Reading 45: Residual Income Valuation-LOS c 习题精选 common, center, present, contrast, 2011

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Session 12: Equity Investments: Valuation Models
Reading 45: Residual Income Valuation

LOS c: Calculate the intrinsic value of a common stock using the residual income model, and contrast the recognition of value in the residual income model to value recognition in other present value models.

 

 

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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Red Shoes’s recent financial statements reported a book value of $11.00 per share; its required rate of return is 9%. Analyst Tony Giancola, CFA, wants to calculate the company’s intrinsic value using a multistage residual income with a high-growth RI for the next 5 years. Giancola creates the following estimates:

PV of interim high-growth RI for the next 5 years is $ 2.90

PV of continuing RI at the end of year 5 is $7.00

Estimated Book Value in 5 years is $14.00
Which of the following is closest to the current intrinsic value of Red Shoes?

A) $18.45.

B) $20.90.

C) $9.90.

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Applying the multistage residual income model:

V₀ = B₀ + PV of interim high-growth RI + PV of continuing RI

= 11.00 + 2.90 + [(7.00) / (1.09)⁵] = $18.45

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Brown Manufacturing’s recent financial statements reported a book value of $9.50 per share; its required rate of return is 10%. Analyst Tony Giancola, CFA, wants to calculate the company’s intrinsic value using a multistage residual income with a high-growth RI for the next 5 years. Giancola creates the following estimates:

PV of interim high-growth RI for the next 5 years is $3.10

At the end of year 5, the PV of continuing RI is $10.00

Estimated Book Value in 5 years is $25.00
Which of the following is closest to the current intrinsic value of Brown Manufacturing?

A) $22.60.

B) $18.81.

C) $13.10.

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Applying the multistage residual income model:

V₀ = B₀ + PV of interim high-growth RI + PV of continuing RI

= 9.50 + 3.10 + [(10.00) / (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 an industry norm.

B) falls to zero over time.

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% in each of the next five years. The required ROE is 8.7%. Current book value is $12.40 per share and the firm pays no dividends. Krieger previously assumed 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) $0.32 per share.

C) $0.64 per share.

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

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

Here is a table containing the relevant values.

Year	Earnings (ROE = 13.60%)	Book Value	Equity Charge (Required ROE = 8.70%)	Residual Income	PV of Residual Income
0		$12.40
1	$1.69	$14.09	$1.08	$0.61	$0.56
2	$1.92	$16.00	$1.23	$0.69	$0.58
3	$2.18	$18.18	$1.39	$0.78	$0.61
4	$2.47	$20.65	$1.58	$0.89	$0.64
5	$2.81	$23.46	$1.80	$1.01	$0.67

Company value = $12.40 + the sum of the residual incomes

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. Instead of discounting the Year 5 residual income by 1 + required ROE, we discount it by 1 + required ROE ? persistence factor. The new values are as follows:

	Book Value	Year 1	Year 2	Year 3	Year 4/5
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.