Question

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.

Answer 1

$144,329.9

Step-by-step explanation:

From the ROE formula we can find net income:

`ROE=(Net Income)/(Sales)*(Sales)/(Total Assets) *(Total Assets)/(Equity)`

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.

`Total Assets=(Sales)/(Turnover)`

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

`Total Assets=(7,000,000)/(4)`

`Total Assets=1,750,000`

2. Find Common Equity.

`Equity=TotalAssets * Equity %`

`Equity=1,750,000*0.75`

`Equity=1,312,500`

3. Replace values.

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

`ROE=(Net Income)/(Sales)*(Sales)/(Total Assets) *(Total Assets)/(Equity)`

`0.11=(Net Income)/(7,000,000) *(7,000,000)/(1,750,000) *(1,750,000)/(1,312,000)`

`0.11=(Net Income)/(7,000,000) *4*1.334`

`0.11=(Net Income)/(7,000,000) *5.335`

It is now easier to clear net income:

`(ROE)/(5.335) *Sales=Net Income`

`(0.11)/(5.335) *7,000,000=Net Income`

`Net Income=144,329.9`