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?48.7%61.5%33.4%50.87%

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?48.7%61.5%33.4%50.87%

BlackTom AI · Accepted Answer

We start by restating the question and the given data to ensure clarity.
Question: What is the IRR for Project B, given the cash flows at the end of each year and a cost of capital of 14%? Cash flows for Project B are: Year 0 = -480,000; Years 1–5 = 280,000 each year.
Answer options to evaluate: 48.7%, 61.5%, 33.4%, 50.87%.
Now, evaluate each option step by step.
Option 1: 48.7%.
- If the IRR were 48.7%, the net present value (NPV) of the future 280,000 annuity over five years would be 280,000 times the present value factor for 5 years at 48.7%. The factor is [1 − (1 + 0.487)^(−5)] / 0.487. Computing (1.487)^5 ≈ 7.27, so (1 + r)^(−5) ≈ 0.138. The factor ≈ (1 − 0.138) / 0.487 ≈ 0.862 / 0.487 ≈ 1.77. Multiply by 280,000 gives ≈ 496,000. Subtract the initial outlay of 480,000, and NPV ≈ +16,000. This suggests the IRR would be slightly higher than 48.7% to bring NPV to zero. Thus 48.7% is not exact; it yields a positive NPV, signaling the true IRR is above this value.
Option 2: 61.5%.
- At 61.5%, the five-year annuity factor is [1 − (1 + 0.615)^(−5)] / 0.615. (1.615)^5 ≈ 10.98, so (1.615)^(−5) ≈ 0.091. The factor ≈ (1 − 0.091) / 0.615 ≈ 0.909 / 0.615 ≈ 1.477. 1.477 × 280,000 ≈ 413,560. NPV ≈ −480,000 + 413,560 = −66,440, which is negative. This implies the IRR is lower than 61.5%, making this option inconsistent with the required break-even condition.
Option 3: 33.4%.
- For 33.4%, compute the annuity factor: (1 + 0.334)^5 ≈ 4.223, so (1.334)^(−5) ≈ 0.237. Factor ≈ (1 − 0.237) / 0.334 ≈ 0.763 / 0.334 ≈ 2.29. 2.29 × 280,000 ≈ 641,200. NPV ≈ −480,000 + 641,200 = +161,200, a substantial positive NPV. This indicates the IRR is higher than 33.4%, not equal to it, so this option is too low.
Option 4: 50.87%.
- At 50.87%, the five-year PV factor is [1 − (1 + 0.5087)^(−5)] / 0.5087. With (1.5087)^5 ≈ 7.82, (1.5087)^(−5) ≈ 0.128, so the factor ≈ (1 − 0.128) / 0.5087 ≈ 0.872 / 0.5087 ≈ 1.715. 1.715 × 280,000 ≈ 480,200. NPV ≈ −480,000 + 480,200 ≈ +200, close to zero.
- This is the only option that aligns with a near-zero NPV, meaning it matches the IRR where the initial outlay is exactly recovered by the discounted future cash inflows, within rounding error. The small positive NPV is attributable to rounding in the intermediate calculations, but the result is consistent with an IRR around 50.87%.
Synthesis across all options:
- The 48.7% case gives a small positive NPV, implying true IRR is slightly higher than 48.7%. 
- The 61.5% case produces a clearly negative NPV, indicating the IRR is lower than 61.5%. 
- The 33.4% case yields a large positive NPV, indicating the IRR is much higher than 33.4%. 
- The 50.87% case yields a near-zero NPV, consistent with the IRR being approximately 50.87%. 
Overall, the evaluation shows that the remaining options do not align with the zero-NPV condition, while the 50.87% option satisfies it within typical rounding precision. Note that final confirmation would come from solving the IRR equation exactly, but the calculations above strongly indicate 50.87% as the correct IRR for Project B.

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