When Capital or Operating Costs Are Non Monotonic

Sometimes operating costs do not increase smoothly and monotonically over time. The same can happen to capital costs. Y\Ten the operating or capital costs are not smooth and monotonic, the one year principle does not apply. The reason that the principle does not apply is that there may be periodic or one-time costs that occur over the course of the next year (as in the case where periodic overhauls are required). These costs may make the cost of keeping the defender for one more year greater than the cost of installing and using the challenger over its economic life. However, there may be a life longer than one year over which the cost of using the defender is less than the cost of installing and using a challenger. Consider this example concerning the potential replacement of a generator.

EXAMPLE 7.9

The Colossal Construction Company uses a generator to produce power at remote sites. The existing generator is now three years old. It cost Sll 000 when purchased. Its current salvage value of S2400 is expected to fall to S1400 next year and S980 the year after, and to continue declining at 30% of current value per year. Its ordinary operating and maintenance costs are now Si000 per year and are expected to rise by S500 per year. There is also a requirement to do an overhaul costing Si000 this year and every third year thereafter.

New fuel-efficient generators have been developed, and Colossal is thinking of replacing its existing generator. It is expected that the new generator technology will be the b est available for the foreseeable future. The new generator sells for $9500. Installation costs are negligible. Other data for the new generator are summarized in Table 7.4.

Table 7.4 Salvage Values and Operating Costs for New Generator

End of Year

Salvage Value

Operating Cost

0

S9500

1

8000

$1000

2

7000

1000

3

6000

1200

4

5000

1500

5

4000

2000

6

3000

2000

2000

2000

8

1000

3000

Should Colossal replace the existing generator with the new type? The MARR is 12%.

We first determine the economic life for the challenger. The calculations are shown in Table 7.5.

Sample calculations for the EAC of keeping the challenger for one, two, and three years are as follows:

Table 7.5 Economic Life of the New Generator

End of Year

Salvage Value

Operating Costs

EAC

1

S8000

SI 000

S3640.00

2

7000

1000

3319.25

3

6000

1200

3236.50

4

5000

1500

3233.07*

5

4000

2000

3290.81

6

3000

2000

3314.16

2000

2000

3318.68

8

1000

3000

3393.52

Lowest equivalent annual cost.

Lowest equivalent annual cost.

EAC(3 years) = (P-S)(A/P, 12%,3) + Si + 1000 + 200(a/F,12%,3) = (9500-6000) (0.41635) + 6000(0.12) + 1000

As the number of years increases, this approach for calculating the EAC becomes more difficult, especially since in this case the operating costs are neither a standard annuity nor an arithmetic gradient. An alternative is to calculate the present worths of the operating costs for each year. The EAC of the operating costs can be found by applying the capital recovery factor to the sum of the present worths for the particular service period considered. This approach is particularly handy when using spreadsheets.

By either calculation, we see in Table 7.5 that the economic life of the generator is four years.

Next, to see if and when the defender should be replaced, we calculate the costs of keeping the defender for one more year. Using the capital recovery formula:

EAC (keep defender 1 more year)

= EAC(capital costs) + EAQoperating costs) = (2400- 1400)(A/P,12%,1) + 1400(0.12) + 2000 = 3288

The equivalent annual cost of using the defender one more year is S3288. This is more than the yearly cost of installing and using the challenger over its economic life. Since the operating costs are not smoothly increasing, we need to see if there is a longer life for the defender for which its costs are lower than for the challenger. This can be done with a spreadsheet, as shown in Table 7.6.

We see that, for an additional life of three years, the defender has a lower cost per year than the challenger, when the challenger is kept over its economic life. Therefore, the defender should not be replaced at this time. Next year a new evaluation should be performed.

Table 7,6 Equivalent Annual Cost of Additional Life for the Defender

Additional Life in Years

Salvage Value

Operating Costs

EAC

0

S2400

1

1400

S2000

S3288

7

980

1500

2722

5

686

2000

2630

4

480

3500

2872

5

336

3000

2924

6

235

3500

3013

0 0

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