Cost Accounting Quiz: Residual Income Ri
8 questions · exam conditions
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Residual Income RiQuestion 1 of 8

Two divisions have identical residual income of $120,000. Division P has operating income of $800,000 and Division Q has operating income of $650,000. If both divisions use a 15% cost of capital, what is the difference in their average operating assets?

$150,000 difference with Division P having more assets
$150,000 difference with Division Q having more assets
$1,000,000 difference with Division P having more assets
$1,000,000 difference with Division Q having more assets
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Cost Accounting Quiz

Cost Accounting Quiz: Residual Income Ri

Practice Residual Income Ri in Cost Accounting with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Residual Income Ri, giving you a quick way to practice the rules, question types, and explanations that matter most for Cost Accounting.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Two divisions have identical residual income of $120,000. Division P has operating income of $800,000 and Division Q has operating income of $650,000. If both divisions use a 15% cost of capital, what is the difference in their average operating assets?

  1. $150,000 difference with Division P having more assets
  2. $150,000 difference with Division Q having more assets
  3. $1,000,000 difference with Division P having more assets (correct answer)
  4. $1,000,000 difference with Division Q having more assets
Explanation: For identical RI: Division P assets = ($800,000 - $120,000) ÷ 0.15 = $680,000 ÷ 0.15 = 4,533,333.DivisionQassets=(4,533,333. Division Q assets = (650,000 - $120,000) ÷ 0.15 = $530,000 ÷ 0.15 = $3,533,333. Difference = $4,533,333 - $3,533,333 = $1,000,000, with P having more. Choice A uses the operating income difference. Choice B has wrong direction. Choice D has wrong direction.

Question 2

Division Z is considering an investment project requiring $500,000 in additional assets that will generate $85,000 in additional operating income annually. The division currently has a residual income of $180,000 and uses a 16% hurdle rate. If accepting this project would change the division's residual income to $185,000, what conclusion can be drawn about the division's current return on investment?

  1. Current ROI is exactly 16.0% and the division is indifferent to the project
  2. Current ROI is less than 16.0% and the project improves overall performance
  3. Current ROI is greater than 17.0% and the project significantly reduces performance
  4. Current ROI is greater than 16.0% and the project reduces overall performance (correct answer)
Explanation: When evaluating investment decisions using residual income, you need to understand how new projects affect both residual income and return on investment (ROI). The key insight is that residual income can increase even when a project's return is below the division's current ROI, as long as it exceeds the hurdle rate. Let's analyze what happens here. The project generates $85,000 operating income on $500,000 invested, yielding a 17% return $(85,000500,000)\left(\frac{85,000}{500,000}\right) .Sincethisexceedsthe16. Since this exceeds the 16% hurdle rate, it adds 5,000 to residual income [85,000−(500,000×0.16)][85,000 - (500,000 × 0.16)], matching the increase from $180,000 to $185,000. However, since the division's residual income only increased by $5,000 despite adding a 17% return project, the division's current ROI must exceed 17%. If the current ROI were 17% or lower, adding a 17% project would either maintain or improve the overall ROI, resulting in a larger residual income increase. Choice A is wrong because a 16% current ROI would mean zero current residual income, not $180,000. Choice B incorrectly assumes the current ROI is below the hurdle rate—impossible given the positive residual income. Choice C correctly identifies that current ROI exceeds 17%, but "significantly reduces performance" overstates the minimal $5,000 increase in residual income. Remember: when residual income increases modestly despite adding a project with returns above the hurdle rate, the division's current performance likely exceeds even the project's return rate.

Question 3

A division reports the following data: Beginning assets $2,000,000, ending assets $2,800,000, operating income $504,000, and minimum required return of 18%. If the company changes its policy from using ending assets to using average assets for residual income calculations, what is the impact on reported residual income?

  1. Decrease of $72,000 due to lower asset base reducing the capital charge
  2. Increase of $72,000 due to lower asset base reducing the capital charge (correct answer)
  3. Decrease of $144,000 due to higher operating income requirements
  4. No change because operating income and required return rate remain constant
Explanation: Using ending assets: RI = 504,000−(504,000 - (2,800,000 × 18%) = $504,000 - $504,000 = 0.Usingaverageassets:Average=(0. Using average assets: Average = (2,000,000 + $2,800,000) ÷ 2 = $2,400,000. RI = 504,000−(504,000 - (2,400,000 × 18%) = $504,000 - $432,000 = $72,000. The change increases RI by $72,000. Choice A has the wrong direction. Choice C uses incorrect calculation. Choice D ignores the asset base change impact.

Question 4

Division X has negative residual income of $(45,000) with operating income of $315,000 and a 20% cost of capital. Management wants to achieve positive residual income of $60,000. If the cost of capital remains unchanged, what percentage increase in operating income is required, assuming average operating assets stay constant?

  1. 18.2% increase by improving operational efficiency and cost management
  2. 20.0% increase through enhanced revenue generation and margin improvement
  3. 42.9% increase requiring substantial operational restructuring and optimization
  4. 33.3% increase via significant process improvements and strategic initiatives (correct answer)
Explanation: When you encounter residual income problems, remember that residual income equals operating income minus the required return on average operating assets. The key insight is working backwards from the desired residual income to find the required operating income change. First, let's find the current average operating assets. Since residual income is operating income minus (cost of capital × average operating assets), we have: -$45,000 = $315,000 - (0.20 × average operating assets). Solving this gives us average operating assets of $1,800,000. To achieve positive residual income of $60,000, the new operating income must equal $60,000 + (0.20 × $1,800,000) = $420,000. This represents an increase from $315,000 to $420,000, or $105,000 additional operating income. The percentage increase is $105,000315,000=0.333=33.3%\frac{105,000}{315,000} = 0.333 = 33.3\% $ Answer D correctly identifies this 33.3% increase. The descriptive language about "significant process improvements and strategic initiatives" appropriately reflects the substantial operational changes needed for such a large income boost. Answer A's 18.2% falls short of the required improvement. Answer B's 20% happens to match the cost of capital rate, but this is coincidental and insufficient. Answer C's 42.9% overshoots the actual requirement, representing unnecessary operational changes. Study tip: In residual income problems, always work backwards from the target. Calculate the required operating income first, then determine the percentage change needed. Don't get distracted by the descriptive language in answer choices—focus on the mathematical requirement.

Question 5

A division manager is evaluating whether to accept a new project. The division currently has operating income of $540,000, average assets of $3,600,000, and uses a 12% hurdle rate. The project requires $800,000 in new assets and will generate $110,000 in additional annual operating income. From a residual income perspective, how will this project affect the division's performance?

  1. Increase residual income by $22,000 significantly improving division performance
  2. Increase residual income by $14,000 making the project financially attractive (correct answer)
  3. Decrease residual income by $14,000 making the project financially unattractive
  4. Have no impact on residual income since project ROI equals hurdle rate
Explanation: When evaluating projects using residual income analysis, you're measuring whether a project creates value beyond the company's required return (hurdle rate). Residual income equals operating income minus a charge for the capital invested at the hurdle rate. Let's calculate the project's impact on residual income. The project generates $110,000 in additional operating income but requires $800,000 in new assets. The capital charge equals the new investment times the hurdle rate: $800,000 × 12% = $96,000. Therefore, the project's residual income contribution is $110,000 - $96,000 = $14,000 positive, making answer B correct. Now let's examine why the other answers miss the mark. Answer A incorrectly calculates 22,000,whichyou′dgetifyoumistakenlyuseda1022,000, which you'd get if you mistakenly used a 10% hurdle rate instead of 12% (110,000 - $80,000 = $30,000... wait, that's still wrong). Answer C shows 14,000asadecrease,whichwouldoccurifyousubtractedtheoperatingincomefromthecapitalchargeinsteadofthereverse.AnswerDclaimsnoimpactbecauseprojectROIequalsthehurdlerate,buttheproject′sROIisactually13.7514,000 as a decrease, which would occur if you subtracted the operating income from the capital charge instead of the reverse. Answer D claims no impact because project ROI equals the hurdle rate, but the project's ROI is actually 13.75% (110,000 ÷ $800,000), which exceeds the 12% hurdle rate. Remember this key insight: any project with an ROI above the hurdle rate will increase residual income, while projects below the hurdle rate will decrease it. The difference between project ROI and hurdle rate, multiplied by the investment, gives you the residual income impact.

Question 6

Metro Corporation evaluates its divisions using residual income with division-specific hurdle rates based on risk profiles. The Electronics Division has been consistently profitable but faces increasing competition.

The Electronics Division reports operating income of $960,000 and average operating assets of $6,000,000. Due to increased market volatility, management raises the division's hurdle rate from 14% to 16%. If the division maintains its current return on investment, what will be the change in residual income?

  1. Decrease of $120,000 due to higher capital charge on existing assets (correct answer)
  2. Decrease of $140,000 reflecting increased risk premium requirements
  3. Increase of $120,000 from improved performance measurement accuracy
  4. No change because return on investment percentage remains constant
Explanation: Original RI = 960,000−(960,000 - (6,000,000 × 14%) = $960,000 - $840,000 = $120,000. New RI = 960,000−(960,000 - (6,000,000 × 16%) = $960,000 - $960,000 = $0. Change = $0 - 120,000=−120,000 = -120,000. The hurdle rate increase of 2% on $6,000,000 assets increases the capital charge by $120,000. Choice B uses an incorrect calculation. Choice C has wrong direction. Choice D ignores the hurdle rate impact.

Question 7

Division A has operating income of $480,000, average operating assets of $2,400,000, and a minimum required rate of return of 16%. If the division's residual income is $96,000, what would be the residual income if average operating assets decreased by 25% while maintaining the same return on investment percentage?

  1. $24,000
  2. $36,000
  3. $72,000 (correct answer)
  4. $96,000
Explanation: First, calculate the current ROI: $480,000 ÷ $2,400,000 = 20%. With 25% decrease in assets: New assets = $2,400,000 × 0.75 = $1,800,000. New operating income = $1,800,000 × 20% = $360,000. New residual income = 360,000−(360,000 - (1,800,000 × 16%) = $360,000 - $288,000 = $72,000. Choice A uses the wrong ROI calculation. Choice B incorrectly applies the 25% reduction to residual income. Choice D assumes residual income stays constant.

Question 8

Company XYZ uses residual income to evaluate its three divisions. Division Beta reported operating income of $350,000 with average operating assets of $1,750,000. The company's weighted average cost of capital is 14%, but Division Beta faces higher risk and uses a 18% hurdle rate. If Division Beta's residual income was $35,000, what operating income would be needed to achieve zero residual income using the company's WACC instead of the division-specific rate?

  1. $245,000 (correct answer)
  2. $280,000
  3. $315,000
  4. $350,000
Explanation: Current RI calculation confirms: 350,000−(350,000 - (1,750,000 × 18%) = $350,000 - $315,000 = $35,000 ✓. For zero RI using 14% WACC: Required operating income = $1,750,000 × 14% = $245,000. Choice B incorrectly uses 16% rate. Choice C uses the current 18% rate. Choice D assumes no change needed.