Residual income and ROI

Good afternoon,

I wonder if you could help me to understand this question from a dec 13 past exam:

Example 2
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 A was selected by a minority of candidates.
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.
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%.

Would you please confirm where (in the equation that results in ROI of 25.83%) the second £20,000 (project net asset) is coming from?

Leonardo