Q17. Assume that a firm has an expected dividend payout ratio of 20%, a required rate of return of 9%, and an expected dividend growth of 5%. What is the firm's estimated price-to-earnings (P/E) ratio?

A)   2.22.

B)   20.00.

C)   5.00.

Q18. Assuming that a company's return on equity (ROE) is 12% and the required rate of return is 10%, which of the following would most likely cause the company's P/E ratio to rise?

A)   The firm's ROE falls.

B)   The inflation rate falls.

C)   The firm's dividend payout rises.

Q19. If a company has a "0" earnings retention rate, the firm's P/E ratio will equal:

A)   k + g

B)   1 / k

C)   D/P + g

Q20. An analyst gathered the following information for a company:

• Risk-free rate = 6.75%
• Expected market return = 15.00%
• Beta = 1.30
• Dividend payout ratio = 55%
• Profit margin = 10.0%
• Total asset turnover = 0.75
• Assets to equity ratio = 2.00

What is the firm’s sustainable growth rate?

A)   6.75%

B)   15.00%.

C)   Tax rate needed to determine answer.

Q21. What is the capital asset pricing model (CAPM) required rate of return for this stock?

A)   10.73%.

B)   19.50%.

C)   17.48%.

Q22. What is the price-earnings ratio for this firm?

A)   18.14X.

B)   5.13X.

C)   22.18X.

Q23. Assuming that the most recent year’s earnings are $2.27, what is the estimated value of the stock using the earnings multiplier method of valuation?

A)   $29.14.

B)   $41.18.

C)   $12.43.

Q24. A company currently has a required return on equity of 14% and an ROE of 12%. All else equal, if there is an increase in a firm’s dividend payout ratio, the stock's value will most likely:

A)   increase.

B)   either increase or decrease.

C)   decrease.

Q17. Assume that a firm has an expected dividend payout ratio of 20%, a required rate of return of 9%, and an expected dividend growth of 5%. What is the firm's estimated price-to-earnings (P/E) ratio? fficeffice" />

A)   2.22.

B)   20.00.

C)   5.00.

Correct answer is C)

The price-to-earnings (P/E) ratio is equal to (D₁/E₁)/(k – g) = 0.2/(.09 – 0.05) = 5.00.

Q18. Assuming that a company's return on equity (ROE) is 12% and the required rate of return is 10%, which of the following would most likely cause the company's P/E ratio to rise?

A)   The firm's ROE falls.

B)   The inflation rate falls.

C)   The firm's dividend payout rises.

Correct answer is B)

§   Decrease in the expected inflation rate. The expected inflation rate is a component of k_e (through the nominal risk free rate). k_e can be represented by the following: nominal risk free rate + stock risk premium, where nominal risk free rate = [(1 + real risk free rate)(1 + expected inflation rate)] – 1.

§   If the rate of inflation decreases, the nominal risk free rate will decrease.

§   k_e will decrease.

§   The spread between k_e and g, or the P/E denominator, will decrease.

§   P/E ratio will increase.

(An increase in the stock risk premium would have the opposite effect.)

§   Decrease in ROE: ROE is a component of g. As g decreases, the spread between k_e and g, or the P/E denominator, will increase, and the P/E ratio will decrease.

§   Increase in dividend payout/reduction in earnings retention. In this case, an increase in the dividend payout will likely decrease the P/E ratio because a decrease in earnings retention will likely lower the P/E ratio. The logic is as follows: Because earnings retention impacts both the numerator (dividend payout) and denominator (g) of the P/E ratio, the impact of a change in earnings retention depends upon the relationship of k_e and ROE. If the company is earning a higher rate on new projects than the rate required by the market (ROE> k_e), investors will likely prefer that the company retain more earnings. Since an increase in the dividend payout would decrease earnings retention, the P/E ratio would fall, as investors will value the company lower if it retains a lower percentage of earnings.

Q19. If a company has a "0" earnings retention rate, the firm's P/E ratio will equal:

A)   k + g

B)   1 / k

C)   D/P + g

Correct answer is B)

P/E = div payout ratio / (k ? g)

where g = (retention rate)(ROE) = (0)(ROE) = 0

Dividend payout = 1 ? retention ratio = 1 ? 0 = 1

P/E = 1 / (k ? 0) = 1 / k

Q20. An analyst gathered the following information for a company:

• Risk-free rate = 6.75%
• Expected market return = 15.00%
• Beta = 1.30
• Dividend payout ratio = 55%
• Profit margin = 10.0%
• Total asset turnover = 0.75
• Assets to equity ratio = 2.00

What is the firm’s sustainable growth rate?

A)   6.75%

B)   15.00%.

C)   Tax rate needed to determine answer.

Correct answer is A)        

Sustainable Growth (g) = ROE × Earnings Retention Rate, or ROE × (1 ? Dividend Payout)

ROE = Profit Margin × Total Asset Turnover × Financial Leverage Multiplier = 0.10 × 0.75 × 2 = 0.15

g = 0.15 × 0.45 = 0.0675, or 6.75%.

Q21. What is the capital asset pricing model (CAPM) required rate of return for this stock?

A)   10.73%.

B)   19.50%.

C)   17.48%.

Correct answer is C)

CAPM Reg. Return = Risk-free Rate + Beta (Market Ret. ? Risk-Free Ret.)

= 6.75 + 1.30 (15.00 ? 6.75) = 17.48

Q22. What is the price-earnings ratio for this firm?

A)   18.14X.

B)   5.13X.

C)   22.18X.

Correct answer is B)

Price / Earnings ratio = (Dividend Payout Ratio) / (k ? g), where k is based on the CAPM required return = 0.55 / (0.1748 ? 0.0675) = 5.13.

Q23. Assuming that the most recent year’s earnings are $2.27, what is the estimated value of the stock using the earnings multiplier method of valuation?

A)   $29.14.

B)   $41.18.

C)   $12.43.

Correct answer is C)

Using the components calculated in prior questions:

P = (Next year's earnings E₁) × (P/E ratio)

Next year's earnings = E₁ = E₀ × (1 + g) = (2.27) × (1.0675) = 2.4232

P = (2.4232)(5.13) = $12.43

Q24. A company currently has a required return on equity of 14% and an ROE of 12%. All else equal, if there is an increase in a firm’s dividend payout ratio, the stock's value will most likely:

A)   increase.

B)   either increase or decrease.

C)   decrease.

Correct answer is A)        

Increase in dividend payout/reduction in earnings retention.In this case, an increase in the dividend payout will likely increase the P/E ratio because a decrease in earnings retention will likely increase the P/E ratio. The logic is as follows: Because earnings retention impacts both the numerator (dividend payout) and denominator (g) of the P/E ratio, the impact of a change in earnings retention depends upon the relationship of k_e and ROE. If the company is earning a lower rate on new projects than the rate required by the market (ROE < k_e), investors will likely prefer that the company pay out earnings rather than investing in lower-yield projects. Since an increase in the dividend payout would decrease earnings retention, the P/E ratio would rise, as investors will value the company higher if it retains a lower percentage of earnings.