Respuesta :
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)
[tex]RoE = Net Profit Margin * Asset turnover Ratio * Equity Multiplier[/tex]
Substituting the values from the question in the DuPont identity we get,
[tex]0.1964 = 0.051 * 2.3 * Equity Multiplier[/tex]
[tex]Equity Multiplier = \frac{0.1964}{0.051*2.3}[/tex]
[tex]Equity Multiplier = 1.674339301 [/tex]
[tex]Equity Multiplier = \frac{Total Assets }{Equity}[/tex]
So,
[tex]\frac{1}{Equity multiplier} =\frac{Equity}{Total Assets}[/tex]
Substituting the value of equity multiplier in the formula above we get,
[tex]\frac{Equity}{Total Assets} = 0.597250509[/tex]
Now,
[tex]\frac{Equity}{Total Assets} + \frac{Debt}{Total Assets} =1[/tex]
So,
[tex]\frac{Debt }{Total Assets} = 1 - \frac{Equity}{Total Assets}[/tex]
[tex]\frac{Debt }{Total Assets} = 1 - 0.597250509 [/tex]
[tex]\frac{Debt }{Total Assets} = 0.402749491 [/tex]
Now that we have the proportions of debt and equity to total assets, we can find the Debt Equity (D/E) ratio as follows:
[tex]\frac{D}{E} = \frac{\frac{Debt}{Total Assets}}{\frac{Equity}{Total Assets}}[/tex]
Substituting the values we get,
[tex]\frac{D}{E} = \frac{0.402749491 }{0.597250509 }[/tex]
[tex]\frac{D}{E} = 0.674339301 [/tex]
