标题: Reading 60: Equity Valuation: Concepts and Basic Tools-LOS e [打印本页]
作者: 1215 时间: 2011-3-30 11:51 标题: [2011]Session14-Reading 60: Equity Valuation: Concepts and Basic Tools-LOS e
Session 14: Equity Analysis and Valuation
Reading 60: Equity Valuation: Concepts and Basic Tools
LOS e: Calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate.
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: 1215 时间: 2011-3-30 11:51
Which of the following statements concerning security valuation is least accurate?
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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 two years, and a required return of 15% is estimated to be worth $18.70 currently. | |
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B) |
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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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: 1215 时间: 2011-3-30 11:52
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: 1215 时间: 2011-3-30 11:52
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: 1215 时间: 2011-3-30 11:52
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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A) |
At the end of two years, Computech's stock will sell for $20.64. | |
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B) |
Computech's stock is currently worth $17.46. | |
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C) |
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: 1215 时间: 2011-3-30 11:52
Given the following information, compute the implied dividend growth rate.
- Profit margin = 10.0%
- Total asset turnover = 2.0 times
- Financial leverage = 1.5 times
- Dividend payout ratio = 40.0%
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%.
作者: 1215 时间: 2011-3-30 11:53
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: 1215 时间: 2011-3-30 11:53
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: 1215 时间: 2011-3-30 11:53
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: 1215 时间: 2011-3-30 11:53
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: 1215 时间: 2011-3-30 11:53
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: 1215 时间: 2011-3-30 11:54
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: 1215 时间: 2011-3-30 11:54
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: 1215 时间: 2011-3-30 11:54
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: 1215 时间: 2011-3-30 11:54
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: 1215 时间: 2011-3-30 11:55
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: 1215 时间: 2011-3-30 11:55
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: 1215 时间: 2011-3-30 11:55
A firm has a profit margin of 10%, an asset turnover of 1.2, an equity multiplier of 1.3, and an earnings retention ratio of 0.5. What is the firm's internal growth rate?
ROE = (Net Income / Sales)(Sales / Total Assets)(Total Assets / Total Equity)
ROE = (0.1)(1.2)(1.3) = 0.156
g = (retention ratio)(ROE) = 0.5(0.156) = 0.078 or 7.8%
作者: 1215 时间: 2011-3-30 11:55
In its latest annual report, a company reported the following:
| Net income |
= $1,000,000 |
| Total equity |
= $5,000,000 |
| Total assets |
= $10,000,000 |
| Dividend payout ratio |
= 40% |
Based on the sustainable growth model, the most likely forecast of the company’s future earnings growth rate is:
g = (RR)(ROE)
RR = 1 ? dividend payout ratio = 1 ? 0.4 = 0.6
ROE = NI / Total Equity = 1,000,000 / 5,000,000 = 1 / 5 = 0.2
Note: This is the "simple" calculation of ROE. Since we are only given these inputs, these are what you should use. Also, if given beginning and ending equity balances, use the average in the denominator.
g = (0.6)(0.2) = 0.12 or 12%
作者: 1215 时间: 2011-3-30 11:56
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: 1215 时间: 2011-3-30 11:56
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: 1215 时间: 2011-3-30 11:56
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: 1215 时间: 2011-3-30 11:56
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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B) |
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: 1215 时间: 2011-3-30 11:56
Which of the following statements about the constant growth dividend discount model (DDM) is least accurate?
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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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B) |
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: 1215 时间: 2011-3-30 11:57
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: 1215 时间: 2011-3-30 11:57
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: 1215 时间: 2011-3-30 11:57
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: 1215 时间: 2011-3-30 11:57
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
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