Solution :
Return on sales = Net income / sales = 6%
Asset turnover = Sales / Assets = 1.5
Asset divided by owners' equity = 1.3
Part A )
We need to find return on equity , we can find this with the help of above ratios.
Return on equity = Net income / Equity
Net income/ equity can be further expanded into three factors
Net income / Equity = Net income / Sales * Sales / Asset * Asset / Equity = 6% * 1.5 * 1.3 = 11.7%
Return on equity = 11.7%
Part B )
It is given that return on sales has been reduced by 5 % and we need to find the increase in leverage ( asset / equity)
Again using the same formula
11.7% = 6% * ( 1-0.05) * 1.5 * Asset / Equity
Asset / equity = 11.7% / ( 6% * 0.95 *1.5 ) = 1.368421
Increase = 1.368421 - 1.3 = 0.068421
% increase = 0.068421 / 1.3 = 0.052632 = 5.2632%
Alternatively we can calculate in this way since one parameter is decreased by 5% hence other parameter should increase by 1/( 1- decrease % ) = 1/(1-0.05) = 1/0.95 = 1.052632
Increase = 1.052633 -1 = 5.2633%
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