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**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 ______.

B. +0.24%

C. -0.8%

A. +1.6%

B. +0.24%

C. -0.8%

Correct Answer: C

= (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%.

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%.

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**User Contributed Comments**
12

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 |