the corresponding annual cost is $8502. Since this is less than the annual cost of the new
machine ($9400), the existing machine should be retained for at least 5 years.
- Determine precisely when the existing machine
should be replaced
Since costs increase beyond the fifth year, the existing machine and the improved model
will be compared on a year-by-year basis. Let BR = cost of retaining existing machine 1
year beyond the Rth year. Then BR = LR(l + i) - LR+l + cR+l. Thus, B 5 = $3000(1.10) -
$2700 + $8500 = $9100. Since this is less than the annual cost of the new model, the ex-
isting machine should not be retired 5 years hence. Continuing, we find B 6 = $2700(1.10)
- $2600 + $9700 = $10,070, which exceeds $9400. Therefore, the existing machine
should be retired 6 years hence.
ECONOMY OF REPLACEMENT UNDER
CONTINUING IMPROVEMENTS
A newly acquired machine costs $40,000, and it has the salvage values and annual operat-
ing costs shown in Table 4. It is anticipated that a new model will become available at the
end of each year. All future models will have first costs and salvage values identical with
those of the present model, but the annual operating cost for a given model will be $600
lower than the corresponding annual operating cost of the preceding model. For example,
the model that becomes available 1 year hence will have an operating cost of $11,400 for
the first year, $12,400 for the second year, etc. Applying an interest rate of 10 percent, de-
termine how long this machine should be held.
Calculation Procedure:
- Establish the excess operating costs in relation to a 1-year life
When the machine is retired, it will be replaced with the model that becomes available at
that date. First assume that the machine is retired at the end of each year. The operating
costs for the next 8 years are shown in Table 5. Now assume that the machine is held for 8
years. Subtracting the values just found from the values in Table 4 gives the excess oper-
ating costs for an 8-year life; these are shown in Table 5. This table also gives the excess
operating costs for every prospective life of the machine. For example, if the machine is
TABLE 4
Salvage value Annual operating
Year at end, $ cost, $
1 25,00 0 12,00 0
2 20,00 0 13,00 0
3 17,00 0 14,60 0
4 15,00 0 16,50 0
5 13,50 0 18,80 0
6 12,00 0 21,50 0
7 11,00 0 24,50 0
8 10,00 0 28,00 0
