve efficiency. The new machine would decrease the variable cost to 4, but increase fixed costs by 15,000.Therevisedbreak−evenpointindollarsis15,000. The revised break-even point in dollars is .

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Solution

To calculate the revised break-even point in dollars, we first need to understand the concept of break-even point. The break-even point is the point at which total cost (fixed costs + variable costs) equals total sales revenue.

Step 1: Calculate the contribution margin per unit. This is the selling price per unit minus the variable cost per unit. With the new machine, the selling price per unit is still 10,andthevariablecostperunitdecreasesto10, and the variable cost per unit decreases to 4. So, the contribution margin per unit is 10−10 - 4 = $6.

Step 2: Calculate the total fixed costs. With the new machine, fixed costs increase by 15,000,sothetotalfixedcostsare15,000, so the total fixed costs are 30,000 + 15,000=15,000 = 45,000.

Step 3: Calculate the break-even point in units. This is the total fixed costs divided by the contribution margin per unit. So, the break-even point in units is 45,000/45,000 / 6 = 7,500 units.

Step 4: Calculate the break-even point in dollars. This is the break-even point in units multiplied by the selling price per unit. So, the break-even point in dollars is 7,500 units * 10/unit=10/unit = 75,000.

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