Question

Question: A company has a profit margin of 8.8%, total asset turnover of 3.7, assets of $88, 000 and liabilities of $25, 000. How would the ROE change if profit margin increases to 9.5%, sales decrease by 5% and all balance sheet items stay the same?

Answer 1

Asset Turnover ratio=Sales/Total assets

3.7=Sales/88,000

Sales=3.7*88,000=325,600

==> Profit margin=Net Income/Sales

8.8%=Net Income/325,600

Net income=8.8%*325,600=28,652.8

==> Equity=Assets-Laibilties=88,000-25,000=63,000

ROE=Net income/Total equity=28,652.8/63,000=45.48%

2. If sales decreases by 5%, then sales would become=325,600*(1-5%)=309,320

Profit margin becomes 9.5% of sales, Net income=9.5%*309,320=29,385.4

ROE=29,385.4/63,000=46.64%

ROE increases by 1.16% (46.64%-45.48%)