Allen Company sells flags with team logos. Allen has fixed costs of $ 875000 per year plus variable costs of $ 12.50 per flag. Each flag sells for $ 25.00.
1-Use the equation approach to compute the number of flags Allen must sell each year to break even.
2- Prepare Allen's contribution margin income statement for the year ended December 31, 2018, for sales of 61 comma 000 flags. (Round your final answers up to the next whole number.)
3-The company is considering an expansion that will increase fixed costs by 40 % and variable costs by $ 2.50 per flag. Compute the new breakeven point in units and in dollars. Should Allen undertake the expansion?
1- To compute the number of flags Allen must sell each year to break even, we can use the equation:
Fixed costs + (Variable costs per unit * Number of units) = Sales revenue
In this case, the fixed costs are $875,000, the variable costs per flag is $12.50, and the sales revenue per flag is $25.00. Let's represent the number of flags Allen must sell each year as 'x'.
875,000 + (12.50 * x) = 25.00 * x
Simplifying the equation:
875,000 + 12.50x = 25.00x
12.50x - 25.00x = - 875,000
-12.50x = -875,000
Dividing both sides of the equation by -12.50:
x = 875,000 / 12.50
x = 70,000
So, Allen must sell 70,000 flags each year to break even.
2- To prepare Allen's contribution margin income statement for the year ended December 31, 2018, for sales of 61,000 flags, we need to calculate the contribution margin, fixed costs, and net income.
Contribution margin = Sales revenue - Variable costs
Contribution margin per flag = $25.00 - $12.50 = $12.50
Contribution margin for 61,000 flags = Contribution margin per flag * 61,000
Contribution margin for 61,000 flags = $12.50 * 61,000
Fixed costs = $875,000
Net Income = Contribution margin - Fixed costs
Net Income = (Contribution margin per flag * 61,000) - $875,000
Calculate the values:
Contribution margin for 61,000 flags = $12.50 * 61,000 = $762,500
Net Income = $762,500 - $875,000
3- If the company is considering an expansion that will increase fixed costs by 40% and variable costs by $2.50 per flag, we need to calculate the new breakeven point in units and in dollars.
New Fixed Costs = 1.40 * $875,000
New Variable Costs per flag = $12.50 + $2.50
New Breakeven Point in Units:
Fixed Costs + (Variable Costs per unit * Number of units) = Sales revenue
Replace the values:
1.40 * $875,000 + ($12.50 + $2.50) * x = $25.00 * x
New Breakeven Point in Dollars:
Contribution margin per flag = $25.00 - ($12.50 + $2.50)
New Breakeven Point in Dollars = New Fixed Costs / Contribution margin per flag
Compare the new breakeven point with the current breakeven point to decide if undertaking the expansion is viable.
1- To compute the break-even point, we need to find the number of flags Allen must sell to cover their fixed costs and variable costs, without generating a profit.
Let's denote:
- B: Break-even point (number of flags).
- FC: Fixed costs per year ($875,000).
- VC: Variable costs per flag ($12.50).
- SP: Selling price per flag ($25.00).
The equation approach to compute the break-even point is as follows:
B = FC / (SP - VC)
Plug in the given values:
B = $875,000 / ($25.00 - $12.50)
Simplifying the equation:
B = $875,000 / $12.50
B = 70,000 flags
Therefore, Allen must sell 70,000 flags each year to break even.
2- To prepare Allen's contribution margin income statement, we need to calculate the sales revenue, variable costs, contribution margin, and contribution margin ratio.
Let's denote:
- SF: Sales revenue from flags.
- VC: Variable costs from flags.
- CM: Contribution margin.
- CMR: Contribution margin ratio.
First, calculate the sales revenue (SF):
SF = Number of flags sold * Selling price per flag
SF = 61,000 * $25.00
SF = $1,525,000
Next, calculate the variable costs (VC):
VC = Number of flags sold * Variable cost per flag
VC = 61,000 * $12.50
VC = $762,500
Now, calculate the contribution margin (CM):
CM = Sales revenue - Variable costs
CM = $1,525,000 - $762,500
CM = $762,500
Finally, calculate the contribution margin ratio (CMR):
CMR = CM / Sales revenue * 100
CMR = $762,500 / $1,525,000 * 100
CMR = 50%
The contribution margin income statement for Allen for the year ended December 31, 2018, for sales of 61,000 flags is as follows:
Sales Revenue: $1,525,000
Variable Costs: $762,500
Contribution Margin: $762,500
Contribution Margin Ratio: 50%
3- To compute the new break-even point (after the expansion), we need to consider the increased fixed costs and variable costs.
Let's denote:
- B2: New break-even point (number of flags).
- FC2: New fixed costs per year (40% increase from $875,000).
- VC2: New variable costs per flag ($12.50 + $2.50).
Calculate the new fixed costs (FC2):
FC2 = $875,000 * 1.40 (40% increase)
FC2 = $1,225,000
Calculate the new variable costs (VC2):
VC2 = $12.50 + $2.50
VC2 = $15.00
Now, calculate the new break-even point (B2):
B2 = FC2 / (SP - VC2)
B2 = $1,225,000 / ($25.00 - $15.00)
B2 = $1,225,000 / $10.00
B2 = 122,500 flags
The new break-even point in units is 122,500 flags, or in dollars it would be:
Break-even point in dollars = B2 * $25.00
Break-even point in dollars = 122,500 * $25.00
Break-even point in dollars = $3,062,500
Finally, whether Allen should undertake the expansion or not depends on various factors such as market demand, expected sales growth, potential profit, and risk assessment. The break-even analysis alone does not provide enough information to make a decision. Further analysis and evaluation are necessary.