spartan1

What is a company’s equity if their return on equity (ROE) is 12%, and their net income is $10 million?

A) $120,000,000.

B) $83,333,333.

C) $1,200,000.

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One of the many ways ROE can be expressed is: ROE = net income / equity
0.12 = $10,000,000 / equity
Equity = $10,000,000 / 0.12 = $83,333,333

spartan1

The traditional DuPont equation shows ROE equal to:

A) net income/sales × sales/assets × assets/equity.

B) EBIT/sales × sales/assets × assets/equity × (1 – tax rate).

C) net income/assets × sales/equity × assets/sales.

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Profit margin × asset turnover × financial leverage. Although net income/assets × sales/equity × assets/sales also yields ROE, it is not the DuPont equation.

spartan1

An analyst has gathered the following information about a company.

• The total asset turnover is 1.2.

• The after-tax profit margin is 10%.

• The financial leverage multiplier is 1.5.

Given this information, the company’s return on equity is:

A) 12%.

B) 9%.

C) 18%.

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ROE = profit margin × total asset turnover × financial leverage
ROE = (0.1)(1.2)(1.5) = 0.18 or 18.0%

spartan1

If a firm has a net profit margin of 0.05, an asset turnover of 1.465, and a leverage ratio of 1.66, what is the firm's ROE?

A) 12.16%.

B) 3.18%.

C) 5.87%.

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One of the many ways to express ROE = net profit margin × asset turnover × leverage ratio
ROE = (0.05)(1.465)(1.66) = 0.1216

spartan1

Given the following information about a firm what is its return on equity (ROE)?

• An asset turnover of 1.2.
• An after tax profit margin of 10%.
• A financial leverage multiplier of 1.5.

A) 0.18.

B) 0.09.

C) 0.12.

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ROE = (EAT / S)(S / A)(A / EQ)
ROE = (0.1)(1.2)(1.5) = 0.18

spartan1

With other variables remaining constant, if profit margin rises, ROE will:

A) fall.

B) increase.

C) remain the same.

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The DuPont equation shows clearly that ROE will increase as profit margin increases, as long as asset turn and leverage do not fall.

spartan1

If a company has a net profit margin of 15%, an asset turnover ratio of 4.5 and a ROE of 18%, what is the equity multiplier?

A) 0.267.

B) 2.667.

C) 0.523.

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There are many different ways to illustrate ROE one of which is:
ROE = (net profit margin)(asset turnover)(equity multiplier)
0.18 = (0.15)(4.5)(equity multiplier)
0.18 ÷ [(0.15)(4.5)] = equity multiplier
0.18 ÷ 0.675 = equity multiplier
0.18 ÷ 0.675 = 0.267

spartan1

When the return on equity equation (ROE) is decomposed using the original DuPont system, what three ratios comprise the components of ROE?

A) Net profit margin, asset turnover, asset multiplier.

B) Net profit margin, asset turnover, equity multiplier.

C) Gross profit margin, asset turnover, equity multiplier.

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The three ratios can be further decomposed as follows:
Net profit margin = net income/sales
Asset turnover = sales/assets
Equity multiplier = assets/equity

spartan1

Which of the following ratios is NOT part of the original DuPont system?

A) Asset turnover.

B) Debt to total capital.

C) Equity multiplier.

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The debt to total capital ratio is not part of the original DuPont system. The firm’s leverage is accounted for through the equity multiplier.

spartan1

Would an increase in net profit margin or in the firm’s dividend payout ratio increase a firm’s sustainable growth rate?

Net profit margin

Dividend payout ratio

A) Yes Yes

B) Yes No

C) No No

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The sustainable growth rate is equal to ROE multiplied by the retention rate. According to the Dupont formula, an increase in net profit margin will result in higher ROE. Thus, an increase in net profit margin will result in a higher growth rate. The retention rate is equal to 1 minus the dividend payout ratio. Thus, an increase in the dividend payout ratio will lower the retention rate and lower the growth rate.