- CFA Exams
- CFA Level I Exam
- Topic 5. Equity Valuation
- Learning Module 26. Residual Income Valuation
- Subject 6. Multistage Residual Income Valuation
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(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 Et) 1.51(Y1) 1.76(Y2) 2.05(Y3)
= 32.04(Y1) 37.33(Y2) 43.49(Y3)
Note that we use the perpetuity ratio since residual income is not expected to grow after year 3.
Plus: Earnings (ROE x BBV) 6.05(Y1) 7.05(Y2) 8.21(Y3)
Less: Dividends (25% of Et) 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 = Earnings3 - Required Rate of Return x BBV3 = 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)/1.091] + [(7.05 - 0.09 x 32.04)/1.092] + [(8.21 - 0.09 x 37.33)/1.093] + 53.89/1.093 = $52.15
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% |