Respuesta :
Answer: The dividend payout ratio is 46.19%.
We follow these steps in order to arrive at the answer:
We begin with the DuPont identity of RoE.
DuPont Identity:
[tex]RoE = Net Profit Margin * Asset Turnover Ratio * Equity Multiplier[/tex]
Now,
[tex]Equity Multiplier = \frac{1}{Debt Ratio}[/tex]
And Debt Ratio is also expressed as:
[tex]Debt Ratio = \frac{D/E}{1+D/E}[/tex]
where D/E represents the Debt-Equity Ratio.
Substituting the value of D/E ratio from the question in the debt ratio formula above we get,
[tex]Debt Ratio = \frac{0.9}{1+0.9}[/tex]
[tex]Debt Ratio = \frac{0.9}{1.9}[/tex]----(1)
Substituting (1) in the equity multiplier formula above we get,
[tex]Equity Multiplier = \frac{1}{\frac{0.9}{1.9}}[/tex]
[tex]Equity Multiplier = \frac{1.9}{0.9}[/tex]
Substituting Equity Multiplier from above and the relevant numbers from the question in the DuPont identity we get,
[tex]RoE = 0.048 * 1.08 * \frac{1.9}{0.9}[/tex]
[tex]RoE = 0.10944[/tex]
The relationship between RoE and earnings growth rate g is given by the following formula:
[tex]RoE = \frac{g}{(1-p)}[/tex], where p is the dividend payout ratio.
Plugging in the values in the formula above we get,
[tex]0.10944 = \frac{0.16}{(1-p)}[/tex]
[tex]1-p = \frac{0.16}{0.10944}[/tex]
[tex]1-p = 1.461988304[/tex]
p = 0.461988304 or 46.19%
