kim226

Assuming the risk-free rate is 5% and the expected return on the market is 12%, what is the value of a stock with a beta of 1.5 that paid a $2 dividend last year if dividends are expected to grow at a 5% rate forever?

A) $20.00.

B) $12.50.

C) $17.50.

---

P0 = D1 / (k − g)
Rs = Rf + β(RM − Rf) = 0.05 + 1.5(0.12 − 0.05) = 0.155
D1 = D0(1 + g) = 2 × (1.05) = 2.10
P0 = 2.10 / (0.155 − 0.05) = $20.00

kim226

If a stock sells for $50 that has an expected annual dividend of $2 and has a sustainable growth rate of 5%, what is the market discount rate for this stock?

A) 7.5%.

B) 10.0%.

C) 9.0%.

---

k = [(D1 / P) + g] = [(2/50) + 0.05] = 0.09, or 9.00%.

kim226

All else equal, if there is an increase in the required rate of return, a stock’s value as estimated by the constant growth dividend discount model (DDM) will:

A) increase or decrease, depending upon the relationship between ke and ROE.

B) decrease.

C) increase.

---

If ke increases, the spread between ke and g widens (increasing the denominator), resulting in a lower valuation.

karoliukas

An analyst has gathered the following data for Webco, Inc:

• Retention = 40%
• ROE = 25%
• k = 14%

Using the infinite period, or constant growth, dividend discount model, calculate the price of Webco’s stock assuming that next years earnings will be $4.25.

A) $63.75.

B) $55.00.

C) $125.00.

---

g = (ROE)(RR) = (0.25)(0.4) = 10%
V = D1 / (k – g)
D1 = 4.25 (1 − 0.4) = 2.55
G = 0.10
K – g = 0.14 − 0.10 = 0.04
V = 2.55 / 0.04 = 63.75

karoliukas

Which of the following statements about the constant growth dividend discount model (DDM) is least accurate?

A) For the constant growth DDM to work, the growth rate must exceed the required return on equity.

B) The constant growth DDM is used primarily for stable mature stocks.

C) In the constant growth DDM dividends are assumed to grow at a constant rate forever.

---

Dividends grow at constant rate forever.
Constant growth DDM is used for mature firms.
k must be greater than g.

karoliukas

Which of the following statements about the constant growth dividend discount model (DDM) is least accurate?

A) For the constant growth DDM to work, the growth rate must exceed the required return on equity.

B) The constant growth DDM is used primarily for stable mature stocks.

C) In the constant growth DDM dividends are assumed to grow at a constant rate forever.

---

Dividends grow at constant rate forever.
Constant growth DDM is used for mature firms.
k must be greater than g.

karoliukas

A stock is expected to pay a dividend of $1.50 at the end of each of the next three years. At the end of three years the stock price is expected to be $25. The equity discount rate is 16 percent. What is the current stock price?

A) $19.39.

B) $24.92.

C) $17.18.

---

The value of the stock today is the present value of the dividends and the expected stock price, discounted at the equity discount rate:
$1.50/1.16 + $1.50/1.162 + $1.50/1.163 + $25.00/1.163 = $19.39

karoliukas

Use the following information on Brown Partners, Inc. to compute the current stock price.

• 
  Dividend just paid = $6.10
• 
  Expected dividend growth rate = 4%
• 
  Expected stock price in one year = $60
• 
  Risk-free rate = 3%
• 
  Equity risk premium = 12%

A) $59.55.

B) $57.48.

C) $57.70.

---

The current stock price is equal to (D1 + P1) / (1 + ke). D1 equals $6.10(1.04) = $6.34. The equity discount rate is 3% + 12% = 15%. Therefore the current stock price is ($6.34 + $60)/(1.15) = $57.70

karoliukas

An investor is considering acquiring a common stock that he would like to hold for one year. He expects to receive both $1.50 in dividends and $26 from the sale of the stock at the end of the year. What is the maximum price he should pay for the stock today to earn a 15 percent return?

A) $23.91.

B) $27.30.

C) $24.11.

---

By discounting the cash flows for one period at the required return of 15% we get: x = (26 + 1.50) / (1+.15)1
(x)(1.15) = 26 + 1.50
x = 27.50 / 1.15
x = $23.91

karoliukas

Assume that a stock paid a dividend of $1.50 last year. Next year, an investor believes that the dividend will be 20% higher and that the stock will be selling for $50 at year-end. Assume a beta of 2.0, a risk-free rate of 6%, and an expected market return of 15%. What is the value of the stock?

A) $45.00.

B) $41.77.

C) $40.32.

---

Using the Capital Asset Pricing Model, we can determine the discount rate equal to 0.06 + 2(0.15 – 0.06) = 0.24. The dividends next year are expected to be $1.50 × 1.2 = $1.80. The present value of the future stock price and the future dividend are determined by discounting the expected cash flows at the discount rate of 24%: (50 + 1.8) / 1.24 = $41.77.