Answer:
To determine the crossover point, we need to find the production volume at which the total cost of each process is equal. Let's denote the production volume as "x."
For Process A:
Fixed cost = $50,000
Variable cost = $10 per unit
Total cost for Process A = Fixed cost + (Variable cost * x)
For Process B:
Fixed cost = $30,000
Variable cost = $15 per unit
Total cost for Process B = Fixed cost + (Variable cost * x)
The selling price for the product is $25 per unit.
To find the crossover point, we'll equate the total costs of both processes and solve for "x."
Total cost for Process A = Total cost for Process B
$50,000 + ($10 * x) = $30,000 + ($15 * x)
Now, let's solve this equation to find the crossover point:
$50,000 + $10x = $30,000 + $15x
$10x - $15x = $30,000 - $50,000
-$5x = -$20,000
x = -$20,000 / -$5
x = 4,000
Therefore, the crossover point occurs at a production volume of 4,000 units.
To determine which process should be chosen above that volume, we'll compare the total costs of each process at a production volume greater than 4,000 units.
For Process A:
Total cost for Process A = $50,000 + ($10 * x)
Total cost for Process A = $50,000 + ($10 * 4,000)
Total cost for Process A = $50,000 + $40,000
Total cost for Process A = $90,000
For Process B:
Total cost for Process B = $30,000 + ($15 * x)
Total cost for Process B = $30,000 + ($15 * 4,000)
Total cost for Process B = $30,000 + $60,000
Total cost for Process B = $90,000
At a production volume greater than 4,000 units, both Process A and Process B have the same total cost of $90,000. Therefore, either process can be chosen above that volume without any cost advantage.