- 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 present value of all the firm's residual?

A. $49.28

B. $52.15

C. $53.89

**Explanation:**Step 1. Beginning Book Value (BBV) 27.50(Y

_{1}) 32.04(Y

_{2}) 37.33(Y

_{3})

Plus: Earnings (ROE x BBV) 6.05(Y

_{1}) 7.05(Y

_{2}) 8.21(Y

_{3})

Less: Dividends (25% of E

_{t}) 1.51(Y

_{1}) 1.76(Y

_{2}) 2.05(Y

_{3})

= 32.04(Y

_{1}) 37.33(Y

_{2}) 43.49(Y

_{3})

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 = 4.85

Step 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.

PV of residual income = [(6.05 - 0.09 x 27.50)/1.09

^{1}] + [(7.05 - 0.09 x 32.04)/1.09

^{2}] + [(8.21 - 0.09 x 37.33)/1.09

^{3}] + 53.89/1.09

^{3}= $52.15

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**User Contributed Comments**
6

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

danlan2 |
g=0.22*0.75=0.165 B1=B0*(1+g)=1.165*B0 RI0=(ROE-r)B0=0.13*B0=3.575 Use C01=1, C02=1.165, C03=1.165^2(1+1/0.09), I=9 to get NPV=14.59 The result is then 14.59*3.575=52.16 |

ThePessimist |
The explanation can be simplified - you can just use the perpetuity instead of adding in year 3 income. Eliminate the year 3 term and instead calculate the perpetuity at the end of year 2: 53.89/(1.09^2) |

dblueroom |
I guess the question meant residual income will remain constant at year 3 level there after. ok that makes sense. I am not sure ThePessimist's simplified version gives the same result. |

rhardin |
I just cannot seem to get this question, no matter how many times I attempt it. Anybody have any easier methods that will work every time? |

hks101 |
danlan's method is much shorter than the explanation. thanks. |

somk |
here was my approach. closed my eyes, pointed my finger. the right answer in 5 seconds. probaility of success:33.3%. propability of screwing up one calculation though i knew the right approach: 1000% |