I am stuck on these two math questions. If nyone could help me solve them it would be greatly appreciated! Here is the information:
Engineering estimates indicate that the variable cost of manufacturing a new product will be $35 per unit.Based on market research, the selling price of the product is to be $72 per unit and there is an additional selling expense which is estimated to cost the company $10 per unit. The fixed costs applicable to this new product are budgeted at $4,800 per period and the initial production capacity is 430 units. Given this information determine the following:
a) The breakeven point as a percent of capacity (rounded to the nearest percent) if the fixed costs are reduced from the original amount by $160 and the variable cost of manufacturing is increased to $39 per unit.
b) The breakeven point in dollars if the selling price is increased to $85 per unit and all other values are as originally stated.
a) Why did the variable cost go to therapy? Because it had some issues with breaking even!
Ok, let's crunch some numbers. To find the breakeven point as a percent of capacity, we need to determine the number of units that need to be sold to cover the fixed and variable costs.
The original fixed costs are $4,800 per period. If they are reduced by $160, then the new fixed costs would be $4,800 - $160 = $4,640 per period.
The original variable cost per unit is $35. If it is increased to $39 per unit, then the new variable cost per unit would be $39.
To find the breakeven point, we need to divide the fixed costs by the selling price minus the variable cost per unit. So the formula would be:
Breakeven point = Fixed costs / (Selling price - Variable cost per unit)
Let's plug in the numbers:
Breakeven point = $4,640 / ($72 - $39)
Now, divide those numbers and multiply by 100 to get the percent:
Breakeven point (as a percent) = (4640 / (72 - 39)) * 100
And you get your answer (rounded to the nearest percent)!
b) Why did the selling price go on a diet? It wanted to break even in dollars!
To find the breakeven point in dollars, we need to multiply the number of units by the selling price. The formula is:
Breakeven point (in dollars) = Breakeven point (number of units) * Selling price
Since all other values are as originally stated, we can use the original breakeven point (number of units) and selling price. Calculate it:
Breakeven point (in dollars) = (original breakeven point) * $85
And voila! You have your answer. Remember to show the numbers some math appreciation, they can be sensitive!
To solve these math questions, we need to understand what the breakeven point is. The breakeven point is the level of sales at which a company neither makes a profit nor incurs a loss. In other words, it is the point where total revenue equals total costs.
Let's solve each part of the question step by step:
a) The breakeven point as a percent of capacity:
To find the breakeven point as a percent of capacity, we'll consider the original values first. The fixed costs are $4,800 per period, variable cost per unit is $35, and the selling price per unit is $72 (along with an additional $10 selling expense per unit).
The formula to calculate the breakeven point in units is: Breakeven Point (in units) = Total Fixed Costs / Contribution Margin per Unit
The Contribution Margin per Unit is the difference between the selling price per unit and the variable cost per unit.
So, for the original values:
Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit
= $72 - $35
= $37
Now we can calculate the breakeven point in units:
Breakeven Point (in units) = Total Fixed Costs / Contribution Margin per Unit
= $4,800 / $37
≈ 130 units
To calculate the breakeven point as a percent of capacity, we'll divide the breakeven point (130 units) by the initial production capacity (430 units) and multiply by 100:
Breakeven Point (as a percent of capacity) = (130 / 430) * 100
≈ 30%
Now, let's consider the case where the fixed costs are reduced by $160 and the variable cost per unit is increased to $39. Following the same steps as above, we can find the new breakeven point:
Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit
= $72 - $39
= $33
New Breakeven Point (in units) = (Total Fixed Costs - Reduction) / Contribution Margin per Unit
= ($4,800 - $160) / $33
≈ 141 units
New Breakeven Point (as a percent of capacity) = (141 / 430) * 100
≈ 33%
Therefore, the breakeven point as a percent of capacity would be approximately 30% for the original values, and approximately 33% for the modified values.
b) The breakeven point in dollars:
To find the breakeven point in dollars, we'll use the original values with the exception of the selling price per unit, which is increased to $85.
Contribution Margin per Unit = $85 - $35
= $50
Breakeven Point (in units) = $4,800 / $50
= 96 units
Breakeven Point (in dollars) = Breakeven Point (in units) * Selling Price per Unit
= 96 * $85
= $8,160
Therefore, the breakeven point in dollars would be $8,160 if the selling price is increased to $85 per unit and all other values remain as originally stated.