I just bought a 2010 Toyota, and I can already tell it’s ready for replacement -
ID: 2575305 • Letter: I
Question
I just bought a 2010 Toyota, and I can already tell it’s ready for replacement -- it has a max of 2 more years to run. I just paid $15,000 for it, and it’ll take $3,000 a year in maintenance to keep it running. I know a guy who will sell me a Prius anytime with an AW of $-10,000. If the salvage value on my Toyota is $10,000 and declining by $3,000 per year, with interest rates at 5%, when should I get the replacement Toyota?
I believe it is after this year and need use AW method but having trouble with the math
Question 1 options:
Right now
After this year
When I have to, after next year
Right now
After this year
When I have to, after next year
Explanation / Answer
Machine should be replaced after the end of second year. (refer below workings)
Determination of optimal replacement period
Year
maintenance cost
Cumulative maintenance cost
Resale Value (S)
Cost-Sale value
T(n)
A(n)
(i)
(ii)
(iii)
(iv)
(v) = (iii)+(v)
(vi) = (v)/n
1
3000
3000
10000
5000
8000
8000
2
3000
6000
6500
8500
14500
7250
In the above table minimum A(n) = $7,250 for n = 2.
Machine should be replaced after the end of second year.
Year
maintenance cost
Cumulative maintenance cost
Resale Value (S)
Cost-Sale value
T(n)
A(n)
(i)
(ii)
(iii)
(iv)
(v) = (iii)+(v)
(vi) = (v)/n
1
3000
3000
10000
5000
8000
8000
2
3000
6000
6500
8500
14500
7250