Jerry is interested in purchasing a washing machine. The price of the machine is $500. The probability that the machine will break down is 20% every year
If the machine breaks down in the first year and Jerry holds a warranty, he receives a new washing machine worth $400 that year. If the machine breaks down after two years and he holds a warranty, he receives a new machine that is worth $300 after the second year. The price of a warranty for two years is $100. The market interest rate is 5%. Is buying the warranty a good investment for Jerry? Explain your answer. Show all the necessary calculations.
If the washing machine breaks down in the first year, Jerry will receive a new machine worth $400.
The present value of this machine is 400/1.05 = 381 approximately.
If the machine breaks down in the second year, Jerry gets a new machine worth $300.
The present value of such a machine is 300/(1.05 )2 = 272 approximately.
Hence the expected value of having the warranty is equal to
0.20 × (381 ) + 0.20 × (272 ) -100 = 76.20 + 54.4 -100 = $30.60.
In this case, since the expected value of an extended warranty is positive, it is a good investment for Jerry.
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