Vargis Corporation has a machining capacity of 217,000 hours per year. Utilization of capacity is normally 85%; it has been as low as 30% and as high as 90%. An analysis of the accounting records revealed the following selected costs:

At a 30% Utilization Rate At a 90% Utilization Rate

Cost A:

Total$457,000 $457,000

Per hour$7.20 ?

Cost B:

Total ? $1,961,000

Per hour$12.50 $12.50

Cost C:

Total$765,000 $1,347,000

Per hour$17.00 $9.09

Vargis uses the high-low method to analyze cost behavior.

Required:

Classify each of the costs as being either variable, fixed, or semivariable.

Calculate amounts for the two unknowns in the preceding table. (Round "Cost A" to 2 decimal places.)

Calculate the total amount that Vargis would expect at a 85% utilization rate for Cost A, Cost B, and Cost C. (Do not round intermediate calculations. Round your final answer to the nearest dollar amount.)

Check the explanation

Explanation:

Machine hours available at different capacity utilizatiion

at 30% = 217000*30% = 65100

at 90% = 217000*90% = 195300

at 85% = 217000*85% =184450

PER HOUR RATE OF COST A AT 90% CAPACITY

Irrespective of capacity utilization fixed cost will remain same

at different capacity utilization cost A is $457000, so that it is Fixed cost

Per hour rate = $457000/195300 hrs

= 2.34 per hour

COST B AT 30% CAPACITY

per hour rate of cost B is remains same in both 30% and 90%

per unit or per hour variable cost will be same at different capacity only if it is Variable cost

So that Cost B at 30% capacity can be calculated as follows

= 12.5*65,100hrs

=$813,750

COSTS THAT WILL INCUR AT 85% CAPACITY UTILIZATION

Cost A = $457,000 (as fixed cost will remain same)

Cost B = $12.5*184450 hrs  

= $2,305,625 (as variable cost rate per hour will remain same)

Cost C:

As it semi-variable cost we have to find out fixed cost within that

for that first we have to calculate variable cost per hour

VC/hr = Change in Variable cost / Change in machine hours

=(1,347,000-765,000) / (195300-65100)

=582000 / 130200

=$4.47

so variable cost at 30% =4.47*65100

=$290,997

variable cost at 90% = 4.47*195300

= $872,991

So fixed cost of C = Total cost of C - Variable cost of

at 30% capacity = 765000 - 290997

= 474003

( checking correctness) at 90% = 1,347,000 - 872991

=47009 (approx)

So, COST C AT 85% capacity utilization

=variable cost + fixed cost

=(4.47*184450hrs) + 474009

=824491.5 + 474009

=$1,298,500.5

TOTAL COST AT 85% CAPACITY UTILIZATION

=cost A+ cost B+ cost C

=$457,000+$2,305,625+$1,298,500.5

=$4,061,125