Question

In: Economics

"Sioux Falls Medical purchased a digital image processing machine three years ago at a cost of...

"Sioux Falls Medical purchased a digital image processing machine three years ago at a cost of $55,000. The machine had an expected life of eight years at the time of purchase and an expected salvage value of $3,000 at the end of the eight years. The old machine has been slow at handling the increased business volume, so management is considering replacing the machine.
A new machine can be purchased for $80,000, including installation costs. Over its five-year life, the machine will reduce cash operating expenses by $23,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless.
The old machine can be sold today for $11,000. The firm`s interest rate for project justification is known to be 12%. The firm does not expect a better machine (other than the current challenger) to be available for the next five years. Assuming that the economic service life of the new machine, as well as the remaining useful life of the old machine, is five years, what is the PRESENT WORTH of the preferred alternative? The answer could be negative. Ignore the effect of taxes and depreciation."

Solutions

Expert Solution

A) Present worth if the machine is replaced:

Year Additional (cost)/savings DF 12% Present worth
0                                 -69,000 (Note 1) 1             -69,000
1                                  23,000 0.89               20,536
2                                  23,000 0.80               18,335
3                                  23,000 0.71               16,371
4                                  23,000 0.64               14,617
5                                  23,000 0.57               13,051
$ 13,910

Note 1: Cost of the machinery: 80,000

(-) Salvage value of the old machine today (11,000)

Outflow in Year 0 $ 69,000

B) Present worth if the machine is not replaced:

Year Additional (cost)/savings DF 12% Present worth
0                                           -   1                       -  
1                                           -   0.89                       -  
2                                           -   0.80                       -  
3                                           -   0.71                       -  
4                                           -   0.64                       -  
5                                    3,000 0.57                 1,702
$ 1,702

Hence, the machine should be replaced immediately since the net present worth ($13,910) is higher than the net present worth worth ($1,702) of the alternative wherein the machine is not replaced.

Note: The cost of $55,000 holds no significance since it is sunk cost (already incurred).


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