Reading 46: Discounted Dividend Valuation - LOS q ～ Q1-5

答案和详解如下：

1.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.

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 percent annual dividend growth in perpetuity. The Middle-Growth scenario calls for 12 percent dividend growth in years 1 through 3, and 3 percent annual growth thereafter. The High-Growth scenario specifies dividend growth year by year, as follows:

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 percent 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 percent for the two lower-growth scenarios, but raise it to 5 percent 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 percent 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 percent, and a weighted average cost of capital (WACC) of only 9 percent. He’s especially impressed that the firm can achieve these growth rates while still maintaining a constant dividend payout ratio of 40 percent, 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 percent 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 percent 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 percent), 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 percent. Dividend growth is expected to decline linearly over six years to 5 percent, and then remain at 5 percent 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 FALSE? 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)   own patents for a very profitable product.

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

D)   have high growth and are expected to maintain that growth for a specific period.

The correct answer was C)

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.

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

A)   11.75%.

B)   6.00%.

C)   11.00%.

D)   12.50%.

The correct answer was C)

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 x {(1 + g_L) x [H x (g_S – g_L)]} + gL

Here,

r = 1.5/30 x {(1+ 0.05) + [(6.0/2) x (0.10 – 0.05)]} + 0.05 = 0.11

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

A)   Ancis’s statement is correct; Nutting’s statement is correct.

B)   Ancis’s statement is incorrect; Nutting’s statement is correct.

C)   Ancis’s statement is correct; Nutting’s statement is incorrect.

D)   Ancis’s statement is incorrect; Nutting’s statement is incorrect.

The correct answer was C)

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.

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

A)   19.0%.

B)   4.0%.

C)   40.0%.

D)   0.3%.

The correct answer was B)

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% (0.40)

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 percent, 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 times (1.20) = $4.80

D₂ = $4.80 dividend in year 1 times (1.15) = $5.52

D₃ = $5.52 dividend in year 2 times (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

= $12.56

Thus, 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 times 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 ) = $63.14

63.14 (0.14 – x) = 6.07 (1+x)

8.84 – 63.14x = 6.07 + 6.07x

2.77 = 69.21 x

0.04 = x

The 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 model:

P₃ = $6.07(1+.04)/(0.14 – .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.

5.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%.

D)   63.1%.

The correct answer was A)

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, and (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%.