- CFA Exams
- CFA Level I Exam
- Study Session 11. Equity Valuation (3)
- Reading 30. Residual Income Valuation
- Subject 4. Fundamental determinants of residual income

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**CFA Practice Question**

Consider the following information for a firm:

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: 40%.

Other information:

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

Assume that the clean surplus relationship holds for the company. If the required rate of return and the profitability are expected to be the same for the next period, the expected residual income for the next period is:

A. $9.92 million.

B. $10.78 million.

C. $11.408 million.

**Explanation:**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. This (profitability) is expected the same for the next period.

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

Book value at the beginning of the next period BV

_{next period}= BV

_{first period}+ Net Income - Dividends = BV + BV x ROE - BV x ROE x Divided payout rate = $80 + $80 x 0.25 - $80 x 0.25 x 0.4 = $92.

RI

_{next period}= Beginning book value of equity

_{next period}x (ROE - cost of equity) = $92 x (0.25 - 0.126) = $11.408.

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**User Contributed Comments**
10

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

mbuechs2 |
I do not understand the last two lines here. Why should the ROE be constant for the 2nd period? If assets and equity increase both by 12 (60% from NI of first period of 20), and profit margin and asset turnover are constant, than ROE decreases. The result would be $10,808. |

lvleow |
Assume the firm maintains its target capital structure. i.e. the D/E ratio. So when equity increases, the firm raises debt, bringing the equity multiplier back to 1/0.8. |

danlan2 |
ROE=2*0.1/0.8=0.25, r=8%*1.2+3%=12.6% B1=B0+E*0.6=B0+0.15*B0=1.15*B0=92 RI=(ROE-r)*B1=(0.25-0.126)*92=11.408 |

volkovv |
Agree with danlan. BV(1) = BV(0) * (1 + g); g = Retention Rate * ROE; g = (1 - .4) * .25 = .15; BV(1) = 80 * 1.15 = 92 |

Hishy |
If assets = 100 and asset turnover = 2, then sales = 200. With net profit margin of 10%, should NI = 20? Why do I have to use BV * ROE? |

Paulvw |
Use Book Value of Equity, not Book Value of Total Assets. Use ROE, not NPM (which is profit margin on sales, not assets). |

albert9 |
Isnt the equity weight .75 instead of .8? |

cminor |
I am an idiot for doing current period not next period. Also retention ratio is a red herring here. |

jorgeandre |
I don't get why the equity weight is 80% instead of 75% |

darbyland |
Equity Weight = Equity / (Equity + Debt) = Equity / Asset. We have Debt / Equity = 0.25. Since we are interested in Equity / Asset, flip D/E to E/D first which would be 4. you can think of it as E = 4 and D = 1, making A = 5. So, E/A = 4/5 = 0.8 |