# CFA Level 2 – Equity Session 11 – Reading 42 Discounted Dividend Valuation

## CFA Level 2 – Equity, Session 11-Reading 42

### Discounted Dividend Valuation – LOS l

#### (Practice Questions, Sample Questions)

1. 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) \$92.23.
B) \$73.68.
C) \$91.11.

Explanation: A) 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

2. An analyst has forecast that Hapex Company, which currently pays a dividend of .

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) \$131.17.
C) \$129.60.

Explanation: C) 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

3. 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.

Explanation: C) 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

4. 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) 1.16.
B) 1.02.
C) 1.20.

Explanation: C) 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

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

A) \$9.72.
B) \$42.37.
C) \$44.49.

Explanation: C) 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

6. 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) \$50.87.
B) \$53.81.
C) \$46.89.

Explanation: A) 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

7. 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) \$46.61.
B) \$47.67.
C) \$47.82.

Explanation: B) 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

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

A) only Nutting is correct.
B) both are incorrect.
C) only Ancis is correct.

Explanation: B) 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.

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

A) 12.50%.
B) 11.75%.
C) 11.00%.

Explanation: 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 × [(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

10. 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) only one is correct.
C) both are incorrect.

Explanation: B) 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.

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

A) 0.3%.
B) 19.0%.
C) 4.0%.

Explanation: C) 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.

12. 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%.

Explanation: 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%

Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with Homework Mules
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Education
Thank you so much, Reaserch writer. you are so helpfull. I appreciate all the hard works. See you.
Customer 452701, February 12th, 2023
Finance
Thank you very much!! I should definitely pass my class now. I appreciate you!!
Customer 452591, June 18th, 2022
Great paper thanks!
Customer 452543, January 23rd, 2023
Psychology
I requested a revision and it was returned in less than 24 hours. Great job!
Customer 452467, November 15th, 2020
Accounting
Thank you for your help. I made a few minor adjustments to the paper but overall it was good.
Customer 452591, November 11th, 2021
Technology
Customer 452551, October 22nd, 2021
Psychology
Thank you. I will forward critique once I receive it.
Customer 452467, July 25th, 2020
Political science
I like the way it is organized, summarizes the main point, and compare the two articles. Thank you!
Customer 452701, February 12th, 2023
Political science
Thank you!
Customer 452701, February 12th, 2023
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend