Last year Rennie Industries had sales of $270,000, assets of $175,000 (which equals total invested capital), a profit margin of 5.3%, and an equity multiplier of 1.2. The CFO believes that the company could reduce its assets by $51,000 without affecting either sales or costs. The firm finances using only debt and common equity. Had it reduced its assets by this amount, and had the debt/total invested capital ratio, sales, and costs remained constant, how much would the ROE have changed

4.04%

Explanation:

Step 1: Calculation of last year return on equity (ROE)

Last year profit = $270,000 × 5.3% = $14,310.00

Asset/Equity = Equity multiplier

Therefore, we have:

$175,000/Last year equity = 1.2

Last year equity = $175,000/1.2 = $145,833.33

Last year ROE = last year profit/Last year equity = $14,310.00/$145,833.33 = 0.0981 or 9.81%

Step 2: Calculation of ROE when asset is reduced by $51,000

Since profit will not change,  

Profit after asset reduction = Last year profit = $14,310.00

New asset value = $175,000 - $51,000 = $124,000

Therefore, we have:

Equity after asset reduction = $124,000/1.2 = $103,333.33

ROE after asset reduction = $14,310.00/$103,333.33 = 0.1385 or 13.85%

Step 3: Calculation of amount of change in ROE

Change in ROE = ROE after asset reduction - Last year ROE = 13.85% - 9.81% = 4.04%

Conclusion

From the calculations above, ROE would change by 4.04% is the reduced by $51,000 based on the other conditions stated.

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