Type one: Purchase price per car $16,000; Annual operating expense per car $4,00
ID: 2623527 • Letter: T
Question
Type one: Purchase price per car $16,000; Annual operating expense per car $4,000; Disposition value per car $4,000; Estimated useful life of the car 4 years
Type two: Purchase price per car $32,000; Annual operating expense per car $3,600; Disposition value per car $5,500; Estimated useful life of the car 6 years
Type three: Purchase price $48,000; Annual operating expense $2,800; Disposition value $8,000; Estimated useful life of the asset 8 years
All cars can be replaced at the end of their asset lives. Using a 6.3 percent discount rate and the equivalent annuity method, which car is the better investment? Please show the NPV, and Equivalent annuity for each type of car.
NPV Equivalent Annuity
Car Type One ____________________ _____________
Car Type Two ____________________ _____________
Car Type Three ____________________ _____________
Which type of car should be chosen?______________________
Explanation / Answer
The pv factor of interest for annuity = [ ((1 + i)n - 1) / ( i*(1 + i)n) ]
i = 6.3% = 0.063
PV factor for Annuity of Car type 1 ; n = 4 : [ ((1 + 0.063)4 - 1) / ( 0.063*(1 + 0.063)4) ] = 3.44
Equivalent Annuity = Annual operating expense * PV factor = 4000*3.44 = 13765.74
PV factor for disposition = [1 / (1 + i)n ] = [ 1 / (1 + 0.063)4 ] = 0.783
PV of Disposition = 4000*0.783 = 3132.75
NPV = -Purchase price - PV(Annuity) + PV(Disposition) = -16000 - 13765.74 + 3132.75 = -$26632.99
PV factor for Annuity of Car type 2 ; n = 6 : [ ((1 + 0.063)6 - 1) / ( 0.063*(1 + 0.063)6) ] = 4.87
Equivalent Annuity = Annual operating expense * PV factor = 3600*4.87 = 17536.73
PV factor for disposition = [1 / (1 + i)n ] = [ 1 / (1 + 0.063)6 ] = 0.693
PV of Disposition = 5500*0.693 = 3812.09
NPV = -Purchase price - PV(Annuity) + PV(Disposition) = -32000 - 17536.73 + 3812.09 = -$45724.64
PV factor for Annuity of Car type 3 ; n = 8 : [ ((1 + 0.063)8 - 1) / ( 0.063*(1 + 0.063)8) ] = 6.14
Equivalent Annuity = Annual operating expense * PV factor = 2800*6.14 = 17182.84
PV factor for disposition = [1 / (1 + i)n ] = [ 1 / (1 + 0.063)8 ] = 0.613
PV of Disposition = 8000*0.613 = 4907.09
NPV = -Purchase price - PV(Annuity) + PV(Disposition) = -48000 - 17182.84 + 4907.09 = -$60275.75
NPV Equivalent Annuity
Car type one -$26632.99 -$13765.74
Car type two -$45724.64 -$17536.73
Car type three -$60275.75 -$17182.84
Car type one should be chosen because of least cost
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