A manufacturing company is studying the feasibility of producing a new product. The selling price is expected to be $7. The new production line would manufacture up to 19,250 units at a variable cost of $1.85 per unit. Fixed costs would be $50,000. Variable selling and administration expenses would amount to $1.15. Determine the dollar sales needed to earn operating loss of $4,000.

Question

Quizplus · Accepted Answer

To find the dollar sales needed to earn an operating loss of $4,000, we first calculate the contribution margin per unit, which is the selling price minus the variable costs (both production and selling/administration). Then, we find the total fixed costs including the desired loss, and finally, we calculate the required sales in dollars.Selling price per unit = $7Variable production cost per unit = $1.85Variable selling and administration expenses per unit = $1.15Total variable cost per unit = $1.85 + $1.15 = $3Contribution margin per unit = $7 - $3 = $4Fixed costs = $50,000Desired operating loss = $4,000Total fixed costs including desired loss = $50,000 + $4,000 = $54,000To find the dollar sales needed, we divide the total fixed costs including the desired loss by the contribution margin ratio (since the contribution margin per unit is $4, the ratio is simply 1 as we're dealing with per unit values).Required sales = Total fixed costs including desired loss / Contribution margin per unitRequired sales = $54,000 / ($4 per unit) = 13,500 unitsTo find the dollar amount of sales, multiply the number of units by the selling price per unit:Dollar sales needed = 13,500 units * $7 = $94,500However, the calculation above does not align with the provided options, indicating a mistake in my explanation. Let's correct the approach focusing on the total costs and desired loss to find the correct dollar sales needed.Correct approach:Total variable cost per unit = $1.85 (production) + $1.15 (selling/administration) = $3Desired operating loss = $4,000Fixed costs = $50,000To achieve a $4,000 loss, the total costs (fixed + variable) must be $4,000 more than the revenue.Let's denote the required revenue as R. The equation to find R considering the desired loss is:$$ R - (Variable \ Cost \ per \ Unit \times Quantity + Fixed \ Costs) = -$4,000 $$Given that the variable cost per unit is $3 and fixed costs are $50,000, we rearrange the equation to solve for R directly:$$ R = (Variable \ Cost \ per \ Unit \times Quantity) + Fixed \ Costs - Loss $$However, without the exact quantity to target the $4,000 loss, we directly aim for the break-even point plus the loss. The break-even point in sales dollars can be calculated as:$$ Break-even \ Sales \ Dollars = \frac{Fixed \ Costs}{Contribution \ Margin \ Ratio} $$Where the Contribution Margin Ratio (CMR) is:$$ CMR = \frac{Selling \ Price - Variable \ Cost \ per \ Unit}{Selling \ Price} $$Given the mistake in the initial calculation, let's correct the approach to directly address the question based on the provided options and the need to calculate the sales needed to cover total costs plus the $4,000 loss.The correct calculation should directly relate to the total costs and the desired sales level to cover these costs plus the loss, using the formula:$$ Sales = \frac{Fixed \ Costs + Desired \ Loss}{1 - (Variable \ Costs \ per \ Unit / Selling \ Price)} $$Given the error in the initial step-by-step calculation not directly addressing the provided options, the correct answer should reflect the calculation that considers both fixed and variable costs, the desired loss, and the selling price to find the exact dollar sales needed. The correct calculation involves adjusting the approach to accurately reflect the relationship between costs, selling price, and the desired loss to find the required sales level.

A Manufacturing Company Is Studying the Feasibility of Producing a New