Question

Lorenzo operates a brushless car wash. Incoming cars are put on an automatic, continuously moving conveyor belt. A car is washed as the conveyor belt carries it from the start station to the finish station. After the car moves off the conveyor belt, workers dry it and clean and vacuum the inside. Workers are managed by a single supervisor.

Lorenzo's accountant wants to estimate total costs in October, when 11,650 cars are expected to be washed. She uses two different methods to estimate total October costs, account analysis and high-low, with number of cars washed as the independent variable for both methods.

For the account analysis method, she developed cost function parameter estimates by analyzing actual costs in February, when 9,600 cars were washed. The following are February total costs and her fixed cost estimates:

Cost Item	Total Cost	Fixed Portion
Soap, cloths, and supplies	$4,800	$0
Water	$5,760	$0
Car wash labor	$28,380	$2,460
Power for conveyor	$12,510	$2,910
Supervisor and cashier	$3,700	$3,700

For the high-low method, she developed cost function parameter estimates by using the actual costs in July and August, when 8,700 and 11,900 cars were washed, respectively. The following are total costs for those two months:

Cost Item	July	August
Soap, cloths, and supplies	$4,350	$5,950
Water	$3,480	$4,760
Car wash labor	$23,380	$31,060
Power for conveyor	$8,960	$11,520
Supervisor and cashier	$3,950	$3,950
Total	$44,120	$57,240

REQUIRED [ROUND PER-UNIT COSTS TO THE NEAREST CENT AND TOTAL COSTS TO THE NEAREST DOLLAR.]

Part A
1. Using account analysis, what is the accountant's estimate of total fixed costs for October?    

2. Using account analysis, what is the accountant's estimate of variable costs per unit for October?   

Part B
1. Using the high-low method, what is the accountant's estimate of total fixed costs for October?    

2. Using the high-low method, what is the accountant's estimate of total variable costs for October?

Answer 1

Answer to Part A:

1.

Estimated Total Fixed Cost for October = $2,460 + $2,910 + $3,700
Estimated Total Fixed Cost for October = $9,070

2.

Total Variable Cost for the Month of February =Total Cost – Total Fixed Cost
Total Variable Cost for the Month of February = $4,800 + $5,760 + $28,380 + $12,510 + $3,700 - $9,070
Total Variable Cost for the Month of February = $46,080

Variable Cost per Unit = 46,080 / 9,600
Variable Cost per Unit = $4.80

Answer to Part B:

1.

As per High-Low Method,
Variable Cost per Unit = (y2 – y1) / (x2 – x1)
Total Cost at the Highest Level of Activity (y2) = $57,240
Total Cost at the Lowest Level of Activity (y1) = $44,120
Total Units at the Highest Level of Activity = 11,900 Units
Total Units at the Lowest Level of Activity = 8,700 Units

Variable Cost per Unit = (57,240 – 44,120) / (11,900 – 8,700)
Variable Cost per Unit = 13,120 / 3,200
Variable Cost per Unit = $4.10

Total Cost = Fixed Cost + Variable Cost * X

For August:
$57,240 = Fixed Cost + ($4.10 * 11,900)
$57,240 = Fixed Cost + $48,790
Fixed Cost = $8,450

For July:
$44,120 = Fixed Cost + ($4.10 * 8,700)
$44,120 = Fixed Cost + $35,670
Fixed Cost = $8,450

2.

Total Variable Cost for the Month of October = $4.10 * 11,650
Total Variable Cost for the Month of October = $47,765