Reading 41: Discounted Dividend Valuation- LOS m～ Q7-12

present, following, investment, interested

Q7. 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) $71.38.

C) $39.50.

Q8. 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.

Q9. What is the price of the UC stock if beta is 1.12?

A) $44.49.

B) $9.72.

C) $42.37.

Correct answer is A)

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

Q10. 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.

Q11. 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.

Q12. 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) own patents for a very profitable product.

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