The NPV and IRR methods, when used to evaluate two equally risky but mutually exclusive projects, will lead to different accept/reject decisions and thus capital budgets if the cost of capital at which the projects' NPV profiles cross is greater than the crossover rate.

Question

BlackTom AI · Accepted Answer

The crossover rate is the discount rate at which the NPVs of the two projects are equal. IRR is the discount rate that makes a single project's NPV zero. NPV ranking depends on the firm’s chosen cost of capital (k); IRR ranking is independent of k. A conflict (different accept/reject or ranking) arises when the firm’s cost of capital lies on the opposite side of the crossover rate relative to which project has the larger IRR—i.e., when the project with the higher IRR does not have the higher NPV at the firm’s k.

1. Relevant concepts
- NPV: present value of cash flows discounted at the firm’s cost of capital; higher NPV preferred.
- IRR: discount rate that sets NPV = 0; project with higher IRR is preferred by the IRR rule.
- Crossover rate (rc): the value of r that solves NPV_A(r) = NPV_B(r). By definition, the “discount rate at which the NPV profiles cross” is the crossover rate.

2. Reasoning step by step
- The statement refers to “the cost of capital at which the projects’ NPV profiles cross” and compares it to “the crossover rate.” These two phrases denote the same concept: rc.
- The statement therefore claims a quantity is greater than itself (that the cost of capital at which they cross is greater than the crossover rate), which is logically impossible.
- The correct condition for an NPV/IRR conflict is: when the firm’s actual cost of capital (k) is on one side of rc and the IRR ranking favors the other project, producing differing decisions. Not the self-contradictory condition stated.

3. Calculations/intermediate steps
- Formally rc solves NPV_A(rc) − NPV_B(rc) = 0. There is no separate “cost of capital at which they cross” distinct from rc.

4. Why the correct answer is correct
- The statement is false because it conflates identical definitions and asserts an impossible inequality; the true cause of NPV/IRR conflict is the position of the firm’s k relative to rc, not a comparison of “the crossing cost” to the crossover rate.

5. Why the other option (True) is incorrect
- Marking True would endorse a self-contradictory condition and misstate the actual criterion for NPV/IRR conflicts.

6. Conclusion
- The correct answer is False, which matches the provided answer.

The NPV and IRR methods, when used to evaluate two equally risky but mutually exclusive projects, will lead to different accept/reject decisions and thus capital budgets if the cost of capital at which the projects' NPV profiles cross is greater than the crossover rate.判断题

类似问题

Projects S and L are equally risky, mutually exclusive, and have normal cash flows. Project S has an IRR of 15%, while Project L’s IRR is 12%. The two projects have the same NPV when the WACC is 7%. Which of the following statements is CORRECT?

If you were evaluating two mutually exclusive projects for a firm with a zero cost of capital, the payback method and NPV method would always lead to the same decision on which project to undertake.

Conflicts between two mutually exclusive projects occasionally occur, where the NPV method ranks one project higher but the IRR method puts the other one first. In theory, such conflicts should be resolved in favor of the project with the higher IRR.

If NPV is zero, then IRR is ………… WACC

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