CMA Study Group

A clear understanding of the ROE formula will surely point to D as being the correct answer.

Recall that ROE combines three ratios, namely the Profit ratio, Asset Turnover and the Equity Multiplier. Thus:

ROE = NI/NS X NS/TA X TA/Equity

For example:
ROE = 40/200 (Profit ratio) X 200/100 (Asset Turnover) X 100/25 (Equity Multiplier)
ROE = 20% X 2 X 4
ROE = 1.6

NOTE: In ratio analysis, the numerator is directly proportional, while the denominator is inversely related to the ratio itself.

Why answer A is wrong
A decrease in the cost ratio (CGS/NS) will naturally increase the Profit ratio, thereby increasing (not decreasing) the ROE. To apply to the original example, if the cost ratio becomes 70% the Profit ratio becomes 30%, and we'll get 2.4 as the revised ROE.

Why answer B is wrong
Debt ratio is Liabilities/Total Asset. Again, based on the above example, the debt ratio is (100-25)/100 or 0.75. If the debt ratio decreases to 0.50, this means the Equity Multiplier dips to 2 (100/50). To calculate the revised ROE, we'll have 20% X 2 X 2, or a lower ROE at 0.80.

Why answer C is wrong
Ultimately, ROE is actually NI/Equity (40/25=1.6).

Choice C assumes that Equity (denominator) increased. Recall that a denominator change causes an inverse effect to the ratio. As denominator increased, ROE will naturally decrease. For instance, if 25 becomes 50, the revised ROE will now be calculated as 40/50 = 0.80 (decreased).

Proving answer D (ROE DECREASES AS TOTAL ASSETS INCREASE)   
If the Total Asset in the original illustration increases to 150, ROE will decrease to 0.533. Here is the revised calculation:

ROE = 40/200 X 200/150 X 150/75
ROE = 0.533

Equity increases (150 - 75 liabilities) as asset increases since the problem stated that all others (liabilities) are assumed to be constant.

I hope the use of hypothetical numbers helped. By the way, here's one trick I use when I encounter this kind of question, I start from the BOTTOM CHOICE. You can surely figure out why.