LOS f: Calculate and interpret the intrinsic value of a share of common stock using a single-stage (constant-growth) residual income model.

Q1. 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.

Q2. 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.

Q3. 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)   $23.23.

B)   $11.28.

C)   $8.10.

LOS f: Calculate and interpret the intrinsic value of a share of common stock using a single-stage (constant-growth) residual income model. fficeffice" />

Q1. 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.

Correct answer is B)

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%

Q2. 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.

Correct answer is B)

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

Q3. 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)   $23.23.

B)   $11.28.

C)   $8.10.

Correct answer is B)

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 %