答案和详解如下！
Question 6
Arshad Khan, CFA, is principal and founding partner of Khan Nolan Beyrout, an asset management firm. Khan and his partner, Christopher Nolan, have concluded that continuing increases in the price of oil are going to make natural gas a more attractive long-term choice as a source of energy. As a result of their analysis, Khan and Nolan have decided to take a position in a natural gas distributor. The Central Texas Energy & Gas Company is one possible choice for investment. The company has been in business for several decades and has a reliable history of paying out 25 percent of its earnings in dividends. Dividend growth at the firm has historically averaged 4.2% per year, with dividends reaching $2.30 per share in the fiscal year just ended. Khan and Nolan agree, however, that the company’s growth rate should increase to 5.0% going forward because of the shift away from oil and towards natural gas. Nolan considers Central Texas Energy & Gas Company a potentially attractive investment because of its very reasonable 6.563 trailing P/E. North Slope Energy Distributors, Inc. is another company that Khan Nolan Beyrout is considering for investment. North Slope is a much younger company than Central Texas and consequently has enjoyed a much higher growth rate in recent years. The company paid out only $1.10 per share in dividends in the most recent fiscal year for a payout ratio of 11%, but dividend growth has been 15% per year. Nolan expects North Slope’s dividend growth rate to decline consistently over the next ten years until it reaches the same long-run growth rate as Central Texas. Because of this rapid dividend growth rate, North Slope trades at a leading P/E of 8.257. Nolan is concerned, however, about the risk in North Slope’s stock if the firm’s dividend growth does not meet his expectations. He tells Khan, “Assuming that the expected rate of return on the stock doesn’t change, if North Slope’s dividend grows 15% for the next three years but the growth rate then suddenly falls to the terminal growth rate of 5%, we would lose over 20% of our investment.” Khan points out, “But even if dividend growth does hit 15% for the next three years and then falls to its terminal value, we’d make nearly 8% on our investment if the terminal growth rate were 5.5% instead of 5%.” Khan argues in favor of investing in Central Texas, saying, “It would only have to earn a 7% ROE in order to fund our expected sustainable growth rate (SGR) of 5%, while maintaining its dividend policy.” Nolan agrees, saying, “If Central Texas’ ROE equals the implied rate of return on equity, the company could more than double the payout ratio and still maintain a 5% growth rate.” Once they complete their analysis, Khan and Nolan decide to invest in Central Texas Energy & Gas. Part 1) In which circumstance is a dividend discount model (DDM) least likely to be an appropriate measure of a stock’s value? A) The investor is a majority shareholder. B) The company has a long history of dividend payments. C) The company has a clear dividend policy that relates to the firm’s earnings. D) The company is a mature firm that generates excess cash flow.
The correct answer was A) The investor is a majority shareholder. A dividend discount model is unlikely to be an appropriate measure of a stock’s value when the investor is a majority shareholder for many reasons, including the fact that a majority owner could change the company’s dividend policy, capital structure, and future growth rate. Dividend discount models can be appropriate valuation measures for a minority stake in a company with a history of dividend payments and a clear dividend policy that relates to the firm’s earnings. Mature companies which generate excess cash flow generally meet these criteria.
This question tested from Session 12, Reading 46, LOS r, (Part 2) Part 2) What is the implied expected rate of return on Central Texas Energy & Gas? A) 5.0%. B) 9.0%. C) 8.2%. D) 4.2%. The correct answer was B) We can calculate the implied expected return using the formula for the justified trailing P/E: Justified trailing P/E = (1 − b) × (1 + g) / (r − g)
6.563 = (0.25) × (1.05) / (r − 0.05)
6.563 = 0.263 / (r − 0.05)
6.563r − (0.05)(6.563) = 0.263
6.563r − 0.328 = 0.263
6.563r = 0.591
r = 0.090 The expected rate of return on Central Texas is 9.0%. Note that we use the expected dividend growth rate of 5.0% rather than the historical growth rate of 4.2% even though it is a trailing P/E because the justified P/E depends on expected growth in dividends. Also note that we did not need to calculate b, the retention ratio, because the term (1 − b) is the payout ratio, which we are given. It is important to realize that calculating a justified P/E ratio will yield the same expected rate of return (or expected value for any other variable) regardless of whether the justified P/E ratio is calculated trailing or leading. We get the same result if we use the formula for justified leading P/E. First, we calculate the leading P/E by adjusting for the expected 5% growth in earnings, (leading P/E = trailing P/E / (1 + g) =) 6.250. Justified leading P/E = payout ratio / (r − g)
6.250 = 0.25 / (r − 0.05)
6.25r − 0.3125 = 0.25
6.25r = 0.5625
r = 0.090 We would also get the same result using the Gordon Growth Model. First, we calculate price. We know that the company pays out 25% of its earnings, so the $2.30 dividend means earnings must have been (4 × $2.30 = ) $9.20 per share. Since trailing P/E is 6.563, we know that price must be (6.563 × $9.20 = ) $60.38. We can calculate the next year’s dividend by increasing the past year’s dividend by 5%, so that the next year’s dividend must be (1.05 × $2.30 = ) $2.415. Now we have the necessary information to use a Gordon Growth Model: r = D1 / P0 + g
r = $2.415 / $60.38 + 0.05
r = 0.04 + 0.05
r = 0.09 It is crucial to understand that all these seemingly different formulas are just different ways of expressing the same fundamental formula: the Gordon Growth Model. Which formula you choose to use on the exam will depend on which one is quickest to solve given the information presented in the question. This question tested from Session 12, Reading 46, LOS r, (Part 2) Part 3) Which statement about a firm’s sustainable growth rate (SGR) is least accurate? A) It assumes that the firm’s debt-to-equity ratio is unchanged. B) The two key variables are the ROA and the retention ratio. C) It tells how quickly a firm can grow using internally generated funds. D) It assumes that the firm does not issue new equity.
The correct answer was B) The two key variables are the ROA and the retention ratio. The SGR is a function of the firm’s ROE, not the ROA. It is possible for the ROA to vary with the return on debt and leave the ROE unaffected.
This question tested from Session 12, Reading 46, LOS r, (Part 2) Part 4) What is the implied expected rate of return on North Slope? A) 7.2%. B) 9.6%. C) 6.8%. D) 10.0%. The correct answer was C) North Slope fits an H-model. We can use the formula that solves an H-model in terms of r: r = (D0/P0 × ((1 + gL ) + (H × (gS – gL)))) + gL First, we have to solve for price. We know that the leading P/E is 8.257. We also know that the most recent dividend was $1.10 and that dividends are expected to grow 15%. That means that next year’s dividend should be (1.15 × $1.10 = ) $1.265 per share. With a dividend payout ratio of 11%, earnings per share were ($1.265/0.11 = ) $11.50. At a forward P/E of 8.257, that means that North Slope must be trading at (8.257 × $11.50 = ) $94.96 per share. Now we can use the formula: r = (D0/P0 × ((1 + gL ) + (H × (gS − gL)))) + gL
r = ($1.10/$94.96 × (1.05 + (5 × (0.15 – 0.05))) + 0.05
r = (0.0116 × (1.05 + 0.5)) + 0.05
r = 0.018 + 0.05
r = 0.068, or 6.8% However, that’s a complex formula to remember on the exam. Alternately, we can use the basic H-model formula: Value = ((D0 × (1 + gL)) + (D0 × H × (gS – gL))) / (r – gL) We set value equal to the current market price of the stock and solve for r: Value = ((D0 × (1 + gL)) + (D0 × H × (gS – gL))) / (r – gL) $94.96 = (($1.10 × 1.05) + ($1.10 × (10/2) × (0.15 – 0.05))) / (r – 0.05)
$94.96 = ($1.155 + ($1.10 × 5 × 0.10)) / (r – 0.05)
$94.96 = ($1.155 + $0.55) / (r – 0.05)
$94.96 = ($1.705) / (r – 0.05)
$94.96r – $4.748 = $1.705
$94.96r = $6.453
r = 0.068 Whichever approach we use, the expected rate of return on North Slope is 6.8%. Note that we cannot use the leading P/E formula for North Slope. The leading P/E formula is based on the Gordon Growth Model, and the Gordon Growth Model does not apply to North Slope because North Slope’s dividend growth rate is not constant. The leading P/E formula can only be used with companies that can be valued using the Gordon Growth Model. This question tested from Session 12, Reading 46, LOS r, (Part 2) Part 5) Regarding the statements made by Khan and Nolan about the risk of their potential investment in North Slope if dividend growth varies from their expectations: A) Khan’s statement is incorrect; Nolan’s statement is incorrect. B) Khan’s statement is correct; Nolan’s statement is correct. C) Khan’s statement is correct; Nolan’s statement is incorrect. D) Khan’s statement is incorrect; Nolan’s statement is correct.
The correct answer was A) Khan’s statement is incorrect; Nolan’s statement is incorrect. If the dividend growth rate of North Slope drops suddenly from 15% to 5%, then it should be valued using a two-stage DDM. The two-stage DDM formula is so complex that it may be quicker and more reliable to construct a table:
| Year 1 | Year 2 | Year 3 | Year 4 | Dividend growth rate | 15% | 15% | 15% | 5% | Expected dividend | 1.265 | 1.455 | 1.673 | 1.757 |
The calculation of the expected dividend is simply the previous year’s dividend multiplied by (1 + g). For example, the dividend in Year 1 is the dividend paid last year of $1.10 multiplied by 1.15 to reflect the 15% growth in expected dividends. Likewise, the dividend in Year 4 is the Year 3 dividend of 1.673 times 1.05 to reflect 5% expected growth. We also need to calculate the terminal value: TV0 = D1 / (r − g)
TV0 = 1.757 / (0.068 − 0.05)
TV0 = 1.757 / 0.018
TV0 = $97.61 Remember that the terminal value is calculated for the current year using next year’s dividends. That means we have calculated the terminal value as of Year 3, not Year 4.
| Year 1 | Year 2 | Year 3 | Dividend | 1.265 | 1.455 | 1.673 | Terminal value |
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| 97.61 | Total cash flow | 1.265 | 1.455 | 99.28 |
We need to calculate the NPV of the future cash flows using a 6.8% discount rate (since the statement specifies that the expected return on the stock does not change.) We use our calculator, setting the discount rate to 6.8% and the cash flows to: CF0 = 0
CF1 = 1.265
CF2 = 1.455
CF3 = 99.28
NPV = $83.95 In the scenario Nolan describes, the stock would fall to $83.95 from its current price of $94.96, a decline of 11.6%. Nolan’s statement is incorrect. In the scenario Khan describes, if the terminal growth rate were 5.5% instead of 5%, the terminal value becomes: TV0 = D1 / (r − g)
TV0 = 1.790 / (0.068 − 0.055)
TV0 = 1.790 / 0.013
TV0 = $137.69 The table becomes:
| Year 1 | Year 2 | Year 3 | Dividend | 1.265 | 1.455 | 1.673 | Terminal value |
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| 137.69 | Total cash flow | 1.265 | 1.455 | 139.365 |
The cash flows become: CF0 = 0
CF1 = 1.265
CF2 = 1.455
CF3 = 139.365
NPV = $116.86 If the terminal growth rate were 5.5% rather than 5%, the stock would rise from the current price of $94.96 to $116.86, an increase of 23%, not “nearly 8%.” Khan’s statement is also incorrect. This question tested from Session 12, Reading 46, LOS r, (Part 2) Part 6) Regarding the statements made by Khan and Nolan about the SGR for Central Texas: A) Khan’s statement is correct; Nolan’s statement is incorrect. B) Khan’s statement is incorrect; Nolan’s statement is incorrect. C) Khan’s statement is correct; Nolan’s statement is correct. D) Khan’s statement is incorrect; Nolan’s statement is correct. The correct answer was A) Khan’s statement is correct; Nolan’s statement is incorrect. The sustainable growth rate formula is: SGR = b × ROE
0.05 = (1 − 0.25) ROE
0.05 = 0.75 ROE
0.07 = ROE The ROE that Central Texas would have to earn to sustain a 5% growth rate with its current dividend policy is 7%. Khan’s statement is correct. Nolan’s statement is incorrect. The market expects equity investors to earn 9% on an investment in Central Texas. If the firm’s ROE equals the implied return on equity of 9%, then: SGR = b × ROE
0.05 = (1 − x) (0.09)
0.05 = 0.09 − 0.09x
-0.04 = -0.09x
0.44 = x If Central Texas’ ROE equals the 9% return to equity investors that the market price implies, the company could increase the dividend payout ratio to 44% and still maintain a 5% growth rate. The potential payout ratio of 44% is not more than double its current ratio of 25%, so Nolan is incorrect. This question tested from Session 12, Reading 46, LOS r, (Part 2)
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发表于 2008-5-17 16:13
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