### CFA Practice Question

There are 534 practice questions for this study session.

### CFA Practice Question

If a firm's profit margin increases by 8%, the debt-to-equity ratio increases from 35% to 55%, and asset turnover falls by 20%, the effect on ROE is ______.

A. +1.6%
B. +0.24%
C. -0.8%

ROE = net income/equity = (net income/sales) x (sales/assets) x (assets/equity)
= (profit margin) x (asset turnover) x (1+debt/equity)
Original assets/equity = 1 + 0.35 = 1.35 and changed assets/equity = 1.55. Therefore, the change in ROE equals (1+8%) x (1-20%) x 1.55/1.35 = 0.992. Thus, ROE falls by 0.8%.

User Comment
aeleina I don't understand...
If D/E increases, TA/E increases too? I thought they are inversely related: TA/E=1-D/E
cbb1 The relationship is

Total assets/equity = 1 + D/E

For example:

100 assets
70 equity
30 debt
the TA/E = 100/70 or 1.42857
the debt/equity = 30/70 or .42857 then add one
haarlemmer As debt-to-equity is .35, asset-to-equity is 1.35 (asset=debt+equity which we assume debt=.35 and equity=1), the rest would be clear.
aafla Debt=Asset - Equity

then divide by Equity --> D/E = A/E - E/E or D/E = A/E - 1 ---> A/E = D/E + 1
A/E = 0.35 + 1 = 1.35
mtcfa Increase in debt/equity reduces equity, but not necessarily assets, therefore TA/equity increases.
surob Good question
Rotigga Remember this: Assets/Equity = Debt/Equity + 1
cfabuzz this is the logic:
say Debt Equity ratio (DER) = 35%
D / E = 0.35
D + E = Asset
0.35 E + E = A
1.35 E = A
A / E = 1.35
msoentoro Sorry, stupid question, why 1.55/1.35 to calculate the increase of equity multiplier side?
abhinavkapoor the question refers to % changes & the effect of these changes in ROE;

Net profit Margin became 1.08 from 1 (8% CHANGE)
Asset Turnover became .8 from 1 (20% change)
Change in % from 1.35 to 1.55 = 20(155-135)/135 = (14.8% CHANGE) = 1.148

1.08 X .8 X 1.148 = .992
Tom0409 How I remember it. Working all the way back through..
debt/equity = 0.35
debt/assets = 0.35/1.35 = 0.259
equity/assets = 1-0.259 = 0.74
assets/equity = 1/0.74 = 1.35
ioanaN profit margin X asset turnover X equity multiplier
equity multiplier=assets/equity=1+debt/equity
(1+0.08)(1-0.2)(1+(1.55-1.35)/1.35)=0.992
decreased by 0.008