Question

MIB William Corp. has $875,000 of assets, and it uses only common equity capital (zero debt). Its sales for the last year were $1,020,000, and its net income was $105,000. Stockholders recently voted in a new management team that has promised to lower costs and get the return on equity up to 20.0%. What profit margin would the firm need in order to achieve the 20% ROE, holding everything else constant?

Answer 1

A profit Maring of 17.16% would be needed to achieve the target ROE of 20% if everything else holds constant

Step-by-step explanation:

Return on Equity is the percent of net income achieve per dollar of equity

It is used to check the management of capital investment. (We give you this much, you generate that)

`(Net Income)/(Average Equity) = ROE`

Where Average Equity:

`$$(Beginning Equity + Ending Equity) / 2`

In this case we have no information about beginning or ending so we go with the vlue provided for Equity: $875,000

Now we can see how much the net income needs to be to achieve 20% ROE

`(Net Income)/(875,000) = 0.20`

Net Income = 175,000

Now, which is the profit margin that generates this net income:

`(Net Income)/(Sales Revenue) = $Profit Margin`

This represents the percentage of sales which turned into profits. It can be interpreted as:

cents of net income per dollar of sale.

Having our target net income, and holding the sales constant we need a profit margin of:

`175,000/1,020,000 = 0.171568`

A profit Maring of 17.16% would be needed to achieve the target ROE of 20%