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

honeycfa

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.

 

honeycfa

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).

honeycfa

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).>

>

honeycfa

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.

honeycfa

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.

honeycfa

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%

honeycfa

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

honeycfa

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.

honeycfa

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.

honeycfa

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