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An IRR root and a discount-rate choice

A root of the NPV equation is a mathematical property of a cash-flow schedule, while a selected discount rate is another model input.

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Read the root condition

For a schedule of equally spaced cash flows, an IRR r solves the sum of discounted flows equal to zero. The equation can have no admissible root, one root or several roots depending on the schedule and domain. A numerical output alone does not explain that structure.

Keep the valuation rate explicit

NPV at a selected rate answers the value of the modeled net cash flows under that discount assumption. Choosing that assumption can involve risk, timing and the task’s required comparison. The root calculation does not by itself specify the appropriate rate.

Inspect one schedule with two roots

For −100, 230, −132 at dates zero, one and two, the roots are 10% and 20%. NPV is positive at 15% and negative at 0%. A rule that simply chooses the higher displayed IRR ignores this rate-dependent profile.

Keep the exercise conclusion within its assumptions

The synthetic schedule makes the equation visible. It does not supply forecasts, risk assessments or a recommended investment. A research report should disclose its flows, horizon, rate assumption and root behavior rather than replace them with a single return label.

Further references