Johnson is trying to decide whether he should keep his presently owned car or pu
ID: 1197434 • Letter: J
Question
Johnson is trying to decide whether he should keep his presently owned car or purchase a more environmentally friendly hybrid. A new car will cost $28,000 and have annual operation and maintenance costs of $1000 per year with an $8000 salvage value in 6 years (which is its estimated economic service life). The presently owned car has a resale value now of $6000; one year from now it will be $4000, two years from now $3000, and 3 years from now$2600. Its operating cost is expected to be $1800 this year, with costs increasing by $200 per year. The presently owned car will definitely not be kept longer than 3 more years. Assuming used cars like the one presently owned will always be available, should the presently owned car be sold now, 1 year from now, 2 years from now, or 3 years from now? Use annual worth calculations at i = 20% per year and show your work. (Show every setup, not just given a numerical answer! )
Explanation / Answer
Present value of New car=-28000-1000*Annuity Factor(20%,6 years)+8000/(1.2^6)
Present value of New car=-28000-1000*3.326+8000/(1.2^6)= -$-28646.8
NPV at year 0 is maximum (least negative ) when old car is sold in year 3 and new car is bought, where NPV =-17413.5
Thus presently owned car should be sold 3 years from now
Old car Sold Now Old car sold in 1 year Old car sold in 2 year Old car sold in 3 year Year 0 1 2 3 Investment in New Car -28646.8 -28646.8 -28646.8 -28646.8 Operation cost -1800 -1600 -1400 Age(years) 0 1 2 3 Salavge value 6000 4000 3000 2600 P.V factor of Annuity(20%,N years) 0 0.833 1.528 2.106 P.V of operation cost=Operaion cost*P.V factor of Annuity 0 -1499.4 -2444.8 -2948.4 P.V of salavge cost=Salavage value/(1.2^N) 6000 3333.333333 2083.333333 1504.62963 Total Present Value=Investment in New Car+P.V of operation cost+P.V of salavge cost -22646.8 -26812.86667 -29008.26667 -30090.57037 NPV at Year 0=Total Present value/(1.2^N) -22646.8 -22344.05556 -20144.62963 -17413.52452Related Questions
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