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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:

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?

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 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?

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

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?

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%.

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 40.m, n)

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 40.o)