an extended warranty is being offered on your new laptop which could cover any r
ID: 3047229 • Letter: A
Question
an extended warranty is being offered on your new laptop which could cover any repair job that could be needed in the next three years. The price of the extended warranty is R740. Your research leads you to believe that the likelihood of a minor repair job in the next three years is 13%, a major repair is 8% and a catastrophic repair is 3%. Without the extended warranty, a minor repair will cost you R800, a major repair will cost you R3200, and a catastrophic repair will cost you R5000. Buying the extended warranty will eliminate all these repair costs. a) calculate expected cost of not buyuing the extended warranty (show your workings) b) would a maximum strategy imply buying the extended warranty? use the relevant costs and calculations to support your argument c) The university buys you 100 laptops per year. Assuming the costs and probabilities for repair are consistent with your research for every laptop the university buys, would you recommend the university buys extended warranties? Use the relevant costs and calculations to support your argument.
Explanation / Answer
a) The expected cost of repair is the probability weighted cost of repair. Here, the expected cost of repair = 0.13 * 800 + 0.08 * 3200 + 0.03 * 5000 = 104 + 256 + 150 = R510.
So, expected cost of not buying the extended warranty = R510.
b) Under the maximum strategy, the maximum loss if we don't buy the extended warranty = R5,000 while the maximum loss if we buy the extended warranty = R740. Hence, under the maximum strategy, to minimise our loss, we should buy the extended warranty.
c) For 100 laptops, the expected cost of not buying extended warranty = R510 * 100 = R51,000.
The cost of buying extended warranty for 100 laptops = R740 * 100 = R74,000
Thus, expected savings of not buying extended warranty = 74000 - 51000 = R23,000.
As this is much greater than the cost of a catastrophic repair, we would recommend that the university should not buy the extended warranties.
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