Kingpin804

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) $33.32.

C) $45.45.

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Dividend payout = 1 − earnings retention rate = 1 − 0.4 = 0.6
RS = Rf + β(RM − Rf) = 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

Kingpin804

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) 5.00.

B) 2.22.

C) 20.00.

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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.

Kingpin804

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.

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• 
  Decrease in the expected inflation rate. The expected inflation rate is a component of ke (through the nominal risk free rate). ke 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.
  • ke will decrease.
  • The spread between ke 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 ke 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 ke and ROE. If the company is earning a higher rate on new projects than the rate required by the market (ROE> ke), 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.

Kingpin804

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

Kingpin804

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) decrease.

C) increase.

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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 ke and ROE. If the company is earning a lower rate on new projects than the rate required by the market (ROE < ke), 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.

Kingpin804

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) not change.

B) decrease.

C) increase.

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

Kingpin804

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) increase.

B) either increase or decrease.

C) 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 ke and ROE. If the company is earning a higher rate on new projects than the rate required by the market (ROE > ke), 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.

Kingpin804

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

A) decrease.

B) either increase or decrease.

C) increase.

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

Kingpin804

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)/(ke - g). As D1/E1 increases, P0/E1 will increase, all else equal.

Kingpin804

All else equal, the price-to-earnings (P/E) ratio of a stable firm will increase if the:

A) dividend payout is decreased.

B) ROE is increased.

C) long-term growth rate is decreased.

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The increase in growth rate will increase the P/E ratio of a stable firm and growth rate can be calculated by the formula g = ROE × retention ratio. All else being equal an increase in ROE will therefore increase the P/E ratio. Note that decreasing the dividend payout ratio and decreasing the long term growth rate will both serve to decrease the P/E ratio.