hariRaj

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) $0.32 per share.

B) $0.16 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.

hariRaj

Assuming that the growth rate is less than the required rate of return (r), an increase in return on equity (ROE) will cause value in a residual income (RI) model to:

A) there is insufficient information to derive the effects of increasing ROE on RI.

B) decrease if ROE is greater than the required rate of return.

C) increase if ROE is greater than the required rate of return.

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An increase (decrease) in ROE increases (decreases) value if the ROE exceeds the required rate of return. This is revealed by the RI valuation expression

hariRaj

Professor Cliff Webley made the following statements in his asset-valuation class:
Statement 1: “Over time, a company’s residual income growth tends to approach the industry average.”
Statement 2: “If actual return on equity equals required return on equity, the residual income model sets the company’s proper market value equal to its book value.”
Statement 3: “The single-stage residual income model should give you the same valuation as the Gordon Growth model.”
Which of Webley’s statements is least accurate?

A) Statement 2.

B) Statement 3.

C) Statement 1.

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Over time, a company’s residual income growth tends to approach zero. It is unlikely that an industry’s average growth rate is zero, so Statement 1 is questionable. The other two statements are accurate.

hariRaj

The single-stage residual income model values a company at:

A) book value plus the present value of the firm’s expected economic profits.

B) book value times a factor determined by the discount rate.

C) book value plus the terminal value discounted at the weighted average cost of capital.

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The single-stage residual income model values a company at book value plus the present value of the firm’s economic profits, or the additional value generated by the firm’s ability to produce returns higher than the cost of equity.

hariRaj

In a single-stage residual income model for a firm with return on equity (ROE) greater than the required rate of return, which statement is least accurate?

A) Market value will be greater than book value.

B) The justified price-to-book value (P/B) ratio will be greater than one.

C) Free cash flow to equity will be positive.

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In a single-stage residual income model with ROE greater than the required rate of return, justified P/B will be greater than one and market value will be greater than book. There is no clear relationship with free cash flow to equity.

hariRaj

In a single-stage residual income model for a firm with return on equity (ROE) greater than the required rate of return, which statement is least accurate?

A) Market value will be greater than book value.

B) The justified price-to-book value (P/B) ratio will be greater than one.

C) Free cash flow to equity will be positive.

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In a single-stage residual income model with ROE greater than the required rate of return, justified P/B will be greater than one and market value will be greater than book. There is no clear relationship with free cash flow to equity.

hariRaj

Assuming that the growth rate is less than the required rate of return (r), a decrease in initial book value will cause value in a residual income (RI) model to:

A) decrease.

B) increase.

C) there is insufficient information to determine the effect on RI.

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A decrease (increase) in initial book value decreases (increases) value. This is revealed by the RI valuation expression:

V0 = B0 + [(ROE – r) / (r – g)]B0

hariRaj

Advanced Instruments reported the following for the end of its fiscal year:

• Revenues = $50.3 million.
• Assets = $33.8 million.
• Liabilities = $13.8 million.
• Earnings per share = $0.68.
• Dividends per share = $0.17.
• Shares outstanding = 5 million.
• Tax rate = 40%.

If the required rate of return is 15%, what is the value of the shares using a single-stage residual income model?

A) $12.77.

B) $7.56.

C) $4.78.

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Retention ratio = (0.68 – 0.17) / 0.68 = 0.75 or 75%
Equity = Assets – liabilities = $33.8 million − $13.8 million = $20 million
Book value per share = Total equity / shares outstanding = $20 million / 5 million = $4.00
ROE = $0.68 / $4.00 = 0.17 or 17%
g = retention ratio × ROE = (0.75) × 0.17 = 0.1275 or 12.75%

hariRaj

Midland Semiconductor has a book value of $10.50 per share. The company’s return on equity is 20%, and its required return on equity is 17%. The dividend payout ratio is 30%. What is the value of the shares using a single-stage residual income model?

A) $10.50.

B) $21.00.

C) $31.50.

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g = retention ratio × ROE = (1 − 0.30) × 0.20 = 0.14 or 14%

hariRaj

Big Sky Ranches reported the following for the end of its fiscal year:

• Revenues = $40.8 million.
• Pretax income = $8.6 million.
• Assets = $53.2 million.
• Liabilities = $27.8 million.
• Dividends per share = $0.35.
• Shares outstanding = 8 million.
• Tax rate = 35%.

The beta for Big Sky Ranches is 1.2, the current risk-free rate is 4.5%, and the expected return on the market is 12.5%.  What is the value of the shares using a single-stage residual income model?

A) $11.28.

B) $23.23.

C) $8.10.

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After tax earnings = Pretax earnings × (1 − T) = 8.6 million × (1 − 0.35) = $5.59 million
EPS = After tax earnings/shares outstanding = $5.59 million / 8 million = $0.70
Retention ratio = (0.70 − 0.35) / 0.70 = 0.50 or 50%
Equity = Assets − liabilities = $53.2 million − $27.8 million = $25.4 million
Book value per share = Total equity/shares outstanding = $25.4 million / 8 million = $3.18
ROE = $0.70 / $3.18 = 0.22 or 22%
g = retention ratio × ROE = (0.50) × 0.22 = 0.11 or 11.00%
Expected return = 0.045 + [0.125 − 0.045]1.2 = 0.1410 or 14.10 %