Question

1 . " 10. An analyst at the Herbert Company calculates the following ratios for Herbert as of the end of fiscal year 2006: 6% Return on sales Asset turnover Assets divided by owners' equity 1.5 times 1.3 a. What is Herbert's return on year-end equity? b. If Herbert's return on sales fell to 5 percent, and its asset turnover remained unchanged, how much would its leverage have to increase to maintain the same ROE?

Answer 1

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%