A company charges $40 for a one-year extended warranty on their product in case the product fails within one year of the purchase date.

Question

A company charges $40 for a one-year extended warranty on their product in case the product fails within one year of the purchase date. They know 1% of their products will fail during this time, and it will cost them $350 to replace a failed product. What is the company’s expected profit (or loss) on each warranty sold?

Answer 1

To calculate the company's expected profit (or loss) on each warranty sold, we can break it down as follows:

Given:

1. Price of the extended warranty: $40
2. Probability of product failure within a year: 1% or 0.01
3. Cost to replace a failed product: $350

Steps:

1. Calculate the expected cost of replacement per warranty sold: The company will incur a cost of $350 only if the product fails. Since there is a 1% (0.01 probability) chance of failure, the expected cost of replacement is:
2. Expected cost = 0.01 × 350 = 3.50
3. Calculate the expected profit: The company's revenue per warranty sold is $40. The expected cost per warranty sold is $3.50. Therefore, the expected profit is:
4. Expected profit = 40 − 3.50 = 36.50

The company's expected profit on each warranty sold is $36.50.

Hope this was helpful.