- CFA Exams
- CFA Level I Exam
- Topic 5. Equity Valuation
- Learning Module 26. Residual Income Valuation
- Subject 6. Multistage Residual Income Valuation

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**CFA Practice Question**

An analyst is conducting a valuation for DEF Corp. This company has a dividend payout ratio of 25% and is expected to exhibit an ROE of 22% over the next three years. Thereafter, the "residual income" will remain constant. If the book value of DEF is currently $27.50, and the required rate of return on equity is 9%, which of the following would best estimate the terminal value of the residual income at the end of year three?

B. $37.65

C. $53.89

A. $27.58

B. $37.65

C. $53.89

Correct Answer: C

Plus: Earnings (ROE x BBV) 6.05(Y1) 7.05(Y2) 8.21(Y3)

Less: Dividends (25% of E

= 32.04(Y1) 37.33(Y2) 43.49(Y3)

Step 1. Beginning Book Value (BBV) 27.50(Y1) 32.04(Y2) 37.33(Y3)

Plus: Earnings (ROE x BBV) 6.05(Y1) 7.05(Y2) 8.21(Y3)

Less: Dividends (25% of E

_{t}) 1.51(Y1) 1.76(Y2) 2.05(Y3)= 32.04(Y1) 37.33(Y2) 43.49(Y3)

Step 2. Compute "residual income" at the end of year 3: (Residual Income)

_{3}= Earnings_{3}- Required Rate of Return x BBV_{3}= 8.21 - 0.09 x 37.33 = 4.85Step 3. Terminal value of residual income: 4.85/0.09 = $53.89.

Note that we use the perpetuity ratio since residual income is not expected to grow after year 3.

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**User Contributed Comments**
5

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

danlan2 |
B2=B0*(1+0.22*0.75)^2=27.5*1.165^2=37.32 RI3=(ROE-r)B2=0.13*37.32=4.85 |

LloydBraun7 |
It was never mentioned that the book value was all equity....it would have to be in order to be able to do ROE*BV. |

Alena1989 |
In Step 2 it should be BBV in the year 2 not 3 (preceding the year of the earnings used in calculation) |

davidt876 |
nice danlan. also the answer is wrong for saying RI3 = E3 - r*BBV3... it should instead be RI3 = E3 - r*BBV2 - which is what danlan references in his answe |

michaelcfa |
The answer is correct. To calculate the residual income of period 3 (RI3) you should use the beginning book value at the end of period 2 , which is also the value at the beginning of period 3: BBV3 (37.33)! |