Question

A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.

If they offer a 2 year extended warranty for $30, what is the company's expected value of each warranty sold?

Answer 1

Explanation:

The expected value of each warranty sold can be calculated using the following formula:

Expected Value = (Probability of Failure without warranty x Replacement Cost without warranty) + (Probability of Failure with warranty x Replacement Cost with warranty) - Cost of Warranty

Probability of Failure without warranty = 0.8% or 0.008 (given)

Replacement Cost without warranty = $200 (given)

Probability of Failure with warranty = 0% (since the product is covered under warranty)

Replacement Cost with warranty = $0 (since the cost of replacement is covered under warranty)

Cost of Warranty = $30 (given)

Expected Value = (0.008 x $200) + (0 x $0) - $30

Expected Value = $1.60 - $30

Expected Value = -$28.40

The company's expected value of each warranty sold is -$28.40, which means that on average, the company can expect to lose $28.40 for every warranty sold. This is because the cost of the warranty ($30) is greater than the expected cost of replacement without the warranty ($1.60). Therefore, it is not beneficial for the company to offer the extended warranty.