Frank recently came to Canberra to study at ANU on a two-year program. He rents an apartment inGreenway and decides to buy a used car. The car costs $15000 and the seller offers an optional warranty for twoyears. With the warranty, the seller will repair (or replace) the car for free if the car fails within two years. Thewarranty costs $1800. We will try to decide if Frank should buy the extended warranty.Frank’s utility index is 𝑢(𝑥0) + 11+𝑟 𝑢(𝑥1) + 1(1+𝑟)2 𝑢(𝑥2), where 𝑥0 is his cash flow right now (either -$15000 or-$16000), 𝑥1 is his cash flow during the first year and 𝑥2 is his cash flow during the second year. Here 𝑟 = 5%. Inall cash flows, we only count the cash flows related to the possible failure of the car. Tuition, wage from part-timejobs, fuel and maintenance of the car are all ignored. The function 𝑢 has the following form:𝑢(𝑥) = 40000 ∗(1 + 𝑥20000)1∕2− 40000.To Frank’s best estimation, the car fails within one year with probability .05 and it survives the first year but failsin the second year with probability .07. If the car survives after 𝑡 years, his cash flow in year 𝑡 is zero; if the carfails in year 𝑡 with no warranty, his cash flow in year 𝑡 is -$15000, the cost of buying a replacement. For simplicity,we ignore the possibility that his replacement car, purchased in Year 1, fails in Year 2.(a) [15 marks] Determine if Frank should buy the warranty; for this part, take all the assumptions as given.(b) [5 marks] Discuss whether it is reasonable to assume that the replacement car does not fail. (Limited to 50words.)(c) [10 marks] Discuss why other cash flows such as tuition and fuel may be ignored in the analysis. (Limited to200 words.)(d) [10 marks] Consultant Bob totally disagrees with our analysis in Part (a). He argues that Frank should switchto public transportation if the car fails before he graduates. Fare is $3.2 everyday and thus about $830 ayear. Therefore, Frank’s cash flow after the failure of the car is -$830 a year without the extended warranty.Therefore, the extended warranty is a joke. Evaluate Bob’s method. (Limited to 200 words.

Four years ago, Victor purchased a very reliable automobile. His warranty has just expired, but the manufacturer has just offered him a 5-year, bumper-to-bumper warranty extension. The warranty costs $3,400. Victor constructs the following probability distribution with respect to anticipated costs if he chooses not to purchase the extended warranty. Cost (in $) 1,000 2,000 5,000 10,000 Probability 0.25 0.45 0.20 0.10

MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $979 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $15,500. Suppose that under the warranty, there is a 6% chance that MotoWin would have to replace the car one time and a 94% chance they wouldn't have to replace the car.If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?To answer, take into account the price of the warranty and the expected value of the cost from replacing the car.MotoWin can expect to make money from offering these warranties.In the long run, they should expect to makedollars on each warranty sold.MotoWin can expect to lose money from offering these warranties.In the long run, they should expect to losedollars on each warranty sold.MotoWin should expect to neither make nor lose money from offering these warranties.

MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $952 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin $13,600. Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.If MotoWin knows that it will sell many of these warranties, should it expect to make or lose money from offering them? How much?To answer, take into account the price of the warranty and the expected value of the cost from replacing the car.MotoWin can expect to make money from offering these warranties.In the long run, they should expect to makedollars on each warranty sold.MotoWin can expect to lose money from offering these warranties.In the long run, they should expect to losedollars on each warranty sold.MotoWin should expect to neither make nor lose money from offering these warranties.

Wade Ellis buys a new car for $16,515.75. He puts 10% down and obtains a simple interest amortized loan for the rest at 1112% interest for four years. (Round your answers to the nearest cent.)(a) Find his monthly payment.

Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $23,900 to the policy holder. Executives at Avicenna are considering offering these policies for $956 each. Suppose that for each holder of a policy there is a 4% chance they will experience property damage in the next five years and a 96% chance they will not.(If necessary, consult a list of formulas.)If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?To answer, take into account the price of the policy and the expected value of the amount paid out to the holder.Avicenna can expect to make money from offering these policies.In the long run, they should expect to makedollars on each policy sold.Avicenna can expect to lose money from offering these policies.In the long run, they should expect to losedollars on each policy sold.Avicenna should expect to neither make nor lose money from offering these policies.