- CFA Exams
- CFA Level I Exam
- Topic 5. Equity Valuation
- Learning Module 26. Residual Income Valuation
- Subject 4. Fundamental Determinants of Residual Income

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**CFA Practice Question**

Consider the following information:

At the beginning of the period:

- Book value of total assets: $100 million.
- Debt/equity ratio: 0.25.

Ratios for the period:

- Total assets turnover: 2.
- Net profit margin: 10%.
- Dividend payout rate: 30%.

Other information:

- Equity premium: 8%.
- Beta: 1.2.
- Risk-free rate: 3%.

The firm's residual income for the period is:

Correct Answer: Beginning book value of equity = total assets x equity weight = $100 x 0.80 = $80.

ROE = Net profit margin x Total asset turnover x Equity multiplier = 0.10 x 2 x (1/0.8) = 0.25.

Required return on equity: risk-free rate + beta x equity premium = 0.03 + 1.2 x .08 = 0.126.

RI = Beginning book value of equity x (ROE - cost of equity) = $80 x (0.25 - 0.126) = $9.92 million.

ROE = Net profit margin x Total asset turnover x Equity multiplier = 0.10 x 2 x (1/0.8) = 0.25.

Required return on equity: risk-free rate + beta x equity premium = 0.03 + 1.2 x .08 = 0.126.

RI = Beginning book value of equity x (ROE - cost of equity) = $80 x (0.25 - 0.126) = $9.92 million.

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**User Contributed Comments**
9

User |
Comment |
---|---|

MGM13 |
Isn't the equity weighting 75%, not 80%? |

hkcfa2 |
Debt/equity ratio: 0.25 => equity is 80% of the total assets. |

NufaNka |
1 / (0,25 + 1) = 0,80 |

danlan2 |
RI=(ROE-r)*E=(1.25*2*0.1-0.126)*80=9.92 |

PASS0808 |
Total asset turnover*net profit margin =NI/TA = 2*10% = 20% =>NI = 20%*100 = 20 M Re *We*asset = charge on equity = 12.6*.8*100 = 10.08 M RI = NI- charge to equity = 20-10.08 = 9.92 |

LloydBraun7 |
Debt:Equity analagy....if your you have 0.25 apples for every orange, it means that for every 1 apple you have 4 oranges. Hence, you have 1 apple for every 5 fruits, so your apples weighting is 20%. |

Leese |
Good question - I'm sure CFA exam will do lots of that...making us fill in the blanks (eg here equity multiplier) |

davcer |
Ni=.10x2x1.25=roe x equity = .25x80= 20 Ri= 20- (80x.126)= 9.92 |

Sp1993 |
Alternative this could be worked out in a simpler way using RI = Net Income - Equity Charge Where Equity Charge = Equity Capital * r Work out r as 0.126 using CAPM inputs given in Q. Equity Capital is 0.8 * 100,000,000 = 80,000,000 Since Total Asset Turnover = 2, Revenue must be 200,000,000 and using the 10% Net Profit Margin we can calculate Net Income as 20,000,000. Finally, 20,000,000 - (80,000,000 * 0.126) = Residual Income Residual Income = 9,920,000 :D |