Abby has just negotiated a $15,000 price on a 2-year-old car and is with the salesman closing the deal. There is a 1-year sales warranty with the pur­chase; however, an extended warranty is available for $2500 that will cover the same repairs and component failures as the 1-year warranty for three additional years. Abby understands this to be a real options situation with the price of the option ($2500) paid to avoid future, unknown costs. To help with her decision, the salesman provided three typical sets of historical data (A, B, C) on estimated repair costs for used cars. The first year is shown as zero because it will be covered by the sales warranty.

Question

The salesman said case C is the base case since it shows that the extended warranty is not needed be­cause the repairs equal the warranty cost. Abby immediately recognized this to be the case only when i = 0%.



(a) If Abby assumes that each repair cost sce­nario has an equal probability of occurring with her car, and money is worth a market interest rate of 8% per year to her, how much should she be willing to pay for the extended warranty that is offered at $2500?

(b) If the base case C actually occurs for her car and she does not purchase the warranty, what is the PW value of the expected future costs at i = 8% per year?

(c) At what market interest rate is case C eco­nomically equivalent to the extended war­ranty cost of $2500 now?

(d) Given all of this analysis, from a purely eco­nomic viewpoint, should Abby pay the $2500 for the extended warranty option? Why?

Answer 1

(a) Find E(PW) after determining E(Rt), the expected repair costs for each year t

E(R2) = 1/3(-500 -1000 -0) = $-500

E(R3) = 1/3(-1200 -1400 -500) = $-1033

E(R4) = 1/3(-850 -400 -2000) = $-1083

E(PW) = -500(P/F,8%,2) -1033(P/F,8%,3) -1083(P/F,8%,4)
= -500(0.8573) -1033(0.7938) - 1083(0.7350)
= $-2045


Without considering noneconomic factors, the warranty is worth an expected $2045, or $455 less than the $2500 extended warranty cost.

(b) PWbase = -500(P/F,8%,3) -2000(P/F,8%,4)
= -500(0.7938) -2000(0.7350)
= $-1867

(c) i = 0%

(d) No, because all of the resulting E(PW) < $2500