Question

Georgeland Cycles makes and sells two models of electric bicycles. The Commuter (a folding model) sells for $2,502.00 and the TourX (a fat-tre trail model) sells for $4,502.00. Unit variable costs for the Commuter are $1,752.00 and for the Tour X$33,202.00. Annual fixed costs at Georgeland are $476,700. The marketing manager estimates that the annual mix of sales is 30 percent Commuter model and 70 percent Touring model. Required: a. How many of each model eblke must Georgeland Cycles sell every year to break even? b. How many of each model ebike must Georgeland Cycles sell every year to earn operating profits of $102.150 before taxes?

Answer 1

To break even, Georgeland Cycles needs to sell approximately 636 units of the Commuter model and 368 units of the TourX model per year. To earn an operating profit of $102,150 before taxes, they should sell around 772 units of the Commuter model and 446 units of the TourX model per year.

Step-by-step explanation:

To calculate the number of each model e-bike Georgeland Cycles must sell every year to break even, we need to consider the contribution margin of each model. The contribution margin is the difference between the selling price and the unit variable cost. For the Commuter model, the contribution margin is $2,502.00 - $1,752.00 = $750.00. For the TourX model, the contribution margin is $4,502.00 - $3,3202.00 = $1,300.00.

a. Break-even Quantity:

To calculate the break-even quantity of each model, we need to divide the annual fixed costs ($476,700) by the contribution margin of each model. For the Commuter model, the break-even quantity is $476,700 / $750 = 635.6, which we can round up to 636 units. For the TourX model, the break-even quantity is $476,700 / $1,300 = 367.4, which we can round up to 368 units.

b. Profit-Maximizing Quantity:

To calculate the profit-maximizing quantity of each model, we need to consider the target operating profit ($102,150) in addition to the fixed costs.

For the Commuter model, the target contribution margin can be calculated as follows:

Target Contribution Margin = Fixed Costs + Target Operating Profit = $476,700 + $102,150 = $578,850.

Dividing the target contribution margin by the contribution margin per unit, we can calculate the profit-maximizing quantity of the Commuter model as $578,850 / $750 = 771.8, which we can round up to 772 units.

Similarly, for the TourX model, the target contribution margin is:

Target Contribution Margin = Fixed Costs + Target Operating Profit = $476,700 + $102,150 = $578,850.

Dividing the target contribution margin by the contribution margin per unit, we can calculate the profit-maximizing quantity of the TourX model as $578,850 / $1,300 = 445.3, which we can round up to 446 units.

Answer 2

To break even, Georgeland Cycles needs to sell 636 units of the Commuter model and 404 units of the TourX model every year. To earn operating profits of $102,150 before taxes, they need to sell 869 units of the Commuter model and 429 units of the TourX model every year.

To break even, Georgeland Cycles needs to sell enough units to cover its fixed costs. The total fixed costs are $476,700. To calculate the break-even point for each model, we can use the formula:

Break-even point = Fixed costs / Contribution margin per unit

For the Commuter model:

Contribution margin per unit = Selling price - Unit variable cost

Contribution margin per unit = $2,502.00 - $1,752.00 = $750.00

Break-even point for Commuter =(476,700) / (750) = 635.6 units

Since we can't sell a fraction of a unit, we round up to 636 units.

For the TourX model:

Contribution margin per unit = Selling price - Unit variable cost

Contribution margin per unit = $4,502.00 - $3,320.00 = $1,182.00

Break-even point for TourX =(476,700) / (1,182) = 403.8 units

Since we can't sell a fraction of a unit, we round up to 404 units.

To earn operating profits of $102,150, we need to consider the contribution margin per unit and the target profit. The formula for calculating the target units is:

Target units = (Fixed costs + Target profit) / Contribution margin per unit

For the Commuter model:

Target units =(476,700 + 102,150) / (750) = 869 units

For the TourX model:

Target units =(476,700 + 102,150) / (1,182) = 429 units