Norwest Property Management (NPM) was founded in 1987 by Henri Rouark. Mr. Rouark had arrived from France several years earlier and had worked in an uncle's hotel in San Francisco, where he obtained a firsthand background in property management. Wishing to be his own boss, he founded his own company, Norwest Property Management.
NPM provides management services to homeowners in popular resort areas. The company contracts with home owners to rent their properties to vacationers during times when the homeowners will not be using their homes. The company charges the homeowners a percentage of the rent as their fee, and the homeowner receives the difference between the rent paid and NPM's fee.
In return for the fee, Mr. Rouark and his staff make all arrangements with the renters and collects rents from them. The company arranges for cleaning the property after renters leave. For an additional fee, at a homeowner's option, NPM will also provide maintenance services.
Under Mr. Rouark's direction, the company has signed contracts with many owners of second homes in the Lake Tahoe, Russian River, and Grass Valley areas of Northern California; in the areas around Klamath Falls and Bend, Oregon; and on the island of Oahu, Hawaii.
NPM has done an excellent job for both homeowners and renters, and the company has prospered as a result. NPM's annual receipts (in millions of dollars) have grown as follows during the past 8 years:
Year 1997 1996 1995 1994 1993 1992 1991 1990
Receipts ($ million) 74.4 57.1 44.3 33.2 25.3 19.8 15.8 12.6
In March 1998, Mr. Rouark was approached by Ms. Isabel Monroe, representing Goliath Home Services (GHS), about buying NPM. GHS is a successful company that provides similar services in Southern California, Nevada, and Arizona and wants to expand further. The company is well financed and is somewhat larger than NPM. Rouark is receptive to the idea of selling his company, provided he can get a good price for it.
Both parties recognize that Rouark's company is well based and positioned to continue to grow in the future. In fact, GHS's interest is based not only on NPM's financial track record since 1990 but also on NPM's future potential. Therefore, in order to help provide a basis for negotiating a fair purchase price, Monroe has projected the NPM's annual receipts to the end of the current year and the next two - that is, to the ends of 1998, 1999, and 2000. In order to be objective and avoid personal bias, Monroe did this by using linear regression analysis.
a. Evaluate the coefficients of a linear regression equation (i.e., the intercept and slope) for projecting the trend of NPM's annual receipts for 1990 to 1997. Provide a complete specification for the linear regression model. The specification should include the equation of the model, with the values for the intercept and slope determined from the data, and a definition of the model's dependent and independent variables. Also include the model's standard error of estimate.
b. Evaluate the coefficient of correlation for the linear regression model.
c. Use the linear regression model determined in part (a) to forecast NPM's annual receipts for 1998, 1999, and 2000.