Question

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 I’m 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!

Answer 1

New Profit margin = Old Profit Margin * 1.15

= 10% * 1.15

= 11.5%

Formula for Total Asset Turnover = Sales ÷ Total Asset

And Old Total Asset Turnover = 2 it means if your total asset is 1 at the same time your sales will be 2 and as per information given in the problem total asset will increase by 50% it means

NewTotal Asset = 1 + 50% = 1.50 but there is no change in sales.

So, New Total Asset Turnover = 2 ÷ 1.5

= 1.3333

Formula for Equity Multiplier = Total Asset ÷ Equity

And old Equity Multiplier = 2, it means if your equity is 1 then total asset will be 2 but in new condition Total asset will increase by 50% so in this condition,

New Total Asset = 2 + 50% = 3 but there is no change in equity.

So, New Equity Multiplier = 3 ÷ 1 = 3

Therefore,

New ROE = 11.5% × 1.3333 × 3

= 45. 99% ie. 46%