Question

Could you explain the answer for me? I’m very confused. Thank you so much!

Because of its age, your car costs $4,000 annually in maintenance expense. You could replace it with a newer vehicle costing $8,000. Both vehicles would be expected to last 4 more years, at which point they will be valueless. If your opportunity cost is 800, by how much must maintenance expense decrease on the newer vehicle to justify its purchase? 94 A. $1,625.40 B. $1,584.63 C. $1,469.08 D. S1,409.54 $8,000 PMT [(1/0.08)-1/0.08(1.08)]: PMT $2,415.37 Maintenance expense decrease required $4,000-2,415.37- $1,584.63

Answer 1

We have following information -

Annual Maintenance expenses of old car = $ 4000

New car cost today = $ 8000

opportunity of cost = 8%

Annual Maintenance of expenses of new car = AM_n

In this case, The difference between Present value(PV) of old car annual maintenance and Present value of new car maintenance at opportunity cost rate, should be at least $ 8000 to make new car preferable.

He has to pay $ 8000 for new car and if his Net present benefits of Annual maintenance is less than $ 8000 then he would loss some money.

Net present benefits of Annual maintenance(AM) = PV of AM of old car - PV of AM of new car

and Net Present benefits of AM should be $ 8000

Thus,

8000 = PV of AM of old car - PV of AM of new car

8000 = 4000*PVAIF(8%,4) - AM_n*PVAIF(8%,4)

8000 = PVAIF(8%,4){4000 - AM_n}

(4000 - AM_n) = 8000/PVAIF(8%,4)

(4000 - AM_n) = 8000/3.3121

(4000 - AM_n) = 2415.37

AM_n = 4000 - 2415.37

AM_n = $ 1584.63

Thus, Annual Maintenance on New Car (AM_n) should be $ 1584.63 to make new car feasible.