(High-low method) Information about SnoCos’ utility cost for the last six months of 2008 follows. The high-low method will be used to develop a cost formula to predict 2009 utility charges, and the number of machine hours has been found to be an appropriate cost driver. Data for the first half of 2008 are not being considered because the utility company imposed a significant rate change as of July 1, 2008. Machine Utility Month Hours Cost July 33,750 $6,500 August 34,000 6,100 September 33,150 5,070 October 32,000 5,980 November 31,250 5,750 December 31,000 5, 860 a. What is the cost formula for utility expense? b. What is the budgeted utility cost for September 2009 if 33,175 machine hours are projected?

To develop a cost formula using the high-low method, we need to find the variable cost per machine hour and the fixed cost component.

Step 1: Find the highest and lowest levels of the cost driver (machine hours).
The highest machine hours = 34,000 (August)
The lowest machine hours = 31,000 (December)

Step 2: Calculate the variable cost per machine hour.
Variable cost = Highest cost - Lowest cost / Highest machine hours - Lowest machine hours

Variable cost = ($6,500 - $5,860) / (34,000 - 31,000)
Variable cost = $640 / 3,000 = $0.213 per machine hour

Step 3: Calculate the fixed cost component.
Using the high or low data point:

At the highest level:
Total cost = Variable cost per machine hour * Machine hours + Fixed cost
$6,500 = $0.213 * 34,000 + Fixed cost
$6,500 = $7,242 + Fixed cost
Fixed cost = $6,500 - $7,242 = -$742 (negative)

At the lowest level:
Total cost = Variable cost per machine hour * Machine hours + Fixed cost
$5,860 = $0.213 * 31,000 + Fixed cost
$5,860 = $6,603 + Fixed cost
Fixed cost = $5,860 - $6,603 = -$743 (negative)

Since both calculations resulted in a negative fixed cost, we can assume that the fixed cost component is zero.

a. The cost formula for utility expense is:
Utility Cost = Variable cost per machine hour * Machine hours

Utility Cost = $0.213 * Machine hours

b. To calculate the budgeted utility cost for September 2009 with 33,175 machine hours, we can use the cost formula:
Budgeted Utility Cost = $0.213 * 33,175
Budgeted Utility Cost = $7,058

To find the cost formula using the high-low method, we need to identify the highest and lowest values for both the machine hours and the utility cost.

1. Identify the highest and lowest values for machine hours:
- The highest machine hours is 34,000 in August.
- The lowest machine hours is 31,000 in December.

2. Identify the highest and lowest values for utility cost:
- The highest utility cost is $6,500 in July.
- The lowest utility cost is $5,070 in September.

Now that we have the high and low values, we can calculate the variable cost per machine hour by using the cost formula:

Variable cost per machine hour = (Cost at High - Cost at Low) / (Machine Hours at High - Machine Hours at Low)

Variable cost per machine hour = ($6,500 - $5,070) / (34,000 - 31,000) = $1,430 / 3,000 = $0.4767 (approx.)

Next, we can calculate the fixed cost by using the cost formula:

Fixed cost = Total cost - (Variable cost per machine hour * Total machine hours)

Let's calculate the total cost at any given point by using the formula:

Total cost = (Variable cost per machine hour * Machine hours) + Fixed cost

Now, let's calculate the fixed cost:

Using the data for December: $5,860 = ($0.4767 * 31,000) + Fixed cost
$5,860 = $14,777 + Fixed cost
Fixed cost = $5,860 - $14,777 = -$8,917 (approx.)

Since the fixed cost cannot be negative, we consider it as zero. Therefore, the cost formula for utility expense is:

Total cost = (Variable cost per machine hour * Machine hours)

So, the cost formula is:
Total cost = $0.4767 * Machine hours

To answer part b of the question, we can use the cost formula to calculate the budgeted utility cost for September 2009.

Budgeted utility cost for September 2009 = $0.4767 * 33,175 machine hours

Calculating the value:

Budgeted utility cost for September 2009 = $15,808.78 (approx.)

Therefore, the budgeted utility cost for September 2009, with a projected 33,175 machine hours, is approximately $15,808.78.