I need help trying to solve for ROA(Return on Total Assets) Finance question.?

Question

Hello I need help solving this finance question. I don't need just the answer I need step by step of how I can get to the answer I would very much appreciate this. Here is the question:

The common stock of J.C. Penney is currently selling at $8 per share, which represents a P/E ratio of 33. If J.C. Penney has 607,210 shares of common stock outstanding, a return on equity of 16 percent, and a debt ratio of 80 percent, what is its Return on Total Assets (ROA)?

Please show me the steps you used to get to the answer Thanks once again!

Answer 1

P/E ratio or Price Earnings Ratio = Mkt price per share/Earnings per share = 33, i.e. 8/EPS = 33, so EPS = 8/33 = 0.242424
If Earnings PER SHARE = 0.242424 and there are 607,210 shares, then total net earnings (or Net Income) must be 0.242424 x 607,210 = 147,202.277

Return on Equity is Net Income/Shareholders' Equity, and we're told RoE is 0.16, so
Net Income/Shareholders' Equity = 0.16. From above we know Net Income is 147,202.277, so Shareholders' Equity must be 147,202.277/0.16 = 920,014.23

Debt ratio is Total Debt/Total Assets = 0.80
so TD = 0.80TA

Total Assets - Total Debt (aka Total liabilities) = Shareholders' Equity
TA - 0.80TA = 920,014.23 (see above)
0.2TA = 920,014.23
TA = 920,014.23/0.2 = 4,600,071.15

Return on Assets is Net Income/Total Assets
We know Net Income is 147,202.277 and Total Assets is 4,600,071.15, so RoA is 147,202.277/4,600,071.15 = 0.032 or 3.2%