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 $50.00.

If they offer a 2 year extended warranty for $5.00, what is the company's expected value of each warranty sold?
The expected value of each warranty sold is ______.

Answer 1

Explanation:

o calculate the expected value of each warranty sold, we need to consider the probability of a product failing within the extended warranty period and the associated costs.

Let's assume that the company sells 1,000 warranties. The cost of selling these warranties would be 1,000 x $5.00 = $5,000.

The probability of a product failing within the extended warranty period is 0.8%. Therefore, out of the 1,000 warranties sold, we can expect 0.8% x 1,000 = 8 products to fail.

The cost of replacing each failed product is $50.00. Therefore, the total cost of replacing the 8 failed products is 8 x $50.00 = $400.00.

The expected value of each warranty sold is calculated as the difference between the revenue generated from selling the warranties and the cost of replacing the failed products, divided by the number of warranties sold.

The revenue generated from selling the warranties is $5.00 x 1,000 = $5,000.

The expected value of each warranty sold is:

($5,000 - $400) / 1,000 = $4.60

Therefore, the company's expected value of each warranty sold is $4.60.