Question

Assume you are given the following relationships for the Brauer Corp:

Sales/Total assets 1.5X
Return on Assets (ROA) 3%
Return on equity (ROE) 3%
Calculate Brauer's profit margin and debt-to-capital ratio assuming the firm uses only debt and common equity, so total assets equal total invested capital.

Answer 1

To calculate Brauer Corp's profit margin, we use the formula (Net Income/Sales). The profit margin is 1.33/X. To calculate Brauer Corp's debt-to-capital ratio, we use the formula (Debt/(Debt + Equity)). The debt-to-capital ratio is 39.39%.

Step-by-step explanation:

To calculate Brauer's profit margin, we can use the formula:

Profit Margin = Net Income / Sales

Since the return on assets (ROA) is 3%, we can determine the net income as:

Net Income = ROA * Total Assets = 3% * Total Assets

And since the sales/total assets ratio is 1.5X, we can determine the sales as:

Sales = 1.5X * Total Assets

Substituting these values into the profit margin formula:

Profit Margin = (3% * Total Assets) / (1.5X * Total Assets)

Profit Margin = 2% / 1.5X = 2/1.5X = 1.33/X

Therefore, the profit margin for Brauer Corp is 1.33/X.

To calculate Brauer's debt-to-capital ratio, we can use the formula:

Debt-to-capital Ratio = Debt / (Debt + Equity)

Given the information, we can determine the debt as the sum of reserves ($30 million), bonds ($50 million), and loans ($50 million). Therefore:

Debt = $30 million + $50 million + $50 million = $130 million

Since we know that the total assets equal the total invested capital, we can determine the total capital as the sum of deposits ($300 million) and equity ($30 million). Therefore:

Total Capital = $300 million + $30 million = $330 million

Substituting these values into the debt-to-capital ratio formula:

Debt-to-capital Ratio = $130 million / $330 million = 0.3939 (or 39.39%)

Therefore, Brauer Corp's debt-to-capital ratio is 39.39%.

Answer 2

Profit margin= 2%

Debt to capital= 0

Step-by-step explanation:

We can find out Profit margin through the formula of ROA

Return on Assets= Asset turnover* Profit margin

We have been give ROA, and ATO

ROA=3%

ATO=1.5X

So, 3%=1.5*X

X=2%

Profit margin is 2%

Now debt to capital

It can be calculated from the Dupont analysis which is

ROE=ROA*Equity multiplier

Equity multiplier is Assets/Equity

so,

3%=3%*x

EM= 1

Now, Equity multiplier tells us how much our assets are financed through equity so if it is 1, means Assets/Equity =1

So, Assets= Equity

So, all the assets are financed through equity. None of the assets are financed through debt. So, it suggest debt is 0

Debt to capital = Debt/Capital = 0/capital = 0