Reading 60: Equity Valuation: Concepts and Basic Tools-LOS h 2011, center, interpret, following, determine

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Session 14: Equity Analysis and Valuation
Reading 60: Equity Valuation: Concepts and Basic Tools

LOS h: Calculate and interpret the following multiples: price to earnings, price to an estimate of operating cash flow, price to sales, and price to book value.

 

 

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) $30.12.

B) $24.80.

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.

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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 firm's dividend payout rises.

C) The inflation rate falls.

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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.

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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) 12.00.

B) 22.73.

C) 14.20.

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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.

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

A) k + g

B) D/P + g

C) 1 / k

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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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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 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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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) decrease.

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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Assume that the expected dividend growth rate (g) for a firm decreased from 5% to zero. Further, assume that the firm's cost of equity (k) and dividend payout ratio will maintain their historic levels. The firm's P/E ratio will most likely:

A) decrease.

B) become undefined.

C) increase.

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The P/E ratio may be defined as: Payout ratio / (k - g), so if k is constant and g goes to zero, the P/E will decrease.

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

A) required return on equity.

B) expected dividend payout ratio.

C) expected stock price in one year.

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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).