Chapter 18 Equity Valuation Models
84. The growth in dividends of Music Doctors, Inc. is expected to be 8%/year for the next
two years, followed by a growth rate of 4%/year for three years; after this five year period, the growth in dividends is expected to be 3%/year, indefinitely. The required rate of return on Music Doctors, Inc. is 11%. Last year's dividends per share were $2.75. What should the stock sell for today?
A) $8.99 B) $25.21 C) $43.76 D) $110.00 E) none of the above
Answer: C Difficulty: Difficult
Rationale:
Calculations are shown below Yr. Dividend PV of Dividend @ 11% 1 $2.75(1.08) = $2.97/(1.11) = $2.6757
2
2 $2.75(1.08) = $3.21/(1.11)2 = $2.6034 3 $2.75(1.08)2(1.04) = $3.34/(1.11)3 = $2.4392 4 $2.75(1.08)2(1.04)2 = $3.47/(1.11)4 = $2.2854 5 $2.75(1.08)2(1.04)3 = $3.61/(1.11)5 = $2.1412 Sum $12.1449
P5 = 3.7164 / (.11 - .03) = $46.4544; PV of P5 = $46.4544/(1.08)5 = $31.6161; PO = $12.1449 + $31.63 = $43.76
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Chapter 18 Equity Valuation Models
85. The growth in dividends of ABC, Inc. is expected to be 15%/year for the next three
years, followed by a growth rate of 8%/year for two years; after this five year period, the growth in dividends is expected to be 3%/year, indefinitely. The required rate of return on ABC, Inc. is 13%. Last year's dividends per share were $1.85. What should the stock sell for today?
A) $8.99 B) $25.21 C) $40.00 D) $27.74 E) none of the above
Answer: D Difficulty: Difficult
Rationale:
Calculations are shown below Yr. Dividend PV of Dividend @ 13% 1 $1.85 (1.15) = $2.13/(1.13) = $1.88
2
2 $1.85 (1.15) = $2.45/(1.13)2 = $1.92 3 $1.85 (1.15)3 = $2.81/(1.13)3 = $1.95 4 $1.85 (1.15)3(1.08) = $3.04/(1.13)4 = $1.86 5 $1.85 (1.15)3(1.08)2 = $3.28/(1.13)5 = $1.78 Sum $9.39
P5 = 3.28 (1.03) / (.13 - .03) = $33.80; PV of P5 = $33.80/(1.13)5 = $18.35; PO = $18.35 + $9.39 = $27.74.
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Chapter 18 Equity Valuation Models
86. The growth in dividends of XYZ, Inc. is expected to be 10%/year for the next two years,
followed by a growth rate of 5%/year for three years; after this five year period, the growth in dividends is expected to be 2%/year, indefinitely. The required rate of return on XYZ, Inc. is 12%. Last year's dividends per share were $2.00. What should the stock sell for today?
A) $8.99 B) $25.21 C) $40.00 D) $110.00 E) none of the above
Answer: B Difficulty: Difficult
Rationale:
Calculations are shown below Yr. Dividend PV of Dividend @ 12% 1 $2.00(1.10) = $2.22/(1.12) = $1.96
2
2 $2.00(1.10) = $2.42/(1.12)2 = $1.9 3 $2.00(1.10)2(1.05) = $2.54/(1.12)3 = $1.81 4 $2.00(1.10)2(1.05)2 = $2.67/(1.12)4 = $1.70 5 $2.00(1.10)2(1.05)3 = $2.80/(1.12)5 = $1.59 Sum $8.99
P5 = 2.80 (1.02) / (.12 - .02) = $28.56; PV of P5 = $28.56/(1.12)5 = $16.21; PO = $16.20 + $8.99 = $25.21.
87. If a firm's required rate of return equals the firm's return on equity, there is no advantage
to increasing the firm's growth. Suppose a no-growth firm had a required rate of return and a ROE of 12% and a stock price of $40. However, if the firm is able to increase the ROE to 15% with a plowback ratio of 50%, what is the present value of growth opportunities now? (Last year's dividends were $2.00/share).
A) $9.78 B) $7.78 C) $10.78 D) $12.78 E) none of the above
Answer: B Difficulty: Difficult
Rationale: g = 0.50 x 15% = 7.5%; P0 = 2 (1.075) / (.12 - .075) = $47.78; $47.78 -
$40.00 = $7.78.
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Chapter 18 Equity Valuation Models
88. If a firm has a required rate of return equal to the ROE A) the firm can increase market price and P/E by retaining more earnings. B) the firm can increase market price and P/E by increasing the growth rate. C) the amount of earnings retained by the firm does not affect market price or the P/E. D) A and B. E) none of the above.
Answer: C Difficulty: Easy
Rationale: If required return and ROE are equal, investors are indifferent as to whether
the firm retains more earnings or increases dividends. Thus, retention rates and growth rates do not affect market price and P/E.
89. According to James Tobin, the long run value of Tobin's Q should tend toward A) 0. B) 1. C) 2. D) infinity. E) none of the above.
Answer: B Difficulty: Easy
Rationale: According to Tobin, in the long run the ratio of market price to replacement
cost should tend toward 1.
90. The goal of fundamental analysts is to find securities A) whose intrinsic value exceeds market price. B) with a positive present value of growth opportunities. C) with high market capitalization rates. D) all of the above. E) none of the above.
Answer: A Difficulty: Easy
Rationale: The goal of analysts is to find an undervalued security.
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Chapter 18 Equity Valuation Models
91. The dividend discount model A) ignores capital gains. B) incorporates the after-tax value of capital gains. C) includes capital gains implicitly. D) restricts capital gains to a minimum. E) none of the above.
Answer: C Difficulty: Moderate
Rationale: The DDM includes capital gains implicitly, as the selling price at any point is
based on the forecast of future dividends.
92. Many stock analysts assume that a mispriced stock will A) immediately return to its intrinsic value. B) return to its intrinsic value within a few days. C) never return to its intrinsic value. D) gradually approach its intrinsic value over several years. E) none of the above.
Answer: D Difficulty: Moderate
Rationale: Many analysts assume that mispricings may take several years to gradually
correct.
93. Investors want high plowback ratios A) for all firms. B) whenever ROE > k. C) whenever k > ROE. D) only when they are in low tax brackets. E) whenever bank interest rates are high.
Answer: B Difficulty: Easy
Rationale: Investors prefer that firms reinvest earnings when ROE exceeds k.
94. Because the DDM requires multiple estimates, investors should A) carefully examine inputs to the model. B) perform sensitivity analysis on price estimates. C) not use this model without expert assistance. D) feel confident that DDM estimates are correct. E) both A and B.
Answer: E Difficulty: Easy
Rationale: Small errors in input estimates can result in large pricing errors using the
DDM. Therefore, investors should carefully examine input estimates and perform sensitivity analysis on the results.
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