1215

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) $40.32.

C) $41.77.

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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.

1215

A firm will not pay dividends until four years from now. Starting in year four dividends will be $2.20 per share, the retention ratio will be 40%, and ROE will be 15%. If k = 10%, what should be the value of the stock?

A) $41.32.

B) $55.25.

C) $58.89.

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g = ROE × retention ratio = ROE × b = 15 × 0.4 = 6%

Based on the growth rate we can calculate the expected price in year 3:

P₃ = D₄ / (k ? g) = 2.2 / (0.10 ? 0.06) = $55

The stock value today is: P₀ = PV (55) at 10% for 3 periods = $41.32

1215

A stock has the following elements: last year’s dividend = $1, next year’s dividend is 10% higher, the price will be $25 at year-end, the risk-free rate is 5%, the market premium is 5%, and the stock’s beta is 1.2.

What happens to the price of the stock if the beta of the stock increases to 1.5? It will:

A) increase.

B) remain unchanged.

C) decrease.

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When the beta of a stock increases, its required return will increase. The increase in the discount rate leads to a decrease in the PV of the future cash flows.

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What will be the current price of the stock with a beta of 1.5?

A) $23.51.

B) $20.23.

C) $23.20.

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k = 5 + 1.5(5) = 12.5%
P₀ = (1.1 / 1.125) + (25 / 1.125) = $23.20

1215

What is the value of a stock that paid a $0.25 dividend last year, if dividends are expected to grow at a rate of 6% forever? Assume that the risk-free rate is 5%, the expected return on the market is 10%, and the stock's beta is 0.5.

A) $17.67.

B) $16.67.

C) $3.53.

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The discount rate is k_e = 0.05 + 0.5(0.10 ? 0.05) = 0.075. Use the infinite period dividend discount model to value the stock. The stock value = D₁ / (k_e – g) = (0.25 × 1.06) / (0.075 – 0.06) = $17.67.

1215

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.

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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

1215

Use the following information and the multi-period dividend discount model to find the value of Computech’s common stock.

• Last year’s dividend was $1.62.
• The dividend is expected to grow at 12% for three years.
• The growth rate of dividends after three years is expected to stabilize at 4%.
• The required return for Computech’s common stock is 15%.

Which of the following statements about Computech's stock is least accurate?

A) At the end of two years, Computech's stock will sell for $20.64.

B) Computech's stock is currently worth $17.46.

C) The dividend at the end of year three is expected to be $2.27.

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The dividends for years 1, 2, and 3 are expected to be ($1.62)(1.12) = $1.81; ($1.81)(1.12) = $2.03; and ($2.03)(1.12) = $2.27. At the end of year 2, the stock should sell for $2.27 / (0.15 – 0.04) = $20.64. The stock should sell currently for ($20.64 + $2.03) / (1.15)² + ($1.81) / (1.15) = $18.71.

1215

Given the following information, compute the implied dividend growth rate.

• Profit margin = 10.0%
• Total asset turnover = 2.0 times
• Financial leverage = 1.5 times
• Dividend payout ratio = 40.0%

A) 4.5%.

B) 18.0%.

C) 12.0%.

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Retention ratio equals 1 – 0.40, or 0.60.
Return on equity equals (10.0%)(2.0)(1.5) = 30.0%.
Dividend growth rate equals (0.60)(30.0%) = 18.0%.

1215

Which of the following statements concerning security valuation is least accurate?

A) A stock to be held for two years with a year-end dividend of $2.20 per share, an estimated value of $20.00 at the end of two years, and a required return of 15% is estimated to be worth $18.70 currently.

B) A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $36.11.

C) A stock with an expected dividend payout ratio of 30%, a required return of 8%, an expected dividend growth rate of 4%, and expected earnings of $4.15 per share is estimated to be worth $31.13 currently.

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A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $37.33 using the DDM where P_o = D₁ / (k ? g). We are given D_o = $3.25, g = 3.5%, and k = 12.5%. What we need to find is D₁ which equals D_o × (1 + g) therefore D₁ = $3.25 × 1.035 = $3.36 thus P_o = 3.36 / (0.125 ? 0.035) = $37.33.

In the answer choice where the stock value is $18.70, discounting the future cash flows back to the present gives the present value of the stock. the future cash flows are the dividend in year 1 plus the dividend and value of the stock in year 2 thus the equation becomes: V_o = 2.2 / 1.15 + (2.2 + 20) / 1.15² = $18.70

For the answer choice where the stock value is $31.13 use the DDM which is P_o = D₁ / (k ? g). We are given k = 0.08, g = 0.04, and what we need to find is next year’s dividend or D₁. D₁ = Expected earnings × payout ratio = $4.15 × 0.3 = $1.245 thus P_o = $1.245 / (0.08 ? 0.04) = $31.13