In: Economics
"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."
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).