Reading 49: Residual Income Valuation - LOS m ～ Q1-3

答案和详解如下：

1．Brown Manufacturing is expected to have a return on equity (ROE) of 15 percent for the next five years and 10 percent thereafter, indefinitely. Its current book value per share as of the beginning of year 1 (i.e., the end of year 0) is $9.50 per share and its required rate of return is 10 percent. The premium over book value at the end of five years is expected to be 40 percent. All earnings are reinvested. The sum of the present values of the residual income estimates over the next five years is $3.10. The projected ending book value in year 5 is $25.00. What is the value of Brown Manufacturing using these inputs?

A)   $13.83.

B)   $10.00.

C)   $12.60.

D)   $18.81.

The correct answer was D)

Applying the finite horizon residual income valuation model:

V₀ = B₀ + sum of discounted RIs + discounted premium

     = 9.50 + 3.10 + [(0.40)(25.00)/(1.10)⁵] = $18.81

2．Valdez Plastics is expected to have a return on equity (ROE) of 15 percent for the next five years and 10 percent thereafter, indefinitely. Its current book value per share as of the beginning of year 1 (i.e., the end of year 0) is $8.50 per share and its required rate of return is 10 percent. The premium over book value at the end of five years is expected to be 40 percent. All earnings are reinvested. The sum of the present values of the residual income estimates over the next five years is $2.10. The projected ending book value in year 5 is $17.80. What is the value of Valdez Plastics using these inputs?

A)   $13.83.

B)   $4.15.

C)   $10.60.

D)   $15.02.

The correct answer was D)

Applying the finite horizon residual income valuation model:

V₀ = B₀ + sum of discounted RIs + discounted premium

     = 8.50 + 2.10 + [(0.40)(17.80)/(1.10)⁵] = $15.02

3．Creative Gardening is expected to have a return on equity (ROE) of 13 percent for the next five years and 10 percent thereafter, indefinitely. Its current book value per share as of the beginning of year 1 (i.e., the end of year 0) is $7.50 per share and its required rate of return is 10 percent. The premium over book value at the end of five years is expected to be 30 percent. All earnings are reinvested. The sum of the present values of the residual income estimates over the next five years is $1.10. The projected ending book value in year 5 is $13.83. What is the value of Creative Gardening using these inputs?

A)   $11.18.

B)   $13.83.

C)   $4.15.

D)   $8.60.

The correct answer was A)

Applying the finite horizon residual income valuation model:

V₀ = B₀ + sum of discounted RIs + discounted premium

     = 7.50 + 1.10 + [(0.30)(13.83)/(1.10)⁵] = $11.18