Reading 43: Residual Income Valuation-LOS c 习题精选 future, center, current, 2010, class

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Session 12: Equity Investments: Valuation Models
Reading 43: Residual Income Valuation

LOS c: Calculate future values of residual income given current book value, earnings growth estimates, and an assumed dividend payout ratio.

 

 

 

Expert Systems (ES) has a beginning book value per share of $6.00, an expected growth rate of 15 percent, current earnings per share of $1.50, and a required rate of return of 17 percent. Assuming that the dividend remains constant at $0.75 per share, what is next year’s expected residual income per share?

A) $0.50.

B) $1.73.

C) $0.58.

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EPS next year = 1.50 × 1.15 = $1.73. Forecast book value per share = BV₀ + EPS – D = 6.00 + 1.50 – 0.75 = $6.75. The per share equity charge is 6.75 × 0.17 = $1.15. Thus, residual income is expected to be 1.73 – 1.15 = $0.58.

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Legend Software Corp. has a current book value per share of $6.00 and expected residual income over the next three years of $0.55, $0.72, and $3.08, respectively. Given a required rate of return on equity of 12%, what is the value of the stock using the residual income model?

A) $3.26.

B) $9.26.

C) $10.35.

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V₀ = 6.00 + [0.55 / 1.12] + [0.72 / (1.12)²] + [3.08 / (1.12)³] = $9.26

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In the residual income approach, value tends to be recognized:

A) later than in other present value-based approaches.

B) earlier than in other present value-based approaches.

C) almost exclusively due to estimated terminal value.

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Value tends to be recognized earlier in the residual income approach than in other present value-based approaches. For instance, a large portion of the total present value of a stock estimated using either forecasted dividends or free cash flows comes from the expected terminal value. Yet, uncertainty about this forecast is usually the greatest of any of the predicted cash flows. Conversely, residual income valuation models usually are less sensitive to terminal value estimates.

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In the residual income approach:

A) uncertainty concerning the estimated terminal value is low.

B) value is recognized earlier than in other present value-based approaches.

C) value is predominately derived from expected terminal value.

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Value tends to be recognized earlier in the residual income approach than in other present value-based approaches. For instance, a large portion of the total present value of a stock estimated using either forecasted dividends or free cash flows comes from the expected terminal value. Yet, uncertainty about this forecast is usually the greatest of any of the predicted cash flows. Conversely, residual income valuation models usually are less sensitive to terminal value estimates.

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Diamond Corp. (DC) has a beginning book value per share of $5.00, an expected growth rate of 15 percent, current earnings per share of $1.20, and a required rate of return of 17 percent. Assuming that the dividend remains constant at $0.55 per share, what is next year’s expected residual income per share?

A) $1.38.

B) $0.50.

C) $0.42.

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EPS next year = 1.20 × 1.15 = $1.38
Forecast book value per share = BV₀ + EPS – D = 5.00 + 1.20 – 0.55 = $5.65
The per share equity charge is 5.65 × 0.17 = $0.961
Thus, residual income is expected to be 1.38 – 0.961 = $0.42

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Expert Systems has a beginning book value per share of $7.00, an expected growth rate of 15%, this year's forecasted earnings per share of $1.25, and a required rate of return of 17. Assuming that the dividend remains constant at $0.75 per share, what is next year’s expected residual income per share?

A) $0.13.

B) $1.44.

C) $0.16.

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EPS next year = 1.25 × 1.15 = $1.44. Forecast book value per share = BV₀ + EPS – D = 7.00 + 1.25 – 0.75 = $7.5. The per share equity charge is 7.5 × 0.17 = $1.28. Thus, residual income is expected to be 1.44 – 1.28 = $0.16.

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Crystal Offerings has a current book value per share (BVPS) of $6.00 and expected residual income over the next three years of $0.45, $0.65, and $4.12, respectively. Given a required rate of return on equity of 12%, what is the value of the stock using the residual income model?

A) $9.85.

B) $11.22.

C) $3.26.

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V₀ = 6.00 + (0.45 / 1.12) + (0.65 / 1.12²) + (4.12 / 1.12³) = $9.85

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Crystal Offerings has a current book value per share of $9.00 and expected residual income over the next three years of $0.55, $0.72, and $3.08, respectively. Given a required rate of return on equity of 12%, what is the value of the stock using the residual income model?

A) $9.26.

B) $12.26.

C) $3.26.

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V₀ = 9.00 + [0.55 / 1.12] + [0.72 / (1.12)²] + [3.08 / (1.12)³] = $12.26