honeycfa

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) 10.00%.

B) 9.78%.

C) 10.25%.

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D₀ (1 + g) / P₀ + g = k

1.00 (1.05) / 20 + 0.05 = 10.25%.

honeycfa

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   $35.25

B) $27.50   $35.25

C) $25.22    $29.80

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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, k_e = 0.10. Alternative:  Using the capital asset pricing model (CAPM), k_e = R_f + Beta * (R_m – R_f) = 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 + k_e)] + [P₁ / (1 + k_e)] = [$2.75 / (1.10)] + [$25.0 / (1.10)] = $25.22. Shortcut: since the growth rate in dividends, g, was equal to k_e, 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 + k_e)] + [D₂/ (1 + k_e)²] + [P₂ / (1 + k_e)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 k_e, 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.

honeycfa

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

honeycfa

Assume that at the end of the next year, Company A will pay a $2.00 dividend per share, an increase from the current dividend of $1.50 per share. After that, the dividend is expected to increase at a constant rate of 5%. If an investor requires a 12% return on the stock, what is the value of the stock?

A) $30.00.

B) $28.57.

C) $31.78.

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P₀ = D₁ / k ? g
D₁ = $2
g = 0.05
k = 0.12
P₀ = 2 / 0.12 ? 0.05 = 2 / 0.07 = $28.57

honeycfa

Company B paid a $1.00 dividend per share last year and is expected to continue to pay out 40% of its earnings as dividends for the foreseeable future. If the firm is expected to earn a 10% return on equity in the future, and if an investor requires a 12% return on the stock, the stock’s value is closest to:

A) $12.50.

B) $17.67.

C) $16.67.

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P₀ = Value of the stock = D₁ / (k ? g)

g = (RR)(ROE)

RR = 1 ? dividend payout = 1 ? 0.4 = 0.6

ROE = 0.1

g = (0.6)(0.1) = 0.06

D₁ = (D₀)(1 + g) = (1)(1 + 0.06) = $1.06

P₀ = 1.06 / (0.12 ? 0.06) = 1.06 / 0.06 = $17.67

honeycfa

Assume that the expected dividend growth rate (g) for a firm decreased from 5% to zero. Further, assume that the firm's cost of equity (k) and dividend payout ratio will maintain their historic levels. The firm's P/E ratio will most likely:

A) decrease.

B) become undefined.

C) increase.

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The P/E ratio may be defined as: Payout ratio / (k - g), so if k is constant and g goes to zero, the P/E will decrease.

honeycfa

Using an infinite period dividend discount model, find the value of a stock that last paid a dividend of $1.50. Dividends are expected to grow at 6 percent forever, the expected return on the market is 12 percent and the stock’s beta is 0.8. The risk-free rate of return is 5 percent.

A) $26.50.

B) $34.57.

C) $32.61.

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First find the required rate of return using the CAPM equation.

k = 0.05 + 0.8(0.12 - 0.05) = 10.6%

$1.50(1.06) /(0.106 - 0.06) = $34.57

honeycfa

A company has just paid a $2.00 dividend per share and dividends are expected to grow at a rate of 6% indefinitely. If the required return is 13%, what is the value of the stock today?

A) $30.29.

B) $34.16.

C) $32.25.

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P₀ = D₁ / (k - g) = 2.12 / (0.13 - 0.06) = $30.29

honeycfa

A firm is expected to have four years of growth with a retention ratio of 100%. Afterwards the firm’s dividends are expected to grow 4% annually, and the dividend payout ratio will be set at 50%. If earnings per share (EPS) = $2.4 in year 5 and the required return on equity is 10%, what is the stock’s value today?

A) $30.00.

B) $13.66.

C) $20.00.

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Dividend in year 5 = (EPS)(payout ratio) = 2.4 × 0.5 = 1.2

P₄ = 1.2 / (0.1 ? 0.04) = 1.2 / 0.06 = $20

P₀ = PV (P₄) = $20 / (1.10)⁴ = $13.66

honeycfa

Bybee is expected to have a temporary supernormal growth period and then level off to a “normal,” sustainable growth rate forever. The supernormal growth is expected to be 25 percent for 2 years, 20 percent for one year and then level off to a normal growth rate of 8 percent forever. The market requires a 14 percent return on the company and the company last paid a $2.00 dividend. What would the market be willing to pay for the stock today?

A) $52.68.

B) $67.50.

C) $47.09.

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First, find the future dividends at the supernormal growth rate(s). Next, use the infinite period dividend discount model to find the expected price after the supernormal growth period ends. Third, find the present value of the cash flow stream.

D₁ = 2.00 (1.25) = 2.50 (1.25) = D₂ = 3.125 (1.20) = D₃ = 3.75
P₂ = 3.75/(0.14 - 0.08) = 62.50
N = 1; I/Y = 14; FV = 2.50; compute PV = 2.19.
N = 2; I/Y = 14; FV = 3.125; compute PV = 2.40.
N = 2; I/Y = 14; FV = 62.50; compute PV = 48.09.
Now sum the PV’s: 2.19 + 2.40 + 48.09 = $52.68.