Sam is buying a refrigerator. He has two choices. A used one, at $475, should la

Question

Sam is buying a refrigerator. He has two choices. A used one, at $475, should last him about three years. A new one, at $1250, would likely last eight years. Both have a scrap value of zero. The interest rate is 8 percent. (a) Which refrigerator has a lower cost? (Use a present worth analysis with repeated lives. Assume operating costs are the same.) (b) If Sam knew that he could resell the new refrigerator after three years for $1000, would this change the answer in part (a)? (Use a present worth analysis with a three-year study period. Assume operating costs are the same.)

Explanation / Answer

The LCM of 3 and 8 is 24.

Present Worth Analysis with repeated lives:

(a) A Used one:

PW = - $475 – 475(P/F,0.08,3) – 474(P/F,0.08,6) - 475(P/F,0.08,9) – 475(P/F,0.08,12) –475(P/F,0.08,15) -475(P/F,0.08,18) –475(P/F,0.08,21) + 0(P/F,0.08,24)

PWu = -$475 -475*0.7938 – 475*0.6301-475*0.5002 -475*0.3971 -475*0.3152 -475*0.2502 -475*0.1986 +0

PWu = -$475 – 379.19 -299.29 -237.59 -188.62 -149.72 -118.84 -94.33

PWu = -$1942.58

A New one:

PWn = -$1250 -1250(P/F,0.08,8) -1250(P/F,0.08,16) + 0(P/F,24)

PWn = -$1250 -1250*0.5402 -1250*0.2918

PWn = -$1250 -675.25 -364.75

PWn = -$2290.

Used one has the lowest PW cost. Select the Used one.

(b) PW analysis for New one with a three-year period:

PWn = -$1250 -1250(P/F,0.08,3)

PWn = -$1250 -1250*0.7938

PWn = -$1250 -1250*0.7938

PWn = -$1250 -992.25

PWn = -$2242.25

The PW of the new one is lower with a 3-year period than the PW of the new one with a repeated lives of 24 years.

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