Assume a conventional project: one initial cash outflow followed by nonnegative inflows, a positive required return r and a unique IRR. Assess these combinations.
Impossible under these assumptions: positive NPV implies total undiscounted inflows exceed the initial outlay, so it is recovered by completion.
Impossible under the conventional-cash-flow assumption because positive NPV requires IRR > r.
Possible. The project may fail to recover its initial outlay even before discounting.
Impossible for the same recovery reason as the first combination.
Impossible under these assumptions because IRR > r implies positive NPV. Non-conventional cash flows require separate analysis.
For each claim, give a justified answer.
No. A hurdle rate is needed to accept or reject an investment; mutually exclusive projects must be ranked by NPV at the relevant rate. Percentage returns can reverse the value ranking when scale or timing differs. Non-conventional cash flows can produce multiple or no IRRs.
No. Payback measures how quickly nominal cash inflows recover the initial outlay. It ignores later cash flows, the time value of money and a risk-adjusted valuation of cash flows. It can be useful as a liquidity screen, not as a measure of value or a guarantee of safety.
For a standalone conventional investment with one initial outflow followed by inflows, NPV is positive exactly when the unique IRR exceeds the appropriate hurdle rate. This agreement does not extend automatically to ranking mutually exclusive projects.
No. Its stated opportunity cost is 15%. For a conventional cash-flow pattern, the appropriate IRR hurdle is 15%, not an arbitrary 20%; use NPV at 15% for the direct value test.
Accept if payback is no longer than a chosen cutoff. It is simple and highlights early cash recovery, but the cutoff is arbitrary and the method can reject value-creating long-lived projects or accept negative-NPV projects.