Reading 56: An Introduction to Security Valuation LOSd习题精 return, factors, develop, required, div

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LOS d: Show how to use the DDM to develop an earnings multiplier model and explain the factors in the DDM that affect a stock's price-to-earnings (P/E) ratio.

According to the earnings multiplier model, all else equal, as the required rate of return on a stock increases, the:

A) P/E ratio will decrease.

B) P/E ratio will increase.

C) earnings per share will increase.

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According to the earnings multiplier model, the P/E ratio is equal to P₀/E₁ = (D₁/E₁)/(k_e - g). As k_e increases, P₀/E₁ will decrease, all else equal.

 

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According to the earnings multiplier model, all else equal, as the dividend payout ratio on a stock increases, the:

A) P/E ratio will decrease.

B) required return on the stock will decrease.

C) P/E ratio will increase.

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According to the earnings multiplier model, the P/E ratio is equal to P₀/E₁ = (D₁/E₁)/(k_e - g). As D₁/E₁ increases, P₀/E₁ will increase, all else equal.

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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) either increase or decrease.

B) increase.

C) decrease.

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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.

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All else equal, if a firm’s return on equity (ROE) increases, the stock’s value as estimated by the constant growth dividend discount model (DDM) will most likely:

A) increase.

B) not change.

C) decrease.

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

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Assume a company's ROE is 14% and the required return on equity is 13%. All else remaining equal, if there is a decrease in a firm’s retention rate, a stock’s value as estimated by the constant growth dividend discount model (DDM) will most likely:

A) decrease.

B) increase.

C) either increase or decrease.

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Increase in dividend payout/reduction in earnings retention. In this case, reduction 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.

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All else equal, an increase in a company’s growth rate will most likely cause its P/E ratio to:

A) increase.

B) decrease.

C) either increase or decrease.

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Increase in g: As g increases, the spread between k_e and g, or the P/E denominator, will decrease, and the P/E ratio will increase.

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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

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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

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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) 15.00%.

B) Tax rate needed to determine answer.

C) 6.75%.

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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%.

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

A) 17.48%.

B) 10.73%.

C) 19.50%.

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

= 6.75 + 1.30 (15.00 ? 6.75) = 17.48

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What is the price-earnings ratio for this firm?

A) 18.14X.

B) 22.18X.

C) 5.13X.

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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.

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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) $12.43.

B) $29.14.

C) $41.18.

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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

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An analyst gathered the following data:

• An earnings retention rate of 40%.
• An ROE of 12%.
• The stock's beta is 1.2.
• The nominal risk free rate is 6%.
• The expected market return is 11%.

Assuming next year's earnings will be $4 per share, the stock’s current value is closest to:

A) $26.67.

B) $45.45.

C) $33.32.

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Dividend payout = 1 ? earnings retention rate = 1 ? 0.4 = 0.6

R_S = R_f + β(R_M ? R_f) = 0.06 + 1.2(0.11 ? 0.06) = 0.12

g = (retention rate)(ROE) = (0.4)(0.12) = 0.048

D₁ = E₁ × payout ratio = $4.00 × 0.60 = $2.40

Price = D₁ / (k – g) = $2.40 / (0.12 – 0.048) = $33.32

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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.

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