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?
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Applying the finite horizon residual income valuation model:
= 7.50 + 1.10 + [(0.30)(13.83)/(1.10)5] = $11.18V0 = B0 + sum of discounted RIs + discounted premium
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:
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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
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:
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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
If a multistage residual income model does not consider a persistence factor, the analyst using the model is most likely assuming that residual income:
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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.
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:
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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 Here is a table containing the relevant values.
Equity charge = prior year book value × required ROE
Residual income = earnings ? equity charge
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.
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