Question

United Motors specializes in producing one specialty vehicle. It is called Surfer and is styled to easily fit multiple surfboards in its back area and​ top-mounted storage racks.

United has the following manufacturing​ costs:

United currently produces 180 vehicles per month

Plant management​ costs, $1,728,000 per year
Cost of leasing​ equipment, $2,856,000 per year
​Workers' wages, $800 per Surfer vehicle produced
Direct materials​ costs: Steel, $1,600 per​ Surfer; Tires, $150 per​ tire, each Surfer takes 5 tires​ (one spare)
City​ license, which is charged monthly based on the number of tires used in​ production:
	​0-500 tires	$70,000
	​501-1,000 tires	$80,000
	more than​ 1,000 tires	$230,000

Requirements

1.	What is the variable manufacturing cost per​ vehicle? What is the fixed manufacturing cost per​ month?
2.	Plot a graph for the variable manufacturing costs and a second for the fixed manufacturing costs per month. How does the concept of relevant range relate to your​ graphs? Explain.
3.	What is the total manufacturing cost of each vehicle if 95 vehicles are produced each​ month? 220 vehicles? How do you explain the difference in the manufacturing cost per​ unit?

Answer 1

(1): Variable mfg. cost per vehicle = cost of steel+tire+wages

= 1600 + (150*5) + 800

= $3,150

Fixed manufacturing cost per month = plant management costs + cost of leasing equipment + city license

= $1,728,000/12 + $2,856,000/12 + 80,000 (as no. of tires = 5*180 = 900)

= 144,000 + 238,000 + 80,000

= $462,000

(2): The graph is shown as an image attachment below. The concept of relevant range can be seen from the fixed manufacturing cost per month graph. We can see that the fixed costs are constant at $542,000 from 0-100 units, then at $462,000 till 200 units and after that stabilizes at $612,000. Thus we can see that fixed costs are fixed only within a relevant range of activity.

(3): Mfg. cost in case of 95 vehicles per month = [(3150*95) + (144,000+238,000) + $70,000]/95

= 751,250/95

= $7,907.89

Mfg. cost in case of 220 vehicles per month =[ (3150*220) + (144,000+238,000) + 230,000)]/220

= 1,305,000/220

= $5,931.82

The difference in manufacturing cost per unit can be attributed to the fact that in case of 220 vehicles the fixed costs are absorbed by a higher number of vehicles and this leads to a reduction in the total cost per vehicle.