Question

CONGRATULATIONS!!!  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 ...
⦁   The overall goal and/or purpose
⦁   The given information
⦁   A time-line for the expected repair costs covered by the warranty
⦁   The present value for each of the repair costs
⦁   The present value of the warranty and the expected profit for the warranty company
⦁   Your conclusion

Answer 1

GOAL: We have to find the find out the better option from the two options, first one being purchasing extended warranty for the period of 4 years at the cost of $1,800 or to incurr the yearly expenses at own cost.

INFORMATION GIVEN: We have been given cost of extended warranty anf yearly maintenance costs that would be incurred along with interest rate.

TIME LINES AND CASH FLOWS:

End of Year	Cash Outflow(Warranty Purchased)	Cash Outflow(No Warranty)
0	-1,800	0
1
2
3
4		-400
5		-500
6		-600
7		-800

PRESENT VALUES:

End of Year	Cash Outflow(Warranty Purchased)	Cash Outflow(No Warranty)	Discounting Factor(1/(1+r)^n)	PV Cash Outflow(Warranty)	PV Cash Outflow(No Warranty)
0	-1,800	0	1	-1800
1			0.932583466
2			0.869711921
3			0.811078957
4		-400	0.756398825		-302.5595301
5		-500	0.705405038		-352.702519
6		-600	0.657849075		-394.709445
7		-800	0.61349917		-490.7993364
			TOTAL	-1800	-1540.77083

Discounting Factor =(1/(1+r)^n)

where r=7%/12 (Divided by 12 for monthly compounding)

n=Year*12 (Multiplied by 12 for monthly compounding)

PRESENT VALUES AND EXPECTED PROFIT OF WARRANTY GIVING COMPANY:

Present value for the amount received for extended warranty will the actual amount of $1,800 only as the amount has been incurred in the current year itself.

Present value for the costs associated with warranty is $1,540.77.

Thus the warranty giving company is contemplating a profit of $259.23 (1800-1540.77).

CONCUSION:

Since, there is a profit of $259.23 for the company, it will obviously try to sell the extended warranty to us. As we all know that one person's profit is another one's expense/loss, the purchaser of car should not buy extended warranty and rather incur the maitenance costs over the period after expiry of original warranty himself. In this way he would be saving $259.23.

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