Finding Sustainable Growth Rate

ok, so questions like this throw me off. I also remember seeing one in the past, where they give you the P/E ratio or something similar and you need to use that. If anyone has that example , that would be appreciated.

Question:

Sales = $800,000

Net Profit Margin = 20%

Sales to Assets = 50%

Equity multiplier = 1.6

Interest expense = $30,000

Dvidiends declared = $32,000

What is the sustainable growth rate?

=(Retention rate) (ROE)

Easy way to find ROE is (.20) (0.5) (1.6) = 16%

Hard way = (.20) (.5) / ((800,000/.5) (1/1.6))

Can someone explain the hard way? I understand the numerator is just net income. But the denominator is a little tricky.

Then the retention rate is 1-dividend payout ratio.

1 - (32,000/ (.20)(800,000). This makes sense.

Thanks!

I, for one, cannot, as the formula you have for “the hard way” doesn’t give (remotely) the same answer as the formula for the easy way. If you get rid of that (800,000/0.5), then they’re the same.

Where’d you find that hard way formula? (Did you, perhaps, omit something?)