Calculating beginning book value per share

CFA Level II Equities
#1

(Schweser Residual Income Valuation EOC q3)

Does anyone know how we get beginning book value per share for 2018-2021 from the below?

For reference, the answer is: 2018: 10.62; 2019: 11.89; 2020: 13.32; 2021: 14.91.

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Josef Robien, CFA, is valuing the common stock of British Cornucopia Bank (BCB) as of December 31, 2017, when the book value per share is £10.62. In this effort, Robien has made the following assumptions:

  • Earnings per share (EPS) will be 20% of the beginning book value per share for each of the next three years.
  • BCB will pay cash dividends equal to 40% of EPS.
  • At the end of three years, BCB’s common stock will trade at four times its book value.
  • Beta for BCB is 0.7, the risk-free rate is 4.5%, and the equity risk premium is 5.0%.

Q: The residual income per share in 2020 and the present value of continuing residual income as of the end of 2019 are closest to:

#2

Beginning book value per share in 2018 = 10.62

EPS in 2018 = 20% * 10.62 = 2.124

Dividend in 2018 = 40% * 2.124 = 0.8496

Ending book value per share in 2018 = Beginning book value per share in 2018 + EPS in 2018 - Dividend in 2018 = 10.62 + 2.124 - 0.8496 = 11.8944, which is essentially beginning book value per share in 2019. Beginning book value per shares for the rest of the periods can be calculated with the same approach.