A special purpose machine can be purchased for $90,000. The operating & maintena

Question

A special purpose machine can be purchased for $90,000. The operating & maintenance expenses for each of the next five years and the market value at the end of each of the next five years are shown below. If the MARR is 15% per year compounded yearly, determine the best time to replace the machine with an identical new machine.

Year                            1                      2                      3                      4                      5

Op. & Main. Exp.       $20K               $25K               $30K               $40K               $60K

MV at the end of yr    $65K               $45K               $30K               $20                  $10K

Explanation / Answer

It is a replacement problem. You have purchased at $90,000. Steps are as follows:

1. Suppose you will replace it after one year. During this one year, you have to pay $20K operating & Maint. exp. Machine of $90K can be sold at $65K. So $90-$65=$25K is depreciation. So sum of depreciation and operating & maint. exp. is $20K+$25K=$45K if replaced after one year.

Next consider replacement after year 2. During this 2 years, total Op. & Main. exp. is $20K in year 1 and $25K in year2. So cumulative Op. & maint. exp. is $20K+$25K=$45K. Further machine will fetch $30K. So depreciation is $90K-$45K=$45K. Total cost of using it for 2 years is $45K+$45K=$90K.

In this manner calculate total cost of using the machine for using 3,4 and 5 years. Results are shown in column (5) of the table below.

2. Now ascertain present value of $1 at 15% discounting rate. Formula is 1/(1.15)^n. It is shown in column (6) of the table.

3. Multiply figure of step 1 with corresponding figure of step 2. You will get total present value of cost incurred for using the machine. See column (7) of the table.

4. Next ascertain cumulative discounting factor from data of step 2. See column (8)

5. Finally divide figure of step 3 by the figure of step4. You will get annual equivalent cost of using the machine. It is shown in step (9)

6. Use the machine till the year where annual operating cost is minimum.

In the table, Annual cost is lowest in year 4. So machine will be used for 4 years and then it will be replaced.

Statement showing annual cost. Year Op. & maint. Depreciation Cumulative Dep.+Op. Discount Present Cumulative Annual Exp. op. &maint & maint factor value discount cost exp. exp. factor (1) (2) (3) (4) (5) (6) (7) (8) (9) 1 20 25 20 45 0.869565 39.13043 0.86956522 45 2 25 45 45 90 0.756144 68.05293 1.62570888 41.86047 3 30 60 75 135 0.657516 88.76469 2.28322512 38.87689 4 40 70 115 185 0.571753 105.7744 2.85497836 37.04909 5 60 80 175 255 0.497177 126.7801 3.3521551 37.82047

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