Question

In: Accounting

Assume that a company wants to separate a mixed cost into its variable and fixed elements...

Assume that a company wants to separate a mixed cost into its variable and fixed elements for cost estimation purposes. It provided the following information:

Month Units Produced Mixed Cost
January 1,050 $ 11,045
February 1,150 $ 11,870
March 1,100 $ 11,560
April 1,250 $ 12,100
May 950 $ 10,800
June 1,280 $ 12,210
July 990 $ 10,970
August 1,010 $ 11,005

Assuming the company produces 1,200 units in September, using least-squares regression, the estimated total amount of the mixed cost would be closest which of the following? (Note: Round your estimate of the variable cost per unit to the nearest penny.)

Multiple Choice

  • $11,950

  • $11,908

  • $12,002

  • $11,985

Solutions

Expert Solution

Month Units Produced Mixed Costs Units produced^2 Units Produced*Mixed Costs
January 1050 11045 1102500 11597250
February 1150 11870 1322500 13650500
March 1100 11560 1210000 12716000
April 1250 12100 1562500 15125000
May 950 10800 902500 10260000
June 1280 12210 1638400 15628800
July 990 10970 980100 10860300
August 1010 11005 1020100 11115050
Total 8780 91560 9738600 100952900
Unit Variable Cost (b) = nΣxy − (Σx)(Σy)
nΣx2 − (Σx)2
= 8*100952900-(8780*91560)
= 8*9738600-(8780)^2
= 3726400/820400
= 4.54217
Total Fixed Cost (a) = Σy − bΣx
n
= 91560-4.542(8780)/8
= 6459.96
b) Equation for utility cost y=a+bx
a Fixed cost
b Unit variable cost
x Units produced
1200 units cost 6459.96+(4.54217*1200)
11911
Option B $11908 is the correct answer.

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