Question

A company estimates that 0.4% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $150.

If they offer a 2 year extended warranty for $11, what is the company's expected value of each warranty sold?

Answer 1

To calculate the company's expected value of each warranty sold, we need to consider the probability of a product failing within 2 years of the purchase, with and without the extended warranty.

Without the extended warranty:

- Probability of product failure = 0.4%

- Replacement cost = $150

Therefore, the expected cost of a product failure without the extended warranty is:

0.4% x $150 = $0.60

With the extended warranty:

- Probability of product failure = 0% (since the warranty covers the 2-year period)

- Cost of the warranty = $11

Therefore, the expected cost of a product failure with the extended warranty is:

0% x $150 = $0

$11 (warranty cost) + $0 = $11

To calculate the overall expected value, we need to weigh these two scenarios by their probabilities:

Expected value = (probability of product failure without warranty) x (expected cost without warranty) + (probability of product failure with warranty) x (expected cost with warranty)

Expected value = (0.4% x $150) + (99.6% x $11)

Expected value = $0.60 + $10.96

Expected value = $11.56

Therefore, the company's expected value of each warranty sold is $11.56.