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.

karoliukas

A company last paid a $1.00 dividend, the current market price of the stock is $20 per share and the dividends are expected to grow at 5 percent forever. What is the required rate of return on the stock?

A) 10.25%.

B) 10.00%.

C) 9.78%.

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D0 (1 + g) / P0 + g = k
1.00 (1.05) / 20 + 0.05 = 10.25%.

karoliukas

Using the one-year holding period and multiple-year holding period dividend discount model (DDM), calculate the change in value of the stock of Monster Burger Place under the following scenarios. First, assume that an investor holds the stock for only one year. Second, assume that the investor intends to hold the stock for two years. Information on the stock is as follows:

• Last year’s dividend was $2.50 per share.
• Dividends are projected to grow at a rate of 10.0% for each of the next two years.
• Estimated stock price at the end of year 1 is $25 and at the end of year 2 is $30.
• Nominal risk-free rate is 4.5%.
• The required market return is 10.0%.
• Beta is estimated at 1.0.

The value of the stock if held for one year and the value if held for two years are:

Year one

Year two

A) $25.22    $29.80

B) $25.22    $35.25

C) $27.50    $35.25

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First, we need to calculate the required rate of return. When a stock’s beta equals 1, the required return is equal to the market return, or 10.0%. Thus, ke = 0.10. Alternative: Using the capital asset pricing model (CAPM), ke = Rf + Beta * (Rm – Rf) = 4.5% + 1 * (10.0% - 4.5%) = 4.5% + 5.5% = 10.0%.
Next, we need to calculate the dividends for years 1 and 2.

• D1 = D0 * (1 + g)   = 2.50 * (1.10) = 2.75
• D2 = D1 * (1 + g)   = 2.75 * (1.10) = 3.03

Then, we use the one-year holding period DDM to calculate the present value of the expected stock cash flows (assuming the one-year hold).

• P0 = [D1/ (1 + ke)] + [P1 / (1 + ke)] = [$2.75 / (1.10)] + [$25.0 / (1.10)] = $25.22. Shortcut: since the growth rate in dividends, g, was equal to ke, the present value of next year’s dividend is equal to last year’s dividend.

Finally, we use the multi-period DDM to calculate the return for the stock if held for two years.

• P0 = [D1/ (1 + ke)] + [D2/ (1 + ke)2] + [P2 / (1 + ke)2] = [$2.75 / (1.10)] + [$3.03 / (1.10)2] + [$30.0 / (1.10)2] = $29.80. Note: since the growth rate in dividends, g, was equal to ke, the present value of next year’s dividend is equal to last year’s dividend (for periods 1 and 2). Thus, a quick calculation would be 2.5 * 2 + $30.00 / (1.10)2  = 29.80.

karoliukas

Baker Computer earned $6.00 per share last year, has a retention ratio of 55%, and a return on equity (ROE) of 20%. Assuming their required rate of return is 15%, how much would an investor pay for Baker on the basis of the earnings multiplier model?

A) $40.00.

B) $74.93.

C) $173.90.

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g = Retention × ROE = (0.55) × (0.2) = 0.11
P0/E1 = 0.45 / (0.15 − 0.11) = 11.25
Next year's earnings E1 = E0 × (1 + g) = (6.00) × (1.11) = $6.66
P0 = 11.25($6.66) = $74.93