### CFA Practice Question

There are 201 practice questions for this study session.

### 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)

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 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%