Last year Kruse Corp had $440,000 of assets (which is equal to its total invested capital), $403,000 of sales, $28,250 of net income, and a debt-to-total-capital ratio of 39%. The new CFO believes the firm has excessive fixed assets and inventory that could be sold, enabling it to reduce its total assets and total invested capital to $252,500. The firm finances using only debt and common equity. Sales, costs, and net income would not be affected, and the firm would maintain the same capital structure (but with less total debt). By how much would the reduction in assets improve the ROE

The reduction in assets would improve the ROE by 7.81%.

Explanation:

This can be calculated as follows:

Previous equity = (100% - Debt-to-total-capital ratio) * Previous total invested capital = (100% - 39%) * $440,000 = 61% * $440,000 = $268,400

Previous return on equity (ROE) = (Net income / Previous equity) * 100 = ($28,250 / $268,400) * 100 = 10.53%

New equity = (100% - Debt-to-total-capital ratio) * New total invested capital = (100% - 39%) * $252,500 = 61% * $252,500 = $154,025

New ROE = (Net income / New equity) * 100 = ($28,250 / $154,025) * 100 = 18.34%

Change in ROE = New ROE - Previous ROE = 18.34% - 10.53% = 7.81%

Since change in ROE is 7.81% and positive, this implies that the reduction in assets would improve the ROE by 7.81%.

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