hariRaj

An analyst is considering the purchase of Rylinks, Inc., which has a price to book value (P/B) ratio of 6.00. Return on equity (ROE) is expected to be 13%, current book value per share is $13.00, and the cost of equity is 11%. What growth rate is implied by the current P/B rate?

A) 0.40%.

B) 10.60%.

C) 11.00%.

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The P/B ratio of 6.00 and the current book value per share of $13.00 imply a current market price of $78.00. This implies a growth rate of:
g = r – [{B0(ROE – r)} / {V0 – B0}] = 0.11 – [{13.00(0.13 – 0.11)} / {78.00 – 13.00}] = 0.1060 = 10.60%.
Note that the reading in the curriculum does not provide this expression directly

hariRaj

An investor is considering the purchase of Robust Econometrics, Inc., which has a price-to-book (P/B) value ratio of 4.50. Return on equity (ROE) is expected to be 14%, the current book value per share (BVPS) is Sf22.50, and the cost of equity is 12%. The growth rate implied by the current P/B ratio is closest to:

A) 11.43%.

B) 12.57%.

C) 8.00%.

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The P/B ratio of 4.50 and the current BVPS of Sf22.50 imply a market price of Sf101.25(4.5 × 22.5). This implies a growth rate of:

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 %

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

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

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

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

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

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.