Danny is interested in buying a Nissan Altima as his next car. It costs $26,000 to buy and its market value (i.e., what Danny could get as salvage value if and when he sells it used) declines by 30% per year from that starting point. Annual maintenance costs begin at $600 in Year 1, grow to $1,100 in Year 2, and continue growing by another $500 per year thereafter. Danny's interest rate is 5%. (a) Determine a general formula for AEC(N), the annual equivalent cost of owning and maintaining a Nissan Altima as a function of the number of years that Danny owns it for before selling it. Fill in the table below by computing the values of AEC(N) for the included values of N. What is the economic service life of the Nissan Altima, N*, and what is AEC(N*)? Service Life (N) Annual Equivalent Cost (AEC(N)) 8 9 10 11 12 While Danny is interested in the Nissan Altima, he currently drives a Honda Civic that he has owned for a while. At its own economic service life, the minimum annual equivalent cost of Danny's Civic is lower than the respective figure for the Altima, which you calculated in part (b). However, the maintenance costs on Danny's Civic are high and rising, so he is contemplating when it will be economically optimal to make the switch, which would mean selling his Civic, buying an Altima, then planning on repeatedly buying and selling Altimas according to their economic service life. The table below shows the market value and annual maintenance cost of Danny's current Civic in each year. When should he make the switch to the Altima? Year Market Value Maintenance Cost 0 $10,000 1 $8,200 $3,000 2 $6,900 $3,800 3 $5,900 $4,700 4 $5,300 $5,700 5 $5,000 $6,800 Danny is interested in buying a Nissan Altima as his next car. It costs $26,000 to buy and its market value (i.e., what Danny could get as salvage value if and when he sells it used) declines by 30% per year from that starting point. Annual maintenance costs begin at $600 in Year 1, grow to $1,100 in Year 2, and continue growing by another $500 per year thereafter. Danny's interest rate is 5%. (a) Determine a general formula for AEC(N), the annual equivalent cost of owning and maintaining a Nissan Altima as a function of the number of years that Danny owns it for before selling it. Fill in the table below by computing the values of AEC(N) for the included values of N. What is the economic service life of the Nissan Altima, N*, and what is AEC(N*)? Service Life (N) Annual Equivalent Cost (AEC(N)) 8 9 10 11 12 While Danny is interested in the Nissan Altima, he currently drives a Honda Civic that he has owned for a while. At its own economic service life, the minimum annual equivalent cost of Danny's Civic is lower than the respective figure for the Altima, which you calculated in part (b). However, the maintenance costs on Danny's Civic are high and rising, so he is contemplating when it will be economically optimal to make the switch, which would mean selling his Civic, buying an Altima, then planning on repeatedly buying and selling Altimas according to their economic service life. The table below shows the market value and annual maintenance cost of Danny's current Civic in each year. When should he make the switch to the Altima? Year Market Value Maintenance Cost 0 $10,000 1 $8,200 $3,000 2 $6,900 $3,800 3 $5,900 $4,700 4 $5,300 $5,700 5 $5,000 $6,800
