Reading 43: Residual Income Valuation-LOS j 习题精选 class, 2010, return, required, interpret

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

LOS j: Calculate and interpret the intrinsic value of a common stock using a multistage residual income model, given the required rate of return, forecasted earnings per share over a finite horizon, and forecasted continuing residual earnings.

 

 

 

Creative Gardening is expected to have a return on equity (ROE) of 13% for the next five years and 10% 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%. The premium over book value at the end of five years is expected to be 30%. 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) $8.60.

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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

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Valdez Plastics is expected to have a return on equity (ROE) of 15% for the next five years and 10% 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%. 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) $15.02.

B) $10.60.

C) $13.83.

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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

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Brown Manufacturing is expected to have a return on equity (ROE) of 15% for the next five years and 10% 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%. The premium over book value at the end of five years is expected to be 40%. 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) $18.81.

B) $12.60.

C) $13.83.

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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

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If a multistage residual income model does not consider a persistence factor, the analyst using the model is most likely assuming that residual income:

A) falls to zero over time.

B) falls to an industry norm.

C) falls to zero immediately.

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The assumption that residual income declines to a long-run level in a mature industry allows for the use of a simpler formula that does not require a persistence factor. Both of the other assumptions listed require an equation that uses the persistence factor.

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Krieger String & Twine expects to generate a return on equity (ROE) of 13.6% over the next five years. The required ROE is 8.7%. Current book value is $12.40 per share. Krieger is expected to earn $1.95 per share next year, and both book value and equity are expected to rise at the rate of ROE every year for the next five years. Krieger currently assumes residual income falls to zero immediately after five years, but has now decided to recalculate its estimated value using a persistence factor of 35%. The difference between the new valuation and the old one is closest to:

A) $0.16 per share.

B) $0.64 per share.

C) $0.32 per share.

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To answer this question, we need to establish the residual values using the following equations:

Equity charge = prior year book value × required ROE
Residual income = earnings ? equity charge

Here is a table containing the relevant values.

Year	Earnings	Book value	ROE	Equity charge	Residual income	Required ROE
0		$12.40	13.60%			8.70%
1	$1.69	$14.09	13.60%	$1.08	$0.61	8.70%
2	$1.92	$16.00	13.60%	$1.23	$0.69	8.70%
3	$2.18	$18.18	13.60%	$1.39	$0.78	8.70%
4	$2.47	$20.65	13.60%	$1.58	$0.89	8.70%
5	$2.81	$23.46	13.60%	$1.80	$1.01	8.70%

 

 

 

 

 

To value the company, we start with current book value, then discount the residual value at the required ROE for the next three years. At year four, we add the year-four residual income ($0.89) and the terminal value, which is Year 5 residual income / (1 + required ROE). That sum is then discounted at the required ROE. Here are the relevant values.

Book Value	Year 1	Year 2	Year 3	Year 4
$12.40	$0.56	$0.58	$0.61	$1.31

Assuming residual value drops to zero after year five, the company is valued at $15.46 per share.

Now, we modify the model to reflect the persistence factor of 35%. The only value that persistence factor effects is the terminal value, which is included in the discounted residual income from Year 4. Instead of discounting the Year 5 residual income by 1 + required ROE, we discount it by 1 + required ROE ? persistence factor. That changes the values as follows:

	Book Value	Year 1	Year 2	Year 3	Year 4
Value	$12.40	$0.56	$0.58	$0.61	$1.62

For a total value of $15.78 per share, or $0.32 higher than the original value.