A problem faced by management is selecting from among alternative production processes which have different fixed and variable costs. For example, management may be considering two alternative production processes. The first has a high fixed cost but low variable cost per unit; the other has a low fixed cost but a high variable cost per unit. Which is the best production process that should be adopted by management?

The tools presented in this chapter can be used to evaluate which production process should be adopted. To illustrate how, assume that the two production processes management is considering have the following cost structure:

PROCESS A PROCESS B

Total fixed cost $500,000 $2,500,000

Variable cost per unit 20 10

Regardless of the production process selected, management expects to sell each unit for $30. Further, the production capacity will be the same for both production processes: 6 million units. First, management should determine the break-even point for process A and process B. For process A, the break-even point is 50,000 units, as shown below:

Break-even point = Total fixed costs.

(in units)

Contribution margin per unit

= $500,000

$30 – $20

= 50,000 units

For process B, the break-even point is 125,000 units, as shown below:

Break-even point = Total fixed costs

(in units)

Contribution margin per unit

= 2,500,000

$30 – $10

= 125,000

Which is the best production system? Is it the one which has the lower break-even point? Not necessarily. The answer depends on what management expects the level of sales will, the probability of achieving that level of sales, and the volatility of sales. For example, suppose that management expects that sales will be 60,000. With process A, a profit will be realized, but with process B, a loss will be sustained. In fact, for any level of sales between 50,001 and 124,999 units, the selection of process A will result in a profit while process B will result in a loss. At any level below 50,000, there will be a loss regardless of the production process selected; however, the loss will be greater with process B.

If sales are expected to be greater than 125,000, both production processes will result in a profit. Which will produce the greatest profit? Management must determine the point at which sales will be the same for both production processes A and B.

Since unit sales will be same regardless of the production process selected, the level of sales that will produce the same profit is that level of sales at which the total costs of both production processes are equal. Solving for this point algebraically, let the subscripts A and B denote the costs associated with process A and process B, respectively. Then the point at which the profit from both production processes will be equal is as follows:

TC_A = TC_B

Since total cost is equal to total variable costs plus total fixed costs, the above equation can be written as

V_A . Q + F_A = V_B . Q + F_B

Solving this equation for Q, we have Sales at which both

production processes = F_B – F_A

produce same profit V_A – V_B

(in units)

In this example, the number of units that must be sold in order to produce the same level of profit is 200,000 units, as shown below:

Sales at which both production process = $2,500,000 – $500,000

$20 – $10

produce processes produce same profit (in units)

= 200,000 units

The following simple income statement verifies that 200,000 units will produce the same level of profits:

	PROCESS A	PROCESS B
Sales (total revenue) (200,000 x $30)	$ 6,000,000	$ 6,000,000
Total variable costs
200,000 x $20	(4,000,000)
200,000 x $10		(2,000,000)
Total fixed costs	(500,000)	(2,500,000)
Profit	$ 1,500,000	$ 1,500,000

Therefore, for sales between 125,000 and 199,999 units, process A will produce the greater profit. If sales are expected to exceed 200,000 units, process B will generate a greater profit.

The relationship between sales and profit for both production processes is shown in Table. The best production process depends on the expected level of sales.

For example, suppose that management expects that sales will be 250,000 units. The profit under process A and process B will be $2,000,000 and $2,500,000, respectively, as shown below:

Profit at 250,000 units = $30(250,000) – $20(250,000) – $500,000 for process A

for process A = $2,000,000

Profit at = $30(250,000)

250,000 units – $10(250,000) –

for process B $2,500,000

= $2,500,000

Although there is a greater profit with process B if actual sales are 250,000 units, there is also greater risk. The margin of safety is 80% and 50% for process A and process B, respectively, as shown below:

Margin of safety for process A =

Expected sales – Break-even sales for process A / Expected sales

= 250,000 – 50,000

250,000

= .80 or 80%

Margin of safety for process B =

Expected sales – Break-even sales for process B / Expected sales

= 250,000 – 125,000

250,000

= .50 or 50%

Consequently, unit sales can decline by as much as 80% and the firm will still break even under process A; however, unit sales can only fall by 50% under process B before a loss will be realized. The best process will depend not only on the expected level of sales, but also on the probability that different levels of sales may be realized.