Last year Central Chemicals had sales of $205,000, assets of $127,500, a profit margin of 5.3%, and an equity multiplier of 1.2.The CFO believes that the company could reduce its assets by $21,000 without affecting either sales or costs.Had it reduced its assets in this amount, and had the debt-to-assets ratio, sales, and costs remained constant, by how much would the ROE have changed?
A) 1.81%
B) 2.02%
C) 2.22%
D) 2.44%
E) 2.68%

Question

Quizplus · Accepted Answer

ROE = profit margin * equity multiplier
Given: Sales = $205,000, Assets = $127,500, Profit Margin = 5.3%, Equity Multiplier = 1.2

ROE = 0.053 * 1.2 = 6.36%

If assets were reduced by $21,000, then new assets would be $106,500 ($127,500 - $21,000). Equity would remain the same.

New ROE = (Net Income/Revenue) * (Revenue/Assets) * (Assets/Equity)
New ROE = [($205,000 - Cost) * 0.053 / $106,500] * $106,500 / $127,500
New ROE = 0.053 * 0.838 + 6.36%
New ROE = 10.52%

Change in ROE = New ROE - Old ROE = 10.52% - 6.36% = 4.16%
Therefore, the ROE would have changed by 4.16%, which is closest to 2.02% (Option B).

Last Year Central Chemicals Had Sales of $205,000, Assets of $127,500