Problems and Questions

1. Respond true or false to the following statements relating to the dividend discount model.

a. The dividend discount model cannot be used to value a high-growth company that pays no dividends.

b. The dividend discount model will undervalue stocks because it is too conservative.

c. The dividend discount model will find more undervalued stocks when the overall stock market is depressed.

d. Stocks that are undervalued using the dividend discount model have generally made significant positive excess returns over long periods (five years or more).

e. Stocks that pay high dividends and have low price/earnings ratios are more likely to be undervalued using the dividend discount model.

2. Ameritech Corporation paid dividends per share of $3.56 in 1992, and dividends are expected to grow 5.5% a year forever. The stock has a beta of 0.90, and the treasury bond rate is 6.25%.

a. What is the value per share, using the Gordon Growth Model?

b. The stock is trading for $80 per share. What would the growth rate in dividends have to be to justify this price?

3. A key input for the Gordon Growth Model is the expected growth rate in dividends over the long term. How, if at all, would you factor in the following considerations in estimating this growth rate?

a. There is an increase in the inflation rate.

b. The economy in which the firm operates is growing very rapidly.

c. The growth potential of the industry in which the firm operates is very high.

d. The current management of the firm is of very high quality.

4. Newell Corporation, a manufacturer of do-it-yourself hardware and housewares, reported earnings per share of $2.10 in 1993, on which it paid dividends per share of $0.69. Earnings are expected to grow 15% a year from 1994 to 1998, during which period the dividend payout ratio is expected to remain unchanged. After 1998, the earnings growth rate is expected to drop to a stable 6%, and the payout ratio is expected to increase to 65% of earnings. The firm has a beta of 1.40 currently, and it is expected to have a beta of 1.10 after 1998. The treasury bond rate is 6.25%.

a. What is the expected price of the stock at the end of 1998?

b. What is the value of the stock, using the two-stage dividend discount model?

5. Church & Dwight, a large producer of sodium bicarbonate, reported earnings per share of $1.50 in 1993 and paid dividends per share of $0.42. In 1993, the firm also reported the following:

Net Income = $30 million

Interest Expense = $0.8 million

Book Value of Debt = $7.6 million

Book Value of Equity = $160 million

The firm faced a corporate tax rate of 38.5%. The market value debt-to -equity ratio is 5%. The treasury bond rate is 7%.

The firm expects to maintain these financial fundamentals from 1994 to 1998, at which time it is expected to become a stable firm, with an earnings growth rate of 6%. The firm's financial characteristics will approach industry averages after 1998. The industry averages are as follows:

Return on Assets = 12.5%

Debt/Equity Ratio = 25%

Interest Rate on Debt = 7%

Church & Dwight had a beta of 0.85 in 1993, and the unlevered beta is not expected to change over time.

a. What is the expected growth rate in earnings, based upon fundamentals, for the high-growth period (1994 to 1998)?

b. What is the expected payout ratio after 1998?

c. What is the expected beta after 1998?

d. What is the expected price at the end of 1998?

e. What is the value of the stock, using the two-stage dividend discount model?

f. How much of this value can be attributed to extraordinary growth? to stable growth?

6. Medtronic Inc., the world's largest manufacturer of implantable biomedical devices, reported earnings per share in 1993 of $3.95 and paid dividends per share of $0.68. Its earnings are expected to grow 16% from 1994 to 1998, but the growth rate is expected to decline each year after that to a stable growth rate of 6% in 2003. The payout ratio is expected to remain unchanged from 1994 to 1998, after which it will increase each year to reach 60% in steady state. The stock is expected to have a beta of 1.25 from 1994 to 1998, after which the beta will decline each year to reach 1.00 by the time the firm becomes stable (the treasury bond rate is 6.25%).

a. Assuming that the growth rate declines linearly (and the payout ratio increases linearly) from 1999 to 2003, estimate the dividends per share each year from 1994 to 2003.

b. Estimate the expected price at the end of 2003.

c. Estimate the value per share, using the three-stage dividend discount model.

7. Kimberly-Clark, a household product manufacturer, reported earnings per share of $3.20 in 1993 and paid dividends per share of $1.70 in that year. The firm reported depreciation of $315 million in 1993, and capital expenditures of $475 million (there were 160 million shares outstanding, trading at $51 per share). This ratio of capital expenditures to depreciation is expected to be maintained in the long term. The working capital needs are negligible. Kimberly-Clark had debt outstanding of $1.6 billion and intends to maintain its current financing mix (of debt and equity) to finance future investment needs. The firm is in a steady state, and earnings are expected to grow 7% a year. The stock had a beta of 1.05 (the treasury bond rate is 6.25%).

a. Estimate the value per share, using the Dividend Discount Model.

b. Estimate the value per share, using the FCFE Model.

c. How would you explain the difference between the two models, and which one would you use as your benchmark for comparison to the market price?

8. Ecolab Inc. sells chemicals and systems for cleaning, sanitizing, and maintenance. It reported earnings per share of $2.35 in 1993 and expected earnings growth of 15.5% a year from 1994 to 1998, and 6% a year after that. The capital expenditure per share was $2.25, and depreciation was $1.125 per share in 1993. Both are expected to grow at the same rate as earnings from 1994 to 1998. Working capital is expected to remain at 5% of revenues, and revenues that were $1,000 million in 1993 are expected to increase 6% a year from 1994 to 1998, and 4% a year after that. The firm currently has a debt ratio [D/(D+E)] of 5% but plans to finance future investment needs (including working capital investments) using a debt ratio of 20%. The stock is expected to have a beta of 1.00 for the period of the analysis, and the treasury bond rate is 6.50%. There are 63 million shares outstanding.

a. Assuming that capital expenditures and depreciation offset each other after 1998, estimate the value per share.

b. Assuming that capital expenditures continue to be 200% of depreciation even after 1998, estimate the value per share.

c. What would the value per share have been if the firm had continued to finance new investments with its old financing mix (5%)? Is it fair to use the same beta for this analysis?

9. Dionex Corporation, a leader in the development and manufacture of ion chromography systems (used to identify contaminants in electronic devices), reported earnings per share of $2.02 in 1993 and paid no dividends. These earnings are expected to grow 14% a year for five years (1994 to 1998) and 7% a year after that. The firm reported depreciation of $2 million in 1993 and capital spending of $4.20 million and had 7 million shares outstanding. The working capital is expected to remain at 50% of revenues, which were $106 million in 1993 and are expected to grow 6% a year from 1994 to 1998 and 4% a year after that. The firm is expected to finance 10% of its capital expenditures and working capital needs with debt. Dionex had a beta of 1.20 in 1993, and this beta is expected to drop to 1.10 after 1998. The treasury bond rate is 7%.

a. Estimate the expected free cash flow to equity from 1994 to 1998, assuming that capital expenditures and depreciation grow at the same rate as earnings.

b. Estimate the terminal price per share (at the end of 1998). Stable firms in this industry have capital expenditures that are 150% of revenues, and maintain working capital at 25% of revenues.

c. Estimate the value per share today, based upon the FCFE model.

10. Biomet Inc., designs, manufactures, and markets reconstructive and trauma devices. It reported earnings per share of $0.56 in 1993, on which it paid no dividends. It had revenues per share in 1993 of $2.91. It had capital expenditures of $0.13 per share in 1993 and depreciation in the same year of $0.08 per share. The working capital was 60% of revenues in 1993 and will remain at that level from 1994 to 1998, while earnings and revenues are expected to grow 17% a year. The earnings growth rate is expected to decline linearly over the following five years to a rate of 5% in 2003. During the high growth and transition periods, capital spending and depreciation are expected to grow at the same rate as earnings, but they are expected to offset each other when the firm reaches steady state. Working capital is expected to drop from 60% of revenues during the 1994-1998 period to 30% of revenues after 2003. The firm has no debt currently, but it plans to finance 10% of its net capital investment and working capital requirements with debt.

The stock is expected to have a beta of 1.45 for the high-growth period (1994-1998), and it is expected to decline to 1.10 by the time the firm goes into steady state (in 2003). The treasury bond rate is 7%.

a. Estimate the value per share, using the FCFE model.

b. Estimate the value per share, assuming that working capital stays at 60% of revenues forever.

c. Estimate the value per share, assuming that the beta remains unchanged at 1.45 forever.

11. Omnicare Inc., which provides pharmacy management and drug therapy to nursing homes, reported earnings per share of $0.85 in 1993 on revenues per share of $12.50. It had negligible capital expenditures, which were covered by depreciation, but had to maintain working capital at 40% of revenues. Revenues and earnings are expected to grow 20% a year from 1994 to 1998, after which the growth rate is expected to decline linearly over three years to 5% in 2001. The firm has a debt ratio of 15%, which it intends to maintain in the future. The stock has a beta of 1.10, which is expected to remain unchanged for the period of the analysis. The treasury bond rate is 7%.

a. Estimate the value per share, using the free cash flow to equity model.

b. Assume now that you find out that the way that Omnicare is going to create growth is by giving easier credit terms to their clients. How would that affect your estimate of value? (Will it increase or decrease?)

c. How sensitive is your estimate of value to changes in the working capital assumption?

12. Which of the following firms is likely to have a higher value from the dividend discount model, a higher value from the FCFE model, or the same value from both models?

a. A firm that pays out less in dividends than it has available in FCFE, but that invests the balance in treasury bonds.

b. A firm that pays out more in dividends than it has available in FCFE, and then issues stock to cover the difference.

c. A firm that pays out, on average, its FCFE as dividends.

d. A firm that pays out less in dividends that it has available in FCFE, but which uses the cash at regular intervals to acquire other firms, with the intent of diversifying.

e. A firm that pays out more in dividends than it has available in FCFE, but borrows money to cover the difference (the firm is already over-levered).

13. Union Pacific Railroad reported net income of $770 million in 1993, after interest expenses of $320 million (the corporate tax rate was 36%). It reported depreciation of $960 million in that year, and capital spending was $1.2 billion. The firm also had $4 billion in debt outstanding on the books, rated AA (carrying a yield to maturity of 8%), trading at par (up from $3.8 billion at the end of 1992). The beta of the stock is 1.05, and there were 200 million shares outstanding (trading at $60 per share), with a book value of $5 billion. Union Pacific paid 40% of its earnings as dividends and working capital requirements are negligible. The treasury bond rate is 7%.

a. Estimate the free cash flow to the firm in 1993.

b. Estimate the value of the firm at the end of 1993.

c. Estimate the value of equity at the end of 1993, and the value per share, using the FCFF approach.

14. Lockheed Corporation, one of the largest defense contractors in the United States, reported EBITDA of $1290 million in 1993, prior to interest expenses of $215 million and depreciation charges of $400 million. Capital Expenditures in 1993 amounted to $450 million, and working capital was 7% of revenues (which were $13,500 million). The firm had debt outstanding of $3.068 billion (in book value terms), trading at a market value of $3.2 billion, and yielding a pre-tax interest rate of 8%. There were 62 million shares outstanding, trading at $64 per share, and the most recent beta is 1.10. The tax rate for the firm is 40%. The treasury bond rate is 7%.

The firm expects revenues, earnings, capital expenditures, and depreciation to grow at 9.5% a year from 1994 to 1998, after which time the growth rate is expected to drop to 4%. (Capital spending will offset depreciation in the steady state period.) The company also plans to lower its debt/equity ratio to 50% for the steady state (which will result in the pre-tax interest rate dropping to 7.5%.)

a. Estimate the value of the firm.

b. Estimate the value of the equity in the firm and the value per share.

15. In the face of disappointing earnings results and increasingly assertive institutional stockholders, Eastman Kodak was considering a major restructuring in 1993. As part of this restructuring, it was considering the sale of its health division, which earned $560 million in earnings before interest and taxes in 1993, on revenues of $5.285 billion. The expected growth in earnings was expected to moderate to 6% between 1994 and 1998 and to 4% after that. Capital expenditures in the health division amounted to $420 million in 1993, while depreciation was $350 million. Both are expected to grow 4% a year in the long term. Working capital requirements are negligible.

The average beta of firms competing with Eastman Kodak's health division is 1.15. While Eastman Kodak has a debt ratio [D/(D+E)] of 50%, the health division can sustain a debt ratio [D/(D+E)] of only 20%, which is similar to the average debt ratio of firms competing in the health sector. At this level of debt, the health division can expect to pay 7.5% on its debt, before taxes. The tax rate is 40%, and the treasury bond rate is 7%.

a. Estimate the cost of capital for the division.

b. Estimate the value of the division.

c. Why might an acquirer pay more than this estimated value?

16. National City Corporation, a bank holding company, reported earnings per share of $2.40 in 1993, and paid dividends per share of $1.06. The earnings had grown 7.5% a year over the prior five years, and were expected to grow 6% a year in the long term (starting in 1994). The stock had a beta of 1.05 and traded for ten times earnings. The treasury bond rate was 7%.

a. Estimate the P/E Ratio for National City Corporation.

b. What long term growth rate is implied in the firmís current PE ratio?

17. The following were the P/E ratios of firms in the aerospace/defense industry at the end of December, 1993, with additional data on expected growth and risk:

Company P/E Ratio Expected Beta Payout

Growth

Boeing 17.3 3.5% 1.10 28%

General Dynamics 15.5 11.5% 1.25 40%

General Motors - Hughes 16.5 13.0% 0.85 41%

Grumman 11.4 10.5% 0.80 37%

Lockheed Corporation 10.2 9.5% 0.85 37%

Logicon 12.4 14.0% 0.85 11%

Loral Corporation 13.3 16.5% 0.75 23%

Martin Marietta 11.0 8.0% 0.85 22%

McDonnell Douglas 22.6 13.0% 1.15 37%

Northrop 9.5 9.0% 1.05 47%

Raytheon 12.1 9.5% 0.75 28%

Rockwell 13.9 11.5% 1.00 38%

Thiokol 8.7 5.5% 0.95 15%

United Industrial 10.4 4.5% 0.70 50%

a. Estimate the average and median P/E ratios. What, if anything, would these averages tell you?

b. An analyst concludes that Thiokol is undervalued, because its P/E ratio is lower than the industry average. Under what conditions is this statement true? Would you agree with it here?

c. Using a regression, control for differences across firms on risk, growth, and payout. Specify how you would use this regression to spot under and overvalued stocks. What are the limitations of this approach?

18. NCH Corporation, which markets cleaning chemicals, insecticides and other products, paid dividends of $2.00 per share in 1993 on earnings of $4.00 per share. The book value of equity per share was $40.00, and earnings are expected to grow 6% a year in the long term. The stock has a beta of 0.85, and sells for $60 per share. The treasury bond rate is 7%.

a. Based upon these inputs, estimate the price/book value ratio for NCH.

b. How much would the return on equity have to increase to justify the price/book value ratio at which NCH sells for currently?

19. You are trying to estimate a price per share on an initial public offering of a company involved in environmental waste disposal. The company has a book value per share of $20 and earned $3.50 per share in the most recent time period. While it does not pay dividends, the capital expenditures per share were $2.50 higher than depreciation per share in the most recent period, and the firm uses no debt financing. Analysts project that earnings for the company will grow 25% a year for the next five years. You have data on other companies in the environment waste disposal business:

Company Price BV/Share EPS DPS Beta Exp.Growth

Air & Water $9.60 $8.48 $0.40 $0.00 1.65 10.5%

Allwaste $5.40 $3.10 $0.25 $0.00 1.10 18.5%

Browning Ferris $29.00 $11.50 $1.45 $0.68 1.25 11.0%

Chemical Waste $9.40 $3.75 $0.45 $0.15 1.15 2.5%

Groundwater $15.00 $14.45 $0.65 $0.00 1.00 3.0%

Intn'l Tech. $3.30 $3.35 $0.16 $0.00 1.10 11.0%

Ionics Inc. $48.00 $31.00 $2.20 $0.00 1.00 14.5%

Laidlaw Inc. $6.30 $5.85 $0.40 $0.12 1.15 8.5%

OHM Corp. $16.00 $5.65 $0.60 $0.00 1.15 9.50%

Rollins $5.10 $3.65 $0.05 $0.00 1.30 1.0%

Safety-Kleen $14.00 $9.25 $0.80 $0.36 1.15 6.50%

The average debt/equity ratio of these firms is 20%, and the tax rate is 40%.

a. Estimate the average price/book value ratio for these comparable firms. Would you use this average P/BV ratio to price the initial public offering.

b. What subjective adjustments would you make to the price/book value ratio for this firm and why?

20. Longs Drug, a large U.S. drugstore chain operating primarily in Northern California, had sales per share of $122 in 1993, on which it reported earnings per share of $2.45 and paid a dividend per share of $1.12. The company is expected to grow 6% in the long term, and has a beta of 0.90. The current T.Bond rate is 7%.

a. Estimate the appropriate price/sales multiple for Longs Drug.

b. The stock is currently trading for $34 per share. Assuming the growth rate is estimated correctly, what would the profit margin need to be to justify this price per share.

21. You have been asked to assess whether Walgreen Company, a drugstore chain, is correctly priced relative to its competitors in the drugstore industry at the end of 1993. The following are the price/sales ratios, profit margins, and other relative details of the firms in the drugstore industry.

Company P/S Ratio Profit Margin Payout Expected Growth Beta

Arbor Drugs 0.42 3.40% 18% 14.0% 1.05

Big B Inc. 0.30 1.90% 14% 23.5% 0.70

Drug Empor. 0.10 0.60% 0% 27.5% 0.90

Fay's Inc. 0.15 1.30% 37% 11.5% 0.90

Genovese 0.18 1.70% 26% 10.5% 0.80

Longs Drug 0.30 2.00% 46% 6.0% 0.90

Perry Drugs 0.12 1.30% 0% 12.5% 1.10

Rite Aid 0.33 3.20% 37% 10.5% 0.90

Walgreen 0.60 2.70% 31% 13.5% 1.15

Based entirely on a subjective analysis, do you think that Walgreen is overpriced because its price/sales ratio is the highest in the industry? If it is not, how would you rationalize its value?