- If each division has the same operating income of $300,000 and the same average operating assets of $2,000,000, which statement about the divisions' performance measures is correct?
Answer: Division X has the highest residual income, and all divisions have identical ROI of 15%
ROI = Operating Income ÷ Average Operating Assets = $300,000 ÷ $2,000,000 = 15% for all divisions (ROI is not adjusted for risk). Residual Income = Operating Income - (Required Rate × Assets). Division X: $300,000 - (8% × $2,000,000) = $140,000. Division Y: $300,000 - (10% × $2,000,000) = $100,000. Division Z: $300,000 - (14% × $2,000,000) = $20,000. Division X has the highest residual income at $140,000. Choice B is wrong because ROI doesn't vary (it's 15% for all). Choice C is wrong because residual income differs due to different required rates. Choice D is wrong because Division Y's residual income ($100,000) doesn't equal WACC × Assets (10% × $2,000,000 = $200,000).
- Both divisions are considering identical investment projects requiring $600,000 in assets and generating $84,000 in annual operating income. Division M currently has an ROI of 13%, and Division N currently has an ROI of 11%. From a residual income perspective, what is the difference in the projects' attractiveness between the two divisions?
Answer: The project is more attractive for Division N, generating $12,000 more residual income than for Division M
Project ROI = $84,000 ÷ $600,000 = 14% for both divisions. For Division M: Project RI = $84,000 - 0.11 × $600,000 = $84,000 - $66,000 = $18,000. For Division N: Project RI = $84,000 - 0.09 × $600,000 = $84,000 - $54,000 = $30,000. Difference = $30,000 - $18,000 = $12,000 in favor of Division N. This makes sense because Division N has a lower required rate of return (9% vs 11%), making the same project more attractive from a residual income standpoint. The project generates positive residual income for both divisions, but $12,000 more for Division N. Choice A is wrong because the residual incomes are different ($18,000 vs $30,000). Choice C reverses the relationship. Choice D is wrong because both generate positive residual income.
- Kappa Division's performance data shows that when average operating assets increased by $300,000, operating income increased by $42,000, ROI decreased from 16% to 15.2%, and residual income increased by $6,000. What is Kappa Division's required rate of return?
Answer: 12%
Let original assets = A, so new assets = A + $300,000. Original operating income = 0.16A. New operating income = 0.16A + $42,000. New ROI = (0.16A + $42,000)/(A + $300,000) = 15.2% = 0.152. Cross-multiplying: 0.16A + $42,000 = 0.152(A + $300,000) = 0.152A + $45,600. Simplifying: 0.16A - 0.152A = $45,600 - $42,000. 0.008A = $3,600, so A = $450,000. Original operating income = 0.16 × $450,000 = $72,000. New operating income = $72,000 + $42,000 = $114,000. Let r = required rate of return. Original RI = $72,000 - r × $450,000. New RI = $114,000 - r × $750,000. Change in RI = ($114,000 - r × $750,000) - ($72,000 - r × $450,000) = $42,000 - r × $300,000 = $6,000. Solving: $42,000 - $6,000 = r × $300,000, so $36,000 = r × $300,000, giving r = 12%. Verification: Original RI = $72,000 - 0.12 × $450,000 = $18,000. New RI = $114,000 - 0.12 × $750,000 = $24,000. Change = $24,000 - $18,000 = $6,000 ✓.
