rgonzalez

An analyst has collected the following data on two companies:

[td=1,1,127] Middle Hickory Co.	Lower Elm Inc.
FCFE	Negative	Positive and growing
Capital investment	Significant	Decreasing

Which dividend-discount model is the best option for valuing the two companies?

Middle Hickory

Lower Elm

A) Two-stage Gordon Growth

B) Gordon Growth Three-stage

C) Three-stage Two-stage

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Middle Hickory is in the initial-growth phase, while Lower Elm is in the transition phase. The three-stage model is appropriate for new, fast-growing companies. The two-stage model is appropriate for companies in the transitional phase.

rgonzalez

In which of the following stages is a firm most likely to distribute the highest proportion of its earnings in the form of dividends?

A) Transition stage.

B) Mature stage.

C) Initial growth stage.

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As a firm matures, the forces of competition begin to deny it opportunities to earn greater than the required return. Faced with this situation, most earnings are distributed to shareholders as dividends. An alternate way of returning capital is through stock repurchases.

rgonzalez

Most firms follow a pattern of growth that includes several stages. The second stage of growth is referred to as the:

A) H-stage.

B) transitional stage.

C) mature stage.

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The second stage is often referred to as the transitional stage. During this stage, the firm’s growth begins to slow as competitive forces build

rgonzalez

In what stage of growth would a firm most likely NOT pay dividends?

A) Transition stage.

B) Declining stage.

C) Initial growth stage.

During the initial growth stage, the firm is able to exploit opportunities to earn greater than the required return. During this stage, earnings are reinvested in the growth opportunities rather than returned to the investors.

rgonzalez

Kyle Star Partners is expected to have earnings in year five of $6.00 per share, a dividend payout ratio of 50%, and a required rate of return of 11%. For year 6 and beyond the dividend growth rate is expected to fall to 3% in perpetuity. Estimate the terminal value at the end of year five using the Gordon growth model.

A) $38.63.

B) $37.50.

C) $27.27.

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The dividend for year 5 is expected to be $3 ($6 times 50%). The dividend for year 6 is then expected to be $3.00 × 1.03 = $3.09. The terminal value using the Gordon growth model is therefore: terminal value = 3.09 / (0.11 − 0.03) = $38.625
P5 = D6 / (k − g)

rgonzalez

Methods for estimating the terminal value in a DDM are least likely to include:

A) the Gordon Growth Model.

B) PVGO.

C) the market multiple approach.

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No matter which dividend discount model we use, we have to estimate a terminal value at some point in the future. There are two ways to do this: using the Gordon growth model and the market multiple approach (i.e., a P/E ratio).

rgonzalez

Q-Partners is expected to have earnings in ten years of $12 per share, a dividend payout ratio of 50%, and a required return of 11%. At that time, ROE is expected to fall to 8% in perpetuity and the trailing P/E ratio is forecasted to be eight times earnings. The terminal value at the end of ten years using the P/E multiple approach and DDM is closest to:

P/E multiple

DDM

A) 96.32 85.71

B) 96.32 89.14

C) 96.00 89.14

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Terminal Value	= P/E × EPS
	= 8 × 12 = 96

D10 = 0.5 × 12 = 6
g = 0.50 × 0.08 = 4%

rgonzalez

Bernadine Nutting has just completed several rounds of job interviews with the valuation group, Ancis Associates. The final hurdle before the firm makes her an offer is an interview with Greg Ancis, CFA, the founder and senior partner of the group. He takes pride in interviewing all potential associates himself once they have made it through the earlier rounds of interviews, and puts candidates through a grueling series of tests. As soon as Nutting enters his office, Ancis tries to overwhelm her with financial information on a variety of firms, including AlphaBetaHydroxy, Inc., Turbo Financial Services, Aultman Construction, and Reality Productions. He begins with AlphaBetaHydroxy, Inc., which trades under the symbol AB and has an estimated beta of 1.4. The firm currently pays $1.50 per year in dividends, but the historical dividend growth rate has varied significantly, as shown in the table below.

AlphaBetaHydroxy, Inc. Historical Dividend Growth
Year	Dividend Growth Rate (%)
−1	+20
−2	+58
−3	−27
−4	−19
−5	+38
−6	+17
−7 and earlier	+3

Ancis says that, given AB’s wildly varying historical dividend growth, he wants to value the firm using 3 different scenarios. The Low-Growth scenario calls for 3% annual dividend growth in perpetuity. The Middle-Growth scenario calls for 12% dividend growth in years 1 through 3, and 3% annual growth thereafter. The High-Growth scenario specifies dividend growth year by year, as follows:

AlphaBetaHydroxy, Inc.                 High-Growth Scenario
Year	Dividend Growth Rate (%)
1	20
2	18
3	16
4	9
5	8
6	7
7 and thereafter	4

Nutting suggests that the scenarios are incomplete, saying that she’d like to include some additional assumptions for the various scenarios. For example, while she would estimate the return on the S& 500 to be 12% regardless of AB’s performance, she would want to vary the outlook for interest rates depending on the scenario. In specific, she’d use a long-term Treasury bond rate of 4% for the two lower-growth scenarios, but raise it to 5% for the two higher-growth scenarios.
Ancis then moves on to Turbo Financial Services. Ancis has been following Turbo for quite some time because of its impressive earnings growth. Earnings per share have grown at a compound annual rate of 19% over the past six years, pushing earnings to $10 per share in the year just ended. He considers this growth rate very high for a firm with a cost of equity of 14%, and a weighted average cost of capital (WACC) of only 9%. He’s especially impressed that the firm can achieve these growth rates while still maintaining a constant dividend payout ratio of 40%, which he expects the firm to continue indefinitely. With a market value of $55.18 per share, Ancis considers Turbo a strong buy.Ancis believes that Turbo will have one more year of strong earnings growth, with EPS rising by 20% in the coming year. He then expects EPS growth to fall 5 percentage points per year for each of the following two years, and achieve its long-term sustainable growth rate of 5% beginning in year four.
Finally, Ancis turns to Aultman Construction, trading at $22 per share (with current EPS of $2.50 and a required return of 18%), and Reality Productions, which currently trades at $30 per share. Reality Production’s current divided is the same as AB’s ($1.50), but the historical dividend growth rate has been a stable 10%. Dividend growth is expected to decline linearly over six years to 5%, and then remain at 5% indefinitely.Ancis begins the valuation test by asking Nutting to value AB with both the two-stage DDM model and the Gordon Growth model, using the scenario most suited to each modeling technique. Nutting answers that the Gordon Growth model gives a valuation for AB that is $1.32 higher than the valuation using the DDM model. After reviewing her analysis, Ancis says that her valuation is incorrect because she should have applied the Gordon Growth model to the High-Growth scenario.
Unhappy with her misuse of the Gordon Growth Model, Ancis asks Nutting to explain the appropriate uses of two other valuation tools: the H-model and three-stage DDM. She says that the H-model is most suited to sustained high-growth companies while three-stage DDM is only appropriate to companies where the dividend growth rate is expected to decline in stages. Ancis says that three-stage DDM does not require a company’s growth rate to decline – it could equally well apply when a company’s growth is expected to be higher in the final stage than in the first. Nutting loses the job.Which of the following statements is least accurate? The two-stage DDM is most suited for analyzing firms that:

A) are expected to grow at a normalized rate after a fixed period of time.

B) are in an industry with low barriers to entry.

C) own patents for a very profitable product.

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The two-stage DDM is well suited to firms that have high growth and are expected to maintain it for a specific period. The assumption that the growth rate drops sharply from high-growth in the initial phase to a stable rate makes this model appropriate for firms that have a competitive advantage, such as a patent, that is expected to exist for a fixed period of time. The model is not useful in analyzing a firm that is in an industry with low barriers to entry. Low barriers to entry are likely to result in increased competition. Therefore, the length of the initial phase of the growth period is indeterminate and probably uneven. (Study Session 11, LOS 39.i)

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Regarding the statements made by Ancis and Nutting about the correct valuation models and values for AB:

A) only Nutting is correct.

B) only Ancis is correct.

C) both are incorrect.

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Both Ancis’s and Nutting’s statements are incorrect.
The Gordon Growth Model assumes that dividends increase at a constant rate perpetually. That fits the Low-Growth scenario, not the Middle or High-Growth scenarios. Thus, Ancis’s statement is incorrect.In the Low-Growth scenario:
The required rate of return is (r) = 0.04 + 1.4(0.12 − 0.04) = 0.152.
The value per share is DPS0(1 + gn) / (r − gn) = [(1.50)(1.03)] / (0.152 − 0.03) = $12.66.

The two-stage DDM model is most suited to a company that has one dividend growth rate for a specified time period and then shifts suddenly to a second dividend growth rate. That best fits the Middle-Growth scenario. In the Middle-Growth scenario,The required rate of return is (r) = 0.05 + (1.4)(0.12 − 0.05) = 0.148.
The value per share is:
The two-stage DDM gives a value for AB that is ($16.44 − $12.66) = $3.78 higher than the value given by the Gordon Growth Model. Thus Nutting’s statement is also incorrect. (Study Session 11, LOS 39.l, m)

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What is the implied required rate of return for Reality Productions?

A) 12.50%.

B) 11.00%.

C) 11.75%.

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The H-model applies to firms where the dividend growth rate is expected to decline linearly over the high-growth stage until it reaches its long-run average growth rate. This most closely matches the anticipated pattern of growth for Reality Productions.The H-model can be rewritten in terms of r and used to solve for r given the other model inputs:
r = D0 / P0 × [(1 + gL) × [H × (gS − gL)] + gL
Here, r = 1.5 / 30 × [(1 + 0.05) + [(6.0 / 2) × (0.10 − 0.05)] + 0.05 = 0.11 (Study Session 11, LOS 39.m)

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Regarding the statements made by Ancis and Nutting about the appropriate uses of the H-model and three-stage DDM:

A) both are correct.

B) both are incorrect.

C) only one is correct.

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Ancis’s statement is technically correct. Although three-stage DDM traditionally uses progressively lower growth rates in each stage, that is not necessary. Three-stage DDM applies when growth rates vary in any manner, as long as they do so in three distinct stages. Nutting’s statement is incorrect because the H-model is not appropriate for a company with sustained dividend growth at any level (high or not). The H-model assumes that the company’s dividend growth rate declines linearly. (Study Session 11, LOS 39.i)

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Based upon its current market value, what is the implied long-term sustainable growth rate of Turbo Financial Advisors?

A) 0.3%.

B) 4.0%.

C) 19.0%.

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The implied long-term rate is the rate that will cause the present value of expected dividends to equal its current market value. Since Ancis provides specific growth rates for Turbo over the next three years, we can use a multi-stage dividend discount model and solve for the long-term growth rate that makes the present value equal to the current market value.First, we calculate Turbo’s expected dividends.
D0 = $10.00 current EPS times the dividend payout ratio of 40%D0 = $4.00 dividend per share in year 0.
Note that the 19% historical dividend growth rate is irrelevant to the current value of the firm. Since the dividend payout ratio is expected to remain constant at 40%, we can use the expected growth rate in earnings to estimate future dividends. EPS growth is forecast at 20% in year 1, 15% in year 2, and 10% in year 3.Multiplying each year’s expected dividend times the relevant forecast growth rate, we calculate:
D1 = ($4.00 dividend in year 0) × (1.20) = $4.80D2 = ($4.80 dividend in year 1) × (1.15) = $5.52
D3 = ($5.52 dividend in year 2) × (1.10) = $6.07 Discounting these back to their present value in year 0 using the cost of equity (the WACC is irrelevant), we find:
Present Value (D1 + D2 + D3) = ($4.80 / 1.141) + ($5.52 / 1.142) + ($6.07 / 1.143)= $4.21 + $4.25 + $4.10
= $12.56Thus, we know that $12.56 of the current $55.18 market value represents the present value of the expected dividends in years 1, 2 and 3. Therefore, the present value of the firm’s dividends for years 4 and beyond must equal ($55.18 - $12.56) = $42.62.
Since the present value of the firm’s dividends beginning in year 4 equals $42.62, the future value in year four will equal ($42.62 × 1.143) = $63.14.Now that we know the value in year 4 of the future stream of steady-growth dividends, we can solve for the growth rate using the Gordon Growth Model:
P3 = [($6.07)(1 + x)] / (0.14 – x ) = $63.1463.14 (0.14 – x) = 6.07 (1+x)
8.84 – 63.14x = 6.07 + 6.07x2.77 = 69.21x
x = 0.04The long-term growth rate that makes Turbo fairly valued is 4% per year.
We can check our calculation by plugging the 4% growth rate we just solved for into the Gordon Growth Model and then plugging that result into the basic multi-stage dividend discount model3 = [($6.07)(1 + 0.04)] / (0.14 − 0.04)
P3 = 6.313 / (.10)P3 = 63.13
(Note that this value varies from the previous calculation by 0.01 because of rounding error.)P0 = ($4.80 / 1.141) + ($5.52 / 1.142) + ($6.07 / 1.143) + ($63.13 / 1.143) = $55.18, which is the current market value. At a 4% growth rate, Turbo is fairly valued.
Note that on the exam, it may be faster to plug each growth rate into the Gordon Growth Model and then plug each of those terminal values into the basic multi-stage formula than to solve for the growth rate. This trial and error method is especially effective if you start with the “middle” growth rate and then decide which value to test next depending on the results of the first calculation. For example, if the first growth rate gives a value for the firm that is too high, you can eliminate all the higher growth rates and try the next lower one. (Study Session 11, LOS 39.n)

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What is the present value of Aultman’s future investment opportunities as a percentage of the market price?

A) 36.9%.

B) 13.9%.

C) 8.1%.

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The present value of the company’s future investment opportunities is also known as PVGO, which can be calculated using the formula: Value = (E / r) + PVGO

where:
E = earnings per share

r = required return

(E / r) is the value of the assets in place

Here, $22 = ($2.5 / 0.18) + PVGO
PVGO = $8.11
The PVGO as a percentage of the market price equals ($8.11 / $22.00) = 36.9%. (Study Session 11, LOS 39.e)

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.