Q13. 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.

Q14. What is the implied required rate of return for Reality Productions?

A)   12.50%.

B)   11.00%.

C)   11.75%.

Q15. Regarding the statements made by Ancis and Nutting about the appropriate uses of the H-model and three-stage DDM:

A)   only one is correct.

B)   both are correct.

C)   both are incorrect.

Q16. Based upon its current market value, what is the implied long-term sustainable growth rate of Turbo Financial Advisors?

A)   4.0%.

B)   0.3%.

C)   19.0%.

Q17. What is the present value of Aultman’s future investment opportunities as a percentage of the market price?

A)   13.9%.

B)   36.9%.

C)   8.1%.

Q13. Regarding the statements made by Ancis and Nutting about the correct valuation models and values for AB: fficeffice" />

A)   only Nutting is correct.

B)   only Ancis is correct.

C)   both are incorrect.

Correct answer is C)

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 + g_n) / (r ? g_n) = [(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 41.m, n)

Q14. What is the implied required rate of return for Reality Productions?

A)   12.50%.

B)   11.00%.

C)   11.75%.

Correct answer is B)

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 + g_L) × [H × (g_S ? g_L)] + g_L

Here, r = 1.5 / 30 × [(1 + 0.05) + [(6.0 / 2) × (0.10 ? 0.05)] + 0.05 = 0.11 (Study Session 11, LOS 41.n)

Q15. Regarding the statements made by Ancis and Nutting about the appropriate uses of the H-model and three-stage DDM:

A)   only one is correct.

B)   both are correct.

C)   both are incorrect.

Correct answer is A)

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 41.j)

Q16. Based upon its current market value, what is the implied long-term sustainable growth rate of Turbo Financial Advisors?

A)   4.0%.

B)   0.3%.

C)   19.0%.

Correct answer is A)

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) = $4.80

D₂ = ($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

= $12.56

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 × 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 = 69.21x

x = 0.04

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 + 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 41.o)

Q17. What is the present value of Aultman’s future investment opportunities as a percentage of the market price?

A)   13.9%.

B)   36.9%.

C)   8.1%.

Correct answer is B)

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 41.f)

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