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标题: Reading 56: An Introduction to Security Valuation LOSd习题精 [打印本页]

作者: honeycfa 时间: 2010-4-22 22:25 标题: [2010]Session 14-Reading 56: An Introduction to Security Valuation LOSd习题精

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.

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.

作者: honeycfa 时间: 2010-4-22 22:25

According to the earnings multiplier model, a stock’s P/E ratio (P₀/E₁) is affected by all of the following EXCEPT the:

A)

required return on equity.

B)

expected stock price in one year.

C)

expected dividend payout ratio.

According to the earnings multiplier model, the P/E ratio is equal to P₀/E₁ = (D₁/E₁)/(k_e- g).

Thus, the P/E ratio is determined by:

The expected dividend payout ratio (D₁/E₁).
The required rate of return on the stock (k_e).
The expected growth rate of dividends (g).

作者: honeycfa 时间: 2010-4-22 22:25

The earnings multiplier model, derived from the dividend discount model, expresses a stock’s P/E ratio (P₀/E₁) as the:

A)

expected dividend payout ratio divided by the difference between the required return on equity and the expected dividend growth rate.

B)

expected dividend payout ratio divided by the sum of the expected dividend growth rate and the required return on equity.

C)

expected dividend in one year divided by the difference between the required return on equity and the expected dividend growth rate.

Starting with the dividend discount model P₀ = D₁/(k_e- g), and dividing both sides by E₁ yields: P₀/E₁ = (D₁/E₁)/(k_e- g)

Thus, the P/E ratio is determined by:

The expected dividend payout ratio (D₁/E₁).
The required rate of return on the stock (k_e).
The expected growth rate of dividends (g).>

作者: honeycfa 时间: 2010-4-22 22:26

If the payout ratio increases, the P/E multiple will:

A)
decrease, if we assume that the growth rate remains constant.

B)

always increase.

C)
increase, if we assume that the growth rate remains constant.

When payout ratio increases, the P/E multiple increases only if we assume that the growth rate will not change as a result.

作者: honeycfa 时间: 2010-4-22 22:26

An analyst gathered the following information about an industry. The industry beta is 0.9. The industry profit margin is 8%, the total asset turnover ratio is 1.5, and the leverage multiplier is 2. The dividend payout ratio of the industry is 50%. The risk-free rate is 7% and the expected market return is 15%. The industry P/E is closest to:

A)
22.73.

B)
12.00.

C)
14.20.

Using the CAPM: k_i = 7% + 0.9(0.15 ? 0.07) = 14.2%.

Using the DuPont equation: ROE = 8% × 1.5 × 2 = 24%.

g = retention ratio × ROE = 0.50 × 24% = 12%.

P/E = 0.5/(0.142 ? 0.12) = 22.73.

作者: honeycfa 时间: 2010-4-22 22:26

A firm has an expected dividend payout ratio of 48 percent and an expected future growth rate of 8 percent. What should the firm's price to earnings ratio (P/E) be if the required rate of return on stocks of this type is 14 percent and what is the retention ratio of the firm?

P/E ratio Retention ratio

A)

6.5   52%

B)

8.0    52%

C)

6.5   48%

P/E = (dividend payout ratio)/(k - g)

P/E = 0.48/(0.14 - 0.08) = 8

The retention ratio = (1 - dividend payout) = (1 - 0.48) = 52%

作者: honeycfa 时间: 2010-4-22 22:26

A firm has an expected dividend payout ratio of 50%, a required rate of return of 12% and a constant growth rate of 6%. If earnings for the next year are expected to be $4.50, the value of the stock today is closest to:

A)

$39.75

B)

$37.50

C)

$33.50

Expected dividend = $4.50 × 0.50 = $2.25

Value today = $2.25 / (0.12 - 0.06) = $37.50

作者: honeycfa 时间: 2010-4-22 22:27

All of the following factors affects the firm’s P/E ratio EXCEPT:

A)
the required rate of return.

B)
growth rates of dividends.

C)
the expected interest rate on the bonds of the firm.

The factors that affect the P/E ratio are the same factors that affect the value of a firm in the infinite growth dividend discount model. The expected interest rate on the bonds is not a significant factor affecting the P/E ratio.

作者: honeycfa 时间: 2010-4-22 22:27

Assuming all other factors remain unchanged, which of the following would most likely lead to a decrease in the market P/E ratio?

A)
A decline in the risk-free rate.

B)
A rise in the stock risk premium.

C)
An increase in the dividend payout ratio.

P/E = (1 - RR)/(k - g)

To lower P/E: RR increases, g decreases and or k increases. Both a decline in the RF rate and a decline in the rate of inflation will reduce k. An increase in the stock's risk premium will increase k.

作者: honeycfa 时间: 2010-4-22 22:27

A stock has a required return of 14% percent, a constant growth rate of 5% and a retention rate of 60%. The firm’s P/E ratio should be:

A)
6.66.

B)
4.44.

C)
5.55.

P/E = (1 - RR) / (k - g) = 0.4 / (0.14 - 0.05) = 4.44

作者: honeycfa 时间: 2010-4-22 22:27

If the expected dividend payout ratio of a firm is expected to rise from 50 percent to 55 percent, the cost of equity is expected to increase from 10 percent to 11 percent, and the firm’s growth rate remains at 5 percent, what will happen to the firm’s price-to-equity (P/E) ratio? It will:

A)
decline.

B)
be unchanged.

C)
increase.

Payout increases from 50% to 55%, cost of equity increases from 10% to 11%, and dividend growth rate stays at 5%, the P/E will change from 10 to 9.16:

P/E = (D/E) / (k – g).

P/E₀ = 0.50 / (0.10 – 0.05) = 10.

P/E₁ = 0.55 / (0.11 – 0.05) = 9.16.

作者: honeycfa 时间: 2010-4-22 22:28

A)
decline.

B)
be unchanged.

C)
increase.

Payout increases from 50% to 55%, cost of equity increases from 10% to 11%, and dividend growth rate stays at 5%, the P/E will change from 10 to 9.16:

P/E = (D/E) / (k – g).

P/E₀ = 0.50 / (0.10 – 0.05) = 10.

P/E₁ = 0.55 / (0.11 – 0.05) = 9.16.

作者: honeycfa 时间: 2010-4-22 22:28

Which of the following is NOT a determinant of the expected price/earnings (P/E) ratio?

A)
Expected dividend payout ratio (D/E).

B)
Average debt to capital ratio (D/C).

C)
Expected growth rate in dividends (g).

The P/E ratio is determined by payout ratio D/E, required return K_e, and expected growth g.

作者: honeycfa 时间: 2010-4-22 22:28

According to the earnings multiplier model, which of the following factors is the least important in estimating a stock’s price-to-earnings ratio? The:

A)
estimated required rate of return on the stock.

B)
expected dividend payout ratio.

C)
historical dividend payout ratio.

P/E = (D₁/E₁)/(k - g)

where:
D₁/E₁= the expected dividend payout ratio
k = estimated required rate of return on the stock
g = expected growth rate of dividends for the stock

The P/E is most sensitive to movements in the denominator.

作者: honeycfa 时间: 2010-4-22 22:28

Use the following information to determine the value of River Gardens’ common stock:

Expected dividend payout ratio is 45%.
Expected dividend growth rate is 6.5%.
River Gardens’ required return is 12.4%.
Expected earnings per share next year are $3.25.

A)
$24.80.

B)
$30.12.

C)
$27.25.

First, estimate the price to earnings (P/E) ratio as: (0.45) / (0.124 – 0.065) = 7.63. Then, multiply the expected earnings by the estimated P/E ratio: ($3.25)(7.63) = $24.80.

作者: honeycfa 时间: 2010-4-22 22:29

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.

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

作者: honeycfa 时间: 2010-4-22 22:29

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.

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

作者: honeycfa 时间: 2010-4-22 22:29

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 inflation rate falls.

B)
The firm's ROE falls.

C)
The firm's dividend payout rises.

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.

作者: honeycfa 时间: 2010-4-22 22:30

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

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

作者: honeycfa 时间: 2010-4-22 22:30

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%.

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%.

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

A)
17.48%.

B)
10.73%.

C)
19.50%.

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

= 6.75 + 1.30 (15.00 ? 6.75) = 17.48

What is the price-earnings ratio for this firm?

A)
18.14X.

B)
22.18X.

C)
5.13X.

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.

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.

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

作者: honeycfa 时间: 2010-4-22 22:31

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.

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.

作者: honeycfa 时间: 2010-4-22 22:31

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.

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.

作者: honeycfa 时间: 2010-4-22 22:31

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.

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.

作者: honeycfa 时间: 2010-4-22 22:31

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.

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.

作者: honeycfa 时间: 2010-4-22 22:32

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.

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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