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The internal rate of return is the discount rate at which the NPV is equal to zero. We are given several NPVs for both projects, each one calculated using a different discount rate. As the discount rate increases, the NPVs decrease. For each project, the rate at which the NPV changes from a positive number to a negative number will be approximately where the NPV will be zero. The IRR will be a rate in between the last positive rate in the table and the first negative rate. We can estimate that from the table. For Project A, at a discount rate of 18%, its NPV is 77. At a discount rate of 20%, its NPV is (26). Therefore, the discount rate at which its NPV will be zero must be somewhere in between 18% and 20%, but closer to 20% because the negative amount (26) is a smaller amount than the positive amount (77). For Project B, at a discount rate of 24%, its NPV is 30. At a discount rate of 26%, its NPV is (11). Therefore, the discount rate at which its NPV will be zero must be somewhere in between 24% and 26%, but closer to 26% because the negative amount (11) is a smaller amount than the positive amount (20). The only answer choice that fulfills both of those ranges is 19.5% and 25.5%. With the answer choices given, there is no need to do any further calculation to interpolate the exact IRR for each project.
At a discount rate of 0% for both projects, Project A has a Net Present Value of $2,220 and Project B has a Net Present Value of $1,240. The internal rate of return is the discount rate at which the NPV is equal to zero; so 0% cannot be the internal rate of return for either project. Look for the rates where the NPV of each project changes from a positive number to a negative number. The rate at which the NPV is zero will be somewhere in between those two rates.
At a discount rate of 20.50%, Project A has a Net Present Value of approximately (48.25). At a discount rate of 26.5%, Project B has a Net Present Value of approximately (20). These NPVs were calculated by interpolating from the data given. The internal rate of return is the discount rate at which the NPV is equal to zero; so 20.5% cannot be the internal rate of return for Project A and 26.5% cannot be the internal rate of return for Project B. Look for the rates where the NPV of each project changes from a positive number to a negative number. The rate at which the NPV is zero will be somewhere in between those two rates.
At a discount rate of 19.0%, Project A has a Net Present Value of approximately 25.5. At a discount rate of 21.5%, Project B has a Net Present Value of approximately 89. These NPVs were calculated by interpolating from the data given. The internal rate of return is the discount rate at which the NPV is equal to zero; so 19.0% cannot be the internal rate of return for Project A and 21.5% cannot be the internal rate of return for Project B. Look for the rates where the NPV of each project changes from a positive number to a negative number. The rate at which the NPV is zero will be somewhere in between those two rates.