honeycfa

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.

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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.

honeycfa

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.

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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.

honeycfa

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).

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

honeycfa

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.

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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.

honeycfa

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.

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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.

honeycfa

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

honeycfa

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.

honeycfa

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 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.

honeycfa

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

honeycfa

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