You have two alternatives for replacing a piece of equipment. You can use altern

Question

You have two alternatives for replacing a piece of equipment. You can use alternative X which costs $100,000 and lasts forever, or you can use alternative Y which costs $75,000 and and lasts n years. What is the useful life of alternative Y which makes the two alternatives equally desirable? Assume equal benefits for both alternatives, an infinite analysis period (with continuing replacement of alternative Y ), and MARR of 10%.

The answer that was given for this problem was n = 15 years, but I'm not sure how to solve the problem to get that answer. Please show all your work and do NOT use Excel. Thanks! (:

Explanation / Answer

Present value of cash inflow for alternative A - present value of cash outflow of alternative A = Present value of cash inflow for alternative B - present value of cash outflow of alternative B

If cash inflow was $12,891 per year the above equation can be written as:

12891/0.1 - 100000 = 12891(P/A, 10%, n) - 75000

103910/12891= (P/A,10%,n)

8.0607= (P/A,10%,n)

Therefore n=15 years.

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