# A new machine costs \$25,000 and has the estimated maximum (physical) life of 5 years.

A new machine costs \$25,000 and has the estimated maximum (physical) life of 5 years. It also has the estimated salvage (market) value (S) and operating and maintenance costs (O&M) in each of the 5 years of use as shown below:

Year n    Sn                O&Mn                    EACn                      MCn

0              \$25,000

1              \$16,000                 \$5,000                   \$16,000                 \$16,000

2              \$13,000                 \$8,000                   \$14,212                 \$12,280

3              \$11,000                 \$11,000                \$14,159                 \$14,040

4              \$10,000                 \$14,000                 \$14,541                 \$15,880

5              \$9,500                   \$17,000                 \$15,181                 \$18,300

Suppose the MARR is 8%. The EACn for keeping the machine n years and the marginal cost MCn of keeping the machine 1 more year during year n can be computed as shown above

Verify that the EAC for keeping the machine 2 years is indeed \$14,212, and the marginal cost of keeping it 1 more year during year 4 is \$15,880 as shown.

What is the economic life of this new machine and what is the corresponding EAC?

If the machine has been used for 2 years and if there is a new machine which can do a similar job with the EAC at its economic useful life being \$16,500, when should the defender be replaced? Assume that the machine (old or new) will be needed for a long time.

Suppose there is no technological change and the candidate for the challenger is exactly the same model as the defender (except it is new of course). Suppose also that the defender has been used for two years and the machine (old or new) will be needed for a long (infinite) time. Determine if and when the defender should be replaced using the PW method. First state why we need to consider only 4 mutually exclusive options.

Then answer the replacement question by first filling the missing entry in the following table:

Option                    Replace defender                                 PW(8%)

1                              Now                                                        ……….

2                              ………………                                      ……….

3                              2 years from now                                 177,488

4                              3 year from now                                  181,633

Thus the defender should be replaced………….year(s) from now.

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