By how much must a firm reduce its assets in order to improve ROA from 10% to 12% if the firm's profit margin is 5% on sales of $4 million?
To find out by how much a firm must reduce its assets in order to improve the Return on Assets (ROA) from 10% to 12%, we need to calculate the current and target ROA, and then use the formula for ROA to determine the asset reduction required.
Here are the steps to calculate the asset reduction:
Step 1: Calculate the current ROA:
ROA = Net Income / Average Total Assets
Given:
Profit Margin = 5% (or 0.05)
Sales = $4 million
To find Net Income, multiply the Profit Margin by the Sales amount:
Net Income = Profit Margin * Sales
Net Income = 0.05 * $4,000,000
Net Income = $200,000
Since the problem doesn't provide information about the firm's assets at the beginning and end of the period, we'll assume that the average total assets remain the same. So we'll consider the Average Total Assets as the current Total Assets.
ROA = Net Income / Average Total Assets
10% = $200,000 / Average Total Assets
Solving for Average Total Assets:
Average Total Assets = $200,000 / 10%
Average Total Assets = $2,000,000
Step 2: Calculate the target ROA:
Target ROA = 12%
Using the same formula as before, we can find the target Net Income:
Target Net Income = Target ROA * Average Total Assets
Target Net Income = 12% * $2,000,000
Target Net Income = $240,000
Step 3: Calculate the asset reduction required:
Asset Reduction = Current Total Assets - Target Total Assets
Since we assumed the Average Total Assets as the current Total Assets, the asset reduction required will be:
Asset Reduction = Average Total Assets - Target Total Assets
Asset Reduction = $2,000,000 - $240,000
Asset Reduction = $1,760,000
Therefore, the firm must reduce its assets by $1,760,000 in order to improve the ROA from 10% to 12% if the firm's profit margin is 5% on sales of $4 million.