The closer the interest rate approaches zero and the shorter the payback period, the closer the results

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The closer the interest rate approaches zero and the shorter the payback period, the closer the results for the nondiscounted and discounted payback periods become. As the interest rate grows and the payback period grows, so too does the difference in the payback period results. But do discounted and nondiscounted payback period versions still give the same conclusions when comparing alternatives?

That is, do both measures always give that alternative Z1 is better than alternative Z2? Would you expect, in general, that the nondiscounted version of payback period will give a similar conclusion to that for discounted payback period, when comparing alternatives?

If not, can you think of an example where they would give different conclusions? The exercise is about comparing alternative investments (not comparing discounted and nondiscounted payback periods for a single investment).

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