ROI and RI

A division currently earns a return on investment (ROI) of 20%. It is considering investing in a project which has a residual income (RI) of $1,000 at an imputed interest charge of 20%.
What is the effect on the division’s ROI if the project is undertaken?
A. Increase
B. Decrease
C. Remain the same
D. Not possible to tell from this information

The correct answer is A
A useful way of answering many ratio analysis questions is to substitute some simple numbers into the problem. For example, if the division currently earns an ROI (operating profit over net assets) of 20%, this could be represented by operating profit of $20,000 and net assets of $100,000. Residual income is calculated by operating profit – (net assets x imputed interest rate). A residual income of $1,000 could be represented by an operating profit of $11,000 less an imputed interest charge of $50,000 x 20%.

Therefore the new ROI would become (existing operating profit + project operating profit) ÷ (existing net assets + project net assets) = ($20,000 + $11,000) ÷ ($100,000 + $20,000) = 25.83% = an increase in ROI.

I do not understand why we do ($20,000 + $11,000) divided by ($100,000 + $20,000)?
Shouldnt we divide by $100,000 + $50,000 due to new capital employed?

Far quicker though is to realise that a project offering a positive residual income at an imputed interest rate of 20% must be offering a return higher than 20%, and therefore must improve the existing ROI of 20%

I do not understand what this means.

Thank you sir