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.
<u>DuPont Identity:</u>
Now,
![Equity Multiplier = \frac{1}{Debt Ratio}](https://tex.z-dn.net/?f=Equity%20Multiplier%20%3D%20%5Cfrac%7B1%7D%7BDebt%20Ratio%7D)
And Debt Ratio is also expressed as:
![Debt Ratio = \frac{D/E}{1+D/E}](https://tex.z-dn.net/?f=Debt%20Ratio%20%3D%20%5Cfrac%7BD%2FE%7D%7B1%2BD%2FE%7D)
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,
![Debt Ratio = \frac{0.9}{1+0.9}](https://tex.z-dn.net/?f=Debt%20Ratio%20%3D%20%5Cfrac%7B0.9%7D%7B1%2B0.9%7D)
----(1)
Substituting (1) in the equity multiplier formula above we get,
![Equity Multiplier = \frac{1}{\frac{0.9}{1.9}}](https://tex.z-dn.net/?f=Equity%20Multiplier%20%3D%20%5Cfrac%7B1%7D%7B%5Cfrac%7B0.9%7D%7B1.9%7D%7D)
![Equity Multiplier = \frac{1.9}{0.9}](https://tex.z-dn.net/?f=Equity%20Multiplier%20%3D%20%5Cfrac%7B1.9%7D%7B0.9%7D)
Substituting Equity Multiplier from above and the relevant numbers from the question in the DuPont identity we get,
![RoE = 0.10944](https://tex.z-dn.net/?f=RoE%20%3D%200.10944)
The relationship between RoE and earnings growth rate g is given by the following formula:
, where p is the dividend payout ratio.
Plugging in the values in the formula above we get,
![0.10944 = \frac{0.16}{(1-p)}](https://tex.z-dn.net/?f=0.10944%20%3D%20%5Cfrac%7B0.16%7D%7B%281-p%29%7D)
![1-p = \frac{0.16}{0.10944}](https://tex.z-dn.net/?f=1-p%20%3D%20%5Cfrac%7B0.16%7D%7B0.10944%7D)
![1-p = 1.461988304](https://tex.z-dn.net/?f=1-p%20%3D%201.461988304)
p = 0.461988304 or 46.19%