Forecasting with Regression Regression is a statistical method that enables us to “fit” a straight line

Forecasting with Regression Regression is a statistical method that enables us to “fit” a straight line

that on average represents the best possible graphical relationship between sales and time. This best “fit” is called the regression line. One way regression can be used is to simply extrapolate future sales based on the trend in past sales. In Exhibit 29.3, let’s look at the sales of Inter- national Business Machines’ sales over the period 1976 through 1999. During much of this period, sales increased each year, hence the sales trend is positive. If we were to connect each point representing sales and time, the result would look almost like a straight line that slopes upward. But we can’t do much with an “almost” straight line. We need

a straight line. Let’s simplify the regression against time by noting the years 1976, 1977, ..., 1999 as 1, 2, ..., 24. Regressing IBM’s sales against time we estimate a regression line described as:

IBM annual sales, in billions =

$3.00 × time

Intercept of

Slope of

line with

the line, in

vertical axis,

billions of

in billions

dollars per year

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EXHIBIT 29.3 Sales of IBM

Panel a: Sales, 1976 through 1999

Panel b: Sales and Fitted Regression Line, 1976 through 1999

This line tells us that on average, from 1976 through 1999, IBM’s sales increased $3.19 billion each year. This regression line is also plot- ted in Exhibit 29.3. You’ll notice that the line intersects the vertical axis at $14.67 billion sales and has a slope (a rate of change in sales each year) of $3.00 billion.

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EXHIBIT 29.3

(Continued) Panel c: Actual Sales and Forecasted Sales for 2000 and 2001

Source: IBM Annual Reports, various years If we assume the current trend continues, we would predict sales to

increase in 2000. Let 2000 be represented as time = 25, then

IBM 2000 sales, in billions = $14.67 + $3 25 ( ) = $89.72 And for 2001 (time = 20):

IBM 2001 sales, in billions = $14.67 + $3 26 ( ) = $92.76 The difference between what was forecasted and what actually

occurred is the forecast error. Were actual 2000 and 2001 sales close to what we predicted? Not really: We have predicted higher sales than actually occurred.

Sales Predicted Actual Sales by Regression Line Forecast Error in Billions

in Billions

in Billions

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EXHIBIT 29.4 Sales and Capital Expenditures for IBM

Predicted Sales for 2000 and 2001, Based on Regression of Sales and Capital Expenditures for 1976–1999

Source: IBM Annual Reports, various years Predicted and actual 2000 and 2001 sales are shown in Exhibit

29.3, panel c. You’ll notice that we overestimated sales. This illustrates

a problem with regression analysis: Past trends do not always continue. Sales growth slowed in 2000 and 2001. Another way of using regression is to look at the relation between two measures, say, sales and capital expenditures. Exhibit 29.4, which shows the relation between sales and capital expenditures for the period 1976 through 1999, indicates that the greater the capital expenditures, the greater IBM’s sales. The straight line shown in this figure is the regres- sion line, which represents the best summary of the relation between IBM’s sales and capital expenditures from 1976 through 1999. Based on the relation between sales and capital expenditures during the 1976–1999 period and using actual capital expenditures for 2000 and 2001, we would have underestimated IBM’s sales in these years using the regression:

Forecast Year

Actual Capital

$88.40 billion $34.30 billion 2001

$54.10 billion

85.97 billion 31.64 billion As you can see, we have forecast errors that are quite large relative to

5.66 billion

54.33 billion

actual sales.

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We also could look at the relation between IBM’s sales and a num- ber of factors, such as IBM’s capital expenditures, a measure of eco- nomic activity such as Gross Domestic Product (GDP), and IBM’s competitor’s capital expenditures. Estimating the relation among these factors over a number of years, combined with forecasts of GDP and competitors’ expenditures, we could predict IBM’s sales for 1994. The more factors we include, the more accurate should be our predictions.

While regression analysis gives us what may seem to be a precise measure of the relationship among variables, there are a number of warnings that the financial manager must heed in using it:

■ Using historical data to predict the future assumes that the past rela- tionships will continue into the future, which is not always true. ■ The period over which the regression is estimated may not be represen- tative of the future. For example, data from a recessionary period of time will not tell much about a period that is predicted to be an eco- nomic boom.

■ The reliability of the estimate is important: If there is a high degree of error in the estimate, the regression estimates may not be useful. ■ The time period over which the regression is estimated may be too short to provide a basis for projecting long-term trends. ■ The forecast of one variable may require forecasts of other variables. For example, you may be convinced that sales are affected by GDP and use regression to analyze this relationship. But to use regression to fore- cast sales, you must first forecast GDP. In this case, your forecast of sales is only as good as your forecast of GDP.

Market Surveys Market surveys of customers can provide estimates of future revenues.

In the case of IBM, we would need to focus on the computer industry and, specifically, on the personal computer, mini-computer, and main- frame computer markets. For each of these markets, we would have to assess IBM’s market share and also the expected sales for each market. We should expect to learn from these market surveys:

■ product development and introductions by IBM and its competitors; and ■ the general economic climate and the projected expenditures on com- puters.

A firm can use its own market survey department to survey its custom- ers. Or it can employ outside market survey specialists.

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