A company has a 10% earning on sales before taxes. If material costs are reduced by $250.000 and everything else remains the same, how much would sales have to increase to earn the same amount?
To calculate how much sales would have to increase in order to earn the same amount after reducing material costs, we need to understand the relationship between earnings on sales and material costs.
Let's break down the calculation step by step:
1. Calculate the earning on sales before reducing material costs:
If the company has a 10% earning on sales before taxes, it means that for every dollar in sales, the company earns $0.10 before taxes.
2. Determine the initial sales amount:
Let's assume the initial sales amount is represented by "X."
3. Calculate the initial earnings on sales:
To find the initial earnings on sales, we multiply the initial sales amount by the earning percentage:
Initial Earnings = X * 10% = 0.10X
4. Determine the reduced material costs:
According to the question, the material costs are reduced by $250,000.
5. Calculate the new sales amount required to earn the same amount after reducing material costs:
Since the earnings on sales remain the same, we can equate the initial earnings to the new earnings:
0.10X = (X + increased sales) * 10%
To simplify the equation, let's distribute the 10% to the increased sales term:
0.10X = X * 10% + increased sales * 10%
After distributing, the equation becomes:
0.10X = 0.10X + increased sales * 10%
Now, let's isolate the increased sales term:
0.10X - 0.10X = increased sales * 10%
0 = increased sales * 10%
Dividing both sides of the equation by 10%, we get:
increased sales = 0 / 10%
This means that increased sales can be any value since multiplying it by 0% gives us 0.
Therefore, sales would not need to increase to earn the same amount of earnings after reducing material costs.