Question

1. Dr. Heimerdinger is starting a company to manufacture his new invention. Dr. Heimerdinger estimates that he will need to produce between 0 and 30,000 units per year. Three equipment alternatives have been identified, with estimated fixed and variable costs as shown below. Determine the ranges of production (number of units produced per year) over which each alternative would be preferable (be exact). Alternative Annual Fixed Costs $100,000 $200,000 $150,000 Annual Variable Costs $20.00 per unit $5.00 per unit $7.50 per unit B с

Answer 1

Solution:

Alternative 'A' has lowest fixed cost and highest variable cost, C's fixed and variable costs are in the middle and B has highest fixed cost and lowest variable cost. Total cost per unit includes variable cost per unit and fixed costs per unit.

As a general principle, the alternative with low fixed cost & high variable cost should have lowest total cost per unit if the production levels are on the lower side and alternative with low variable cost & high fixed costs should have lowest total cost per unit when the production is on the higher side.

Let's look at different alternatives through the following calculations and draw conclusions:

Note 1: Comparison of A and B Annual variable Annual fixed costs costs (per unit) 1,00,000.0 20.0 2,00,000.0 5.0 Difference -1,00,000.0 15.0 We can see that A has lesser fixed costs of $100,000 and excess variable costs of $15 per unit. Lets calculate the level of production at which the benefit of lower fixed costs is compensated by higher variable costs per unit Production at which total cost per unit of A and B will be equal = (B's fixed costs - A's fixed costs)/(A's variable cost p.u - B's variable cost p.u.) Production at which total cost per unit of A and B will be equal = (200,000 - 100,000)/(20-5) Production at which total cost per unit of A and B will be equal = 6,666.67 units [Production level 1] Note 2: Comparison of B and C Annual variable Annual fixed costs costs (per unit) 2,00,000.0 5.0 1,50,000.0 7.5 Difference 50,000.0 -2.5 We can see that C has lesser fixed costs of $100,000 and excess variable costs of $2.5 per unit. Lets calculate the level of production at which the benefit of lower fixed costs is compensated by higher variable costs per unit Production at which total cost per unit of B and C will be equal = (B's fixed costs - C's fixed costs)/(C's variable cost p.u - B's variable cost p.u.) Production at which total cost per unit of B and C will be equal = (200,000-150,000)/(7.5-5)= 20,000 units Production at which total cost per unit of A and B will be equal = 20,000 units [Production level 2]

A Note 3: Comparison of A and C Annual variable Annual fixed costs costs (per unit) 1,00,000.0 20.0 1,50,000.0 7.5 Difference -50,000.0 12.5 We can see that C has lesser fixed costs of $100,000 and excess variable costs of $2.5 per unit. Lets calculate the level of production at which the benefit of lower fixed costs is compensated by higher variable costs per unit Production at which total cost per unit of A and C will be equal = (C's fixed costs - A's fixed costs)/(A's variable cost p.u - C's variable cost p.u.) Production at which total cost per unit of A and C will be equal = (1,50,000-100,000)/(20-7.5)= 4,000 units Production at which total cost per unit of A and C will be equal = 4,000 units [Production level 3] Note 4: Comparison of A B and C at all levels calculated above Annual fixed costs Annual variable costs (per unit) Production Level 1 (Units) Total Cost per unit Production Level 2 (Units) Total Cost per unit Production Level 3 (Units) Total Cost per unit 1,00,000.0 20.0 6,666.7 (Note 1) 6,666.7 (Note 1) 35.00 [20+(100000/6666.7)] 35.00 [5+(200000/6666.7)] 20,000 (Note 2) 20,000 (Note 2) 25.00 [20+(100000/20000)] 15.00 [5+(200000/20000)] 4,000 (Note 3) 4,000 (Note 3) 4,000 (Note 3) 45.00 [20+(100000/4000)] 55.00 [5+(200000/4000)] 2,00,000.0 1,50,000.0 6,666.7 (Note 1) 30.00 [7.5+(150000/6666.7)] 20,000 (Note 2) 15.00 [7.5+(150000/20000)] 45.00 [7.5+(150000/4000)]

Conclusion:- Using the above table and Notes 1, 2 and 3, the following is available A Production range at which the alternative Reason (Refer Note 4 for total cost at different levels mentioned below) is preferred At 4,000 units B's total cost is 55 per unit whereas A and C have equal costs of 45 per unit. Since, A's fixed costs is lower and variable costs 0-3,999 units is higher than C, therefore till 3999 units A's total cost will be lower than C and at levels above 4,000 units the total cost of C will be lower than A At 20,000 units A's total cost is 25 per unit whereas B and C have equal costs of 15 per unit. Since, C's fixed costs is lower and variable 20,001-30,000 units costs is higher than B, therefore till 19,999 units C's total cost will be lower than B and at levels above 20,000 units the total cost of B will be lower than C At 20,000 units A's total cost is 25 per unit whereas B and C have equal costs of 15 per unit. Since, C's fixed costs is lower and variable 4,001-19,999 units costs is higher than B, therefore till 19,999 units C's total cost will be lower than B and at be lower than C