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...