A company estimates that 5% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $100. if they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words, so the expected value will be 0)

Answer: $5

Explanation:

Let N = number of products

c = cost of extended warranty

In order for the company to get break even, the total amount of revenue that they will collect from extended warranty should be the same as the total revenue that they will collect from replacement fees because once they offer an extended warranty for one unit of product, they will lose revenue from the replacement fee that they collect for one unit of product.

Since 5% of the products are estimated to fail, the number of defective products is 5% of N = 0.05N. (Recall that N is the number of product and we change 5% to decimal which is 0.05)

So, the revenue from the replacement fees is given by

Revenue from replacement fee = (number of defective products) * (replacement fee)

= 0.05N * $100

= 5N

Moreover,

Revenue from extended warranty = (Cost of extended warranty) * (Number of products)

= c * N

= cN

As we mentioned earlier, to get into break-even

Revenue from extended warranty = Revenue from replacement fee

cN = 5N

c = $5 (Since we are looking for the value of c, divide both sides by N.)

Hence, the cost of the extended warranty should be $5.