Division X has an ROI of 20% on a divisional investment of $30,000,000. Margin is 1%. The imputted interest rate charged by top management to Division X is 15%.

I know the formula on how to find sales using the Margin formula which as follows below:

Margin = net operating income / sales

Then this becomes: sales = net operating income / margin

However, I am stumbled on getting the net operating income from this question.

I'm making two assumptions. One is that "investment" is meaning assets and not equity. (ROI and ROA usually mean the same thing, but I've seen exceptions.) Two, that they're wanting the DuPont. However, I'm not sure what that 15% is for. That part I'm not familiar with, so perhaps someone else can shed light on that one.

\text{ROI\ =\ \frac{income}{invested\ assets}}

But the extended equation is:

\text{ROI\ =\ \frac{income}{sales}\ x\ \frac{sales}{invested\ assets}}

(If you were to cancel out sales, you'd be back to the original equation. But the point of this is to see the "pieces" as well.)

In other words:

\text{ROI\ =\ profit\ margin\ x\ asset turnover}

You have ROI and margin. Plug those in and solve for turnover. They also gave you invested assets, or what I'm assuming to be invested assets. Once you have the turnover, you can plug that in and solve for sales, then plug that in and solve for income.

Now, this is the way I see most books wanting it done. However, notice that if you use the original equation, you can plug in the 20% and the assets, and solve straight for the income. I just about never see that though.

And again, I'm not sure how that interest is coming into play. In accounting we don't get into this stuff too in depth, and if this is a finance class, which would use this stuff way more, that might be getting into some finance thing I just don't remember. Which could make me full of it here. But this is my "accounting-view" assessment of the situation.

I'm making two assumptions. One is that "investment" is meaning assets and not equity. (ROI and ROA usually mean the same thing, but I've seen exceptions.) Two, that they're wanting the DuPont. However, I'm not sure what that 15% is for. That part I'm not familiar with, so perhaps someone else can shed light on that one.

\text{ROI\ =\ \frac{income}{invested\ assets}}

But the extended equation is:

\text{ROI\ =\ \frac{income}{sales}\ x\ \frac{sales}{invested\ assets}}

(If you were to cancel out sales, you'd be back to the original equation. But the point of this is to see the "pieces" as well.)

In other words:

\text{ROI\ =\ profit\ margin\ x\ asset turnover}

You have ROI and margin. Plug those in and solve for turnover. They also gave you invested assets, or what I'm assuming to be invested assets. Once you have the turnover, you can plug that in and solve for sales, then plug that in and solve for income.

Now, this is the way I see most books wanting it done. However, notice that if you use the original equation, you can plug in the 20% and the assets, and solve straight for the income. I just about never see that though.

And again, I'm not sure how that interest is coming into play. In accounting we don't get into this stuff too in depth, and if this is a finance class, which would use this stuff way more, that might be getting into some finance thing I just don't remember. Which could make me full of it here. But this is my "accounting-view" assessment of the situation.

Thanks for clarifying what investments is in the first place. I just needed some clarification so far. I'm glad I solved it by myself using the ROI and the associated formulaes.