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CFA Program Level 1 | Equity InvestmentsPages
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2023
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CFA Level 1 - Equity Investments Session 14 - Reading 60 Equity Valuation: Concepts and Basic Tools-LOS e (Notes, Practice Questions, Sample Questions) 1. Given the following estimated ﬁnancial results, value the stock of FishnChips, Inc., using the inﬁnite period dividenddiscount model (DDM). Sales of $1,000,000.Earnings of $150,000.Total assets of $800,000.Equity of $400,000.Dividend payout ratio of 60.0%.Average shares outstanding of 75,000.Real risk free interest rate of 4.0%.Expected inﬂation rate of 3.0%.Expected market return of 13.0%.Stock Beta at 2.1.The per share value of FishnChips stock is approximately: (Note:Carry calculations out to at least 3 decimal places.) A) Unable to calculate stock value because ke < g.B) $17.91. C) $26.86. [Explanation]: Here, we are given all the inputs we need. Usethe following steps to calculate the value of the stock:First, expand the inﬁnite period DDM:DDM formula: P0 = D1 / (ke – g)D1> >
= (Earnings × Payout ratio) / average number of sharesoutstanding> >>>= ($150,000 × 0.60) / 75,000 = $1.20> >ke> >= nominal risk free rate + [beta × (expected market return –nominal risk free rate)]Note: Nominal risk-free rate= (1 + real risk free rate) × (1 + expected inﬂation) – 1= (1.04)×(1.03) – 1 = 0.0712, or 7.12%.ke= 7.12% + [2.1 × (13.0% ? 7.12%)] = 0.19468g= (retention rate × ROE)Retention= (1 – Payout) = 1 – 0.60 = 0.40.ROE= (net income / sales)(sales / total assets)(total assets / equity)= (150,000 / 1,000,000)(1,000,000 / 800,000)(800,000 /400,000)= 0.375g= 0.375 × 0.40 = 0.15Then, calculate: P0 = D1 / (ke – g) = $1.20 / (0.19468 ? 0.15) =26.86. 2. Which of the following statements concerning security valuation is least accurate? A) A stock to be held for two years with a year-end dividend of$2.20 per share, an estimated value of $20.00 at the end of twoyears, and a required return of 15% is estimated to be worth$18.70 currently. B) A stock with a dividend last year of $3.25 per share, anexpected dividend growth rate of 3.5%, and a required returnof 12.5% is estimated to be worth $36.11.
C) A stock with an expected dividend payout ratio of 30%, arequired return of 8%, an expected dividend growth rate of 4%,and expected earnings of $4.15 per share is estimated to beworth $31.13 currently. [Explanation]: A stock with a dividend last year of $3.25 pershare, an expected dividend growth rate of 3.5%, and arequired return of 12.5% is estimated to be worth $37.33 usingthe DDM where Po = D1 / (k ? g). We are given Do = $3.25, g =3.5%, and k = 12.5%. What we need to ﬁnd is D1 which equals Do× (1 + g) therefore D1 = $3.25 × 1.035 = $3.36 thus Po = 3.36 /(0.125 ? 0.035) = $37.33.In the answer choice where the stock value is $18.70,discounting the future cash ﬂows back to the present givesthe present value of the stock. the future cash ﬂows are thedividend in year 1 plus the dividend and value of the stock inyear 2 thus the equation becomes: Vo = 2.2 / 1.15 + (2.2 + 20) /1.152 = $18.70For the answer choice where the stock value is $31.13 use theDDM which is Po = D1 / (k ? g). We are given k = 0.08, g = 0.04,and what we need to ﬁnd is next year’s dividend or D1. D1 =Expected earnings × payout ratio = $4.15 × 0.3 = $1.245 thus Po= $1.245 / (0.08 ? 0.04) = $31.13 3. What is the value of a stock that paid a $0.25 dividend last year, if dividends are expected to grow at a rate of 6% forever?Assume that the risk-free rate is 5%, the expected return on themarket is 10%, and the stock's beta is 0.5. A) $17.67. B) $16.67.C) $3.53.
[Explanation]: The discount rate is ke = 0.05 + 0.5(0.10 ? 0.05)= 0.075. Use the inﬁnite period dividend discount model tovalue the stock. The stock value = D1 / (ke – g) = (0.25 × 1.06) /(0.075 – 0.06) = $17.67 4. An analyst has gathered the following data for Webco, Inc: Retention = 40%ROE = 25%k = 14%Using the inﬁnite period, or constant growth, dividend discountmodel, calculate the price of Webco’s stock assuming that nextyears earnings will be $4.25. A) $63.75. B) $55.00.C) $125.00. [Explanation]: g = (ROE)(RR) = (0.25)(0.4) = 10%V = D1 / (k – g)D1 = 4.25 (1 ? 0.4) = 2.55G = 0.10K – g = 0.14 ? 0.10 = 0.04V = 2.55 / 0.04 = 63.75 5. Use the following information and the multi-period dividend discount model to ﬁnd the value of Computech’s commonstock. Last year’s dividend was $1.62.The dividend is expected to grow at 12% for three years.
The growth rate of dividends after three years is expected tostabilize at 4%.The required return for Computech’s common stock is 15%.Which of the following statements about Computech's stock isleast accurate? A) At the end of two years, Computech's stock will sell for$20.64. B) Computech's stock is currently worth $17.46. C) The dividend at the end of year three is expected to be $2.27. [Explanation]: The dividends for years 1, 2, and 3 are expectedto be ($1.62)(1.12) = $1.81; ($1.81)(1.12) = $2.03; and ($2.03)(1.12)= $2.27. At the end of year 2, the stock should sell for $2.27 /(0.15 – 0.04) = $20.64. The stock should sell currently for($20.64 + $2.03) / (1.15)2 + ($1.81) / (1.15) = $18.71 6. Given the following information, compute the implied dividend growth rate. Proﬁt margin = 10.0%Total asset turnover = 2.0 timesFinancial leverage = 1.5 timesDividend payout ratio = 40.0% A) 4.5%. B) 18.0%. C) 12.0%. [Explanation]: Retention ratio equals 1 – 0.40, or 0.60.Return on equity equals (10.0%)(2.0)(1.5) = 30.0%.Dividend growth rate equals (0.60)(30.0%) = 18.0%
7. Use the following information and the dividend discount model to ﬁnd the value of GoFlower, Inc.’s, common stock. Last year’s dividend was $3.10 per share.The growth rate in dividends is estimated to be 10% forever.The return on the market is expected to be 12%.The risk-free rate is 4%.GoFlower’s beta is 1.1. A) $34.95. B) $121.79. C) $26.64. [Explanation]: The required return for GoFlower is 0.04 +1.1(0.12 – 0.04) = 0.128 or 12.8%. The expect dividend is($3.10)(1.10) = $3.41. GoFlower’s common stock is then valuedusing the inﬁnite period dividend discount model (DDM) as($3.41) / (0.128 – 0.10) = $121.79 8. Assuming the risk-free rate is 5% and the expected return on the market is 12%, what is the value of a stock with a beta of 1.5that paid a $2 dividend last year if dividends are expected togrow at a 5% rate forever? A) $12.50.B) $17.50. C) $20.00. [Explanation]: P0 = D1 / (k ? g)Rs = Rf + β (RM ? Rf) = 0.05 + 1.5(0.12 ? 0.05) = 0.155 D1 = D0(1 + g) = 2 × (1.05) = 2.10P0 = 2.10 / (0.155 ? 0.05) = $20.00
9. Assume that a stock paid a dividend of $1.50 last year. Next year, an investor believes that the dividend will be 20% higherand that the stock will be selling for $50 at year-end. Assume abeta of 2.0, a risk-free rate of 6%, and an expected marketreturn of 15%. What is the value of the stock? A) $45.00.B) $40.32. C) $41.77. [Explanation]: Using the Capital Asset Pricing Model, we candetermine the discount rate equal to 0.06 + 2(0.15 – 0.06) =0.24. The dividends next year are expected to be $1.50 × 1.2 =$1.80. The present value of the future stock price and thefuture dividend are determined by discounting the expectedcash ﬂows at the discount rate of 24%: (50 + 1.8) / 1.24 = $41.77 10. A ﬁrm will not pay dividends until four years from now. Starting in year four dividends will be $2.20 per share, theretention ratio will be 40%, and ROE will be 15%. If k = 10%, whatshould be the value of the stock? A) $41.32. B) $55.25.C) $58.89 [Explanation]: g = ROE × retention ratio = ROE × b = 15 × 0.4 = 6%Based on the growth rate we can calculate the expected pricein year 3:P3 = D4 / (k ? g) = 2.2 / (0.10 ? 0.06) = $55
The stock value today is: P0 = PV (55) at 10% for 3 periods =$41.32
LOS e CFA Level 1 - Equity Investments Session 14 - Reading 60 Equity Valuation: Concepts and Basic Tools
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