Question

Jack corp. Has a profit margin of 5.1 percent, total asset turnover of 2.3, and roe of 19.64 percent. What is this firm's debt-equity ratio? (do not round intermediate calculations and round your answer to 2 decimal places,
e.G., 32.16.)

Answer 1

Answer: Jack Corp's D/E ratio is 0.67.

We follow these steps to arrive at the answer:

We begin with the DuPont Identity for Return on Equity (RoE)

$RoE = Net Profit Margin * Asset turnover Ratio * Equity Multiplier$

Substituting the values from the question in the DuPont identity we get,

$0.1964 = 0.051 * 2.3 * Equity Multiplier$

$Equity Multiplier = \frac{0.1964}{0.051*2.3}$

$Equity Multiplier = 1.674339301$

$Equity Multiplier = \frac{Total Assets }{Equity}$

So,

$\frac{1}{Equity multiplier} =\frac{Equity}{Total Assets}$

Substituting the value of equity multiplier in the formula above we get,

$\frac{Equity}{Total Assets} = 0.597250509$

Now,

$\frac{Equity}{Total Assets} + \frac{Debt}{Total Assets} =1$

So,

$\frac{Debt }{Total Assets} = 1 - \frac{Equity}{Total Assets}$

$\frac{Debt }{Total Assets} = 1 - 0.597250509$

$\frac{Debt }{Total Assets} = 0.402749491$

Now that we have the proportions of debt and equity to total assets, we can  find the Debt Equity (D/E) ratio as follows:

$\frac{D}{E} = \frac{\frac{Debt}{Total Assets}}{\frac{Equity}{Total Assets}}$

Substituting the values we get,

$\frac{D}{E} = \frac{0.402749491 }{0.597250509 }$

$\frac{D}{E} = 0.674339301$