Question

The assistant is unsure how to classify the utilities costs in the radiology department, since these costs do not exhibit either strictly variable or strictly fixed cost behaviour. Utilities costs are very high in the department due to a CT scanner that draws a large amount of power and is kept running at all times. The scanner cannot be turned off due to the long warm-up period required for its use. When the scanner is used to scan a patient, it consumes an additional burst of power. The assistant has accumulated the following data on utilities costs and use of the scanner since the first of the year: Month Number of Scans Utilities Cost January $4,250 February 85 6,300 March 7,000 April 10,400 May 14,000 June 110 8,500 July 16,000 August 11,700 September 210 15,100 October 13,500 40 100 150 200 260 160 180 The chief administrator has informed her assistant that the utilities cost is probably a mixed cost that will have to be broken down into its variable and fixed cost elements by use of a scattergraph. The assistant feels, however, that if an analysis of this type is necessary, the high- low method should be used because it is easier and quicker to use than other methods. REQUIRED: 1. Using the high-low method, estimate a cost formula for utilities. Express the formula in the form Ya+bX 2. Draw a scattergraph and interpret your values. 3. Perform a regression analysis and interpret your values. 4. Estimate the total utilities cost for November if the hospital plans to perform 167 scans.

Answer 1

High point in calculation July.

Mixed cost = a+bx

b=(cost @ highest level - cost @ lowest level)/highest level - lowest level

= ($16,000-$4,250)/260-40

= $11,750/220

= $53.41

$16,000 = Fixed cost + ($53.41*260)

$16,000 = Fixed cost + $13,887.6

Fixed cost = $16,000-$13,887.6

= $2,113.4

Total cost for 55 scans is

= $2,113.4 + (53.41*55)

= $2,113.4 + $2,937.55

Total cost = $5,051