标题: Reading 56: An Introduction to Security Valuation LOSc习题精 [打印本页]
作者: honeycfa 时间: 2010-4-22 22:07 标题: [2010]Session 14-Reading 56: An Introduction to Security Valuation LOSc习题精
LOS c, (Part 1): Calculate and interpret the value of a preferred stock using the dividend discount model (DDM).
The yield on a company’s 7.5%, $50 par preferred stock is 6%. The value of the preferred stock is closest to:
The preferred dividend is 0.075($50) = $3.75. The value of the preferred = $3.75 / 0.06 = $62.50.
作者: honeycfa 时间: 2010-4-22 22:08
A preferred stock’s dividend is $5 and the firm’s bonds currently yield 6.25%. The preferred shares are priced to yield 75 basis points below the bond yield. The price of the preferred is closest to:
Preferred stock yield (Kp) = bond yield – 0.75% = 6.25% ? 0.75% = 5.5%
Value = dividend / Kp = $5 / 0.055 = $90.91.
作者: honeycfa 时间: 2010-4-22 22:08
Assuming a discount rate of 15%, a preferred stock with a perpetual dividend of $10 is valued at approximately:
The formula for the value of preferred stock with a perpetual dividend is: D / kp, or 10.0 / 0.15 = $66.67.
作者: honeycfa 时间: 2010-4-22 22:08
Calculate the value of a preferred stock that pays an annual dividend of $5.50 if the current market yield on AAA rated preferred stock is 75 basis points above the current T-Bond rate of 7%.
kpreferred = base yield + risk premium = 0.07 + 0.0075 = 0.00775
ValuePreferred = Dividend / kpreferred
Value = 5.50 / 0.0775 = $70.97
作者: honeycfa 时间: 2010-4-22 22:09
A company has 8 percent preferred stock outstanding with a par value of $100. The required return on the preferred is 5 percent. What is the value of the preferred stock?
The annual dividend on the preferred is $100(.08) = $8.00. The value of the preferred is $8.00/0.05 = $160.00.
作者: honeycfa 时间: 2010-4-22 22:09
If a preferred stock that pays a $11.50 dividend is trading at $88.46, what is the market’s required rate of return for this security?
From the formula: ValuePreferred Stock = D / kp, we derive kp = D / ValuePreferred Stock = 11.50 / 88.46 = 0.1300, or 13.00%.
作者: honeycfa 时间: 2010-4-22 22:09
A company has 6% preferred stock outstanding with a par value of $100. The required return on the preferred is 8%. What is the value of the preferred stock?
The annual dividend on the preferred is $100(.06) = $6.00. The value of the preferred is $6.00/0.08 = $75.00.
作者: honeycfa 时间: 2010-4-22 22:09
What is the value of a preferred stock that is expected to pay a $5.00 annual dividend per year forever if similar risk securities are now yielding 8%?
作者: honeycfa 时间: 2010-4-22 22:10
The preferred stock of the Delco Investments Company has a par value of $150 and a dividend of $11.50. A shareholder’s required return on this stock is 14%. What is the maximum price he would pay?
Value of preferred = D / kp = $11.50 / 0.14 = $82.14
作者: honeycfa 时间: 2010-4-22 22:10
LOS c, (Part 2): Calculate and interpret the value of a common stock using the dividend discount model (DDM).
An analyst projects the following pro forma financial results for Magic Holdings, Inc., in the next year:
- Sales of $1,000,000
- Earnings of $200,000
- Total assets of $750,000
- Equity of $500,000
- Dividend payout ratio of 62.5%
- Shares outstanding of 50,000
- Risk free interest rate of 7.5%
- Expected market return of 13.0%
- Stock Beta at 1.8
If the analyst assumes Magic Holdings, Inc. will produce a constant rate of dividend growth, the value of the stock is closest to:
Infinite period DDM: P0 = D1 / (ke – g)
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D1 |
= (Earnings × Payout ratio) / average number of shares outstanding |
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= ($200,000 × 0.625) / 50,000 = $2.50. |
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ke |
= risk free rate + [beta × (expected market return – risk free rate)] |
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ke |
= 7.5% + [1.8 × (13.0% - 7.5%)] = 17.4%. |
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g |
= (retention rate × ROE) |
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Retention = (1 – Payout) = 1 – 0.625 = 0.375. |
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ROE = net income/equity |
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= 200,000/500,000 = 0.4 |
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g |
= 0.375 × 0.4 = 0.15. |
P0 = D1 / (ke – g) = $2.50 / (0.174 - 0.15) = 104.17.
作者: honeycfa 时间: 2010-4-22 22:10
Which of the following statements about the constant growth dividend discount model (DDM) in its application to investment analysis is FALSE? The model:
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is best applied to young, rapidly growing firms. | |
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can’t be applied when g > K. | |
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can’t handle firms with variable dividend growth. | |
The model is most appropriately used when the firm is mature, with a moderate growth rate, paying a constant stream of dividends. In order for the model to produce a finite result, the company’s growth rate must not exceed the required rate of return.
作者: honeycfa 时间: 2010-4-22 22:11
A firm pays an annual dividend of $1.15. The risk-free rate (RF) is 2.5%, and the total risk premium (RP) for the stock is 7%. What is the value of the stock, if the dividend is expected to remain constant?
If the dividend remains constant, g = 0.
P = D1 / (k-g) = 1.15 / (0.095 - 0) = $12.10
作者: honeycfa 时间: 2010-4-22 22:12
Given the following estimated financial results, value the stock of FishnChips, Inc., using the infinite period dividend discount 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.)
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A) |
Unable to calculate stock value because ke < g. | |
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Here, we are given all the inputs we need. Use the following steps to calculate the value of the stock:
First, expand the infinite period DDM:
DDM formula: P0 = D1 / (ke – g)
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D1 |
= (Earnings × Payout ratio) / average number of shares outstanding |
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= ($150,000 × 0.60) / 75,000 = $1.20 |
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ke |
= nominal risk free rate + [beta × (expected market return – nominal risk free rate)] |
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Note: Nominal risk-free rate |
= (1 + real risk free rate) × (1 + expected inflation) – 1 |
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= (1.04)×(1.03) – 1 = 0.0712, or 7.12%. |
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ke |
= 7.12% + [2.1 × (13.0% ? 7.12%)] = 0.19468 |
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g |
= (retention rate × ROE) |
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Retention |
= (1 – Payout) = 1 – 0.60 = 0.40. |
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ROE |
= (net income / sales)(sales / total assets)(total assets / equity) |
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= (150,000 / 1,000,000)(1,000,000 / 800,000)(800,000 / 400,000) |
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= 0.375 |
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g |
= 0.375 × 0.40 = 0.15 |
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Then, calculate: P0 = D1 / (ke – g) = $1.20 / (0.19468 ? 0.15) = 26.86.
作者: honeycfa 时间: 2010-4-22 22:12
Which of the following statements concerning security valuation is least accurate?
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A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $36.11. | |
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B) |
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 two years, and a required return of 15% is estimated to be worth $18.70 currently. | |
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C) |
A stock with an expected dividend payout ratio of 30%, a required return of 8%, an expected dividend growth rate of 4%, and expected earnings of $4.15 per share is estimated to be worth $31.13 currently. | |
A stock with a dividend last year of $3.25 per share, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $37.33 using the 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 gives the present value of the stock. the future cash flows are the dividend in year 1 plus the dividend and value of the stock in year 2 thus the equation becomes: Vo = 2.2 / 1.15 + (2.2 + 20) / 1.152 = $18.70
For the answer choice where the stock value is $31.13 use the DDM 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
作者: honeycfa 时间: 2010-4-22 22:12
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.
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 valued using the infinite period dividend discount model (DDM) as ($3.41) / (0.128 – 0.10) = $121.79.
作者: honeycfa 时间: 2010-4-22 22:12
Which of the following is a shortcoming(s) of the constant growth dividend discount model?
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Small differences in key assumptions can produce widely varying values. | |
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Firms with temporary high-growth expectations have characteristics that are inconsistent with model. | |
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Both of these choices are correct. | |
The constant growth dividend discount model cannot be used to value firms that are experiencing supernormal growth and are very dependent on the assumed values of k and g.
作者: honeycfa 时间: 2010-4-22 22:13
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 the market is 10%, and the stock's beta is 0.5.
The discount rate is ke = 0.05 + 0.5(0.10 ? 0.05) = 0.075. Use the infinite period dividend discount model to value the stock. The stock value = D1 / (ke – g) = (0.25 × 1.06) / (0.075 – 0.06) = $17.67.
作者: honeycfa 时间: 2010-4-22 22:13
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 1.5 that paid a $2 dividend last year if dividends are expected to grow at a 5% rate forever?
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) = 2.10
P0 = 2.10 / (0.155 ? 0.05) = $20.00
作者: honeycfa 时间: 2010-4-22 22:13
If a stock sells for $50 that has an expected annual dividend of $2 and has a sustainable growth rate of 5%, what is the market discount rate for this stock?
k = [(D1 / P) + g] = [(2/50) + 0.05] = 0.09, or 9.00%.
作者: honeycfa 时间: 2010-4-22 22:14
Regarding the estimates required in the constant growth dividend discount model, which of the following statements is most accurate?
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Dividend forecasts are less reliable than estimates of other inputs. | |
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The model is most influenced by the estimates of "k" and "g." | |
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The variables "k" and "g" are easy to forecast. | |
The relationship between "k" and "g" is critical - small changes in the difference between these two variables results in large value fluctuations.
作者: honeycfa 时间: 2010-4-22 22:14
All else equal, if there is an increase in the required rate of return, a stock’s value as estimated by the constant growth dividend discount model (DDM) will:
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increase or decrease, depending upon the relationship between ke and ROE. | |
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If ke increases, the spread between ke and g widens (increasing the denominator), resulting in a lower valuation.
作者: honeycfa 时间: 2010-4-22 22:14
An analyst has gathered the following data for Webco, Inc:
- Retention = 40%
- ROE = 25%
- k = 14%
Using the infinite period, or constant growth, dividend discount model, calculate the price of Webco’s stock assuming that next years earnings will be $4.25.
g = (ROE)(RR) = (0.25)(0.4) = 10%
V = D1 / (k – g)
D1 = 4.25 (1 ? 0.4) = 2.55
G = 0.10
K – g = 0.14 ? 0.10 = 0.04
V = 2.55 / 0.04 = 63.75
作者: honeycfa 时间: 2010-4-22 22:14
Using the constant growth dividend discount model to value a firm whose growth rate is greater than its required return on equity would result in a value that is:
For the constant growth DDM to work k must be greater than g.
作者: honeycfa 时间: 2010-4-22 22:15
The constant-growth dividend discount model would typically be most appropriate in valuing a stock of a:
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moderate growth, "mature" company. | |
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rapidly growing company. | |
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new venture expected to retain all earnings for several years. | |
Remember, the infinite period DDM has the following assumptions:
- The stock pays dividends and they grow at a constant rate.
- The constant growth rate, g, continues for an infinite period.
- k must be greater than g. If not, the math will not work.
If any one of these assumptions is not met, the model breaks down. The infinite period DDM doesn’t work with growth companies. Growth companies are firms that currently have the ability to earn rates of return on investments that are currently above their required rates of return. The infinite period DDM assumes the dividend stream grows at a constant rate forever while growth companies have high growth rates in the early years that level out at some future time. The high early or supernormal growth rates will also generally exceed the required rate of return. Since the assumptions (constant g and k > g) don’t hold, the infinite period DDM cannot be used to value growth companies.
作者: honeycfa 时间: 2010-4-22 22:15
Which of the following statements about the constant growth dividend discount model (DDM) is FALSE?
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For the constant growth DDM to work, the growth rate must exceed the required return on equity. | |
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The constant growth DDM is used primarily for stable mature stocks. | |
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C) |
In the constant growth DDM dividends are assumed to grow at a constant rate forever. | |
Dividends grow at constant rate forever.
Constant growth DDM is used for mature firms.
k must be greater than g.
作者: honeycfa 时间: 2010-4-22 22:15
A stock is expected to pay a dividend of $1.50 at the end of each of the next three years. At the end of three years the stock price is expected to be $25. The equity discount rate is 16 percent. What is the current stock price?
The value of the stock today is the present value of the dividends and the expected stock price, discounted at the equity discount rate:
$1.50/1.16 + $1.50/1.162 + $1.50/1.163 + $25.00/1.163 = $19.39
作者: honeycfa 时间: 2010-4-22 22:16
Use the following information on Brown Partners, Inc. to compute the current stock price.
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Dividend just paid = $6.10
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Expected dividend growth rate = 4%
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Expected stock price in one year = $60
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Risk-free rate = 3%
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Equity risk premium = 12%
The current stock price is equal to (D1 + P1) / (1 + ke). D1 equals $6.10(1.04) = $6.34. The equity discount rate is 3% + 12% = 15%. Therefore the current stock price is ($6.34 + $60)/(1.15) = $57.70
作者: honeycfa 时间: 2010-4-22 22:16
An investor is considering acquiring a common stock that he would like to hold for one year. He expects to receive both $1.50 in dividends and $26 from the sale of the stock at the end of the year. What is the maximum price he should pay for the stock today to earn a 15 percent return?
By discounting the cash flows for one period at the required return of 15% we get: x = (26 + 1.50) / (1+.15)1
(x)(1.15) = 26 + 1.50
x = 27.50 / 1.15
x = $23.91
作者: honeycfa 时间: 2010-4-22 22:17
Assume that a stock paid a dividend of $1.50 last year. Next year, an investor believes that the dividend will be 20% higher and that the stock will be selling for $50 at year-end. Assume a beta of 2.0, a risk-free rate of 6%, and an expected market return of 15%. What is the value of the stock?
Using the Capital Asset Pricing Model, we can determine 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 the future dividend are determined by discounting the expected cash flows at the discount rate of 24%: (50 + 1.8) / 1.24 = $41.77.
作者: honeycfa 时间: 2010-4-22 22:17
The following data pertains to a common stock:
- It will pay no dividends for two years.
- The dividend three years from now is expected to be $1.
- Dividends are expected to grow at a 7% rate from that point onward.
If an investor requires a 17% return on this stock, what will they be willing to pay for this stock now?
time line = $0 now; $0 in yr 1; $0 in yr 2; $1 in yr 3.
P2 = D3/(k - g) = 1/(.17 - .07) = $10
Note the math. The price is always one year before the dividend date.
Solve for the PV of $10 to be received in two years.
FV = 10; n = 2; i = 17; compute PV = $7.30
作者: honeycfa 时间: 2010-4-22 22:17
A firm will not pay dividends until four years from now. Starting in year four dividends will be $2.20 per share, the retention ratio will be 40%, and ROE will be 15%. If k = 10%, what should be the value of the stock?
g = ROE × retention ratio = ROE × b = 15 × 0.4 = 6%
Based on the growth rate we can calculate the expected price in 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
作者: honeycfa 时间: 2010-4-22 22:18
Utilizing the infinite period dividend discount model, all else held equal, if the required rate of return (Ke) decreases, the model yields a price that is:
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increased, due to a smaller spread between required return and growth. | |
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reduced, due to increased spread between growth and required return. | |
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reduced, due to the reduction in discount rate. | |
The denominator of the single-stage DDM is the spread between required return Ke, and expected growth rate, g. The smaller the denominator, all else held equal, the larger the computed value.
作者: honeycfa 时间: 2010-4-22 22:18
A stock has the following elements: last year’s dividend = $1, next year’s dividend is 10% higher, the price will be $25 at year-end, the risk-free rate is 5%, the market premium is 5%, and the stock’s beta is 1.2.
What happens to the price of the stock if the beta of the stock increases to 1.5? It will:
When the beta of a stock increases, its required return will increase. The increase in the discount rate leads to a decrease in the PV of the future cash flows.
What will be the current price of the stock with a beta of 1.5?
k = 5 + 1.5(5) = 12.5%
P0 = (1.1 / 1.125) + (25 / 1.125) = $23.20
作者: honeycfa 时间: 2010-4-22 22:18
What value would be placed on a stock that currently pays no dividend but is expected to start paying a $1 dividend five years from now? Once the stock starts paying dividends, the dividend is expected to grow at a 5 percent annual rate. The appropriate discount rate is 12 percent.
P4 = D5/(k-g) = 1/(.12-.05) = 14.29
P0 = [FV = 14.29; n = 4; i = 12] = $9.08.
作者: honeycfa 时间: 2010-4-22 22:19
Assume a company has earnings per share of $5 and this year paid out 40% in dividends. The earnings and dividend growth rate for the next 3 years will be 20%. At the end of the third year the company will start paying out 100% of earnings in dividends and earnings will increase at an annual rate of 5% thereafter. If a 12% rate of return is required, the value of the company is approximately:
First, calculate the dividends in years 0 through 4: (We need D4 to calculate the value in Year 3)
D0 = (0.4)(5) = 2
D1 = (2)(1.2) = 2.40
D2 = (2.4)(1.2) = 2.88
D3 = E3 = 5(1.2)3 = 8.64
g after year 3 will be 5%, so
D4 = 8.64 × 1.05 = 9.07
Then, solve for the terminal value at the end of period 3 = D4 / (k ? g) = 9.07 / (0.12 ? 0.05) = $129.57
Present value of the cash flows = value of stock = 2.4 / (1.12)1 + 2.88 / (1.12)2 + 8.64 / (1.12)3 + 129.57 / (1.12)3 = 2.14 + 2.29 + 6.15 + 92.22 = 102.80
作者: honeycfa 时间: 2010-4-22 22:19
Use the following information and the multi-period dividend discount model to find the value of Computech’s common stock.
- 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 to stabilize at 4%.
- The required return for Computech’s common stock is 15%.
Which of the following statements about Computech's stock is least accurate?
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At the end of two years, Computech's stock will sell for $20.64. | |
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Computech's stock is currently worth $17.46. | |
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The dividend at the end of year three is expected to be $2.27. | |
The dividends for years 1, 2, and 3 are expected to 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.
作者: honeycfa 时间: 2010-4-22 22:19
An analyst gathered the following information about a company:
- The stock is currently trading at $31.00 per share.
- Estimated growth rate for the next three years is 25%.
- Beginning in the year 4, the growth rate is expected to decline and stabilize at 8%.
- The required return for this type of company is estimated at 15%.
- The dividend in year 1 is estimated at $2.00.
The stock is undervalued by approximately:
The high “supernormal” growth in the first three years and the decrease in growth thereafter signals that we should use a combination of the multi-period and finite dividend growth models (DDM) to value the stock.
Step 1: Determine the dividend stream through year 4
- D1 = $2.00 (given)
- D2 = D1 × (1 + g) = 2.00 × (1.25) = $2.50
- D3 = D2 × (1 + g) = $2.50 × (1.25) = $3.13
- D4 = D3 × (1 + g) = $3.13 × (1.08) = $3.38
Step 2: Calculate the value of the stock at the end of year 3 (using D4)
- P3 = D4 / (ke – g) = $3.38 / (0.15 – 0.08) = $48.29
Step 3: Calculate the PV of each cash flow stream at ke = 15%, and sum the cash flows. Note: We suggest you clear the financial calculator memory registers before calculating the value. The present value of:
- D1 = 1.74 = 2.00 / (1.15)1, or FV = -2.00, N = 1, I/Y = 15, PV = 1.74
- D2 = 1.89 = 2.50 / (1.15)2, or FV = -2.50, N = 2, I/Y = 15, PV = 1.89
- D3 = 2.06 = 3.13 / (1.15)3, or FV = -3.13, N = 3, I/Y = 15, PV = 2.06
- P3 = 31.75 = 48.29 / (1.15)3, or FV = -48.29, N = 3, I/Y = 15, PV = 31.75
- Sum of cash flows = 37.44.
- Thus, the stock is undervalued by 37.44 – 31.00 = approximately 6.40.
Note: Future values are entered in a financial calculator as negatives to ensure that the PV result is positive. It does not mean that the cash flows are negative. Also, your calculations may differ slightly due to rounding. Remember that the question asks you to select the closest answer.
作者: honeycfa 时间: 2010-4-22 22:20
The last dividend paid on a common stock was $2.00, the growth rate is 5% and investors require a 10% return. Using the infinite period dividend discount model, calculate the value of the stock.
2(1.05) / (0.10 - 0.05) = $42.00
作者: honeycfa 时间: 2010-4-22 22:20
Day and Associates is experiencing a period of abnormal growth. The last dividend paid by Day was $0.75. Next year, they anticipate growth in dividends and earnings of 25% followed by negative 5% growth in the second year. The company will level off to a normal growth rate of 8% in year three and is expected to maintain an 8% growth rate for the foreseeable future. Investors require a 12% rate of return on Day.
What is the approximate amount that an investor would be willing to pay today for the two years of abnormal dividends?
First find the abnormal dividends and then discount them back to the present.
$0.75 × 1.25 = $0.9375 × 0.95 = $0.89.
D1 = $0.9375; D2 = $0.89.
At this point you can use the cash flow keys with CF0 = 0, CF1 = $0.9375 and CF2 = $0.89.
Compute for NPV with I/Y = 12. NPV = $1.547.
Alternatively, you can put the dividends in as future values, solve for present values and add the two together.
What would an investor pay for Day and Associates today?
Here we find P2 using the constant growth dividend discount model.
P2 = $0.89 × 1.08 / (0.12 – 0.08) = $24.03.
Discount that back to the present at 12% for 2 periods and add it to the answer in the previous question.
N = 2; I/Y = 12; PMT = 0; FV = $24.03; CPT &rarr PV = $19.16.
Add $1.55 (the present value of the abnormal dividends) to $19.16 and you get $20.71.
作者: honeycfa 时间: 2010-4-22 22:20
Calculate the value of a common stock that last paid a $2.00 dividend if the required rate of return on the stock is 14 percent and the expected growth rate of dividends and earnings is 6 percent. What growth model is an example of this calculation?
Value of stock Growth model
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A) |
| $26.50 |
Supernormal growth | | |
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|
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$2(1.06)/0.14 - 0.06 = $26.50.
This calculation is an example of the Gordon Growth Model also known as the constant growth model.
作者: honeycfa 时间: 2010-4-22 22:21
A company last paid a $1.00 dividend, the current market price of the stock is $20 per share and the dividends are expected to grow at 5 percent forever. What is the required rate of return on the stock?
D0 (1 + g) / P0 + g = k
1.00 (1.05) / 20 + 0.05 = 10.25%.
作者: honeycfa 时间: 2010-4-22 22:21
Using the one-year holding period and multiple-year holding period dividend discount model (DDM), calculate the change in value of the stock of Monster Burger Place under the following scenarios. First, assume that an investor holds the stock for only one year. Second, assume that the investor intends to hold the stock for two years. Information on the stock is as follows:
- Last year’s dividend was $2.50 per share.
- Dividends are projected to grow at a rate of 10.0% for each of the next two years.
- Estimated stock price at the end of year 1 is $25 and at the end of year 2 is $30.
- Nominal risk-free rate is 4.5%.
- The required market return is 10.0%.
- Beta is estimated at 1.0.
The value of the stock if held for one year and the value if held for two years are:
Year one Year two
First, we need to calculate the required rate of return. When a stock’s beta equals 1, the required return is equal to the market return, or 10.0%. Thus, ke = 0.10. Alternative: Using the capital asset pricing model (CAPM), ke = Rf + Beta * (Rm – Rf) = 4.5% + 1 * (10.0% - 4.5%) = 4.5% + 5.5% = 10.0%.
Next, we need to calculate the dividends for years 1 and 2.
- D1 = D0 * (1 + g) = 2.50 * (1.10) = 2.75
- D2 = D1 * (1 + g) = 2.75 * (1.10) = 3.03
Then, we use the one-year holding period DDM to calculate the present value of the expected stock cash flows (assuming the one-year hold).
- P0 = [D1/ (1 + ke)] + [P1 / (1 + ke)] = [$2.75 / (1.10)] + [$25.0 / (1.10)] = $25.22. Shortcut: since the growth rate in dividends, g, was equal to ke, the present value of next year’s dividend is equal to last year’s dividend.
Finally, we use the multi-period DDM to calculate the return for the stock if held for two years.
- P0 = [D1/ (1 + ke)] + [D2/ (1 + ke)2] + [P2 / (1 + ke)2] = [$2.75 / (1.10)] + [$3.03 / (1.10)2] + [$30.0 / (1.10)2] = $29.80. Note: since the growth rate in dividends, g, was equal to ke, the present value of next year’s dividend is equal to last year’s dividend (for periods 1 and 2). Thus, a quick calculation would be 2.5 * 2 + $30.00 / (1.10)2 = 29.80.
作者: honeycfa 时间: 2010-4-22 22:21
Baker Computer earned $6.00 per share last year, has a retention ratio of 55%, and a return on equity (ROE) of 20%. Assuming their required rate of return is 15%, how much would an investor pay for Baker on the basis of the earnings multiplier model?
g = Retention × ROE = (0.55) × (0.2) = 0.11
P0/E1 = 0.45 / (0.15 ? 0.11) = 11.25
Next year's earnings E1 = E0 × (1 + g) = (6.00) × (1.11) = $6.66
P0 = 11.25($6.66) = $74.93
作者: honeycfa 时间: 2010-4-22 22:22
Assume that at the end of the next year, Company A will pay a $2.00 dividend per share, an increase from the current dividend of $1.50 per share. After that, the dividend is expected to increase at a constant rate of 5%. If an investor requires a 12% return on the stock, what is the value of the stock?
P0 = D1 / k ? g
D1 = $2
g = 0.05
k = 0.12
P0 = 2 / 0.12 ? 0.05 = 2 / 0.07 = $28.57
作者: honeycfa 时间: 2010-4-22 22:22
Company B paid a $1.00 dividend per share last year and is expected to continue to pay out 40% of its earnings as dividends for the foreseeable future. If the firm is expected to earn a 10% return on equity in the future, and if an investor requires a 12% return on the stock, the stock’s value is closest to:
P0 = Value of the stock = D1 / (k ? g)
g = (RR)(ROE)
RR = 1 ? dividend payout = 1 ? 0.4 = 0.6
ROE = 0.1
g = (0.6)(0.1) = 0.06
D1 = (D0)(1 + g) = (1)(1 + 0.06) = $1.06
P0 = 1.06 / (0.12 ? 0.06) = 1.06 / 0.06 = $17.67
作者: honeycfa 时间: 2010-4-22 22:22
Assume that the expected dividend growth rate (g) for a firm decreased from 5% to zero. Further, assume that the firm's cost of equity (k) and dividend payout ratio will maintain their historic levels. The firm's P/E ratio will most likely:
The P/E ratio may be defined as: Payout ratio / (k - g), so if k is constant and g goes to zero, the P/E will decrease.
作者: honeycfa 时间: 2010-4-22 22:23
Using an infinite period dividend discount model, find the value of a stock that last paid a dividend of $1.50. Dividends are expected to grow at 6 percent forever, the expected return on the market is 12 percent and the stock’s beta is 0.8. The risk-free rate of return is 5 percent.
First find the required rate of return using the CAPM equation.
k = 0.05 + 0.8(0.12 - 0.05) = 10.6%
$1.50(1.06) /(0.106 - 0.06) = $34.57
作者: honeycfa 时间: 2010-4-22 22:23
A company has just paid a $2.00 dividend per share and dividends are expected to grow at a rate of 6% indefinitely. If the required return is 13%, what is the value of the stock today?
P0 = D1 / (k - g) = 2.12 / (0.13 - 0.06) = $30.29
作者: honeycfa 时间: 2010-4-22 22:23
A firm is expected to have four years of growth with a retention ratio of 100%. Afterwards the firm’s dividends are expected to grow 4% annually, and the dividend payout ratio will be set at 50%. If earnings per share (EPS) = $2.4 in year 5 and the required return on equity is 10%, what is the stock’s value today?
Dividend in year 5 = (EPS)(payout ratio) = 2.4 × 0.5 = 1.2
P4 = 1.2 / (0.1 ? 0.04) = 1.2 / 0.06 = $20
P0 = PV (P4) = $20 / (1.10)4 = $13.66
作者: honeycfa 时间: 2010-4-22 22:24
Bybee is expected to have a temporary supernormal growth period and then level off to a “normal,” sustainable growth rate forever. The supernormal growth is expected to be 25 percent for 2 years, 20 percent for one year and then level off to a normal growth rate of 8 percent forever. The market requires a 14 percent return on the company and the company last paid a $2.00 dividend. What would the market be willing to pay for the stock today?
First, find the future dividends at the supernormal growth rate(s). Next, use the infinite period dividend discount model to find the expected price after the supernormal growth period ends. Third, find the present value of the cash flow stream.
D1 = 2.00 (1.25) = 2.50 (1.25) = D2 = 3.125 (1.20) = D3 = 3.75
P2 = 3.75/(0.14 - 0.08) = 62.50
N = 1; I/Y = 14; FV = 2.50; compute PV = 2.19.
N = 2; I/Y = 14; FV = 3.125; compute PV = 2.40.
N = 2; I/Y = 14; FV = 62.50; compute PV = 48.09.
Now sum the PV’s: 2.19 + 2.40 + 48.09 = $52.68.
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