In: Accounting
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
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. | |