Part 7 of 8:

You also learned that the crossover rate is unique.

The crossover rate is approximately 11.07%. At that point, both NPVA and NPVB are still positive ( $43,705 approx.)

From this information, you can conclude that the IRR of Project A will be lower than the IRR of Project B.

Question

Part 7 of 8:

You also learned that the crossover rate is unique.

The crossover rate is approximately 11.07%. At that point, both NPVA and NPVB are still positive ( $43,705 approx.)

From this information, you can conclude that the IRR of Project A will be lower than the IRR of Project B.

BlackTom AI · Accepted Answer

The prompt presents a statement about IRRs based on the given crossover rate and NPVs, so we need to examine what each piece of information means.

First, recall the key concepts: the crossover rate is the discount rate at which the NPVs of two projects are equal. At that rate, the two projects have the same NPV. If the crossover rate is 11.07%, and at that rate both NPVs are still positive (about $43,705), this tells us that the discount rate of 11.07% is below the IRR of each project (since NPV > 0 when the discount rate is less than the IRR for a given project).

With that in mind, consider option by option:

- Analyzing the claim that Project A’s IRR will be lower than Project B’s IRR: The information given (the crossover rate and the fact that both NPVs are positive at that rate) does not provide a direct comparison of the two IRRs. Knowing that both IRRs are greater than 11.07% (since their NPVs are positive at 11.07%) tells us only that both projects’ IRRs exceed 11.07%. It does not establish which IRR is higher. Therefore, the statement asserting A’s IRR is lower than B’s is not supported by the data provided.

- Why this conclusion is not guaranteed: The crossover rate is precisely where NPVs are equal, not where the ordering of IRRs is determined. Even if at 11.07% both NPVs are positive, it could be that IRR(A) > IRR(B) or IRR(A) < IRR(B); the given information is silent on their relative magnitudes beyond the fact that both exceed 11.07%. Hence a definite comparison cannot be drawn from these details alone.

- Potential misinterpretations to avoid: If someone thinks "positive NPV at 11.07% means A is better than B" they would be conflating NPV at a particular discount rate with the inherent ranking of IRRs. Positive NPV at a rate simply indicates the rate is below that project’s IRR; it does not establish which IRR is higher.

- Additional nuance: The fact that the crossover rate exists and their NPVs are positive there implies that both projects have IRRs above 11.07%, but the relative gap between IRR(A) and IRR(B) is determined by the shape of each project's cash flows and is not deducible from the provided statement alone. Therefore, the assertion that IRR(A) is lower than IRR(B) is not justified.

In summary, the given information does not allow us to conclude which project has the higher IRR; it only tells us both IRRs exceed 11.07% because NPVs are positive at that rate. This makes the statement false or at least not provable from the data provided.

COMM_V 298 201-207 2024W2 Class 16: Capital Budgeting Practice Quiz 2

Part 7 of 8: You also learned that the crossover rate is unique. The crossover rate is approximately 11.07%. At that point, both NPVA and NPVB are still positive ( $43,705 approx.) From this information, you can conclude that the IRR of Project A will be lower than the IRR of Project B.

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