Sources: Company annual reports.

Sources: Company annual reports.

A. A multiple regression model with each paper and forest products company's rate of return on stockholders' equity (ROE) as the dependent Y variable and firm size (BV), growth (GR), and leverage (LTD) as independent X variables gives the following results (t statistics in parentheses):

ROE = 2.689 - 9.09E-05 BV + 0.216 GR - + 0.107 LTD (0.40) (-0.22) (2.27) (0.76)

How would you interpret these findings?

B. What suggestions might you make for a more detailed study of the determinants of profitability for paper and forest products companies versus other types of companies?

ST10.1 Solution

A. As is typically the case, the constant in such a regression has no economic meaning. Clearly, the intercept should not be used to suggest the rate of return on stockholders' equity for a paper and forest products company that has zero values for the book value of stockholders' equity, growth, and leverage. Zero values for all of these variables are not observed for any of these paper and forest products companies, and extrapolation beyond the range of actual observations is always dangerous.

The coefficient estimate of -9.09E-05 for total assets implies that a $1 million rise in stockholders' equity would lead to an average -0.00009% decline in the ROE. However, the coefficient on this measure of firm size is not statistically significant at the a = 0.1 level with a calculated t statistic value of -0.22, meaning that it is not possible to argue on the basis of these data that there is any strong link between profitability and firm size in the paper and forest products industry. Although business leaders regard the accounting book value of assets in place as a favorable indication of the firm's ability to earn attractive rates of return in the future, the downturn in industry profitability in 2001 led to especially severe profit prob lems for industry leaders. Controversies tied to environmental concerns, like the spotted-owl crisis, make matters even worse for large companies that are convenient targets of consumer activists and regulators.

The coefficient estimate of 0.216 for growth implies that a 1% rise in growth leads to an average 0.216% increase in ROE. The growth coefficient is statistically significant at the a = 0.05 level with a calculated t statistic value of 2.27, meaning that it is possible to be more than 95% confident that growth has a statistically significant affect on ROE. The probability of observing such a large t statistic when there is in fact no relation between ROE and growth is less than 5%.

The coefficient estimate of 0.107 for LTD implies that a 1% rise in leverage leads to an average 0.107% increase in ROE. However, this effect is not significant at even the a = 0.1 level, meaning theat there is no strong link between ROE and leverage in the sample analyzed. Given rather tepid economic growth, high financial leverage had no beneficial effect of boosting profitability during the 2001 sample period.

The R2 = 27.2% is quite modest and indicates the share of variation in ROE that can be explained by the model as a whole. This relatively low level of explained variation must be interpreted in light of the very small sample size involved. The standard error of the Y estimate of SEE = 4.371% is the average amount of error encountered in estimating ROE using this multiple regression model. If the u error terms are normally distributed about the regression equation, as would be true when large samples of more than 30 or so observations are analyzed, there is a 95% probability that observations of the dependent variable will lie within the range Y ± (1.96 X SEE), or within roughly two standard errors of the estimate. The probability is 99% that any givenY will lie within the rangeY ± (2.576 X SEE), or within roughly three standard errors of its predicted value. When very small samples of data are analyzed, as is the case here, "critical" t values slightly larger than two or three are multiplied by the SEE to obtain the 95% and 99% confidence intervals.

Precise critical t values obtained from a t table, such as that found in Appendix C, are t*14a=0 05 = 2.145 (at the 95% confidence level) and t*14a=0 01 = 2.977 (at the 99% confidence level) for df = 18 - 4 = 14. This means that actual ROE can be expected to fall in the range Y ± (2.145 X 4.371), or Y ± 9.376, with 95% confidence; and within the range Y ± (2.977 X4.371), or Y ± 13.012, with 99% confidence.

B. Collection of a broader and more descriptive sample of data is a necessary first step in a more detailed study of the determinants of the return on stockholders' equity for paper and forest products companies. With only 18 observations of annual data, the regression technique is clearly handicapped in this application. Perhaps a pooled cross-section sample of annual data over the past 5 years, or n = 90 (= 18 X 5) observations, would provide a sufficiently broad sample of data to offer a meaningful perspective on the determinants of profitability for forest and paper products companies. In addition, a larger sample of data would make it possible to investigate the potential role of additional independent variables, such as the level of advertising spending, the role of regional economic growth, and so on.

ST10.2 Perfect Competition and Monopoly. The City of Columbus, Ohio, is considering two proposals to privatize municipal garbage collection. First, a leading waste disposal firm has offered to purchase the city's plant and equipment at an attractive price in return for an exclusive franchise on residential service. A second proposal would allow several individual workers and small companies to enter the business without any exclusive franchise agreement or competitive restrictions. Under this plan, individual companies would bid for the right to provide service in a given residential area. The city would then allocate business to the lowest bidder.

The city has conducted a survey of Columbus residents to estimate the amount that they would be willing to pay for various frequencies of service. The city has also estimated the total cost of service per resident. Service costs are expected to be the same whether or not an exclusive franchise is granted.

A. Complete the following table.

Trash Pickups Price per Total Marginal Total Marginal per Month Pickup Revenue Revenue Cost Cost

Trash Pickups Price per Total Marginal Total Marginal per Month Pickup Revenue Revenue Cost Cost

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