Question

X Company is unhappy with a machine that they bought just a year ago for $40,000. It is considering replacing it with a new machine that will save significant operating costs. Operating costs with the current machine are $67,000 per year; operating costs with the new machine are expected to be $47,000 per year. Both machines will last for 6 more years.The current machine can be sold immediately for $7,000 but will have no salvage value at the end of 6 years. The new machine will cost $72,000 and have a salvage value of $3,000 in 6 years.

Assuming a discount rate of 7%, what is the net present value of replacing the current machine?

Answer 1

Understanding the question

The question does not have .......... tax rates. So, we need not be concerned about depreciation.

Thus the difference between operating costs ....... i.e 67000 and 47000 = 20000 shall be the annual cash in flow due to replacement. In the year 6, there is additional cash flow of 3000 due to salvage of new machine.

Investment at the t = 0 shall be ........... cost of new machine - sale of old machine = 72000 - 7000 = 65000

Answering the question

Investment = 65000

Annual cash flow = 20000

PVIFA for 6 years at 7% discount rate = [ 1 - (1+r)^-n ] /r = [ 1 - (1.07)^-6 ] / 0.07 = 4.7665397

PV for 6th Year at 7% discount rate = (1+r)^-n = (1.07)^-6 = 0.66634222

NPV = Present value of all cash in flows - Investment

= 20000 * 4.7665397 + 3000 * 0.66634222 - 65000

= 32,329.82 ................... is the NPV of replacing the current machine.