Auto Shoppe is considering the purchase of a new engine computer code reader for

Question

Auto Shoppe is considering the purchase of a new engine computer code reader for $45,500. Auto Shoppe can charge $80 for the service of reading the codes from a single car engine, while the actual cost of the reading would only be $15 per car engine.

a. How many cars would need their engine computer codes read by Auto Shoppe for it to break-even on this purchase?

b. 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 500 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 The manager says this is because, “…those sorts of engine computer code readers go out of date very quickly, so if we don’t get our money back soon, we will probably just wind up replacing the machine before it ever breaks even.”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 break-even when it reads the codes from 500 car engines?

Explanation / Answer

a. Break even units:

Contribution margin = price charged from single car engine - cost of reading per car engine = 80 - 15 = $65

Fixed cost (price of the reader) = 45,500

Break even units = Fixed costs/(price per unit - variable cost per unit) = fixed cost/contribution margin

= 45,500/65 = 692.31 cars

b. If the number of units = 500 cars, total fixed costs per unit = $15. let the price charged per car be "x"

so, using the formula: Break even units = Fixed costs/(price per unit - variable cost per unit)

500 = 45,500/(x - 15)

x - 15 = 45,500/500

x-15 = 91

or x = $106. This is price that Auto Shoppe need to charge for the service of reading each car engine to break even.

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