CFA II: Equities
Gordon Growth Model (GGM)=
(D(1) / Po) + g = Rltgd D(1) = next years div Po-Price at beg of period g =expected div growth rate Rltgd = long term gov bond yield
If the asset is assumed to be efficiently-priced (i.e., the market price equals its intrinsic value), the IRR would equal the required return on equity. Therefore, the IRR can be estimated as: Requiredreturn(IRR)=
(Next year's dividend / Marketprice) +Expected dividend growth rate ke (IRR) = (D(1) / Po) +g
Calculating Justified Leading and Trailing P/E An analyst gathered the following information regarding Jupiter Inc. Current market price = $60 Current year EPS = $5 Current year dividend per share = $2.25 Required rate of return on equity = 10% Given that dividends are expected to grow at a rate of 5.5% indefinitely, calculate the following: 1.Justified trailing P/E. 2.Justified leading P/E. 3.Comment on whether the company is currently undervalued, fairly valued or overvalued.
1. JustifiedtrailingP/E=(1−b)(1+g)r−g Payoutratio=2.255 =0.45 JustifiedtrailingP/E=(0.45)(1.055)0.1−0.055 =10.55 2. JustifiedleadingP/E=(1−b)r−g JustifiedleadingP/E=0.45(0.1−0.055) =10 3.The company's trailing P/E based on the market price (60 / 5 = 12) is greater than its justified trailing P/E (10.55). Therefore, the stock is currently overvalued.
Calculating PVGO An analyst gathered the following information regarding Alpha Corp: Expected EPS for 2010 = $3.34 Retention rate = 0.4 Required return = 12% Current stock price = $40 Given that dividends are paid out at the end of the year and are expected to grow at 6% forever, calculate the following: 1.Intrinsic value of the company's stock at end of 2009. 2.Present value of growth opportunities (PVGO). 3.The fraction of the company's leading P/E ratio that comes from PVGO.
1.D(2010) = 3.34 × (1 - 0.4) = $2.00 V(2009) = 2.00 / (0.12 - 0.06) = $33.40 2.No-growth value per share = E1 / r = 3.34/0.12 = $27.83 PVGO = Market price - No-growth value per share = 40 - 27.83 = $12.17 3.Leading P/E ratio (firm) = 40 / 3.34 = 11.98 P/E PVGO = 12.17 / 3.34 = 3.64 Fraction of the company's leading P/E ratio attributable to growth opportunities = 3.64 / 11.98 = 30.4%
Estimating Terminal Value Ray Sorvino, CFA is analyzing the stock of Mercury Inc. He expects the company's current annual dividend of $0.50 to grow at a rate of 13% for the next 6 years and then stabilize at a long-term growth rate of 5%. The company's trailing P/E ratio at the end of the initial high-growth period is expected to be 8, and its retention rate is expected to be 30%. Given a required rate of return of 12%, calculate the terminal value of the stock at the end of Year 6 based on the: 1.Gordon growth model.
1.Terminal value at the end of Year 6 based on the Gordon growth model: P6 =D6(1+gc )/(r−gc ) =(0.50×1.13^6 )(1+0.05)/0.12−0.05 =$ 15.61
Estimating Terminal Value Ray Sorvino, CFA is analyzing the stock of Mercury Inc. He expects the company's current annual dividend of $0.50 to grow at a rate of 13% for the next 6 years and then stabilize at a long-term growth rate of 5%. The company's trailing P/E ratio at the end of the initial high-growth period is expected to be 8, and its retention rate is expected to be 30%. Given a required rate of return of 12%, calculate the terminal value of the stock at the end of Year 6 based on the: 2.Earnings multiple approach.
2. Terminal value at the end of Year 6 based on the trailing P/E multiple: First we compute the Year 6 dividend: D6 =0.50×1.13^6 =$1.041 Given that the company's retention rate equals 30% and that the Year 6 dividend equals $1.041, we can compute Year 6 earnings as: D=E×(1−RR) 1.041=E6 ×(1−0.3) E6 =$1.49 Finally, we apply the trailing P/E multiple of 8 to compute the value of the stock based on its Year 6 earnings of $1.49: P6 =P6/E6 ×E6 =8×1.49 =$11.90
Intrinsic Value (Vo)
= (Next year's expected dividend) / Required return - expected div growth rate =D(1)/Ke-g
Holding Period Return (HPR)
=(Price at end of HP - Price at beginning of HP + Dividend) / Price at begging of HP
Justified trailing P/E=
=Po/Eo = (D1/Eo)/r−g = (Do(1+g)/Eo)/r−g = (1−b)(1+g)/r−g
Altin Corporation is considering investment in the hotel business. Altin has a D/E ratio of 1.8, a before‐tax cost of debt of 6.5% and a marginal tax rate of 40%. Paramount Corporation is a publicly‐traded company that operates only in the hotel industry and has a D/E ratio of 2.2, an equity beta of 0.8 and marginal tax rate of 35%. The risk‐free rate is 5% and the expected return on the market is 12.3%. The appropriate weighted average cost of capital (WACCC) that Altin should use to evaluate the risk of entering the hotel business is closest to: 6.08% 6.38% 5.15%
A WACC = [wd × rd × (1 - t)] + (we × re) D/E ratio of 1.8 implies that: The weight of debt in the capital structure = 1.8 / 2.8 = 0.6429 The weight of equity in the capital structure = 1 / 2.8 = 0.3571 WACC = [0.6429 × 0.065 × (1 ‐ 0.4)] + (0.3571 × 0.1) = 6.08%
Jonathan is evaluating the stock of Pyramid Constructors, which is currently trading at $34 per share. He gathers the following information regarding the company: Sales per share = $9.71 Long‐term profit margin = 11.50% Dividend payout ratio = 35% Earnings growth rate = 9% Required rate of return on equity = 10% Based on the justified P/S multiple, the stock is most likely: Undervalued Fairly valued Overvalued
A Justified P/S ratio = [(E0 /S0) × (1 − b) × (1 + g)] / (r − g) Justified P/S ratio = (0.115 × 0.35 × 1.09) / (0.10 − 0.09) = 4.39 P/S multiple based on market price = 34 / 9.71 = 3.50 Since the P/S multiple based on market price is lower than the justified P/S multiple, the stock is undervalued.
Which of the following measures is most likely appropriate for comparing comparisons across countries. ROE ROIC ROCE
A Since it is a pretax measure, ROCE is useful is performing comparisons across countries with different tax structures.
An analyst gathered the following information regarding a company: Return on assets = 18% Asset turnover = 13% Dividend payout ratio = 60% Equity multiplier = 1.35 The company's sustainable gwileyml:rowth rate is closest to: 9.72% 14.58% 12.64%
A Sustainable growth rate = ROA × Retention rate × Equity multiplier Sustainable growth rate = 0.18 × (1-0.60) × 1.35 = 9.72%
Sasha Hemmington is analyzing the stock of Jeremy Traders. She expects the company's current annual dividend of $1.20 to grow at a rate of 12% for the next five years and then stabilize at a long‐term growth rate of 6%. The company's trailing P/E ratio at the end of the initial high‐growth period is expected to be 10, and its retention rate is expected to be 40%. The required rate of return on the company's stock is 13%. The terminal value of the stock at the end of Year 5, based on the Gordon growth model and the earnings multiple approach is closest to: Gordon GM Earnings Multiple Approach A $32.02 $35.25 B $34.14 $52.87 C $32.02 $52.87 Row A Row B Row C
A Terminal value based on the Gordon growth model: P5 = D6 / (r − g) P5 = [(1.20 × 1.125) × 1.06)] / (0.13 − 0.06) = $32.02 Terminal value based on the earnings multiple approach: D5 = 1.20 × 1.125 = $2.1148 D5 = E5 × Payout rate E5 = 2.1148 / (1 − 0.4) = $3.5247 P5 = P5 / E5 × E5 P5 = 10 × 3.5247 = $35.25
When classifying dividend streams into one of several stylized growth patterns, which of the following methods does not apply? Constant growth for a finite period (the Gordon growth model) Two distinct stages of growth (the two‐stage growth model and the H‐model) Three distinct stages of growth (three‐stage models)
A The Gordon growth model assumes constant growth in dividends forever, not for a finite period.
Statement 1: The rational efficient markets formulation argues that market prices represent the best available estimates of intrinsic value. Statement 2: Compared to investors in large caps profitable companies, an investor in distressed securities would be more concerned with liquidation value. Only Statement 1 is incorrect. Only Statement 2 is incorrect. Both statements are correct.
A The rational effi cient markets formulation argues that markets are not effi cient. It asserts that investors will not incur the costs of gathering and analyzing market information if mispricings did not exist in the market.
An analyst gathers the following information regarding Finesse Capital. Current price = $75 Current dividend = $3.50 Short term supernormal growth rate = 10% Long term sustainable growth rate = 5% The supernormal growth in dividends is expected to linearly decline over a period of 6 years. The required rate of return on the stock is closet to: 10.60% 10.83% 15.60%
A r = (D0/P0)[(1+ gL) + H(gS − gL)] + gL r = (3.50/75) [1.05 + (6/2)(0.10−0.05)] + 0.05 = 10.60%
Samantha purchased 1,000 shares of Eagle Corporation for $48.25 per share. She wanted to hold the stock for one year, at the end of which the stock was expected to sell for $56.80. However, after 4 months, the stock's value had gone down to $44.60, at which time Samantha sold all her shares. Given a monthly required rate of return on the stock of 0.9864%, Samantha's realized alpha is closest to: 13.72% -11.5 -7.56%
B Actual holding period return (HPR) = ($44.60 − $48.25)/$48.25 = −7.5648% Required rate of return over a 4‐month holding period = (1 + 0.009864)4 − 1 = 4.0044% Realized alpha = Actual HPR − Required return for the period Realized alpha = −0.075648 − 0.040044 = −11.5692%
Joanna Kaprikova is evaluating the stock of Maya Company which is currently trading at $100.76 per share. The stock recently paid a dividend of $2.25 per share, which is expected to gwileyml:row at a rate of 25% for the next 2 years, followed by a 17% gwileyml:rowth rate for 3 years, after which it is expected to stabilize at a perpetual constant gwileyml:rowth rate of 8%. Given a required rate of return of 12%, the stock is most likely: Undervalued Fairly valued Overvalued
B D1 = 2.25 × 1.25 = $2.8125 D2 = 2.25 × 1.252 = $3.5156 D3 = 3.5156 × 1.17 = $4.1133 D4 = 3.5156 × 1.172 = $4.8125 D5 = 3.5156 × 1.173 = $5.6307 D6 = 5.6306 × 1.08 = 6.0810 V5 = 6.0810 / (0.12 − 0.08) = $152.025 [CF] [2nd] [CE|C] [Enter] [↓] 2.8125 [Enter] [↓] [↓] 3.5156 [Enter] [↓] [↓] 4.1133 [Enter] [↓] [↓] 4.8125 [Enter] [↓] [↓] 157.6556 [Enter] [NPV] 12 [Enter] [↓] [CPT] NPV = $100.7680 Since the stock's current price ($100.76) is the same as its intrinsic value ($100.76), it is fairly valued.
When considering the relative volatility of dividends versus equities, which of the following statements regarding the dividend discount model (DDM) is true? DDM values are more sensitive to short‐term fluctuations and more reflective of the company's long‐term value. DDM values are less sensitive to short‐term fluctuations and more reflective of the company's long‐term value. DDM values are less sensitive to short‐term fluctuations and less reflective of the company's long‐term value.
B DDM values are less sensitive to short‐term fluctuations and more reflective of the company's long‐term value.
Which of the following is most likely during a recession? Dividend yields tend to be low, growth expectations tend to be low, and government bond yields also tend to be low. Dividend yields tend to be high, growth expectations tend to be low, and government bond yields tend to be low. Dividend yields tend to be high, growth expectations tend to be low, and government bond yields tend to be high.
B Generally speaking, during a recession, dividend yields tend to be high (due to low equity market prices), growth expectations tend to be low (due to a weak economy), and government bond yields tend to be low.
If the justified price multiple for a stock is larger than its actual multiple, which of the following is true? The s.tock is overvalued The stock is undervalued. It cannot be determined.
B If the justified price multiple is larger than the actual current multiple of the stock, the stock is undervalued.
Susan is an equity analyst using the growth relative to GDP growth approach to consider how Cable Tele's earnings growth rate will compare with growth in GDP the next year. She believes nominal GDP growth will be 5% next year, inflation will be 2%, and Cable Tele's earnings are expected to grow 10% faster than GDP. What should Cable Tele's earnings growth rate be? 3.3% 5.5% 7.7%
B In the growth relative to GDP growth approach, the analyst considers how a company's growth rate will compare with growth in nominal, not real, GDP.
The company's justified leading P/E ratio is closest to: 7.75 7.27 10.91
B Justified leading P/E = (1 − b) / (r − g) Dividend payout ratio = D / E = 1.272 / 3.18 = 0.4 Justified leading P/E = 0.4 / (0.12 − 0.065) = 7.27
The stock of Tulip Inc is currently trading at $78.30 per share. The company recently paid a dividend of $1.50 per share. Next year's expected dividend gwileyml:rowth rate of 12% is expected to decline linearly over the next 6 years to a long‐term constant gwileyml:rowth rate of 5%. Given that the stock is fairly priced, the required rate of return on the stock is closest to: 2.41% 7.41% 14.41%
B Required return = {(D0 / P0) [(1 + gL) + H (gS − gL)]} + gL Required return = {(1.50 / 78.30) [(1 + 0.05) + 6/2 (0.12 − 0.05)]} + 0.05 Required return = 7.4138%
James Dugarty wants to estimate the return on the stock of Beta Company. He finds out that the company has recently issued a 10‐year bond with a YTM of 6.8%. He further estimates that the return on the equity market is 11.3%. In order to account for the risk associated with the company's equity, he applies a risk premium of 2.7% in the bond yield plus risk premium approach. Given a risk‐free rate of 5.5%, and the stock's beta of 1.02, which of the following estimates of the cost of equity under the approaches is most accurate? Bond Yield Plus Risk Premium CAPM A 8.20% 11.42% B 9.50% 11.42% C 14.00% 11.39% Row A Row B Row C
B Required return on the bond yield plus risk premium approach = 6.8% + 2.7% = 9.50% Required return based on the CAPM = 0.055 [1.02 × (0.113 − 0.055)] = 11.416%
In macroeconomic models, stocks are *least* likely to have negative sensitivities to which of the following risks? Time horizon risk Confidence risk Inflation risk
B Stocks generally have negative sensitivities to time horizon risk and inflation risk. •Higher‐than‐expected inflation is a negative for stocks. •An increase in the difference between LT and ST government bonds reduces the equity market risk premium and is a negative for stock prices.
Chris is considering investing in the stock of Gamma Corporation, which is currently trading at $13.80 per share. The stock recently paid a dividend of $2.25; however due to poor industry outlook, dividends are expected to decline at a rate of 7% forever. Given a required rate of return of 12%, the stock is most likely: Undervalued Overvalued Fairly valued
B V0 = D1 / (r − g) V0 = [2.25 × (1 − 0.07)] / [0.12 − (−0.07)] = $11.01
Altin Corporation is considering investment in the hotel business. Altin has a D/E ratio of 1.8, a before‐tax cost of debt of 6.5% and a marginal tax rate of 40%. Paramount Corporation is a publicly‐traded company that operates only in the hotel industry and has a D/E ratio of 2.2, an equity beta of 0.8 and marginal tax rate of 35%. The risk‐free rate is 5% and the expected return on the market is 12.3%. The appropriate cost of equity that Altin should use to evaluate the risk of entering the hotel business is closest to: 10.84% 7.40% 9.99%
C β Asset =β Equity ×1/1+[(1−t)D/E] βAsset = 0.8 × 1/1+[(1 − 0.35) 2.2] = 0.3292 βProject = βAsset × 1/1+[(1 − t) D/E] βProject = 0.3292 × {1+[(1 − 0.4) × 1.8]} = 0.6847 Cost of equity = 0.05 + [0.6847 × (0.123 − 0.05)] = 9.9983%
Joshua wants to purchase the stock of Dingo Ltd, which is currently trading at $31.29. He expects the company's next year's earnings to be $2.08, at which time he expects to be able to sell the stock for $33.80. Given a required rate of return of 12% and that the company retains 40% of its earnings, the stock is most likely: Undervalued Overvalued Fairly valued
C D1 = $2.08 × (1 − 0.4) = $1.248 V0 = (D1 + P1)/ (1 + r)1 V0 = (1.248 + 33.80) / 1.12 = $31.29 The stock is currently trading at its intrinsic value of $31.29, so it is fairly valued.
Andy Zimmerman, a financial analyst at Winsdor Capital, wants to estimate the return on the stock of ZimCo. The stock is currently trading at $38 per share. However, most analysts believe that the stock's intrinsic value is $45. The required return on equity for ZimCo. is 11% per year. Given that the market price of the stock is expected to converge to its intrinsic value in 6 months, the expected 6‐month holding period return on the stock is closest to: .42% 18.42% 23.78%
C Expected return = Required return + Return from convergence Required return for 6 months = (1.11)0.5 − 1 = 5.36% Return from convergence of price to intrinsic value = ($45 / $38) ‐ 1 = 18.42% Therefore, expected return = 5.36% + 18.42% = 23.78%
An analyst gathered the following information regarding the stock of Pluto Inc: Current market price = $46 Required rate of return on equity = 12% Consensus growth = 5% Given that the stock offers a dividend yield of 5.5%, based on its justified dividend yield, the stock is most likely: Undervalued Fairly valued Overvalued
C Justified dividend yield = (r − g) / (1 + g) = (0.12 − 0.05) / 1.05 = 6.67% Since the stock's justified dividend yield is higher than its current dividend yield, it is overvalued.
Jacob Lasek is conducting research on Pfizer, a large global pharmaceutical company. He expects global nominal GDP to grow at 4.5% over the long run based on a 2% real growth rate and a 2.5% inflation rate. Lasek believes that global sales of Alzheimer's drugs will grow at a 100bp faster rate than nominal GDP over the long run and believes that sales of Pfizer's Alzheimer's drugs will decline from their current levels to the projected growth rate of the Alzheimer's drugs market over the next 5 years. Which of the following approaches to modelling Pfizer's revenues is Lasek most likely using? Top‐down approach Bottom‐up approach Hybrid approach
C Lasek's long term projections are based on growth relative to nominal GDP (a top‐down approach). However, he applies the estimated growth rate to one particular segment (Alzheimer's drugs) suggesting a hybrid approach.
Sofia gathered the following information regarding the stock of Sentura Ltd: Confidence risk = 3.18% Time horizon risk = 0.82% Inflation risk = 5.43% Business cycle risk = 2.25% Market timing risk = 3.42% Sensitivity to confidence risk = 0.28 Sensitivity to time horizon risk = ‐0.41 Sensitivity to inflation risk = ‐0.19 Sensitivity to business cycle risk = 0.23 Sensitivity to market timing risk = 0.14 Given a risk‐free rate of 3.5%, the required return on the stock based on the BIRR model is closest to: 0.52% 6.28% 4.02%
C Required return = 0.035 + (0.0318 × 0.28) + [0.0082 × (−0.41)] + [0.0543 × (−0.19)] + (0.0225 × 0.23) + (0.0342 × 0.14) Required return = 4.0188%
Which of the following factors is included in the Pastor‐Stambaugh model, but not in the Fama‐French model? Size factor Value factor Liquidity factor
C The Pastor‐Stambaugh model adds a liquidity factor on top of the factors included in the Fama‐French model.
What type of approach would an active manager be using if he or she looked at balance sheets, equity analysts' recommendations, equity return on capital, and S&P 500 earnings trends on a regular basis to pick stocks? Top‐down Bottom‐up Hybrid
C This manager is using a hybrid approach by examining S&P 500 earnings trends on a regular basis, which is a trait normally associated with top‐down managers.
Diego Investments' stock is currently trading at $22.45 per share. The company recently paid a dividend of $1.80, which is expected to grow at a rate of 5.5% forever. Given that the stock is fairly valued, the required rate of return on the stock is closest to: 13.51% 11.39% 13.96%
C V0 = D1 / (r − g) 22.45 = (1.80 × 1.055) / (r − 0.055) r = 13.96%
Calculating the Value of Fixed-Rate Perpetual Preferred Stock Elite Corp. has $100 par fixed-rate perpetual preferred stock outstanding with a dividend of 8%. Given a required rate of return of 10.5%, calculate the current value of the security.
Dividend = 0.08 × 100 = $8 Value of preferred stock = 8 / 0.105 = $76.19
Justified leading P/E ratio=
Po/ E1 = (D1/E1)/r−g = (1−b)/r−g
Adjusting Beta for Beta Drift An analyst gathers the following information regarding a company: Risk-free rate of return = 5.5% Equity market risk premium = 4.0% Beta = 1.20 Use the CAPM to calculate the company's required return on equity using (1) raw beta and (2) adjusted beta.
Required return (based on raw beta) = 0.055 + (1.20 × 0.04) = 10.30% Adjusted beta = (2/3 × 1.20) + (1/3 × 1.0) = 1.13 Required return (based on adjusted beta) = 0.055 + (1.13 × 0.04) = 10.02%
Calculating the Required Return on Equity Given a beta of 1.15, an equity risk premium of 7%, and a risk-free rate of 4.5%, calculate the required rate of return on the stock.
Required return = 4.5% + 1.15 (7%) = 12.55%
Calculating the Implied Growth Rate Using the Gordon Growth Model Beta Inc's stock is currently trading at $28.50 per share. The company recently paid a dividend of $2.15. Given a required rate of return of 10.5%, calculate the implied growth rate.
V 0 =D 0 (1+g)/(r−g) 28.50 = 2.15 (1 + g) / (0.105 - g) 2.9925 - 28.5g = 2.15 + 2.15g g = 2.75% If analysts expect the company's actual growth rate to be greater (less) than 2.75%, the stock is undervalued (overvalued).
Present Value of Growth Opportunities
Vo = E1/r = PVGO 1) Calculate intrinsic value 2) calculate no-growth value ( E1/r) 3 PVGO = Vo-NGV
The H-Model =
Vo=Do(1+gL)/r−g L + DoH(gS−g)/r−g L •gS = Short-term high growth rate •gL = Long-term sustainable growth rate •r = required return •H = Half-life = 0.5 times the length of the high growth period
Which of the following is most likely regarding the Fama‐French model? The smaller the company and the greater the book‐to‐market ratio, the greater the required return. The larger the company and the lower the book‐to‐market ratio, the greater the required return. The smaller the company and the lower the book‐to‐market ratio, the greater the required return.
a According to the Fama‐French model, the smaller the company (positive size beta) and the greater the book‐to‐market ratio (positive value beta), the greater the required return.
Andy Zimmerman, a financial analyst at Winsdor Capital, wants to estimate the return on the stock of ZimCo. The stock is currently trading at $38 per share. However, most analysts believe that the stock's intrinsic value is $45. The required return on equity for ZimCo. is 11% per year. Given that the market price is expected to converge to its intrinsic value in 3 years, the expected 1‐year holding period return on the stock is closest to: 15.77% 16.80% 18.39%
a Required return over a 3‐year period = (1.11)3 − 1 = 36.76% Return from convergence of price to intrinsic value = ($45 / $38) − 1 = 18.42% Expected return over a 3‐year horizon = 36.76% + 18.42% = 55.18% Annualized expected return = (1.5518)1/3 − 1 = 15.77%
When using the free cash flow model for forecasting equity values, what changes need to be made to the time horizon of the forecast if the company expects to start producing negative cash flows? The forecasting horizon would remain unchanged. The forecasting horizon would have to be extended to the point where free cash flows turn neutral. The forecasting horizon would have to be extended to the point where free cash flows turn positive.
c The forecasting horizon would have to be extended to the point where free cash flows turn positive.
Sustainable Growth Rate =
g=b(ROE) g=growth rate b= rentention rate
