Answer:
To break even, the expected revenue from selling extended warranties should be equal to the expected cost of replacing the failed products. Let's calculate these values.
Assuming the company sells 1000 products, 4% of them (i.e. 40 products) are expected to fail after the original warranty period but within 2 years of the purchase. Each replacement costs $300, so the total expected cost of replacements is:
40 x $300 = $12,000
To calculate the expected revenue from selling extended warranties, we need to know how many customers will buy them. Let's assume that the company offers the extended warranty for $x and that p% of customers buy it. Then the expected revenue from selling extended warranties is:
1000 x p x $x
We want the expected value to be 0, so:
1000 x p x $x = $12,000
Solving for $x, we get:
$x = $12,000 / (1000 x p)
Now we need to find the value of p that makes $x equal to the cost of the extended warranty. Let's assume that the cost of the extended warranty is $y. Then:
$x = $y
$12,000 / (1000 x p) = $y
p = $12,000 / (1000 x $y)
Substituting the given values, we get:
p = $12,000 / (1000 x $300)
p = 0.04
So the company needs to sell the extended warranty to 4% of customers to break even. The price of the extended warranty should be:
$x = $12,000 / (1000 x 0.04)
$x = $3
Therefore, the company should charge $3 for the extended warranty to break even