PROBLEM 10

You are considering adding a new product to your firm's existing product line. It should cause a 15 percent increase in your total margin (i.e., new TM = old TM x 1.15), but it will also require a 50 percent increase in total assets (i.e., new TA = old TA x 1.5). You expect to finance this asset growth entirely by debt. If the following ratios were computed before the change, what will be the new return on equity if the new product is added and sales remain constant?

Ratios before new product

Total margin 10%

Total assets turnover 2

Equity multiplier 2

From a previous Chegg Post, these were the answers:

Old profit margin is 10%, new profit margin will be 15% higher at the same sales, so new PAT margin = 10%*1.15 = 11.5%

Next, Total asset turnover = Sales/Total assets =2, information is given that Total assets will increase by 50% and sales will remain same

So new Sales/ Total assets = 2/1.5, solving this sales/ Total assets = 1.3333, which is new asset turnover ratio

Next Equity multiplier = Total asset/Equity = 2, in the new case Total assets will increase 50% while equity will remain same as all incremental funding will be through debt only

So Total assets/Equity = 2*1.5 =3, so New Total assets/Equity = 3

Now the New ROE = 11.5% * 1.3333 * 3 = 46% is the answer

My question: What Im not understanding is the reasoning behind the multiplication and division. Why do you divide your old Total Asset Turnover by the increase in assets? Why do you multiply the equity multiplier by the increase in assets as well? Why are we not using the equation for New Total Assets in our answer?

Thanks!