Dr. Thomas is starting a company to manufacture his new invention. Dr. Thomas es

Question

Dr. Thomas is starting a company to manufacture his new invention. Dr. Thomas 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           Annual Variable Costs

A                                   $100,000                            $20.00 per unit

B                                   $200,000                            $5.00 per unit

C                                   $150,000                            $7.50 per unit

Explanation / Answer

We need to calculate the number of units for which the total cost would be equal for the alternatives to find out the required number of units for each one.

For alternatives A and B:

Let the required number of units be x.

For total costs to be equal for the two alternatives, $100,000+  ($20.00*x) = $200,000 +  ($5.00*x)

or, 15x = $100,000 or x= 6666.67 units

So, if there are only A and B, then below 6666.67 units alternative A is better and above 6666.67 units alternative B should be considered. This is because the fixed cost is lesser in case of alternative A than B.

For alternatives B and C:

For total costs to be equal for the two alternatives, $200,000+  ($5.00*x) = $150,000 +  ($7.50*x)

or, 2.5x = $50,000 or x= 20000 units

So, if there are only B and C, then below 20000 units alternative C is better and above 20000 units alternative B should be considered. This is because the fixed cost is lesser in case of alternative C than B.

For alternatives A and C:

For total costs to be equal for the two alternatives, $100,000+  ($20.00*x) = $150,000 +  ($7.50*x)

or, 12.5x = $50,000 or x= 4000 units

So, if there are only A and C, then below 4000 units alternative A is better and above 4000 units alternative C should be considered.This is because the fixed cost is lesser in case of alternative A than C.

Finally, from the three conditions we can state that the following alternatives should be considered as per the number of units to be manufactured:

0-4000 units: Alternative A

4000-20000 units: Alternative C

20000-30000 units: Alternative B

Please revert to me if you have any queries.

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