$($B$)$ Apply the DuPont model $($which disaggregates the performance of managers into three componentsprofitability, asset utilization, and financial leverage$)$ to analyze financial performance of Diamond during $20092011.$ Specifically, do the following:

$($i$)$For fiscal years $2009,2010,$ and $2011,$ compute ROA $($return on assets$)$ defined as after$-$tax operating income divided by average total assets and its decomposition into return on sales $($after$-$tax operating income divided by sales$),$ and asset turnover $($sales divided by average total assets$).$ What are the major reasons for the change in ROA over this period $(20092011)?$ How have the recent acquisitions affected Diamond's profitability and ROA of Diamond?

$($ii$)$For fiscal years $2009,2010,$ and $2011,$ compute the ROCE $($return on common stockholders' equity$)$ defined as net income to common stockholders divided by average stockholders' equity and its decomposition into profit margin for ROCE $($net income to common stockholders divided by sales$),$ asset turnover $($sales divided by average total assets$),$ and capital structure leverage $($average total assets divided by average stockholders' equity$).$

$($iii$)$While Diamond's ROA and ROCE both went down in $2011$ compared to $2009,$ the relative reduction in the ROCE is much less. Why?