Question

1. Step Costs, Relevant Range

   Bellati Inc. produces large industrial machinery. Bellati has a machining department and a group of direct laborers called machinists. Each machinist can machine up to 500 units per year. Bellati also hires supervisors to develop machine specification plans and oversee production within the machining department. Given the planning and supervisory work, a supervisor can oversee, at most, three machinists. Bellati's accounting and production history shows the following relationships between number of units produced and the annual costs of supervision and materials handling (by machinists):

   Units Produced	Direct Labor			Supervision
   0–500	$ 36,000			$ 40,000
   501–1,000	72,000			40,000
   1,001–1,500	108,000			40,000
   1,501–2,000	144,000			80,000
   2,001–2,500	180,000			80,000
   2,501–3,000	216,000			80,000
   3,001–3,500	252,000			120,000
   3,501–4,000	288,000			120,000

   Required:

   1. On your own paper, prepare a graph that illustrates the relationship between direct labor cost and number of units produced in the machining department. (Let cost be the vertical axis and number of units produced be the horizontal axis.) Would you classify this cost as a strictly variable cost, a fixed cost, or a step cost?
   

   2. On your own paper, prepare a graph that illustrates the relationship between the cost of supervision and the number of units produced. (Let cost be the vertical axis and number of units produced be the horizontal axis.) Would you classify this cost as a strictly variable cost, a fixed cost, or a step cost?
   

   3. Suppose that the normal range of production is between 1,400 and 1,500 units and that the exact number of machinists are currently hired to support this level of activity. Further suppose that production for the next year is expected to increase by an additional 500 units. What is the increase in the cost of direct labor? Cost of supervision?

   Cost of direct labor $
   Cost of supervision $

Answer 1

1. The following graph shows the relationship betweenn direct labour cost and number of units produced. The graph shows a liner relationship for the batch of units and it is a variable cost for batch and the variable cost per unit varies for once the number of units produced crossed the batch. Hence it is step variable cost.

Example: At 500 units the total direct labour cost is 36000 which means that cost per unit is $72 (36000/500).

If the number of units produced is 600, the total direct labour cost will be 72000, where the cost per unit will be 120(72000/600). Hence it is step variable cost

2. The following graph shows the relationship between the number of units produced and supervision cost. the cost is fixed till 1500 units are produced and the cost increased to 80000 if the number of units produced exceeds 1500 units. Hence it is a step fixed cost.

3. It is given that normal range of production is 1400-1500 units. In the given case the direct labour cost will be 1,08,000. and the supervision cost will be 40000.

If the level of production increased by 500 units, then the labour cost will be increased by 36000 if the level of units produced is above 1500 units. and the supervision cost also be increased by $ 40000 if the production is above 1500 units.

If the production is above 1500 units then,

Cost of labour = 144000, Cost of supervision = 80000

If the production is 1500 units, then

Cost of labour = 108000, Cost of supervision = 40000