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%.

---

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

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%.

---

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

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.

---

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

A company reports January 1, 2002, retained earnings of $8,000,000, December 31, 2002, retained earnings of $10,000,000, and 2002 net income of $5,000,000. The company has 1,000,000 shares outstanding and dividends are expected to grow at a rate of 5% per year. What is the expected dividend at the end of 2003?

A) $3.15.

B) $3.00.

C) $13.65.

The first step is to determine 2002 dividends paid as ($8,000,000 + $5,000,000 − 10,000,000) = $3,000,000. The next step is to find the dividend per share ($3,000,000 / 1,000,000 shares) = $3.00 per share. Applying the 5% growth rate, next year’s expected dividend is $3.15, or $3.00 × 1.05.

invic

Jax, Inc., pays a current dividend of $0.52 and is projected to grow at 12%. If the required rate of return is 11%, what is the current value based on the Gordon growth model?

A) $58.24.

B) unable to determine value using Gordon model.

C) $39.47.

---

The Gordon growth model cannot be used if the growth rate exceeds the required rate of return.

invic

A firm currently pays a dividend of $1.77, which is expected to grow at a rate of 4%. If the required return is 10%, what is the current value of the shares using the Gordon growth model?

A) $29.76.

B) $30.68.

C) $29.50.

---

The current value of the shares is $30.68:

V0 = [$1.77(1 + 0.04)] / (0.10 – 0.04)] = $30.68

invic

Jand, Inc., currently pays a dividend of $1.22, which is expected to grow at 5%. If the current value of Jand’s shares based on the Gordon model is $32.03, what is the required rate of return?

A) 8%.

B) 9%.

C) 7%.

---

The required return is 9%: r = [$1.22(1 + 0.05) / $32.03] + 0.05 = 0.09 or 9%.

invic

A firm's dividend per share in the most recent year is $4 and is expected to grow at 6% per year forever. If its shareholders require a return of 14%, the value of the firm's stock (per share) using the single-stage dividend discount model (DDM) is:

A) $50.00.

B) $53.00.

C) $28.57.

---

The value of the firm's stock is: $4 × [1.06 / (0.14 − 0.06)] = $53.00

invic

IAM, Inc. has a current stock price of $40.00 and expects to pay a dividend in one year of $1.80. The dividend is expected to grow at a constant rate of 6% annually. IAM has a beta of 0.95, the market is expected to return 11%, and the risk-free rate of interest is 4%. The expected stock price two years from today is closest to:

A) $43.49.

B) $41.03.

C) $43.94.

---

invic

JAD just paid a dividend of $0.80. Analysts expect dividends to grow at 25% in the next two years, 15% in years three and four, and 8% for year five and after. The market required rate of return is 10%, and Treasury bills are yielding 4%. JAD has a beta of 1.4. The estimated current price of JAD is closest to:

A) $45.91.

B) $25.42.

C) $29.34.

---

JAD’s stock price today can be calculated using the three-stage model. Start by finding the value of the dividends for the next four years with the two different dividend growth rates.

D1 = D0(1+g) = $0.80(1.25) = $1.00
D2 = D1(1+g) = $1.00(1.25) = $1.25
D3 = D2(1+g) = $1.25(1.15) = $1.4375
D4 = D3(1+g) = $1.4375(1.15) = $1.6531

(Alternatively, you could use your financial calculators to solve for the future value to find D1, D2, D3, and D4.)
Next find the value of the stock at the beginning of the constant growth period using the constant dividend discount model:

The easiest way to proceed is to use the NPV function in the financial calculator.
CF0 = 0; CF1 = 1.00; CF2 = 1.25; CF3 = 1.4375; CF4 = 1.6531 + 40.57 = 42.22
I = 12.4; NPV = 29.34
The value of the firm today is $29.34 per share.