invic

Suppose the equity required rate of return is 10%, the dividend just paid is $1.00 and dividends are expected to grow at an annual rate of 6% forever. What is the expected price at the end of year 2?

A) $29.78.

B) $28.09.

C) $27.07.

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The terminal value is $29.78, and that is the price an investor should be willing to pay at the end of year 2. The correct answer is shown below.

Year	Dividend
1	$1.0600
2	$1.1236
3	$1.1910
V3:	$1.191/(0.10 – 0.06) = $29.78

invic

Zephraim Axelrod, CFA, is trying to determine whether Allegheny Mining is a good investment. He decides to use the Gordon Growth model to calculate how much dividend growth shareholders can expect. To that end, he determines the following:

• Share price: $18.12.
• Dividend: $0.32 per share.
• Beta: 1.94.
• Industry average estimated returns: 15%.
• Risk-free rate: 5.5%.
• Equity risk premium: 6.3%

Based only on the information above, the implied dividend growth rate is closest to:

A) 10.27%.

B) 15.68%.

C) 19.89%.

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We have the price and dividend. We need the required rate of return to use the Gordon Growth model to calculate implied dividend growth. Using the capital asset pricing model, the required return = risk-free rate + (beta × equity risk premium) = 17.72%.
Price = [dividend × (1 + dividend growth rate)] / [required return − growth rate]
18.12 = [0.32 × (1 + dividend growth rate)] / [0.1772 − dividend growth rate]
18.12 × [0.1772 − dividend growth rate] = 0.32 + 0.32 × dividend growth rate
3.2112 − 18.12 × dividend growth rate = 0.32 + 0.32 × dividend growth rate
2.8912 = 18.44 × dividend growth rate
1 = 6.3779 × dividend growth rate
Dividend growth rate = 15.68%

invic

In its most recent quarterly earnings report, Smith Brothers Garden Supplies said it planned to increase its dividend at an annual rate of 13% for the foreseeable future. Analyst Clinton Spears has an annual return target of 15.5% for Smith Brothers stock. He decides to use the dividend-growth rate to back out another return estimate to test against his. Smith Brothers stock trades for $55 per share and earned $3.01 per share over the last 12 months. The company paid a dividend of $2.15 per share during the 12-month period, and its dividend-growth rate for the last five years was 9.2%.
Using the Gordon Growth model, the required annual return for Smith Brothers stock is closest to:

A) 13.47%.

B) 17.42%.

C) 19.18%.

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The Gordon Growth model is as follows:
Price = [dividend × (1 + dividend growth rate)] / [required return − growth rate]
55 = [2.15 × 1.13] / [required return − 0.13]
55 = 2.4295 / [required return − 0.13]
22.6384 = 1 / [required return − 0.13]
[Required return − 0.13] = 0.04417
Required return = 0.17417 = 17.42%

invic

Analyst Louise Dorgan has put together a short fact sheet on two companies, Benson Orchards and Terra Firma Development.

<P [td=1,1,122]Benson Orchards	Terra Firma Development
Price/earnings ratio	18.5	<P [/td]
Most recent dividend	$0.56 per share	$1.67 per share
Estimated stock return	15%	<P [/td]
Estimated market return	<P [td=1,1,183]13%
Beta	1.2	1.7
Trailing profits	$5.16 per share	<P [/td]
Stock-market value	$123 million	$1.678 billion
Shares outstanding	<P [td=1,1,183]875 million

The risk-free rate is 3.6%, and Dorgan estimates the stock market’s equity risk premium as 7.5%.
Using only the data presented above, can Dorgan create a Gordon Growth model for:

Benson Orchards

Terra Firm Development

A) Yes Yes

B) Yes No

C) No No

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To calculate a growth rate using the Gordon Growth model, we use four variables (one being the growth rate itself). If we have any three of the variables, we can solve for the fourth. The four variables are: stock price, dividend, required return, and dividend growth rate. The data presented are sufficient for the calculation of three of the variables for both companies.
Benson Orchards
We know the most recent dividend and the estimate stock return. From the P/E ratio and the trailing profits, we can determine the stock price. From those three pieces of data, we can calculate the dividend growth rate.
Terra Firma
We have the dividend. We can determine the stock price by dividing market value by shares outstanding. We can derive the estimated stock return using the capital asset pricing model. From those three statistics, we can create a Gordon Growth model and solve for the dividend-growth rate.

invic

Xerxes, Inc. forecasts earnings to be permanently fixed at $4.00 per share. Current market price is $35 and required return is 10%. Assuming the shares are properly priced, the present value of growth opportunities is closest to:

A) -$5.00.

B) +$3.50.

C) +$5.00.

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Share price = (no-growth earnings / required return) + PVGO
35 = (4 / 0.10) + PVGO
PVGO = -$5.00

invic

The required rate of return for an asset is often difficult to determine, but if we know the growth prospects and the current earnings of a firm we can determine the implied required rate of return from the:

A) dividend rate.

B) earnings retention rate.

C) market price.

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The required rate of return is implicit in the asset’s market price and can be determined with the present value of growth opportunities.

invic

Tri-coat Paints has a current market value of $41 per share with a earnings of $3.64. What is the present value of its growth opportunities (PVGO) if the required return is 9%?

A) $3.92.

B) $0.56.

C) $1.27.

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The PVGO is $0.56:

PVGO = $41 – ($3.64 / 0.09) = $0.56

invic

Obsidian Glass Company has current earnings of $2.22, a required return of 8%, and the present value of growth opportunities (PVGO) of $8.72. What is the current value of Obsidian’s shares?

A) $57.17.

B) $10.94.

C) $36.47.

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The current value is $36.47. V0 = ($2.22 / 0.08) + $8.72 = $36.47

invic

Ambiance Company has a current market price of $42, a current dividend of $1.25 and a required rate of return of 12%. All earnings are paid out as dividends. What is the present value of Ambiance’s growth opportunities (PVGO)?

A) $38.85.

B) $31.58.

C) $16.71.

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The PVGO is $31.58:

PVGO = $42 – ($1.25 / 0.12) = $31.58

invic

A firm has the following characteristics:

• Current share price $100.00.
• Current earnings $3.50.
• Current dividend $0.75.
• Growth rate 11%.
• Required return 13%.

Based on this information and the Gordon growth model, what is the firm’s justified trailing price to earnings (P/E) ratio?

A) 11.9.

B) 8.9.

C) 11.3.

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The justified trailing P/E is 11.9:

P0 / E0 = [($0.75)(1 + 0.11)/$3.50] / (0.13 – 0.11) = 11.8929