rgonzalez

UC Inc. is a high-tech company that currently pays a dividend of $2.00 per share. UC’s expected growth rate is 5%. The risk-free rate is 3% and market return is 9%.What is the beta implied by a market price of $40.38?

A) 1.20.

B) 1.16.

C) 1.02.

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40.38 = 2.10 / (r − 0.05)
r = 2.10 / 40.38 + 0.05 = 0.1020
From CAPM:
r = 0.03 + b(0.09 − 0.03)
0.1020 = 0.03 + 0.06b
b = 1.20

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What is the price of the UC stock if beta is 1.12?

A) $44.49.

B) $9.72.

C) $42.37.

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From CAPM:
r = 0.03 + b(0.09 − 0.03)
r = 0.03 + 1.12(0.06)
r = 0.0972
V0= D1 / (r − g)
      = 2.00(1 + 0.05) / (0.0972 − 0.05)
      = 2.10 / 0.0472 = $44.49

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Assuming a beta of 1.12, if UC is expected to have a growth rate of 10% for the first 3 years and 5% thereafter, what is the price of UC stock?

A) $53.81.

B) $46.89.

C) $50.87.

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D1 = 2(1.10) = 2.20
D2 = 2.20(1.10) = 2.42
D3 = 2.42(1.10) = 2.662
D4 = 2.662(1.05) = 2.795
V3 = D4 / (r − g)
      = (2.795) / (0.0972 − 0.05)
      = 59.22  
V0 = [2.20 / 1.0972] + [2.42 / (1.0972)2] + [(2.662 + 59.22) / (1.0972)3]
      = $50.87

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Assuming a beta of 1.12, if UC’s growth rate is 10% initially and is expected to decline steadily to a stable rate of 5% over the next three years, what is the price of UC stock?

A) $47.67.

B) $46.61.

C) $47.82.

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Given: D0 = 2.00; gL = 0.05; gS = 0.10; H = (3 / 2) = 1.50; and r = 0.0972
V0 = {[D0(1 + gL)] + [D0 × H × (gS − gL)]} / (r − gL)
V0 = [2(1.05) + 2(1.50)(0.10 − 0.05)] / (0.0972 − 0.05)
     = 2.25 / 0.0472 = $47.67

rgonzalez

An analyst for a small European investment bank is interested in valuing stocks by calculating the present value of its future dividends. He has compiled the following financial data for Ski, Inc.:

	Earnings per Share (EPS)
Year 0	$4.00
Year 1	$6.00
Year 2	$9.00
Year 3	$13.50

Note: Shareholders of Ski, Inc., require a 20% return on their investment in the high growth stage compared to 12% in the stable growth stage. The dividend payout ratio of Ski, Inc., is expected to be 40% for the next three years. After year 3, the dividend payout ratio is expected to increase to 80% and the expected earnings growth will be 2%. Using the information contained in the table, what is the value of Ski, Inc.'s, stock?

A) $43.04.

B) $39.50.

C) $71.38.

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The dividends in the next four years are:

Year 1: 6 × 0.4 = 2.4
Year 2: 9 × 0.4 = 3.6
Year 3: 13.5 × 0.4 = 5.4
Year 4: (13.5 × 1.02) × 0.8 = 11.016

The terminal value of the firm (in year 3) is 11.016 / (0.12 − 0.02) = 110.16. Value per share = 2.4 / (1.2)1 + 3.6 / (1.2)2+ 5.4 / (1.2)3 + 110.16 / (1.2)3 = $71.38.

rgonzalez

An analyst has compiled the following financial data for ABC, Inc.:

ABC, Inc. Valuation Scenarios
Item	Scenario 1	Scenario 2	Scenario 3	Scenario 4
Year 0 Dividends per Share	$1.50	$1.50	$1.50	$1.50
Long-term Treasury Bond Rate	4.0%	4.0%	5.0%	5.0%
Expected Return on the S&P 500	12.0%	12.0%	12.0%	12.0%
Beta	1.4	1.4	1.4	1.4
g (growth rate in dividends)	0.0%	3.0%	Years 1-3, g=12.0% After Year 3, g=3.0%	Year 1, g=20% Year 2, g=18% Year 3, g=16% Year 4, g=9% Year 5, g=8% Year 6, g=7% After Year 6, g=4%

If year 0 dividend is $1.50 per share, the required rate of return of shareholders is 15.2%, what is the value of ABC, Inc.'s stock price using the H-Model? Assume that the growth in dividends has been 20% for the last 8 years, but is expected to decline 3% per year for the next 5 years to a stable growth rate of 5%.

A) $19.85.

B) $24.26.

C) $20.95.

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Use the H-Model to value the firm. The H-Model assumes that the initial growth rate (ga) will decline linearly to the stable growth rate (gn). The high growth period is assumed to last 2H years. Hence, the value per share = DPSo(1 + gn) / (r − gn) + DPSo × H × (ga − gn) / (r − gn)

(1.5 × 1.05) / (0.152 − 0.05) + [1.5 × (5 / 2) × (0.20 − 0.05)] / (0.152 − 0.05)

1.575 / 0.102 + 0.5625 / 0.102
15.44 + 5.51 = $20.95

rgonzalez

An analyst has forecast that Apex Company, which currently pays a dividend of $6.00, will continue to grow at 8% for the next two years and then at a rate of 5% thereafter. If the required return is 10%, based on a two-stage model what is the current value of Apex shares?

A) $126.24.

B) $127.78.

C) $133.13.

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The current value of Apex shares is $133.13:

V0 = [($6 × 1.08) / 1.10] + [($6 × (1.08)2) / 1.102] + [ ($6 × (1.08)2 × 1.05) / (1.102 × (0.10 – 0.05))] = $133.13

rgonzalez

A company’s stock beta is 0.76, the market return is 10%, and the risk-free rate is 4%. The stock will pay no dividends for the first two years, followed by a $1 dividend and $2 dividend, respectively. An investor expects to sell the stock for $10 at the end of four years. What price is an investor willing to pay for this stock?

A) $9.42.

B) $11.03.

C) $10.16.

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The first step is to determine the required rate of return as 4% + [(10% – 4%) × 0.76] or 8.56% per year. The second step is to determine the present value of all future expected cash flows, including the terminal $10 stock price, discounted back four years to today. The solution is shown below.

Year	CF
1	0
2	0
3	1
4	2
4	10

0/1.0856 + 0/(1.0856)2 + 1/(1.0856)3 + (2 + 10)/(1.0856)4 = $9.42

rgonzalez

An analyst has forecast that Hapex Company, which currently pays a dividend of $6.00, will grow at a rate of 8%, declining to 5% over the next two years, and remain at that rate thereafter. If the required return is 10%, based on an H-model what is the current value of Hapex shares?

A) $126.24.

B) $129.60.

C) $131.17.

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The current value of Hapex shares is $129.60:

V0 = [$6(1 + 0.05) + $6(2/2)(0.08 – 0.05)] / (0.10 – 0.05) = $129.60

rgonzalez

An analyst has forecasted dividend growth for Triple Crown, Inc., to be 8% for the next two years, declining to 5% over the following three years, and then remaining at 5% thereafter. If the current dividend is $4.00, and the required return is 10%, what is the current value of Triple Crown shares based on a three-stage model?

A) $73.68.

B) $91.11.

C) $92.23.

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V0 = $4(1.08) / 1.10 + $4(1.08)2 / (1.10)2 + [$4(1 + 0.08)2(3/2)(0.08 – 0.05) + $4(1.08)2(1.05)] / [(1.10)2(0.10 – 0.05)] = $92.23

rgonzalez

James Malone, CFA, covers GNTX stock, which is currently trading at $45.00 and just paid a dividend of $1.40. Malone expects the dividend growth rate to decline linearly over the next six years from 25% in the short run to 6% in the long run. Malone estimates the required return on GNTX to be 13%. Using the H-model, the value of GNTX is closest to:

A) $33.40.

B) $17.55.

C) $32.60.

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The estimated value of GNTX using the H-model is calculated as follows:

rgonzalez

If we increase the required rate of return used in a dividend discount model, the estimate of value produced by the model will:

A) decrease.

B) increase.

C) remain the same.

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The required rate of return is used in the denominator of the equation. Increasing this factor will decrease the resulting value.

rgonzalez

Which of the following groups of statistics provides enough data to calculate an implied return for a stock using the two-stage DDM?

A) Short-term growth rate, long-term growth rate, stock price, trailing 12-month profits.

B) Yield, stock price, historical dividend-growth rate, historical profit-growth rate.

C) P/E ratio, trailing 12-month profits, short-term PEG ratio, long-term PEG ratio, yield.

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To calculate an implied return using the two-stage DDM, we need the stock price, the dividend, a short-term growth rate, and a long-term growth rate. In the correct answer, we can derive the stock price from the P/E ratio and profits, then derive the dividend from the price and the yield. Given the P/E ratio, we can also distill growth rates using the PEG ratios. Admittedly, earnings-growth rates aren’t the same as dividend-growth rates, but analysts routinely use either in their models. More to the point, this is the only answer in which we can come up with even imperfect data for all the needed variables. One choice does not provide us with a way to find the dividend. The other option does not give us the needed short-term and long-term growth rates.