Replacement decisionsIn this case using this approach was not too laborious because the lowest common
multiple (LCM) is only 12 years. Suppose, however, that we were considering
replacement after either eight or nine years? Here the LCM is 72 years. If we were also
considering a seven-year possibility, the LCM would be 504 years. Clearly, we need
a more practical approach.
An alternative approach is to imagine that we were able to rent a vehicle, to be
replaced with a new one either after three years or after four years. In either case also
imagine that the rent is of a fixed annual amount and that payment is made at the end
of each year. If we could deduce the annual rent that would represent the equivalent
cost, in NPV terms, to £6,712 (three-year replacement) and £7,713 (four-year replace-
ment) (see ‘Unhelpful solution’ above), we could make a valid comparison between
the two replacement policies.Replace after Replace after
Year 3 years 4 years
££
0 Cost of a new vehicle (10,000) (10,000)
1––
2––
3 PV of the disposal proceeds:
£5,000 ×[1/(1.00 +0.15)^3 ] 3,288
PV of the cost of a new vehicle:
£10,000 ×[1/(1.00 +0.15)^3 ] (6,575)
4 PV of the disposal proceeds:
£4,000 ×[1/(1.00 +0.15)^4 ] 2,287
PV of the cost of a new vehicle:
£10,000 ×[1/(1.00 +0.15)^4 ] (5,718)
5––
6 PV of the disposal proceeds:
£5,000 ×[1/(1.00 +0.15)^6 ] 2,162
PV of the cost of a new vehicle:
£10,000 ×[1/(1.00 +0.15)^6 ] (4,323)
7––
8 PV of the disposal proceeds:
£4,000 ×[1/(1.00 +0.15)^8 ] 1,308
PV of the cost of a new vehicle:
£10,000 ×[1/(1.00 +0.15)^8 ] (3,269)
9 PV of the disposal proceeds:
£5,000 ×[1/(1.00 +0.15)^9 ] 1,421
PV of the cost of a new vehicle:
£10,000 ×[1/(1.00 +0.15)^9 ] (2,843)
10 – –
11 – –
12 PV of the disposal proceeds:
£5,000 ×[1/(1.00 +0.15)^12 ] 935
£4,000 ×[1/(1.00 +0.15)^12 ] 748
Net present cost of owning the vehicles 15,935 14,644Now that we are able to make a valid comparison we can see that it is less costly to
replace the vehicles after four years.Helpful but
laborious
solution