ESTIMATION OF GROWTH RATES
The value of a firm is ultimately determined not by current cash flows but by expected future cash flows. The estimation of growth rates in earnings and cash flows is therefore central to doing a reasonable valuation. Growth rates can be obtained in many ways: they can be based upon past growth; drawn from estimates made by other analysts who follow the firm; or related to the firm's fundamentals. Since each of these approaches yields some valuable information, it makes sense to blend them to arrive at one composite growth rate to use in the valuation. This chapter examines different approaches to estimating future growth, and discusses the determinants of growth.
Question 1 - Arithmetic and Geometric Means
The following are the earnings per share of Thermo Electron, a company that designs cogeneration and resource recovery plants, from 1987 to 1992:
|Year |EPS |
|1987 |0.67 |
|1988 |0.77 |
|1989 |0.90 |
|1990 |1.10 |
|1991 |1.31 |
|1992 |1.51 |

A. Estimate the arithmetic average growth rate in earnings per share from 1987 to 1992.
B. Estimate the geometric average growth rate in earnings per share from 1987 to 1992.
C. Why are the growth rates different?
Question 2 - Linear and Log-linear Models of Earnings Growth
Consider again the example of Thermo Electron, described in the prior example, using the historical data from 1987 to 1992.
A. Estimate the growth rate from a linear regression model.
B. Estimate the growth rate from a log-linear regression model.
C. Project the earnings per share in 1993 using both models.
Question 3 - Dealing with Negative Earnings
The earnings per share from 1987 to 1993 are reported below for McDonnell Douglas, an aircraft manufacturer with extensive defense contracts:
|Year |EPS |
|1987 |7.27 |
|1988 |7.91 |
|1989 |-0.97 |
|1990 |-2.64 |
|1991 |8.42 |
|1992 |-0.06 |
|1993 |10.75 |

A. Estimate the geometric average growth rate in earnings from 1987 to 1993.
B. Estimate the arithmetic average growth rate in earnings from 1987 to 1993, using a correction for the negative earnings.
C. Estimate the growth rate in earnings, using the linear regression model.
Question 4 - Earnings Growth and ROE
Johnson and Johnson, a leading manufacturer of healthcare products, had a return on equity in 1992 of 31.4%, and paid out 36% of its earnings as dividends. It earned a net income of $1,625 million on a book value of equity of $5,171 million. As a consequence of healthcare reform, it is expected that the return on equity will drop to 25% in 1993 and that the dividend payout ratio will remain unchanged.
A. Estimate the growth rate in earnings based upon 1992 numbers.
B. Estimate the growth rate in 1993, when the ROE drops from 31.4% to 25%.
C. Estimate the growth rate after 1993, assuming that 1993 numbers can be sustained.
Question 5 - Earnings Growth, Leverage, and Risk
Eastman Kodak was, in the view of many observers, in serious need of restructuring in 1994. In 1993, the firm reported the following:
Net Income = $1,080 million
Interest Expense = $ 550 million
The firm also had the following estimates of debt and equity in the balance sheet:
Equity (Book Value) = $6,000 million
Debt (Book Value) = $6,880 million
The firm also paid out total dividends of $660 million in 1993. The stock was trading at $63, and there were 330 million shares outstanding. (It faced a corporate tax rate of 40%.) Eastman Kodak had a beta of 1.10.
Analysts believe that Kodak could take the following restructuring actions to improve its financial strength: ï It could sell its chemical division, which has a total book value of assets of $2,500 million and has only $100 million in earnings before interest and taxes. ï It could use the cash to pay down debt and improve its bond rating (leading to a decline in the interest rate to 7%). ï It could reduce the dividend payout ratio to 50% and reinvest more back into the business.
A. What is the expected growth rate in earnings, assuming that 1993 numbers remain unchanged?
B. What is the expected growth rate in earnings, if the restructuring plan described above is put into effect?
C. What will the beta of the stock be, if the restructuring plan is put into effect?
Question 6 - Adjusting Inputs For Firm Type
Computer Associates makes software that enables computers to run more efficiently. It is still in its high-growth phase and has the following financial characteristics:
Return on Assets = 25%
Dividend Payout Ratio = 7%
Debt/Equity Ratio = 10%
Interest rate on Debt = 8.5%
Corporate tax rate = 40%
It is expected to become a stable firm in ten years.
A. What is the expected growth rate for the high-growth phase?
B. Would you expect the financial characteristics of the firm to change once it reaches a steady state? What form do you expect the change to take?
C. Assume now that the industry averages for larger, more stable firms in the industry are as follows:
Industry Average Return on Assets = 14%
Industry Average Debt/Equity Ratio = 40%
Industry Average Interest Rate on Debt = 7%
Industry Average Dividend Payout ratio = 50%
D. What would you expect the growth rate in the stable growth phase to be?
Question 7 - Weighting Different Estimates of Growth Rate
The following are a number of valuation scenarios, where multiple estimates of growth are available. Specify how you weight the different growth rates and why.
A. A cyclical firm, whose earnings have dropped significantly (historical growth rate is negative) as a consequence of a recession, but which you believe has bottomed out and is in the process of recovering. The firm is heavily followed by analysts, who have a good track record in forecasting earnings growth.
B. A troubled firm, whose earnings have dropped significantly because of a combination of bad luck and bad management, but which is now restructuring. You have fairly good information on the form the restructuring will take and its expected impact. Analysts follow the firm, but their track record is spotty.
C. A healthy firm, where the estimates of growth from history, analysts, and fundamentals are fairly close.
D. A firm, which has a long and fairly reliable history of earnings growth, but which has just sold off three divisions (comprising almost half of the market value of the firm). Analysts follow the stock, but base forecasts primarily on historical growth.