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

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

1215

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) $20.71.

B) $24.03.

C) $18.65.

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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.

1215

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) $74.93.

B) $40.00.

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

1215

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) $28.57.

B) $30.00.

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

1215

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) $16.67.

C) $17.67.

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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

1215

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

1215

A firm has a profit margin of 10%, an asset turnover of 1.2, an equity multiplier of 1.3, and an earnings retention ratio of 0.5. What is the firm's internal growth rate?

A) 6.7%.

B) 7.8%.

C) 4.5%.

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ROE = (Net Income / Sales)(Sales / Total Assets)(Total Assets / Total Equity)

ROE = (0.1)(1.2)(1.3) = 0.156

g = (retention ratio)(ROE) = 0.5(0.156) = 0.078 or 7.8%

1215

In its latest annual report, a company reported the following:

Net income	= $1,000,000
Total equity	= $5,000,000
Total assets	= $10,000,000
Dividend payout ratio	= 40%

Based on the sustainable growth model, the most likely forecast of the company’s future earnings growth rate is:

A) 6%.

B) 12%.

C) 8%.

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g = (RR)(ROE)

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

ROE = NI / Total Equity = 1,000,000 / 5,000,000 = 1 / 5 = 0.2
Note: This is the "simple" calculation of ROE. Since we are only given these inputs, these are what you should use. Also, if given beginning and ending equity balances, use the average in the denominator.

g = (0.6)(0.2) = 0.12 or 12%

1215

 

An analyst projects the following pro forma financial results for Magic Holdings, Inc., in the next year:

• Sales of $1,000,000
• Earnings of $200,000
• Total assets of $750,000
• Equity of $500,000
• Dividend payout ratio of 62.5%
• Shares outstanding of 50,000
• Risk free interest rate of 7.5%
• Expected market return of 13.0%
• Stock Beta at 1.8

If the analyst assumes Magic Holdings, Inc. will produce a constant rate of dividend growth, the value of the stock is closest to:

A) $104

B) $19

C) $44

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Infinite period DDM: P₀ = D₁ / (k_e – g)

D1	= (Earnings × Payout ratio) / average number of shares outstanding
	= ($200,000 × 0.625) / 50,000 = $2.50.
ke	=  risk free rate + [beta × (expected market return – risk free rate)]
ke	=  7.5% + [1.8 × (13.0% - 7.5%)] = 17.4%.
g	=    (retention rate × ROE)
		Retention = (1 – Payout) = 1 – 0.625 = 0.375.
		ROE  = net income/equity
				= 200,000/500,000 = 0.4
g	= 0.375 × 0.4 = 0.15.

P₀ = D₁ / (k_e – g) = $2.50 / (0.174 - 0.15) = 104.17.