Question

Auto Shoppe is considering the purchase of a new engine computer code reader for $30,000. Auto Shoppe can charge $50 for the service of reading the codes from a single car engine, while the actual cost of the reading would only be $10 per car engine. Suppose that the manager of Auto Shoppe is concerned about this purchase, and has stated that if Auto Shoppe were to buy the new engine computer code reader, "..the machine needs to pay for itself by the time we use it to read the codes of 200 car engines." The manager says this is because, "…those sorts of engine computer code readers go out of date very quickly, so if we don’t get our money back soon, we will probably just wind up replacing the machine before it ever breaks even." What would Auto Shoppe need to charge for the service of reading each car engine, to just break-even when it reads the codes from 200 car engines?

Answer 1

Answer:

Auto Shoppe

For Auto Shoppe to just break-even when it reads the codes from 200 car engines, it would charge $160 for the service of reading each car engine.

Explanation:

a) Data and Calculations:

Fixed cost of new engine computer code reader = $30,000

Service charge for reading the code from a single car engine = $50

Variable cost of reading per car engine = $10

Number of engines to read their codes = 200

To break-even, total costs must equal total revenue

Total costs = Fixed costs + Variable costs

= $30,000 + $10 * 200

= $32,000

Therefore, revenue should be equal to $32,000

The amount to charge in order to break-even is:

= $160 ($32,000/200)

b) This implies that to break-even at $50 selling price, the number of engines should be increased to 750 ($30,000/$40).  This is because the contribution margin per unit = $40 ($50 - $10) and the fixed costs = $30,000.