### CFA Practice Question

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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?

A. \$27.58
B. \$37.65
C. \$53.89

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.