honeycfa

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

honeycfa

Utilizing the infinite period dividend discount model, all else held equal, if the required rate of return (K_e) 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 K_e, and expected growth rate, g. The smaller the denominator, all else held equal, the larger the computed value.

honeycfa

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) decrease.

B) increase.

C) remain unchanged.

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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

honeycfa

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.

honeycfa

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) $102.80.

C) $55.69.

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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

honeycfa

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.

honeycfa

An analyst gathered the following information about a company:

• The stock is currently trading at $31.00 per share.
• Estimated growth rate for the next three years is 25%.
• Beginning in the year 4, the growth rate is expected to decline and stabilize at 8%.
• The required return for this type of company is estimated at 15%.
• The dividend in year 1 is estimated at $2.00.

The stock is undervalued by approximately:

A) $15.70.

B) $6.40.

C) $0.00.

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The high “supernormal” growth in the first three years and the decrease in growth thereafter signals that we should use a combination of the multi-period and finite dividend growth models (DDM) to value the stock.

Step 1: Determine the dividend stream through year 4

• D₁ = $2.00 (given)
• D₂ = D₁ × (1 + g) = 2.00 × (1.25) = $2.50
• D₃ = D₂ × (1 + g) = $2.50 × (1.25) = $3.13
• D₄ = D₃ × (1 + g) = $3.13 × (1.08) = $3.38

Step 2: Calculate the value of the stock at the end of year 3 (using D₄)

• P₃ = D₄ / (k_e – g) = $3.38 / (0.15 – 0.08) = $48.29

Step 3: Calculate the PV of each cash flow stream at k_e = 15%, and sum the cash flows. Note: We suggest you clear the financial calculator memory registers before calculating the value. The present value of:

• D₁ = 1.74 = 2.00 / (1.15)¹, or FV = -2.00, N = 1, I/Y = 15, PV = 1.74
• D₂ = 1.89 = 2.50 / (1.15)², or FV = -2.50, N = 2, I/Y = 15, PV = 1.89
• D₃ = 2.06 = 3.13 / (1.15)³, or FV = -3.13, N = 3, I/Y = 15, PV = 2.06
• P₃ = 31.75 = 48.29 / (1.15)³, or FV = -48.29, N = 3, I/Y = 15, PV = 31.75
• Sum of cash flows = 37.44.
• Thus, the stock is undervalued by 37.44 – 31.00 = approximately 6.40.

Note: Future values are entered in a financial calculator as negatives to ensure that the PV result is positive. It does not mean that the cash flows are negative. Also, your calculations may differ slightly due to rounding. Remember that the question asks you to select the closest answer.

honeycfa

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) $40.00.

B) $42.00.

C) $13.33.

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

honeycfa

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) $1.55.

B) $1.62.

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.

honeycfa

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   Supernormal growth

B) $25.00   Gordon growth

C) $26.50   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.