Return on operating assets = 25%
Operating asset turnover = 5 times
Operating assets = $20 million
Degree of operating leverage = 4 times
How to slove?
To solve for Return on Operating Assets (ROOA), we can use the formula:
ROOA = Operating Income / Operating Assets
Given that ROOA = 25% and Operating Assets = $20 million, we need to find the Operating Income.
The Operating Asset Turnover Ratio is given as 5 times. This ratio measures the efficiency of a company in generating sales from its operating assets. We can calculate it using the formula:
Operating Asset Turnover = Sales / Operating Assets
In this case, we are given that the Operating Asset Turnover is 5 times. Therefore, we can rearrange the formula to solve for Sales:
Sales = Operating Asset Turnover * Operating Assets
Sales = 5 * $20 million = $100 million
Now, considering the formula for Degree of Operating Leverage (DOL):
DOL = % Change in Operating Income / % Change in Sales
In this case, the Degree of Operating Leverage is given as 4 times. We have already calculated sales to be $100 million. Therefore, we can rearrange the formula to solve for % Change in Operating Income:
4 = % Change in Operating Income / % Change in Sales
From this, we can determine that a 1% change in sales will result in a 4% change in Operating Income.
Now, let's calculate the Operating Income:
ROOA = Operating Income / Operating Assets
0.25 = Operating Income / $20 million
Solving for Operating Income:
Operating Income = 0.25 * $20 million = $5 million
Therefore, the Operating Income is $5 million.