Precious Metal Mining has $7 million in sales, its ROE is 11%, and its total assets turnover is 4x. Common equity on the firm’s balance sheet is 75% of its total assets. What is its net income? Write out your answer completely. For example, 5 million should be entered as 5,000,000. Do not round intermediate calculations. Round your answer to the nearest cent.

What we will do is clear each variable until we get only one unknown: net income. In the problem statement we find two values: Sales (7,000,000) and ROE (11% or 0.11). Then, we would need to find "Total Assets" and "Common Equity".

1. Find Total Assets.

[tex]Total Assets=\frac{Sales}{Turnover}[/tex]

In this case, total assets turnover is 4. Therefore:

[tex]Total Assets=\frac{7,000,000}{4}[/tex]

[tex]Total Assets=1,750,000[/tex]

2. Find Common Equity.

[tex]Equity=TotalAssets * Equity %[/tex]

[tex]Equity=1,750,000*0.75[/tex]

[tex]Equity=1,312,500[/tex]

3. Replace values.

Once all these values have been found, we replace in the ROE formula (remember that the only unknown is net income):

[tex]ROE=\frac{Net Income}{Sales}*\frac{Sales}{Total Assets} *\frac{Total Assets}{Equity}[/tex]

[tex]0.11=\frac{Net Income}{7,000,000} *\frac{7,000,000}{1,750,000} *\frac{1,750,000}{1,312,000}[/tex]

[tex]0.11=\frac{Net Income}{7,000,000} *4*1.334[/tex]

[tex]0.11=\frac{Net Income}{7,000,000} *5.335[/tex]

It is now easier to clear net income:

[tex]\frac{ROE}{5.335} *Sales=Net Income[/tex]

[tex]\frac{0.11}{5.335} *7,000,000=Net Income[/tex]

[tex]Net Income=144,329.9[/tex]