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%33.4%50.87%61.5%

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%33.4%50.87%61.5%

BlackTom AI · Accepted Answer

We start by restating the problem: we need the IRR for Project B, where the cash flows (end of year) are: Year 0 = -480,000, and Years 1–5 each = 280,000. The IRR is the discount rate r that makes the net present value (NPV) zero: -480,000 + 280,000*(PV annuity factor for 5 years at rate r) = 0.

Option A: 48.7%. To assess this, compute the present value factor for 5 years at r = 0.487. The annuity factor (1 - (1+r)^-5)/r would be approximately (1 - 1/(1.487)^5)/0.487. Since (1.487)^5 is roughly 7–7.5, its reciprocal is about 0.13–0.15, giving an annuity factor near 0.85–0.87 divided by 0.487, which would be around 1.7–1.8. Multiply by 280,000 gives roughly 476,000–504,000, which is close to the initial 480,000 but slightly under or over depending on the exact exponent; overall this rate tends to produce an NPV near zero but not precisely aligned. In practice, solving more precisely shows a slight mismatch with zero NPV at this rate.

Option B: 33.4%. At r = 0.334, the 5-year annuity factor (1 - (1.334)^-5)/0.334 is significantly larger than at 48.7%, leading to a present value well above 480,000 when multiplied by 280,000. That would produce a positive NPV, meaning this rate is too low to achieve NPV = 0 for this project. Therefore this IRR estimate understates the rate needed for zero NPV.

Option C: 50.87%. This is very close to the rate we get when solving more precisely. Using r ≈ 0.5087, the 5-year discount factor (1 - (1.5087)^-5)/0.5087 yields an annuity factor near 1.714. Multiplying by 280,000 gives about 480,000, which matches the initial outlay of 480,000, yielding NPV ≈ 0. Small numerical rounding errors can tweak the exact NPV to be exactly zero. This indicates the IRR around 50.87% is consistent with the cash flows provided.

Option D: 61.5%. At a rate this high, the present value of the five subsequent 280,000 cash inflows would be much smaller. The annuity factor for 5 years at 61.5% is quite low (significantly less than 1.7), so the total PV of inflows would fall short of 480,000, producing a negative NPV. Therefore this rate is too high to achieve NPV = 0 for Project B.

Putting the pieces together, the rate that brings the present value of the five 280,000 inflows in line with the 480,000 initial outlay is around 50.8%. In numerical terms, the IRR calculation aligns with an answer near 50.87%, while the other options deviate due to either underestimating or overestimating the required discount rate to achieve zero NPV for this cash-flow pattern.

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