Lorenzo operates a brushless car wash. Incoming cars are put on an automatic, co
ID: 2418509 • Letter: L
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 December, when 11,350 cars are expected to be washed. She uses two different methods to estimate total December 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 June, when 9,500 cars were washed. The following are June total costs and her fixed cost estimates:
Total Cost
Fixed Portion
$5,700
$0
$3,800
$0
$26,030
$2,280
$12,210
$2,710
$3,100
$3,100
For the high-low method, she developed cost function parameter estimates by using the actual costs in April and May, when 8,600 and 11,900 cars were washed, respectively. The following are total costs for these two months:
April
May
$1,720
$2,380
$5,160
$7,140
$25,720
$34,630
$10,240
$13,210
$3,650
$3,650
REQUIRED [ROUND PER-UNIT COSTS TO TWO DECIMAL PLACES AND TOTAL COSTS TO THE NEAREST DOLLAR.]
Part A (6 tries; 5 points)
1. Using account analysis, what is the accountant's estimate of total fixed costs for December?
2. Using account analysis, what is the accountant's estimate of total variable costs for December?
Part B (6 tries; 5 points)
1. Using the high-low method, what is the accountant's estimate of total fixed costs for December?
2. Using the high-low method, what is the accountant's estimate of variable costs per unit for December?
Total Cost
Fixed Portion
Soap, cloths, and supplies$5,700
$0
Water$3,800
$0
Car wash labor$26,030
$2,280
Power for conveyor$12,210
$2,710
Supervisor and cashier$3,100
$3,100
Explanation / Answer
Part A:
Estimation of Total Fixed cost and Total Variable cost for December using Account Analysis:
From the given Actual costs in June, when 9500(x) cars were washed:
Total cost of all items (Y) = 5,700+ 3,800+ 26,030+ 12,210+ 3,100 = 50,840
Total fixed costs (TFC) = 2,280+ 2,710+ 3,100 = 8,090
This implies, Total Variable cost = 50,840 - 8,090 = $42,750
Here, Variable cost per unit (VC) = 42,750/9,500 = $4.50
Hence, the cost formula is Y = VCx + TFC wherein Y represents Total cost
VC represents Variable cost per unit,
x represents level of activity and
TFC represents Total Fixed Cost
Therefore, Y = 4.50x + 8,090
(1). Total Fixed cost for December = $8,090 [Because, fixed cost remains constant at any level of activity]
(2). Total Variable cost for 11,350 cars in December = 4.50* 11,350 cars = $51,075
PART B:
Estimation of Total Fixed cost and Total Variable cost for December using High-Low method:
From the given data:
Total cost for April (X1) = 1,720+ 5,160+ 25,720+ 10,240+ 3,650= $46,490
Total cost for May (X2) = 2,380+ 7,140+ 34,630+ 13,210+ 3,650 = $61,010
Total cars washed in April (Y1) = 8,600
Total cars washed in May (Y2) = 11,900
In the above, X2 is the high activity level, Y2 is the total cost at the high activity level
X1 is the low activity level, Y1 is the total cost at the low activity level
Now, Variable cost per unit = [Y2-Y1] / [X2-X1]
= [61,010 - 46,490] / [11,900- 8,600]
= 14,520 / 3,300
= $4.40 per unit
Finding fixed cost: Y= VCx + TFC
46,490 = 4.40*8,600 + TFC [ Total cost & activity for April are considered]
TFC = $8,650
Now,
1. Total Fixed costs for December = $8,650
2. Variable cost per unit for December = $4.40
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