Answer:
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.