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A company estimates that 0.5% 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 $27, what is the company's expected value
of each warranty sold?
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Notice that 0.5% = 0.005.
The expected profit of selling each warranty is
27 - 0.005*200 dollars = 27 - 1 = 26 dollars.
Here $27 is what the customer pays for the 2-years warranty,
and 0.005*200 = 1 dollar is the company's average expense per unit to cover the replacement.
The net 27 - 1 = 26 dollars is the expected company's profit of each warranty sold.
$26 is the price which the customer does agree to pay to the company for peace in mind.
Solved and explained.
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To me, the presented input data seems to be strange, unfair and unrealistic.
Double check if 0.5% is correct value in your post.
It is more likely that it is 5%.