Question

You just agreed to a deal that will make you the proud new owner of a beautiful new convertible. The car comes with a three-year warranty. Please consider the purchase of the extended warranty which has a purchase price of $1,800, today (the day you purchased your NEW car). The extended warranty covers the 4 years immediately after the three-year warranty expires. You estimate that the yearly expenses that would have been covered by the extended warranty are $400 at the end of the first year of the extension, $500 as the end of the second year of the extension, $600 at the end of the third year of the extension, and $800 at the end of the fourth year of the extension. Assume that money during this time can earn interest at a rate of 7% compounded monthly. Will you decide to buy the warranty? Your formal solutions should include:______.1. The overall goal and/or purpose

2. The given information
3. A time-line for the expected repair costs covered by the warranty
4. The present value for each of the repair costs
5. The present value of the warranty and the expected profit for the warranty company
6. Your conclusion

Answer 1

1. The overall goal and/or purpose

The overall goal of this analysis is to determine if you would actually save money by purchasing the extended warranty.

2. The given information

You can calculate this by determining the present value of the expected repair costs that will be covered by the warranty and determine which is higher; the warranty or the repairs

3. A time-line for the expected repair costs covered by the warranty

• initial investment -$1,800
• cash flow year 4 = $400
• cash flow year 5 = $500
• cash flow year 6 = $600
• cash flow year 7 = $800

4. The present value for each of the repair costs

the discount rate is 7%, so the present value of each repair cost is:

• PV cash flow year 4 = $400 / 1.07⁴ = $305
• PV cash flow year 5 = $500 / 1.07⁵ = $356
• PV cash flow year 6 = $600 / 1.07⁶ = $400
• PV cash flow year 7 = $800 / 1.07⁷ = $498
• total $1,559

5. The present value of the warranty and the expected profit for the warranty company

the present value of the warranty is $1,800, so the car company is making $1,800 - $1,559 = $241 in profits by selling you the warranty

6. Your conclusion

You shouldn't buy the extended warranty (negative NPV)