The bottom half presents the relative root mean squared errors for the corresponding estimators and values for N. across all three estimation approaches for each stock index. In columns (3) and (5), results printed in italic denote the overall smallest estimation errors, i.e. For each estimator, four different values of N are considered ( N = 5, 10, 30 and 50) and the one with the smallest average estimation error is chosen. The top half presents relative estimation biases based on the simple arithmetic mean, the truncated arithmetic mean and the Cooper estimator.
As a result, the moderate underestimation effect of the detailed planning period is a fairly appropriate offset of the overestimation effect of the terminal value that is heavily discounted. Since the average index return rate is in the area of 20% for the KOSPI and the other emerging economies, this implies very small discount factors for longer time horizons. Although the bias of the Cooper estimator is often enormous for the terminal values on a stand-alone basis, this does not distort the overall firm value that much because the value contribution of the terminal value for N = 30 or N = 50 is very small, especially for the indices of the emerging market economies. The underlying reason is that the Cooper estimator slightly underestimates values in the detailed planning period. Simple arithmetic mean and Cooper estimator, give different lengths of the detailed planning period and different cash flow growth rates. We therefore take a closer look at possible consequences of variations in annual cash flow growth rates for bias problems.Īverage relative estimation biases for three indices (Dow Jones, DAX and KOSPI) in three countries (United States, Germany and South Korea) for two different estimators. However, this conclusion is based on the assumption that expected firm cash flows per year are constant over time. Results are quite similar for all three countries. Without such a truncation, the Cooper estimator proves superior to the simple arithmetic mean of historical rates of return. Moreover, this may also render ‘truncation’ a good idea to resolve the problem of the upwards biased arithmetic mean estimator. Thus, high values of N imply the advantage that severe distortions that can be observed especially regarding terminal value estimates have only minor relevance for total firm value estimation result. Moreover, for N = 30 and N = 50, the contribution of the terminal value to overall firm value is limited. Generally, values for N of 30–50 seem to be good choices.
#THE ARTMATIC MEAN SERIES#
There seems to be a country-specific inner optimum for N which is the greater the smaller is the time series of historical rates of return. In contrast, the correctness of the Cooper estimator critically depends on the length of the detailed planning period. Precision results for firm value estimation (in percent of the corresponding true value) based on the simple arithmetic mean and the Cooper estimator according to the average relative estimation bias and the root mean squared error for three different indices (Dow Jones, DAX and KOSPI) from three different countries (United States, Germany and South Korea). For the same reasons, the bias regarding the arithmetic mean estimator is smaller for the DAX than for the KOSPI with differences, however, not as pronounced as in comparison to the Dow Jones. A second reason is the smaller standard deviation of the Dow Jones yearly returns. This is a consequence of the considerably longer time series of returns available for the Dow Jones. However, the bias regarding the arithmetic mean estimator is much smaller for the Dow Jones than for the DAX and the KOSPI. In line with the theoretical considerations of Section 12.2, the arithmetic mean estimator is generally upwardly biased. In particular, the success of the arithmetic mean that the estimator does not depend much on the length N of the detailed planning period. Regarding their basic structure, the results are quite similar for all three indices. We start by a detailed comparison of estimation results for the Dow Jones, the DAX and the KOSPI based on the arithmetic mean of historical return realizations and the corresponding Cooper estimator according to Table 12.2.
0 kommentar(er)
