I am considering adding a new product to my firm's existing product line

I am considering adding a new product to my firm's existing product line. It will cause a 15 percent increase in my profit margin (i.e., new PM = old PM ´ 1.15), but it will also require a 50 percent increase in total assets (i.e., new TA = old TA ´ 1.5). I expect to finance this asset growth entirely by debt. If the following ratios were computed before the change, what will be the new ROE if the new product is added and sales remain constant?

Ratios before new product:

Profit margin = 0.10
Total assets turnover = 2.00
Equity multiplier = 2.00

Old

Profit margin = 0.10
Total assets turnover = 2.00
Equity multiplier = 2.00

New

Profit margin = 0.115 =1.15x0.10
Total assets turnover =Sales / Total Assets = Sales / New Assets
= Sales / (1.5 Old Assets) = (Sales / Old Assets)/1.5=
Equity multiplier = 1.3333 =2/1.5
Equity multiplier =Total Assets / Total Equity = 1.5 Old Assest / Equity = 3 =1.5x2

ROE = Profit Margin X Total Assets Turnover x Equity Multiplier= 0.115 x 1.3333 x 3 = 0.46

Answer: ROE= 0.46