A firm's ROE equals 47%. Its financial leverage equals 1.8 and its asset turnover is 0.8. If the firm's total net sales equal $1.35 million, its net income equals
________.
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A. B. C. D.B
ROE = net income/equity = (net income/sales)*(sales/assets)*(assets/equity) = (net income/sales)*(asset turnover)*(financial leverage) Therefore, net income =
0.47*1.35/(0.8*1.8) million = 440,625.
To solve this problem, we'll use the DuPont formula, which decomposes the return on equity (ROE) into its components: net profit margin, asset turnover, and financial leverage. The formula for ROE is:
ROE = Net Profit Margin × Asset Turnover × Financial Leverage
Given information: ROE = 47% Financial Leverage = 1.8 Asset Turnover = 0.8 Total Net Sales = $1.35 million
We need to find the net income, so let's rearrange the formula to solve for net income:
Net Income = ROE / (Net Profit Margin × Asset Turnover × Financial Leverage)
We can substitute the given values into the formula:
Net Income = 0.47 / (Net Profit Margin × 0.8 × 1.8)
Now we need to solve for the net profit margin. We can use the formula:
Net Profit Margin = Net Income / Total Net Sales
Rearranging the formula, we have:
Net Income = Net Profit Margin × Total Net Sales
Substituting the given values:
Net Income = Net Profit Margin × $1.35 million
Now we have two equations for net income, so let's combine them:
Net Income = 0.47 / (Net Profit Margin × 0.8 × 1.8) = Net Profit Margin × $1.35 million
We can simplify the equation by canceling out the Net Profit Margin terms:
0.47 / (0.8 × 1.8) = $1.35 million
Simplifying further:
0.47 / 1.44 = $1.35 million
Cross-multiplying:
0.47 = 1.44 × $1.35 million
Solving for $1.35 million:
$1.35 million = 0.47 / 1.44
$1.35 million = 0.3264 million
Converting million to dollars:
$1.35 million = $326,400
Therefore, the net income equals $326,400.
Unfortunately, none of the given answer choices match the calculated net income of $326,400.