The following data pertains to activity and utility cost for two recent periods: Utility cost is a mixed cost with both fixed and variable components. Using the high-low method, the cost formula for utility cost is:
A)Y = $1.00 X
B)Y = $1.25 X
C)Y = $4,000 + $0.50 X
D)Y = $1,500 + $1.25 X

Question

The following data pertains to activity and utility cost for two recent periods:  Utility cost is a mixed cost with both fixed and variable components. Using the high-low method, the cost formula for utility cost is:
A)Y = $1.00 X 
B)Y = $1.25 X 
C)Y = $4,000 + $0.50 X 
D)Y = $1,500 + $1.25 X

Quizplus · Accepted Answer

Using the high-low method:
Variable cost per unit = (Total cost at high activity level - Total cost at low activity level) / (High activity level - Low activity level)
= ($14,000 - $8,000) / (12,000 - 8,000) = $1.00 per unit

Fixed cost = Total cost - Variable cost * Total units
= $14,000 - $1.00 * 12,000 = $2,000

The cost formula is therefore: Y = $2,000 + $0.50X
However, we can see that this formula is inconsistent with the low activity level of 8,000 units. When X = 8,000, Y should be $6,000 according to this formula, but the data shows that actual cost was only $8,000 at the low activity level. Therefore, we need to adjust the fixed cost component upwards to match the actual cost at the low activity level.

Adjusted fixed cost = Actual cost - Variable cost * Actual units
= $8,000 - $1.00 * 8,000 = $4,000

The final cost formula is: Y = $4,000 + $0.50X, which is equivalent to choice C.

The Following Data Pertains to Activity and Utility Cost for Two