karoliukas

The following data pertains to a common stock:

• It will pay no dividends for two years.
• The dividend three years from now is expected to be $1.
• Dividends are expected to grow at a 7% rate from that point onward.

If an investor requires a 17% return on this stock, what will they be willing to pay for this stock now?

A) $10.00.

B) $ 7.30.

C) $ 6.24.

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time line = $0 now; $0 in yr 1; $0 in yr 2; $1 in yr 3.
P2 = D3/(k - g) = 1/(.17 - .07) = $10
Note the math. The price is always one year before the dividend date.
Solve for the PV of $10 to be received in two years.
FV = 10; n = 2; i = 17; compute PV = $7.30

karoliukas

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) $55.25.

B) $41.32.

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

karoliukas

Utilizing the infinite period dividend discount model, all else held equal, if the required rate of return (Ke) decreases, the model yields a price that is:

A) increased, due to a smaller spread between required return and growth.

B) reduced, due to increased spread between growth and required return.

C) reduced, due to the reduction in discount rate.

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The denominator of the single-stage DDM is the spread between required return Ke, and expected growth rate, g. The smaller the denominator, all else held equal, the larger the computed value.

karoliukas

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) $23.20.

C) $20.23.

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

karoliukas

What value would be placed on a stock that currently pays no dividend but is expected to start paying a $1 dividend five years from now? Once the stock starts paying dividends, the dividend is expected to grow at a 5 percent annual rate. The appropriate discount rate is 12 percent.

A) $9.08.

B) $8.11.

C) $14.29.

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P4 = D5/(k-g) = 1/(.12-.05) = 14.29
P0 = [FV = 14.29; n = 4; i = 12] = $9.08.

karoliukas

Assume a company has earnings per share of $5 and this year paid out 40% in dividends. The earnings and dividend growth rate for the next 3 years will be 20%. At the end of the third year the company will start paying out 100% of earnings in dividends and earnings will increase at an annual rate of 5% thereafter. If a 12% rate of return is required, the value of the company is approximately:

A) $92.92.

B) $55.69.

C) $102.80.

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First, calculate the dividends in years 0 through 4: (We need D4 to calculate the value in Year 3)
D0 = (0.4)(5) = 2
D1 = (2)(1.2) = 2.40
D2 = (2.4)(1.2) = 2.88
D3 = E3 = 5(1.2)3 = 8.64
g after year 3 will be 5%, so
D4 = 8.64 × 1.05 = 9.07
Then, solve for the terminal value at the end of period 3 = D4 / (k − g) = 9.07 / (0.12 − 0.05) = $129.57
Present value of the cash flows = value of stock = 2.4 / (1.12)1 + 2.88 / (1.12)2 + 8.64 / (1.12)3 + 129.57 / (1.12)3 = 2.14 + 2.29 + 6.15 + 92.22 = 102.80

karoliukas

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) Computech's stock is currently worth $17.46.

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

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.

karoliukas

The last dividend paid on a common stock was $2.00, the growth rate is 5% and investors require a 10% return. Using the infinite period dividend discount model, calculate the value of the stock.

A) $42.00.

B) $40.00.

C) $13.33.

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2(1.05) / (0.10 - 0.05) = $42.00

karoliukas

Day and Associates is experiencing a period of abnormal growth. The last dividend paid by Day was $0.75. Next year, they anticipate growth in dividends and earnings of 25% followed by negative 5% growth in the second year. The company will level off to a normal growth rate of 8% in year three and is expected to maintain an 8% growth rate for the foreseeable future. Investors require a 12% rate of return on Day.What is the approximate amount that an investor would be willing to pay today for the two years of abnormal dividends?

A) $1.62.

B) $1.55.

C) $1.83.

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First find the abnormal dividends and then discount them back to the present.
$0.75 × 1.25 = $0.9375 × 0.95 = $0.89.
D1 = $0.9375; D2 = $0.89.
At this point you can use the cash flow keys with CF0 = 0, CF1 = $0.9375 and CF2 = $0.89.
Compute for NPV with I/Y = 12. NPV = $1.547.
Alternatively, you can put the dividends in as future values, solve for present values and add the two together.

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What would an investor pay for Day and Associates today?

A) $24.03.

B) $18.65.

C) $20.71.

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Here we find P2 using the constant growth dividend discount model.
P2 = $0.89 × 1.08 / (0.12 – 0.08) = $24.03.
Discount that back to the present at 12% for 2 periods and add it to the answer in the previous question.
N = 2; I/Y = 12; PMT = 0; FV = $24.03; CPT &rarr PV = $19.16.
Add $1.55 (the present value of the abnormal dividends) to $19.16 and you get $20.71.

karoliukas

Calculate the value of a common stock that last paid a $2.00 dividend if the required rate of return on the stock is 14 percent and the expected growth rate of dividends and earnings is 6 percent.  What growth model is an example of this calculation?

Value of stock

Growth model

A) $26.50    Gordon growth

B) $26.50    Supernormal growth

C) $25.00    Gordon growth

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$2(1.06)/0.14 - 0.06 = $26.50.
This calculation is an example of the Gordon Growth Model also known as the constant growth model.