Red’s Furniture Manufacturing produces a line of tables and chairs from specialty hardwoods. It makes three different styles of chairs, and each chair takes about the same amount of direct labor time to manufacture. Shawn Hargrove was the company’s new cost accountant and was preparing a direct labor cost budget for 20X5. The previous cost accountant had always estimated direct labor costs based on a regression of the cost against the number of chairs produced using monthly data from the prior four years. This approach seemed to be economically plausible, so Shawn began his cost estimate by following the method used in prior years. However, Shawn was not pleased with his regression results.
Shawn thought about ways to improve the cost function estimate. He realized that the past cost information did not take into account pay raises. Every January, the company gives its employees a cost of living pay increase. Each of the past four years, the employees had received a 2% raise. He learned from management that a 2% raise is planned for 20X5, too. Shawn thought that prior years’ labor costs should be increased to 20X5 pay levels to provide a more accurate prediction of 20X5 costs. He planned to adjust prior year pay using the following formula:
Labor cost at 20X5 level = Labor cost at prior pay level X (1.02)t
Where t = 1 for 20X4
t = 2 for 20X3
t = 3 for 20X2
t = 4 for 20X1
Shawn also considered the degree to which direct labor costs vary with production. The Company’s policy is to increase the number of workers when production volumes increase, and to decrease the number of workers when production volumes decrease. However, it often takes time for the company to hire qualified new workers, and the managers often delay laying employees off when volumes decline. Thus, at least some lag is evident between the time that production volumes change and labor costs change. Shawn thought that an additional cost driver for direct labor costs might be the prior month’s volume of chairs produced.
The data provide monthly direct labor costs and number of chairs produced for the past four years. These data are available at the Web site www.wiley.com/college/eldenburg

REQUIRED
A. Estimate the cost function using the same method as in prior years. Explain why Shawn was displeased with the results.
B. Explain why the annual pay increases cause a problem with the cost function estimated in part (A). In what way is the cost function miss-measured?
C. Use the formula developed by Shawn to adjust the labor cost data for pay increases. Re-estimate the cost function. Explain whether you consider it to be a reasonable cost function for estimating 20X5 direct labor costs.
D. To the analysis you performed in part (C), add a second independent variable for the number of chairs produced in the preceding month. Re-estimate the cost function. Do the statistics suggest that it is a reasonable cost function?
E. Explain what the two independent variable coefficients from part (D) mean in terms of the cost function.
F. Do you agree that both independent variables should be used to estimate 20X5 direct labor costs? Why or why not?