Question at position 2 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the IRR for Project B?50.87%61.5%48.7%33.4%

Question

Question at position 2 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the IRR for Project B?50.87%61.5%48.7%33.4%

BlackTom AI · Accepted Answer

Question restatement: You’re evaluating Project B with cash flows (end of year): Year 0 = -480,000; Years 1–5 = +280,000 each year. The cost of capital is 14%, and you’re asked to identify the IRR for Project B from the provided options.

Option by option analysis:
- Option A: 50.87%
  To gauge whether this IRR is plausible, consider computing the net present value (NPV) at this rate. The present value factor for year 1 at IRR ≈ 50.87% is 1 / (1 + 0.5087) ≈ 0.661. The inflow of 280,000 thus has a present value of about 184,900. For year 2, the factor is 1 / (1.5087)^2 ≈ 0.437, giving ~122,040. Year 3 uses ≈ 0.289, giving ~80,900. Year 4 ≈ 0.191, giving ~53,500. Year 5 ≈ 0.127, giving ~35,500. Summing inflows: roughly 184,900 + 122,040 + 80,900 + 53,500 + 35,500 ≈ 477,840. Subtract the initial outflow 480,000 gives an NPV near -2,160, very close to zero, indicating IRR ≈ 50.87% is a plausible root. Therefore, this option could be the true IRR.
- Option B: 61.5%
  If IRR were 61.5%, the discount factor for year 1 would be 1 / 1.615 ≈ 0.619, giving PV ≈ 173,320 for the 280,000 inflow. Year 2 uses 1 / (1.615)^2 ≈ 0.383, giving ≈ 107,240. Year 3 uses ≈ 0.237, giving ≈ 66,360. Year 4 ≈ 0.147, giving ≈ 41,160. Year 5 ≈ 0.091, giving ≈ 25,480. Total PV of inflows ≈ 413,560. Net present value ≈ 413,560 − 480,000 ≈ −66,440, which is substantially negative. This indicates IRR is lower than 61.5%, so 61.5% is not the IRR.
- Option C: 48.7%
  With IRR at 48.7%, the year-1 PV factor is 1 / 1.487 ≈ 0.672, so PV of the first inflow ≈ 188,160. Year 2 factor ≈ 0.452, PV ≈ 126,560. Year 3 factor ≈ 0.303, PV ≈ 84,840. Year 4 factor ≈ 0.203, PV ≈ 56,840. Year 5 factor ≈ 0.136, PV ≈ 38,080. Sum ≈ 494,480. NPV ≈ 494,480 − 480,000 ≈ +14,480, which is positive, meaning IRR is higher than 48.7% if NPV is to go to zero. Hence 48.7% is not the IRR.
- Option D: 33.4%
  At IRR 33.4%, the year-1 PV factor is 1 / 1.334 ≈ 0.750, giving PV ≈ 210,000. Year 2 factor ≈ 0.561, PV ≈ 157,080. Year 3 factor ≈ 0.421, PV ≈ 117,880. Year 4 factor ≈ 0.316, PV ≈ 88,480. Year 5 factor ≈ 0.237, PV ≈ 66,360. Sum ≈ 639,800. Net NPV ≈ 639,800 − 480,000 ≈ +159,800, which is clearly far from zero. This IRR is too low given the large inflows, so this option is not correct.

In summary, evaluating the IRR by comparing the NPV at each rate shows that the inflows are best balanced to zero out the initial outflow around the 50% range; the other rates produce clearly nonzero NPVs of either negative or positive sign. The reasoning above illustrates why each alternative deviates from the IRR that makes NPV zero at the cash flow pattern of Project B.

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Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table] Year | Project A 0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000 [/table]48.86%53.33%52.29%54.38%

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Question at position 2 (3 marks, difficulty level: Easy) What is the IRR of this project? [table] Year | Project A 0 | -380,000 1 | 180,000 2 | 280,000 3 | 280,000 4 | 280,000 5 | 80,000 [/table]48.86%52.29%54.38%53.33%

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