Reading 50- Equity Valuation: Concepts & Basic Tools

price multiples advantages

-predict future returns -widely used -easily available -time series comparison -cross sectional comparison -EV/EBITDA

asset-based models disadvantages:**

-MV debt hard to obtain -MV different than book values -do not account for intangible assets -assets difficult to value during hyperinflation

discounted cash flow advantages

-based on PV of future cash flows -widely accepted and used

asset-based models advantages:

-floor values: A-L= E 100-20=80 -works for assets that have easily determinable market values (tangible short-term assets) -works for companies that report fair values

discounted cash flow disadvantages

-inputs have to be estimated -estimates sensitive to inputs

present value of a non-callable, non-convertible PERPETUAL preferred share

V0= D0/r

present value of a non-callable, non-convertible preferred stock

V0=∑ D/(1+r) + F/(1+r) (similar to DDM but P1 is replaced by F) F= preferred stock's par value

The two-stage model is best for valuing _______ companies.

transitioning from growth to mature stage

price multiples disadvantages:

-lagging (historical) price multiples -cannot be comparable when firms are different sizes -impacted by economic conditions -might conflict with fundamental method -sensitive to different accounting methods -negative denominator

What is the intrinsic value of a company's stock if dividends are {EXPECTED TO GROW AT 5% INTO THE FUTURE}, the most recent dividend was $1, and investors' required rate of return for this stock is 10%? *hint: expected to grow= multiply numerator by 1+ expected growth rate

1*(1.05)/(.1-.05)= 21 P0= D1(1+g)/ (r-g)

Calculate EV/EBITDA:

1. short-term debt book value= book value of total debt- book value of long-term debt 2. market value of total debt= market value of long-term debt + short-term debt 3. market value of total equity= stock price * number of shares 4. enterprise value= sum of debt + equity- cash 5. EV/EBITDA= enterprise value/ (given in the problem) multiple 10 > 9= overvalued

Missed Questions

11 13 14 15* 16 17

law of one price

2 identical assets should sell at the same price (multiples based on comparables)

Witronix is a rapidly growing U.S. company that has increased free cash flow to equity and dividends at an average rate of 25% per year for the last four years. The present value model that is most appropriate for estimating the value of this company is a: A) multistage dividend discount model. B) Gordon growth model. C) single stage free cash flow to equity model.

A A multistage model is the most appropriate model because the company is growing dividends at a higher rate than can be sustained in the long run. Though the company may be able to grow dividends at a higher-than-sustainable 25% annual rate for a finite period, at some point dividend growth will have to slow to a lower, more sustainable rate. The Gordon growth model is appropriate to use for mature companies that have a history of increasing their dividend at a steady and sustainable rate. A single stage free cash flow to equity model is similar to the Gordon growth model, but values future free cash flow to equity rather than dividends.

One advantage of using price-to-book value (PBV) multiples for stock valuation is that: A) it is a stable and simple benchmark for comparison to the market price. B) most of the time it is close to the market value. C) book value of a firm can never be negative.

A Book value provides a relatively stable measure of value that can be compared to the market price. For investors who mistrust the discounted cash flow estimates of value, it provides a much simpler benchmark for comparison. Book value may or may not be closer to the market value. A firm may have negative book value if it shows accounting losses consistently.

? 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? A) $23.91. B) $27.30. C) $24.11.

A 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

Assuming that a company's return on equity (ROE) is 12% and the required rate of return is 10%, which of the following would most likely cause the company's P/E ratio to rise? A) The inflation rate falls. B) The firm's ROE falls. C) The firm's dividend payout rises.

A Decrease in the expected inflation rate. The expected inflation rate is a component of ke (through the nominal risk free rate). ke can be represented by the following: nominal risk free rate + stock risk premium, where nominal risk free rate = [(1 + real risk free rate)(1 + expected inflation rate)] - 1. If the rate of inflation decreases, the nominal risk free rate will decrease. ke will decrease. The spread between ke and g, or the P/E denominator, will decrease. P/E ratio will increase. (An increase in the stock risk premium would have the opposite effect.) Decrease in ROE: ROE is a component of g. As g decreases, the spread between ke and g, or the P/E denominator, will increase, and the P/E ratio will decrease. Increase in dividend payout/reduction in earnings retention. In this case, an increase in the dividend payout will likely decrease the P/E ratio because a decrease in earnings retention will likely lower the P/E ratio. The logic is as follows: Because earnings retention impacts both the numerator (dividend payout) and denominator (g) of the P/E ratio, the impact of a change in earnings retention depends upon the relationship of ke and ROE.* If the company is earning a higher rate on new projects than the rate required by the market (ROE> ke), investors will likely prefer that the company retain more earnings. Since an increase in the dividend payout would decrease earnings retention, the P/E ratio would fall, as investors will value the company lower if it retains a lower percentage of earnings.

Which of the following statements about the constant growth dividend discount model (DDM) is least accurate? A) For the constant growth DDM to work, the growth rate must exceed the required return on equity. B) The constant growth DDM is used primarily for stable mature stocks. C) In the constant growth DDM dividends are assumed to grow at a constant rate forever.

A Dividends grow at constant rate forever. Constant growth DDM is used for mature firms. k must be greater than g.

Which of the following is a disadvantage of using price-to-sales (P/S) multiples in stock valuations? A) The use of P/S multiples can miss problems associated with cost control. B) It is difficult to capture the effects of changes in pricing policies using P/S ratios. C) P/S multiples are more volatile than price-to-earnings (P/E) multiples.

A Due to the stability of using sales relative to earnings in the P/S multiple, an analyst may miss problems of troubled firms concerning its cost control. P/S multiples are actually less volatile than P/E ratios, which is an advantage in using the P/S multiple. Also, P/S ratios provide a useful framework for evaluating effects of pricing changes on firm value.

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.) A) $26.86. B) Unable to calculate stock value because ke < g. C) $17.91.

A 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) D1 = (Earnings × Payout ratio) / average number of shares outstanding = ($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%)] = 0.19468 g = (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) = 0.375 g = 0.375 × 0.40 = 0.15 Then, calculate: P0 = D1 / (ke - g) = $1.20 / (0.19468 − 0.15) = 26.86.

An argument against using the price to cash flow (P/CF) valuation approach is that: A) non-cash revenue and net changes in working capital are ignored when using earnings per share (EPS) plus non-cash charges as an estimate. B) cash flows are not as easy to manipulate or distort as EPS and book value. C) price to cash flow ratios are not as volatile as price-to-earnings (P/E) multiples.

A Items affecting actual cash flow from operations are ignored when the EPS plus non-cash charges estimate is used. For example, non-cash revenue and net changes in working capital are ignored. Both remaining responses are arguments in favor of using the price to cash flow approach.

An argument against using the price-to-earnings (P/E) valuation approach is that: A) earnings can be negative. B) research shows that P/E differences are significantly related to long-run average stock returns. C) earnings power is the primary determinant of investment value.

A Negative earnings render the P/E ratio useless. Both remaining factors increase the usefulness of the P/E approach.

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? A) $28.57. B) $30.00. C) $31.78.

A P0 = D1 / k − g D1 = $2 g = 0.05 k = 0.12 P0 = 2 / 0.12 − 0.05 = 2 / 0.07 = $28.57 ------------- V0= 2/1.12 + 2(1.05)/[1.12(.12-.05)]= $28.57

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. A) $9.08. B) $8.11. C) $14.29.

A P4 = D5/(k-g) = 1/(.12-.05) = 14.29 P0 = [FV = 14.29; n = 4; i = 12] = $9.08.

Which of the following statements regarding price multiples is most accurate? A) An advantage of the price/sales ratio is that it is meaningful even for distressed firms. B) A disadvantage of the price/book value ratio is that it is not an appropriate measure for firms that primarily hold liquid assets. C) A rationale for using the price/cash flow ratio is that there is only one clear definition of cash flow.

A The P/S ratio is meaningful even for distressed firms, since sales revenue is always positive. This is not the case for the P/E and P/BV ratios, which can be negative. In the P/BV ratio book value is an appropriate measure of net asset value for firms that primarily hold liquid assets. Analysts use several different definitions of cash flow (CFO, adjusted CFO, FCFE, EBITDA, etc.) to calculate P/CF ratios. When earnings are negative, the P/E ratio is meaningless.

The current price of XYZ, Inc., is $40 per share with 1,000 shares of equity outstanding. Sales are $4,000 and the book value of the firm is $10,000. What is the price/sales ratio of XYZ, Inc.? A) 10.000. B) 0.010. C) 4.000.

A The price/sales ratio is (price per share)/(sales per share) = (40)/(4,000/1,000) = 10.0. Alternatively, the price/sales ratio may be thought of as the market value of the company divided by its sales, or (40 × 1,000)/4,000, or 10.0 again.

All else equal, a firm will have a higher Price-to-Earnings (P/E) multiple if: A) the stock's beta is lower. B) return on equity (ROE) is lower. C) retention ratio is higher.

A To increase P/E ratio, lower the retention ratio, lower k and or increase g. A lower beta would lead to a lower stock risk premium and a lower k.

One advantage of price/sales (P/S) multiples over price to earnings (P/E) and price-to-book value (PBV) multiples is that: A) P/S can be used for distressed firms. B) P/S is easier to calculate. C) Regression shows a strong relationship between stock prices and sales.

A Unlike the PBV and P/E multiples, which can become negative and not meaningful, the price/sales multiple is meaningful even for distressed firms (that may have negative earnings or book value).

? 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. A) $63.75. B) $55.00. C) $125.00.

A 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

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? A) $25.00. B) $12.10. C) $16.03.

B If the dividend remains constant, g = 0. P = D1 / (k-g) = 1.15 / (0.095 - 0) = $12.10

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? A) $150.00. B) $54.76. C) $82.14.

C Value of preferred = D / kp = $11.50 / 0.14 = $82.14

Which of the following statements concerning security valuation is least accurate? A) The best way to value a company with no current dividend but who is expected to pay dividends in three years is to use the temporary supernormal growth (multistage) model. B) A firm with a $1.50 dividend last year, a dividend payout ratio of 40%, a return on equity of 12%, and a 15% required return is worth $18.24. C) The best way to value a company with high and unsustainable growth that exceeds the required return is to use the temporary supernormal growth (multistage) model.

B A firm with a $1.50 dividend last year, a dividend payout ratio of 40%, a return on new investment of 12%, and a 15% required return is worth $20.64. The growth rate is (1 - 0.40) × 0.12 = 7.2%. The expected dividend is then ($1.50)(1.072) = $1.61. The value is then (1.61) / (0.15 - 0.072) = $20.64.

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 two years, 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, an expected dividend growth rate of 3.5%, and a required return of 12.5% is estimated to be worth $36.11. 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.

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 $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

According to the earnings multiplier model, all else equal, as the required rate of return on a stock increases, the: A) P/E ratio will increase. B) P/E ratio will decrease. C) earnings per share will increase.

B According to the earnings multiplier model, the P/E ratio is equal to P0/E1 = (D1/E1)/(ke − g). As ke increases, P0/E1 will decrease, all else equal.

Of the following types of firm, which is most suitable for P/B ratio analysis? A) A firm with accounting standards different from other firms. B) A firm with accounting standards consistent to other firms. C) A service industry firm without significant fixed assets.

B Assuming consistent accounting standards across firms, P/B ratios can reveal signs of misvaluation across firms.

Given the following information, compute price/book value. Book value of assets = $550,000 Total sales = $200,000 Net income = $20,000 Dividend payout ratio = 30% Operating cash flow = $40,000 Price per share = $100 Shares outstanding = 1000 Book value of liabilities = $500,000 A) 5.5X. B) 2.0X. C) 2.5X.

B Book value of equity = $550,000 - $500,000 = $50,000 Market value of equity = ($100)(1000) = $100,000 Price/Book = $100,000/$50,000 = 2.0X

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? A) $30.00. B) $13.66. C) $20.00.

B 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

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? A) $1.62. B) $1.55. C) $1.83. What would an investor pay for Day and Associates today? A) $24.03. B) $18.65. C) $20.71.

B 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. -------------------------------------------------------------------------------- C 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.

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? A) $67.50. B) $52.68. C) $47.09.

B 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.

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: A) increase or decrease, depending upon the relationship between ke and ROE. B) decrease. C) increase.

B If ke increases, the spread between ke and g widens (increasing the denominator), resulting in a lower valuation.

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: A) $19 B) $104 C) $44

B Infinite period DDM: P0 = D1 / (ke - g) D1 = (Earnings × Payout ratio) / average number of shares outstanding = ($200,000 × 0.625) / 50,000 = $2.50. ke = risk free rate + [beta × (expected market return - risk free rate)] ke = 7.5% + [1.8 × (13.0% - 7.5%)] = 17.4%. g = (retention rate × ROE) Retention = (1 - Payout) = 1 - 0.625 = 0.375. ROE = net income/equity = 200,000/500,000 = 0.4 g = 0.375 × 0.4 = 0.15. P0 = D1 / (ke - g) = $2.50 / (0.174 - 0.15) = 104.17.

Gwangwa Gold, a South African gold producer, has as its primary asset a mine which is shown on the balance sheet with a value of R100 million. An analyst estimates the market value of this mine to be 90% of book value. The company's balance sheet shows other assets of R20 million and liabilities of R40 million, and the analyst feels that the book value of these items reflects their market values. Using the asset-based valuation approach, what should the analyst estimate the value of the company to be? A) R80 million. B) R70 million. C) R110 million.

B Market value of assets = 0.9(R100 million) + R20 million = R110 million Market value of liabilities = R40 million Estimated net value of company = R110 million − R40 million = R70 million.

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: A) $12.50. B) $17.67. C) $16.67.

B 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

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? A) 6.7%. B) 7.8%. C) 4.5%.

B 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%

The Sustainable Growth Rate is equal to: A) (ROE) x (1+RR). B) (ROE) x (RR). C) (ROE) x (1-RR).

B The Sustainable Growth Rate is equal to the return on the equity portion of new investments (ROE) multiplied by the firm's retention rate (RR).

Which of the following statements about the constant growth dividend discount model (DDM) in its application to investment analysis is least accurate? The model: A) can't be applied when g > K. B) is best applied to young, rapidly growing firms. C) is inappropriate for firms with variable dividend growth.

B 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.

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.

B 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.

One advantage to using the price/book value (P/B) ratio over using the price/earnings (P/E) ratio is that P/B can be used when: A) stock markets are volatile. B) earnings or cash flows are negative. C) the firm is in a slow growth phase.

B When earnings are negative, P/E ratios cannot be used but P/B ratios can be used. The firm's rate of growth and the volatility of markets do not suggest advantages of using P/B ratios rather than P/E ratios.

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: A) 6%. B) 12%. C) 8%.

B 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%

? 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? A) $40.00. B) $74.93. C) $173.90.

B 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

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? A) $10.00. B) $ 7.30. C) $ 6.24.

B 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

Use the following information on Brown Partners, Inc. to compute the current stock price. Dividend just paid = $6.10 Expected dividend growth rate = 4% Expected stock price in one year = $60 Risk-free rate = 3% Equity risk premium = 12% A) $59.55. B) $57.48. C) $57.70.

C 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

Which of the following is a disadvantage of using the price-to-book value (PBV) ratio? A) Book value may not mean much for manufacturing firms with significant fixed costs. B) Firms with negative earnings cannot be evaluated with the PBV ratios. C) Book values are affected by accounting standards, which may vary across firms and countries.

C The disadvantages of using PBV ratios are: 1.Book values are affected by accounting standards, which may vary across firms and countries. 2.Book value may not mean much for service firms without significant fixed costs. 3.Book value of equity can be made negative by a series of negative earnings, which limits the usefulness of the variable.

The yield on a company's 7.5%, $50 par preferred stock is 6%. The value of the preferred stock is closest to: A) $12.50. B) $50.00. C) $62.50.

C The preferred dividend is 0.075($50) = $3.75. The value of the preferred = $3.75 / 0.06 = $62.50.

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: A) $15.70. B) $0.00. C) $6.40.

C 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.

Which of the following is NOT an advantage of using price-to-book value (PBV) multiples in stock valuation? A) Book value is often positive, even when earnings are negative. B) PBV ratios can be compared across similar firms if accounting standards are consistent. C) Book values are very meaningful for firms in service industries.

C Book values are NOT very meaningful for firms in service industries.

Which of the following is least likely a reason the price to cash flow (P/CF) model has grown in popularity? A) CFs are generally more difficult to manipulate than earnings. B) CFs are used extensively in valuation models. C) CFs are more easily estimated than future dividends.

C CFs are not easier to estimate than dividends.

An analyst studying Albion Industries determines that the average EV/EBITDA ratio for Albion's industry is 10. The analyst obtains the following information from Albion's financial statements: EBITDA = £11,000,000 Market value of debt = £30,000,000 Cash = £1,000,000 Based on the industry's average enterprise value multiple, what is the equity value of Albion Industries? A) £110,000,000. B) £80,000,000. C) £81,000,000.

C Enterprise value = Average EV/EBITDA × company EBITDA = 10 × £11,000,000 = £110,000,000 Enterprise value = Equity value + debt − cash Equity value = Enterprise value − debt + cash = £110,000,000 − £30,000,000 + £1,000,000 = £81,000,000

The price to book value ratio (P/BV) is a helpful valuation technique when examining firms: A) with older assets compared to those with newer assets. B) with the same stock prices. C) that hold primarily liquid assets.

C P/BV analysis works best for firms that hold primarily liquid assets.

If the payout ratio increases, the P/E multiple will: A) decrease, if we assume that the growth rate remains constant. B) always increase. C) increase, if we assume that the growth rate remains constant.

C When payout ratio increases, the P/E multiple increases only if we assume that the growth rate will not change as a result.

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: A) increase. B) remain unchanged. C) decrease. ---- What will be the current price of the stock with a beta of 1.5? A) $23.51. B) $23.20. C) $20.23.

C 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. ------------ B k = 5 + 1.5(5) = 12.5% P0 = (1.1 / 1.125) + (25 / 1.125) = $23.20

General, Inc., has net income of $650,000 and one million shares outstanding. The profit margin is 6 percent and General, Inc., is selling for $30.00. The price/sales ratio is equal to: A) 0.65. B) 10.83. C) 2.77.

C 6% profit margin = $650,000/x; x (sales) = $10,833,333. Sales per share = $10.83 M/1,000,000 = $10.83 per share. P/Sales = $30.00/$10.83 = 2.77.

Enterprise Value (EV)=

MV equity + MV debt + MV preferred stock - Cash - Short-term Investments Therefore, Equity value (MV equity)= EV- Debt + Cash

justified P/E

P/E based on fundamentals derived from Gordon growth model d/(r-g) P0/E1=p/(r-g), where p= payout ratio the justified P/E ratio is very sensitive to inputs (r and g)

trailing P/E=

current stock price/ last year's (12 months) earnings per share take average of trailing P/E's and multiply by current year 4 EPS $4

Gordon growth model (constant growth model)

annual growth rate of dividends, g, is constant. dividend D1= D0(1+g) dividend D2= D0(1+g)^2 dividend D3= D0/(1+g)^3...

present value model (discounted cash flow model)

estimate intrinsic value of security as present value of future benefits -dividend discount model (DDM) -free cash flow to equity model (FCFE) (-) not used for companies that have only 1 year of data available

multistage model is useful for

firms with nonconstant growth

when should you use the Gordon growth model? (key words)

forever infinitely indefinitely just paid, recently paid, current dividend= last dividend D0 will pay, is expected to pay= D1

higher P/E

higher dividend payout ratio higher growth in sales

lower P/E

higher level of debt (bc higher risk and higher required return on equity k in the denominator)

asset-based model

intrinsic value of common stock is estimated as total value of [assets- liabilities] & preferred stock book value (carrying value)

dividend discount model (DDM)

intrinsic value of stock= PV of future dividends + expected selling price in one year V0=D1/(1+r) + P1/(1+r)

market price is more likely to be correct for a security when

many analysts follow security

if analyst is more confident of his input values,

more likely to conclude that security is overvalued

free cash flow to equity (FCFE)= represents cash that could be paid out to common shareholders a measure of dividend-paying capacity

net income + depreciation - increase in working capital- fixed capital investment (FCInv)- debt principal repayments + new debt issues discount expected future FCFE by required rate of return on equity: V0= sum FCFE/(1+r)^t

P/B

price divided by book value of equity per share

P/CF

price divided by cash flow per share cash flow= operating or free cash flow

multiplier model (market multiple model)

price multiples or enterprise value multiples P/E, P/S, P/B, EV (-) MV debt hard to obtain

P/E ratio

price to earnings per share a low P/E= buy

P/S

price to sales per share 1. sales revenue/ number of shares 2. divide stock price by sales per share P/S

price multiple

ratio that compares share price with some monetary flow or value (-) doesn't consider the future

dividend displacement earnings:* An increase in the dividend payout ratio will (hint: g= (1- dividend payout ratio)*ROE justified forward P/E= p/(r-g)

reduce firm's growth rate net effect on firm value is ambiguous* (because have to take into account value of r in d/(r-g) P/E ratio is inversely related to r & directly related to g. payout ratio p is ambiguous "dividend displacement of earnings"

gordon growth model is useful for

stable, mature, noncyclical firms

(-) using price multiples based on comparables

stock may be overvalued by comparable method; undervalued by fundamental method different accounting methods price multiples greatly affected by economic conditions

multiple-year holding period DDM

sum present value of dividends over holding period and the estimated terminal (ending) value

when to use an asset-based model for valuation:

tangible assets non-hyperinflation market (fair) values are easily determinable ex. airline company- routes, landing rights, and leases of airport facilities have substantial value

the more confident the investor is about the appropriateness of the valuation model,

the more likely investor is to take an investment position in an overvalued/ undervalued stock

the larger the % difference between market prices & estimated values,

the more likely the investor is to take a position based on estimate of intrinsic (fundamental) value

if competitor or industry average EV/EBITDA is ABOVE that of the firm, the firm is relatively

undervalued

one-year holding period (DDM)

value of stock= present value of any dividends during the year + present value of expected price of stock at end of year

The fundamental P/E ratio is _______ to its inputs.

very sensitive as difference between r and g widens, the value of the stock falls, and vice versa (-) small changes in difference between r and g can cause large changes in stock's value

The three-stage model is best for valuing _______ companies.

young companies that are just entering the growth phase.