The following data has been provided for a company’s most recent year of operations:

Return on investment 20%
Average operating assets $ 100,000
Minimum required rate of return 15%

The residual income for the year was closest to:

Question

The following data has been provided for a company’s most recent year of operations:

Return on investment    20%
Average operating assets    $ 100,000
Minimum required rate of return    15%

The residual income for the year was closest to:

BlackTom AI · Accepted Answer

To analyze the residual income question, I’ll first restate the data and the formula involved.
We have: Return on investment (ROI) = 20% on Average operating assets of $100,000, and Minimum required rate of return (MRRR) = 15% on the same asset base. Residual income (RI) is calculated as: RI = Operating income − (MRRR × Average operating assets).
Now evaluate each option step by step.
Option  "$20,000": This number represents the operating income rather than RI. It is found by applying ROI to assets (0.20 × $100,000 = $20,000). However, RI requires subtracting the minimum required return on the asset base, not simply reporting income. Therefore this option corresponds to operating income, not residual income.
Option  "$3,000": This value could come from a miscalculation, such as subtracting a portion of the required return or misapplying the rate. If you subtract 15% of $100,000 from $20,000, you get $20,000 − $15,000 = $5,000, not $3,000. Hence $3,000 does not align with the RI formula given.
Option  "$5,000": This aligns with the residual income formula. Compute operating income as 0.20 × $100,000 = $20,000, and compute the required return as 0.15 × $100,000 = $15,000. Subtracting gives $20,000 − $15,000 = $5,000. This is exactly the RI amount implied by the data.
Option  "$15,000": This value matches the total minimum required return in dollars (MRRR × assets). While it represents the cost of capital component, RI subtracts this amount from operating income; it is not the residual income itself. Treating $15,000 as RI would ignore the actual operating income figure and thus misstate RI.
In summary, the key idea is to separate the generation of operating income from the cost of capital on the asset base, and then apply the subtraction to obtain RI. The correct approach yields an RI of $5,000, derived from $20,000 operating income minus $15,000 in required return on assets.

The following data has been provided for a company’s most recent year of operations: Return on investment 20% Average operating assets $ 100,000 Minimum required rate of return 15% The residual income for the year was closest to:单项选择题

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