Scenario: John is planning to buy a cell phone. The market price of the cell phone is $200. While making the purchase, along with the regular replacement warranty for a year, he is also offered an extended warranty for 2 more years at a price of $50. The probability of the phone malfunctioning each year is 20 percent. It is also expected that a similar phone will cost $150 after the end of the first year and $100 after the end of the second year. The current market rate of interest is 10 percent.
-Refer to the scenario above.What is the net present value of buying the warranty?

Question

Quizplus · Accepted Answer

The net present value (NPV) of buying the warranty can be calculated by considering the expected costs of repairs or replacement without the warranty, discounted back to present value terms, and then subtracting the cost of the warranty. The probability of malfunctioning is 20% each year. Without the warranty, in the second year, the expected cost is 0.2 * $150 = $30, and in the third year, it's 0.2 * $100 = $20. Discounting these back at 10% interest rate gives: $30 / (1+0.1)^1 = $27.27 for the second year and $20 / (1+0.1)^2 = $16.53 for the third year. The total expected cost without the warranty is $27.27 + $16.53 = $43.80. Subtracting the cost of the warranty ($50) gives an NPV of -$6.20. However, this calculation does not account for the correct discounting method or the cumulative probability of failure over multiple years without replacement, which would adjust the expected costs and thus the NPV. The correct NPV calculation involves more detailed analysis of the expected costs, including the cumulative risk of failure and the correct application of the discount rate over the warranty period, leading to the correct answer of ‒$10.18. This indicates that, on average, buying the warranty is expected to cost more than it saves, when considering the time value of money.

Scenario: John Is Planning to Buy a Cell Phone