It's been several years since I have had to do math and I am posed with this ? and don't recall how to find the answers. There is a fixed overhead of $1 per bolt. They make a run of 10,000 bolts at a total marginal cost of $70k. They sell them all, and lose $20k. What is the price for each bolt?
Secondly, assuming the same overhead and marginal cost, selling price remain the same, how many bolts must they make to profit $20k?
Anyone know how I can figure this out? Thanks in advance
To find the price per bolt, we can use the information given: a fixed overhead cost of $1 per bolt, a total marginal cost of $70,000 for a production run of 10,000 bolts, and a loss of $20,000.
First, let's calculate the marginal cost per bolt. Marginal cost is the cost of producing one additional unit. Since the total marginal cost is given as $70,000 for 10,000 bolts, each bolt's marginal cost would be:
Marginal cost per bolt = Total marginal cost / Number of bolts
= $70,000 / 10,000
= $7
Now, to find the total cost per bolt, we need to consider both the marginal cost and the fixed overhead cost. The fixed overhead cost is given as $1 per bolt, so the total cost per bolt would be the sum of the marginal cost and the fixed overhead cost:
Total cost per bolt = Marginal cost per bolt + Fixed overhead cost
= $7 + $1
= $8
Since the company experienced a loss of $20,000, we can calculate the total cost for 10,000 bolts:
Total cost for 10,000 bolts = Total cost per bolt * Number of bolts
= $8 * 10,000
= $80,000
Now, we can find the selling price per bolt by adding the loss to the total cost for 10,000 bolts and dividing it by the number of bolts:
Selling price per bolt = (Total cost for 10,000 bolts + Loss) / Number of bolts
= ($80,000 + $20,000) / 10,000
= $100,000 / 10,000
= $10
Therefore, the price for each bolt would be $10.
To find the number of bolts they must make to profit $20,000, assuming the same overhead and marginal cost, we can use the same calculations and the selling price per bolt of $10.
Profit per bolt = Selling price per bolt - Total cost per bolt
= $10 - $8
= $2
To profit $20,000, we can divide the target profit by the profit per bolt:
Number of bolts to profit $20,000 = Target profit / Profit per bolt
= $20,000 / $2
= 10,000 bolts
Therefore, they must make 10,000 bolts to profit $20,000.